>> d // MathMLForm >> squared[1, 2] You can view the box structure of a formatted
>> d + 1 // MathMLForm expression using ToBoxes: >> ToBoxes[m + n] though string delimiters are not shown in the de- For instance, you can override MakeBoxes to for- fault output form: >> InputForm[%] mat lists in a different way: [ ] >> MakeBoxes[{items___}, RowBox {"m", "+", "n"} StandardForm] := RowBox[{"[", Sequence @@ Riffle[MakeBoxes /@ {items}, " "], "]"}] Graphics Introduction Examples
>> {1, 2, 3} Two-dimensional graphics can be created us- [123] ing the function Graphics and a list of graphics However, this will not be accepted as input to primitives. For three-dimensional graphics see Mathics anymore: the following section. The following primitives are available: >> [1 2 3] Circle[{x, y}, r] >> Clear[MakeBoxes] draws a circle. Disk[{x, y}, r] By the way, MakeBoxes is the only built-in sym- draws a filled disk. bol that is not protected by default: Rectangle[{x1, y1}, {x2, y2}] >> Attributes[MakeBoxes] [ ] draws a filled rectangle. HoldAllComplete Polygon[{{x1, y1}, {x2, y2}, ...}] draws a filled polygon. MakeBoxes must return a valid box construct: Line[{{x1, y1}, {x2, y2}, ...}] >> MakeBoxes[squared[args___], draws a line. StandardForm] := squared[args] ^ Text[text,{x, y}] 2 draws text in a graphics.
>> squared[1, 2] Power[squared[1, 2], 2]isnotavalidboxstructure.
16 >> Graphics[{Circle[{0, 0}, 1]}] such as Black, White, Red, Green, Blue, etc. >> Graphics[{Red, Disk[]}]
>> Graphics[{Line[{{0, 0}, {0, 1}, {1, 1}, {1, -1}}], Rectangle[{0, Table of hues: 0}, {-1, -1}]}] >> Graphics[Table[{Hue[h, s], Disk [{12h, 8s}]}, {h, 0, 1, 1/6}, {s , 0, 1, 1/4}]]
Colors can be added in the list of graphics primi- Colors can be mixed and altered using the fol- tives to change the drawing color. The following lowing functions: ways to specify colors are supported: Blend[{color1, color2}, ratio] RGBColor[r, g, b] mixes color1 and color2 with ratio, where specifies a color using red, green, and a ratio of 0 returns color1 and a ratio of 1 blue. returns color2. CMYKColor[c, m, y, k] Lighter[color] White specifies a color using cyan, magenta, yel- makes color lighter (mixes it with ). Darker[ ] low, and black. color Hue[h, s, b] makes color darker (mixes it with Black). specifies a color using hue, saturation, and brightness. GrayLevel[l] specifies a color using a gray level. All components range from 0 to 1. Each color function can be supplied with an additional ar- gument specifying the desired opacity (“alpha”) of the color. There are many predefined colors,
17 >> Graphics[{Lighter[Red], Disk[]}] >> Graphics3D[Polygon[{{0,0,0}, {0,1,1}, {1,0,0}}]]
Graphics produces a GraphicsBox: >> Head[ToBoxes[Graphics[{Circle []}]]] GraphicsBox Colors can also be added to three-dimensional primitives. >> Graphics3D[{Orange, Polygon [{{0,0,0}, {1,1,1}, {1,0,0}}]}, 3D Graphics Axes->True]
Three-dimensional graphics are created using the function Graphics3D and a list of 3D prim- itives. The following primitives are supported so far:
Polygon[{{x1, y1, z1}, {x2, y2, z3}, ...}] draws a filled polygon. Line[{{x1, y1, z1}, {x2, y2, z3}, ...}] draws a line. Point[{x1, y1, z1}] draws a point.
Graphics3D produces a Graphics3DBox: >> Head[ToBoxes[Graphics3D[{Polygon []}]]] Graphics3DBox
Plotting Introduction Examples
Mathics can plot functions:
18 >> Plot[Sin[x], {x, 0, 2 Pi}] You can use a custom coloring function: >> DensityPlot[x ^ 2 + 1 / y, {x, 1.0 -1, 1}, {y, 1, 4}, ColorFunction 0.5 -> (Blend[{Red, Green, Blue}, #]&)] 1 2 3 4 5 6 −0.5 −1.0
You can also plot multiple functions at once: >> Plot[{Sin[x], Cos[x], x ^ 2}, {x , -1, 1}]
1.0
0.5
−1.0 −0.5 0.5 1.0 One problem with DensityPlot is that it’s still very slow, basically due to function evaluation −0.5 being pretty slow in general—and DensityPlot has to evaluate a lot of functions. Three-dimensional plots are supported as well: Two-dimensional functions can be plotted using >> Plot3D[Exp[x] Cos[y], {x, -2, DensityPlot: 1}, {y, -Pi, 2 Pi}] >> DensityPlot[x ^ 2 + 1 / y, {x, -1, 1}, {y, 1, 4}]
19 3. Examples
Contents
Linear algebra ..... 21 Dice ...... 22 Curve sketching .... 20
Curve sketching Being different from 0, all three points are actual inflection points. f is not defined where its de- Let’s sketch the function nominator is 0: >> f[x_] := 4 x / (x ^ 2 + 3 x + 5) >> Solve[Denominator[f[x]] == 0, x] {{ √ } 3 I The derivatives are: x− > − − 11 , { 2 2 }} >> {f’[x], f’’[x], f’’’[x]} // √ 3 I Together x− > − + 11 { ( ) 2 2 −4 −5 + x2 ( ) 2 , These are non-real numbers, consequently f is 5 + 3x + x2 ( ) defined on all real numbers. The behaviour of f 8 −15 − 15x + x3 ( ) at the boundaries of its definition: 3 , 5 + 3x + x2 >> Limit[f[x], x -> Infinity] ( ) } −24 −20 − 60x − 30x2 + x4 0 ( ) 4 5 + 3x + x2 >> Limit[f[x], x -> -Infinity] 0 To get the extreme values of f, compute the ze- roes of the first derivatives: Finally, let’s plot f: >> extremes = Solve[f’[x] == 0, x] >> Plot[f[x], {x, -8, 6}] {{ √ } { √ }} x− > − 5 , x− > 5 0.5 − − − − And test the second derivative: 8 6 4 −20.5 2 4 6 >> f’’[x] /. extremes // N −1.0 { − } 1.65086, 0.064079 −1.5 Thus, there is a local maximum at x = Sqrt[5] −2.0 and a local minimum at x = -Sqrt[5]. Com- −2.5 pute the inflection points numerically, chopping imaginary parts close to 0: >> inflections = Solve[f’’[x] == 0, x] // N // Chop Linear algebra {{x− > −1.0852} , {x− > − 3.21463} , {x− > 4.29983}} Let’s consider the matrix >> A = {{1, 1, 0}, {1, 0, 1}, {0, Insert into the third derivative: 1, 1}}; >> f’’’[x] /. inflections {−3.67683, 0.694905, 0.00671894}
20 >> MatrixForm[A] >> B . (RandomInteger[100] * %[[1]] 1 1 0 + s) 1 0 1 {1, 2, 3} 0 1 1
We can compute its eigenvalues and eigenvec- tors: Dice >> Eigenvalues[A] Let’s play with dice in this example. A Dice { − } 2, 1, 1 object shall represent the outcome of a series of rolling a dice with six faces, e.g.: >> Eigenvectors[A] >> Dice[1, 6, 4, 4] {{1, 1, 1} , {1, − 2, 1} , {−1, 0, 1}} Dice [1, 6, 4, 4] A: This yields the diagonalization of Like in most games, the ordering of the individ- >> T = Transpose[Eigenvectors[A]]; ual throws does not matter. We can express this MatrixForm[T] by making Dice Orderless: 1 1 −1 >> SetAttributes[Dice, Orderless] 1 −2 0 1 1 1 >> Dice[1, 6, 4, 4] Dice [1, 4, 4, 6] >> Inverse[T] . A . T // MatrixForm 2 0 0 A dice object shall be displayed as a rectangle 0 −1 0 with the given number of points in it, positioned 0 0 1 like on a traditional dice: >> Format[Dice[n_Integer?(1 <= # <=
>> % == DiagonalMatrix[Eigenvalues[ 6 &)]] := Block[{p = 0.2, r = A]] 0.05}, Graphics[{EdgeForm[Black ], White, Rectangle[], Black, True EdgeForm[], If[OddQ[n], Disk We can solve linear systems: [{0.5, 0.5}, r]], If[MemberQ[{2, >> LinearSolve[A, {1, 2, 3}] 3, 4, 5, 6}, n], Disk[{p, p}, r ]], If[MemberQ[{2, 3, 4, 5, 6}, {0, 1, 2} n], Disk[{1 - p, 1 - p}, r]], If [MemberQ[{4, 5, 6}, n], Disk[{p, >> A.% 1 - p}, r]], If[MemberQ[{4, 5, {1, 2, 3} 6}, n], Disk[{1 - p, p}, r]], If In this case, the solution is unique: [n === 6, {Disk[{p, 0.5}, r], Disk[{1 - p, 0.5}, r]}]}, >> NullSpace[A] ImageSize -> Tiny]] {}
>> Dice[1] Let’s consider a singular matrix: >> B = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
>> MatrixRank[B] 2 The empty series of dice shall be displayed as an
>> s = LinearSolve[B, {1, 2, 3}] empty dice: { } 1 2 >> Format[Dice[]] := Graphics[{ − , , 0 EdgeForm[Black], White, 3 3 Rectangle[]}, ImageSize -> Tiny]
>> NullSpace[B] {{1, − 2, 1}}
21 >> Dice[] >> Dice[a___] + Dice[b___] := Dice[ Sequence @@ {a, b}] TagPlusinDice[a___] + Dice[b___]isProtected. $Failed
Any non-empty series of dice shall be displayed We can now combine dice: as a row of individual dice: >> Dice[1, 5] + Dice[3, 2] + Dice >> Format[Dice[d___Integer?(1 <= # [4] <= 6 &)]] := Row[Dice /@ {d}]
>> Dice[1, 6, 4, 4]
Let’s write a function that returns the sum of the rolled dice: Note that Mathics will automatically sort the >> DiceSum[Dice[d___]] := Plus @@ { given format rules according to their “general- d} ity”, so the rule for the empty dice does not get overridden by the rule for a series of dice. >> DiceSum @ Dice[1, 2, 5] We can still see the original form by using 8 InputForm: And now let’s put some dice into a table: >> Dice[1, 6, 4, 4] // InputForm >> Table[{Dice[Sequence @@ d], Dice [1, 4, 4, 6] DiceSum @ Dice[Sequence @@ d]}, {d, {{1, 2}, {2, 2}, {2, 6}}}] We want to combine Dice objects using the + op- // TableForm erator: >> Dice[a___] + Dice[b___] ^:= Dice [Sequence @@ {a, b}] 3
The ^:= (UpSetDelayed) tells Mathics to asso- 4 ciate this rule with Dice instead of Plus, which is protected—we would have to unprotect it first: 8
It is not very sophisticated from a mathematical point of view, but it’s beautiful.
22 4. Django-based Web Interface
In the future, we plan on providing an interface ments to the this interface. to Jupyter as a separate package. When you enter Mathics in the top after the However currently as part Mathics, we dis- Mathics logo and the word “Mathics” you’ll see tribute a browser-based interface using long- a menubar. term-release (LTS) Django 3.2. It looks like this: Since a Jupyter-based interface seems preferable to the home-grown interface described here, it is doubtful whether there will be future improve-
Contents
Loading and Persistence of Mathics URIs ...... 23 Deleting Definitions in a Saving, Loading, and Worksheets 24 Session ...... 25 Deleting Keyboard Commands . 25 Worksheets .... 24 Saving Worksheets 24
URIs http://localhost:8000 The single-page application; the main For the most part, the application is a single- page. page application. Assuming your are running http://localhost:8000/about locally or on a host called localhost using the A page giving: default port, 8000, here are some URLs and what they do: • the software versions of this package and version information of important software this uses.
• directory path information for the cur- rent setup • machine information • system information http://localhost:8000/doc An on-line formatted version of the doc- umentation, which include this text. You can see this as a right side frame of the main page, when clicking "?" on the right- hand upper corner.
23 Saving, Loading, and Deleting A popup menu should appear with the list of Worksheets saved worksheets with an option to either load or delete the worksheet. Worksheets exist in the browser window only Loading and Deleting Worksheets and are not stored on the server, by default. To save all your queries and results, use the Save button which is the middle graphic of the menu Worksheets exist in the browser window only bar. It looks like this: and are not stored on the server, by default. To save all your queries and results, use the Save button which is the middle graphic of the menu bar. It looks like this: Depending on browser, desktop, and OS- settings, the "Ctrl+S" key combination may do the same thing. settings, the "Ctrl+S" key combination may do the same thing. Saved worksheets can be loaded or deleted us- ing the File Open button which is the left-most Saved worksheets can be loaded or deleted us- ing the File Open button which is the left-most button in the menu bar. It looks like this: Depending on browser, desktop, and OS- settings, the "Ctrl+O" key combination may do the same thing. A popup menu should appear with the list of Depending on browser, desktop, and OS- saved worksheets with an option to either load settings, the "Ctrl+O" key combination may do or delete the worksheet. the same thing. A popup menu should appear with the list of saved worksheets with an option to either load Saving Worksheets or delete the worksheet. Worksheets exist in the browser window only Persistence of Mathics and are not stored on the server, by default. To save all your queries and results, use the Save Definitions in a Session button which is the middle graphic of the menu bar. It looks like this: When you use the Django-based Web interface of Mathics, a browser session is created. Cookies have to be enabled to allow this. Your session holds a key which is used to access your defini- Depending on browser, desktop, and OS- tions that are stored in a database on the server. settings, the "Ctrl+S" key combination may do As long as you don’t clear the cookies in your the same thing. browser, your definitions will remain even when This implies that you should not store sensitive, Saved worksheets can be loaded or deleted us- private information in Mathics variables when ing the File Open button which is the left-most using the online Web interface. In addition to button in the menu bar. It looks like this: their values being stored in a database on the server, your queries might be saved for debug- ging purposes. However, the fact that they are Depending on browser, desktop, and OS- transmitted over plain HTTP should make you settings, the "Ctrl+O" key combination may do aware that you should not transmit any sensitive the same thing. information. When you want to do calculations
24 with that kind of stuff, simply install Mathics lo- Shift+Return cally! This evaluates the current cell (the most If you are using a public terminal, to erase all important one, for sure). On the right- your definitions and close the browser window. hand side you may also see an "=" but- When you use Mathics in a browser, use the com- ton which can be clicked to do the same mand Quit[] or its alias, Exit[]. thing. Normally, when you reload the current page Ctrl+D in a browser using the default url, e.g This moves the cursor over to the docu- http:localhost:8000, all of the previous in- mentation pane on the right-hand side. put and output disappears, even though defini- From here you can preform a search for a tions as described above do not, unless Quit[] pre-defined Mathics function, or symbol. or Exit[] is entered as described above. Clicking on the "?" symbol on the right- However if you want a URL that will that hand side does the same thing. records the input entered the Generate Input Hash Ctrl+C button does this. The button looks like this: This moves the cursor back to document code pane area where you type Mathics expressions Ctrl+S For example, assuming you have a Mathics Save worksheet server running at port 8000 on localhost, Ctrl+O and you enter the url http://localhost:8000/ Open worksheet #cXVlcmllcz14, you should see a single line of Right Click on MathML output input containing x entered. Opens MathJax Menu Of course, what the value of this is when evalu- ated depends on whether x has been previously Of special note is the last item on the list: right- defined. click to open the MathJax menu. Under “Math Setting”/“Zoom Trigger”, if the zoom trigger Keyboard Commands is set to a value other then “No Zoom”, then when that trigger is applied on MathML format- There are some keyboard commands you can ted output, the MathML formula pop up a win- use in the Django-based Web interface of Math- dow for the formula. The window can show the ics. formula larger. Also, this is a way to see out- put that is too large to fit on the display since the window allows for scrolling. Keyboard commands behavior depends the browser used, the operating system, desk- top settings, and customization. We hook into the desktop “Open the current doc- ument” and “Save the current document” functions that many desktops provide. For example see: https://help.ubuntu.com/ community/KeyboardShortcuts#Finding_ keyboard_shortcuts Often, these shortcut keyboard command are only recognized when a text field has focus; otherwise,the browser might do some browser- specific actions, like setting a bookmark etc.
25 Part II.
Reference of Built-in Symbols
26 1. Date and Time
Dates and times are represented symbolically; computations can be performed on them. Date object can also input and output dates and times in a wide range of formats, as well as handle calendars. Contents
DateString ...... 29 TimeConstrained ... 30 AbsoluteTime ..... 27 $DateStringFormat .. 29 TimeRemaining .... 30 AbsoluteTiming .... 27 EasterSunday ..... 29 TimeUsed ...... 30 DateDifference .... 28 Now ...... 30 $TimeZone ...... 30 DateList ...... 28 Pause ...... 30 Timing ...... 31 DateObject ...... 28 SessionTime ...... 30 DatePlus ...... 29 $SystemTimeZone .. 30
AbsoluteTime AbsoluteTiming
AbsoluteTime[] AbsoluteTiming[expr] gives the local time in seconds since evaluates expr, returning a list of the ab- epoch January 1, 1900, in your time zone. solute number of seconds in real time that AbsoluteTime[{y, m, d, h, m, s}] have elapsed, together with the result ob- gives the absolute time specification cor- tained. responding to a date list. AbsoluteTime["string"] >> AbsoluteTiming[50!] gives the absolute time specification for a { given date string. 0.000186443, 30 414 093 ˜ AbsoluteTime[{"string",{e1, e2, ...}}] ˜201 713 378 043 612 608 166 ˜ takgs the date string to contain the ele- ˜064 768 844 377 641 568 ˜ ments "ei". ˜960 512 000 000 000 000}
>> AbsoluteTime[] >> Attributes[AbsoluteTiming] 3.83674 × 109 {HoldAll, Protected}
>> AbsoluteTime[{2000}] 3 155 673 600
>> AbsoluteTime[{"01/02/03", {"Day ", "Month", "YearShort"}}] 3 253 046 400
>> AbsoluteTime["6 June 1991"] 2 885 155 200
>> AbsoluteTime[{"6-6-91", {"Day", "Month", "YearShort"}}] 2 885 155 200
27 DateDifference >> DateList[3155673600] {2 000, 1, 1, 0, 0, 0.} DateDifference[date1, date2] >> DateList[{2003, 5, 0.5, 0.1, returns the difference between date1 and 0.767}] date2 in days. DateDifference[date1, date2, unit] {2 003, 4, 30, 12, 6, 46.02} returns the difference in the specified unit. >> DateList[{2012, 1, 300., 10}] DateDifference[date1, date2,{unit1, {2 012, 10, 26, 10, 0, 0.} unit2, ...}] represents the difference as a list of inte- >> DateList["31/10/1991"] ger multiples of each unit, with any re- {1 991, 10, 31, 0, 0, 0.} mainder expressed in the smallest unit. >> DateList["1/10/1991"] Theinterpretationof 1/10/ >> DateDifference[{2042, 1, 4}, {2057, 1, 1}] 1 991isambiguous. { } 5 476 1 991, 1, 10, 0, 0, 0.
>> DateDifference[{1936, 8, 14}, >> DateList[{"31/10/91", {"Day", " {2000, 12, 1}, "Year"] Month", "YearShort"}}] {64.3425, Year} {1 991, 10, 31, 0, 0, 0.}
>> DateDifference[{2010, 6, 1}, >> DateList[{"31 10/91", {"Day", " {2015, 1, 1}, "Hour"] ", "Month", "/", "YearShort"}}] {40 200, Hour} {1 991, 10, 31, 0, 0, 0.}
>> DateDifference[{2003, 8, 11}, If not specified, the current year assumed {2003, 10, 19}, {"Week", "Day"}] >> DateList[{"5/18", {"Month", "Day {{9, Week} , {6, Day}} "}}] {2 021, 5, 18, 0, 0, 0.} DateList DateObject DateList[] returns the current local time in the form DateObject[...] {year, month, day, hour, minute, second}. Returns an object codifiyng DateList.... DateList[time] returns a formatted date for the number >> DateObject[{2020, 4, 15}] of seconds time since epoch Jan 1 1900. [ ] DateList[{y, m, d, h, m, s}] Wed 15 Apr 2 020 00:00:00 GTM − 5 converts an incomplete date list to the standard representation. DateString[string] returns the formatted date list of a date string specification. DateString[string,{e1, e2, ...}] returns the formatted date list of a string obtained from elements ei.
>> DateList[0] {1 900, 1, 1, 0, 0, 0.}
28 DatePlus The current date and time: >> DateString[]; DatePlus[date, n] >> DateString[{1991, 10, 31, 0, 0}, finds the date n days after date. {"Day", " ", "MonthName", " ", DatePlus[date,{n,"unit"}] "Year"}] finds the date n units after date. DatePlus[date, {{n1,"unit1"}, {n2," 31 October 1 991 unit2"}, ...}] >> DateString[{2007, 4, 15, 0}] finds the date which is n_i specified units after date. Sun 15 Apr 2 007 00:00:00 DatePlus[n] >> DateString[{1979, 3, 14}, {" n finds the date days after the current DayName", " ", "Month", "-", " date. YearShort"}] DatePlus[offset] finds the date which is offset from the Wednesday 03-79 current date. Non-integer values are accepted too: Add 73 days to Feb 5, 2010: >> DateString[{1991, 6, 6.5}] >> DatePlus[{2010, 2, 5}, 73] Thu 6 Jun 1 991 12:00:00 {2 010, 4, 19} Add 8 weeks and 1 day to March 16, 1999: $DateStringFormat >> DatePlus[{2010, 2, 5}, {{8, " Week"}, {1, "Day"}}] $DateStringFormat {2 010, 4, 3} gives the format used for dates generated by DateString. DateString >> $DateStringFormat {DateTimeShort} DateString[] returns the current local time and date as a string. EasterSunday DateString[elem] returns the time formatted according to elems. EasterSunday[year] DateString[{e1, e2, ...}] returns the date of the Gregorian Easter concatinates the time formatted accord- Sunday as {year, month, day}. ing to elements ei. DateString[time] >> EasterSunday[2000] returns the date string of an Absolute- { } Time. 2 000, 4, 23 DateString[{y, m, d, h, m, s}] >> EasterSunday[2030] returns the date string of a date list spec- ification. {2 030, 4, 21} DateString[string] returns the formatted date string of a date string specification. Now DateString[spec, elems] formats the time in turns of elems. Both spec and elems can take any of the above Now formats. gives the current time on the system.
29 >> Now Aborted and the results will not affect the state of [Sat 31 Jul 2 021 18:21:12 GTM − 5] the mathics kernel.
Pause TimeRemaining
Pause[n] TimeRemaining[] pauses for n seconds. Gives the number of seconds re- maining until the earliest enclosing TimeConstrained will request the cur- >> Pause[0.5] rent computation to stop. TimeConstrained[expr, t, failexpr] returns failexpr if the time constraint is not SessionTime met.
If TimeConstrained is called out of a TimeCon- SessionTime[] strained expression, returns ‘Infinity‘ returns the total time in seconds since this >> TimeRemaining[] session started. ∞
>> SessionTime[] >> TimeConstrained[1+2; Print[ 32.9581 TimeRemaining[]], 0.9] 0.899142 $SystemTimeZone TimeUsed
$SystemTimeZone gives the current time zone for the com- TimeUsed[] puter system on which Mathics is being returns the total CPU time used for this run. session, in seconds.
>> $SystemTimeZone >> TimeUsed[] −5. 35.0274
TimeConstrained $TimeZone
TimeConstrained[expr, t] $TimeZone evaluates expr, stopping after t gives the current time zone to assume for seconds. dates and times. TimeConstrained[expr, t, failexpr] returns failexpr if the time >> $TimeZone constraint is not met. −5.
Possible issues: for certain time-consuming functions (like simplify) which are based on sympy or other libraries, it is possible that the evaluation continues after the timeout. How- ever, at the end of the evaluation, the function will return $
30 Timing
Timing[expr] measures the processor time taken to evaluate expr. It returns a list containing the measured time in seconds and the re- sult of the evaluation.
>> Timing[50!] {0.000217321, 30 414 093 ˜ ˜201 713 378 043 612 608 166 ˜ ˜064 768 844 377 641 568 ˜ ˜960 512 000 000 000 000}
>> Attributes[Timing] {HoldAll, Protected}
31 2. Input and Output
Contents
MatrixForm ...... 35 Right ...... 38 BaseForm ...... 32 Message ...... 35 Row ...... 38 BoxData ...... 32 MessageName (::) .. 35 StandardForm ..... 38 Center ...... 33 NonAssociative .... 35 StringForm ...... 38 Check ...... 33 NumberForm ..... 35 Subscript ...... 38 Format ...... 33 Off ...... 36 Subsuperscript .... 38 FullForm ...... 33 On ...... 36 Superscript ...... 38 General ...... 33 OutputForm ...... 36 SympyForm ...... 39 Grid ...... 34 Postfix (//) ...... 36 Syntax ...... 39 Infix ...... 34 Precedence ...... 37 TableForm ...... 39 InputForm ...... 34 Prefix (@) ...... 37 TeXForm ...... 39 Left ...... 34 Print ...... 37 TextData ...... 39 MakeBoxes ...... 34 PythonForm 37 ...... ToBoxes ...... 40 MathMLForm ..... 35 Quiet ...... 38
BaseForm >> BaseForm[12, -3] Positivemachine BaseForm[expr, n] −sizedintegerexpectedatposition2inBaseForm[12, prints numbers in expr in base n. − 3]. MakeBoxes[BaseForm[12, − 3], >> BaseForm[33, 2] StandardForm]isnotavalidboxstructure. 100 0012 >> BaseForm[12, 100] >> BaseForm[234, 16] Requestedbase100mustbebetween2and36. ea 16 MakeBoxes[BaseForm[12, 100],
>> BaseForm[12.3, 2] StandardForm]isnotavalidboxstructure.
1 100.010011001100110012
>> BaseForm[-42, 16] BoxData − 2a16
>> BaseForm[x, 2] BoxData[...] x is a low-level representation of the con- tents of a typesetting cell. >> BaseForm[12, 3] // FullForm BaseForm [12, 3]
Bases must be between 2 and 36:
32 Center Raw objects cannot be formatted: >> Format[3] = "three"; Center Cannotassigntorawobject3. is used with the ColumnAlignments op- tion to Grid or TableForm to specify a Format types must be symbols: centered column. >> Format[r, a + b] = "r"; Formattypea + bisnotasymbol.
Formats must be attached to the head of an ex- Check pression: >> f /: Format[g[f]] = "my f"; Check[expr, failexpr] Tagfnotfoundortoodeepforanassignedrule. evaluates expr, and returns the result, un- less messages were generated, in which case it evaluates and failexpr will be re- FullForm turned. Check[expr, failexpr, {s1::t1,s2::t2 ,...}] FullForm[expr] checks only for the specified messages. displays the underlying form of expr.
Return err when a message is generated: >> FullForm[a + b * c] >> Check[1/0, err] Plus [a, Times [b, c]] Infiniteexpression1/0encountered. >> FullForm[2/3] err Rational [2, 3] Check only for specific messages: >> FullForm["A string"] >> Check[Sin[0^0], err, Sin::argx] "A string" Indeterminateexpression00encountered. Indeterminate
>> Check[1/0, err, Power::infy] General Infiniteexpression1/0encountered. err General is a symbol to which all general-purpose messages are assigned. Format >> General::argr ‘1‘ called with 1 argument; Format[expr] holds values specifying how expr should ‘2‘ arguments are expected. be printed. >> Message[Rule::argr, Rule, 2] Rulecalledwith1argument; 2argumentsareexpected. Assign values to Format to control how par- ticular expressions should be formatted when printed to the user. >> Format[f[x___]] := Infix[{x}, "~ Grid "] Grid[{{a1, a2, ...}, {b1, b2, ...}, >> f[1, 2, 3] ...}] ∼ ∼ 1 2 3 formats several expressions inside a
>> f[1] GridBox. 1
33 >> Grid[{{a, b}, {c, d}}] >> InputForm[f’[x]] [ ] a b Derivative [1] f [x] c d >> InputForm[Derivative[1, 0][f][x ]] [ ] Infix Derivative [1, 0] f [x]
Infix[expr, oper, prec, assoc] displays expr with the infix operator oper, Left with precedence prec and associativity as- soc. Left is used with operator formatting con- Infix can be used with Format to display certain structs to specify a left-associative oper- forms with user-defined infix notation: ator. >> Format[g[x_, y_]] := Infix[{x, y }, "#", 350, Left]
>> g[a, g[b, c]] MakeBoxes a# (b#c) MakeBoxes[expr] >> g[g[a, b], c] is a low-level formatting primitive that a#b#c converts expr to box form, without eval- uating it. >> g[a + b, c] \( ... \) (a + b) #c directly inputs box objects.
>> g[a * b, c] ab#c String representation of boxes >> \(x \^ 2\) >> g[a, b] + c SuperscriptBox [x, 2] c + a#b >> \(x \_ 2\) >> g[a, b] * c SubscriptBox [x, 2] c (a#b) >> \( a \+ b \% c\) >> Infix[{a, b, c}, {"+", "-"}] UnderoverscriptBox [a, b, c] a + b − c >> \( a \& b \% c\) UnderoverscriptBox [a, c, b] InputForm >> \(x \& y \) [ ] OverscriptBox x, y InputForm[expr]
displays expr in an unambiguous form >> \(x \+ y \) suitable for input. [ ] UnderscriptBox x, y
>> InputForm[a + b * c] a + b ∗ c MathMLForm >> InputForm["A string"] "A string" MathMLForm[expr] displays expr as a MathML expression.
34 >> MathMLForm[HoldForm[Sqrt[a^3]]] MessageName (::) identifies a message.
>> MathMLForm[\[Mu]] MessageName is the head of message IDs of the >> FullForm[a::b] # This can causes the TeX to fail # » MessageName [a, "b"] MathMLForm[Graphics[Text["µ"]]] # = ... = ... The second parameter tag is interpreted as a string. >> FullForm[a::"b"] MatrixForm MessageName [a, "b"]
MatrixForm[m] displays a matrix m, hiding the underly- NonAssociative ing list structure. NonAssociative >> Array[a,{4,3}]//MatrixForm is used with operator formatting con- a [1, 1] a [1, 2] a [1, 3] structs to specify a non-associative oper- ator. a [2, 1] a [2, 2] a [2, 3] a [3, 1] a [3, 2] a [3, 3] a [4, 1] a [4, 2] a [4, 3] NumberForm
Message NumberForm[expr, n] prints a real number expr with n-digits of Message[symbol::msg, expr1, expr2, ...] precision. NumberForm[expr,{n, f }] displays the specified message, replacing n f placeholders in the message text with the prints with -digits and digits to the corresponding expressions. right of the decimal point.
>> NumberForm[N[Pi], 10] >> a::b = "Hello world!" Hello world! 3.141592654
>> >> Message[a::b] NumberForm[N[Pi], {10, 5}] Helloworld! 3.14159
>> a::c := "Hello ‘1‘, Mr 00‘2‘!" Off >> Message[a::c, "you", 3 + 4] Helloyou, Mr007! Off[symbol::tag] turns a message off so it is no longer printed.
>> Off[Power::infy]
35 >> 1 / 0 >> OutputForm[Graphics[Rectangle ComplexInfinity []]]
>> Off[Power::indet, Syntax::com]
>> {0 ^ 0,} {Indeterminate, Null}
On
On[symbol::tag] turns a message on for printing.
>> Off[Power::infy]
>> 1 / 0 ComplexInfinity Postfix (//)
>> On[Power::infy] x // f >> 1 / 0 is equivalent to f [x]. Infiniteexpression1/0encountered.
ComplexInfinity >> b // a a [b]
OutputForm >> c // b // a a [b [c]]
OutputForm[expr] The postfix operator // is parsed to an expres- displays expr in a plain-text form. sion before evaluation: >> Hold[x // a // b // c // d // e // f] >> OutputForm[f’[x]] [ ] ′ f [x] Hold f [e [d [c [b [a [x]]]]]]
>> OutputForm[Derivative[1, 0][f][x ]] [ ] Precedence Derivative [1, 0] f [x] Precedence[op] >> OutputForm["A string"] returns the precedence of the built-in op- A string erator op.
>> Precedence[Plus] 310.
>> Precedence[Plus] < Precedence[ Times] True Unknown symbols have precedence 670:
36 >> Precedence[f] >> Print["The answer is ", 7 * 6, 670. "."] Other expressions have precedence 1000: Theansweris42. >> Precedence[a + b] 1 000. PythonForm
Prefix (@) PythonForm[expr] returns an approximate equivalent of expr in Python, when that is possible. We f @ x assume that Python has sympy imported. f [x]. is equivalent to No explicit import will be include in the result. >> a @ b
a [b] >> PythonForm[Infinity]
>> a @ b @ c math.inf
a [b [c]] >> PythonForm[Pi]
>> Format[p[x_]] := Prefix[{x}, sympy.pi "*"] >> E // PythonForm
>> p[3] sympy.E ∗3 >> {1, 2, 3} // PythonForm >> Format[q[x_]] := Prefix[{x}, "~ [1, 2, 3] ", 350]
>> q[a+b] Quiet ∼ (a + b)
>> q[a*b] Quiet[expr,{s1::t1, ...}] ∼ ab evaluates expr, without messages {s1:: t1, ...} being displayed. >> q[a]+b Quiet[expr, All] ∼ b+ a evaluates expr, without any messages be- ing displayed. The prefix operator @ is parsed to an expression Quiet[expr, None] before evaluation: evaluates expr, without all messages be- >> Hold[a @ b @ c @ d @ e @ f @ x] [ [ [ [ [ [ ]]]]]] ing displayed. Hold a b c d e f [x] Quiet[expr, off , on] evaluates expr, with messages off being suppressed, but messages on being dis- Print played.
Evaluate without generating messages: Print[expr, ...] >> Quiet[1/0] prints each expr in string form. ComplexInfinity
>> Print["Hello world!"] Same as above: Helloworld! >> Quiet[1/0, All] ComplexInfinity
37 >> a::b = "Hello"; >> "A string" A string >> Quiet[x+x, {a::b}] 2x >> f’[x] ′ f x >> Quiet[Message[a::b]; x+x, {a::b [ ] }] 2x StringForm >> Message[a::b]; y=Quiet[Message[a ::b]; x+x, {a::b}]; Message[a::b ]; y StringForm[str, expr1, expr2, ...] displays the string str, replacing place- Hello holders in str with the corresponding ex- Hello pressions. 2x
>> Quiet[x + x, {a::b}, {a::b}] >> StringForm["‘1‘ bla ‘2‘ blub ‘‘ InQuiet[x + x, {a :: b}, bla ‘2‘", a, b, c] {a :: b}]themessagename(s){a :: b}appearinboththelistofmessagestoswitchofa bla b blub c bla b fandthelistofmessagestoswitchon. [ ] Quiet x + x, {a::b} , {a::b} Subscript Right Subscript[a, i] displays as a_i. Right is used with operator formatting con- structs to specify a right-associative op- >> Subscript[x,1,2,3] // TeXForm erator. x_{1,2,3}
Row Subsuperscript
Row[{expr, ...}] Subsuperscript[a, b, c] ∧ formats several expressions inside a displays as $a_b c$. RowBox.
>> Subsuperscript[a, b, c] // TeXForm ∧ StandardForm a_b c
StandardForm[expr] displays expr in the default form. Superscript
>> StandardForm[a + b * c] Superscript[x, y] ∧ a + bc displays as x y.
>> StandardForm["A string"] >> Superscript[x,3] // TeXForm A string ∧ x 3 StandardForm is used by default:
38 SympyForm >> Table[Style[Graphics[{EdgeForm[{ Black}], RGBColor[r,g,b], Rectangle[]}], SympyForm[expr] ImageSizeMultipliers->{0.2, 1}], returns an Sympy expr in Python. Sympy {r,0,1,1/2}, {g,0,1,1/2}, {b is used internally to implement a number ,0,1,1/2}] // TableForm of Mathics functions, like Simplify.
>> SympyForm[Pi^2] pi**2
>> E^2 + 3E // SympyForm exp(2) + 3*E
Syntax
Syntax is a symbol to which all syntax messages are assigned.
>> 1 +
>> Sin[1)
>> ^ 2
>> 1.5‘‘
TableForm
TableForm[expr] displays expr as a table. TeXForm
>> TableForm[Array[a, {3,2}], TableDepth->1] TeXForm[expr] {a [1, 1] , a [1, 2]} displays expr using TeX math mode com- {a [2, 1] , a [2, 2]} mands. {a [3, 1] , a [3, 2]} >> TeXForm[HoldForm[Sqrt[a^3]]] ∧ A table of Graphics: \sqrt{a 3}
TextData
TextData[...] is a low-level representation of the con- tents of a textual cell.
39 ToBoxes
ToBoxes[expr] evaluates expr and converts the result to box form.
Unlike MakeBoxes, ToBoxes evaluates its argu- ment: >> ToBoxes[a + a] [ ] RowBox {2,, a}
>> ToBoxes[a + b] [ ] RowBox {a, +, b}
>> ToBoxes[a ^ b] // FullForm SuperscriptBox ["a", "b"]
40 3. Procedural Programming
Procedural programming is a programming ply contain a series of computational steps to paradigm, derived from imperative program- be carried out. Any given procedure might be ming, based on the concept of the procedure called at any point during a program’s execu- call. This term is sometimes compared and con- tion, including by other procedures or itself. trasted with Functional Programming. Procedural functions are integrated into Mathics Procedures (a type of routine or subroutine) sim- symbolic programming environment.
Contents
FixedPoint ...... 42 NestWhile ...... 44 Abort ...... 41 FixedPointList ..... 43 Return ...... 44 Break ...... 41 For ...... 43 Switch ...... 44 Catch ...... 42 If 43 Throw 45 CompoundExpression ...... (;) ...... 42 Interrupt ...... 43 Which ...... 45 Continue ...... 42 Nest ...... 43 While ...... 45 Do ...... 42 NestList ...... 44
Abort Catch
Abort[] Catch[expr] aborts an evaluation completely and re- returns the argument of the first Throw turns $Aborted. generated in the evaluation of expr. Catch[expr, form]
>> Print["a"]; Abort[]; Print["b"] returns value from the first Throw[value, a tag] for which form matches tag. $Aborted Catch[expr, form, f ] returns f [value, tag].
Break Exit to the enclosing Catch as soon as Throw is evaluated: >> Catch[r; s; Throw[t]; u; v] Break[] t exits a For, While, or Do loop. Define a function that can “throw an exception”:
>> n = 0; >> f[x_] := If[x > 12, Throw[ overflow], x!] >> While[True, If[n>10, Break[]]; n =n+1] The result of Catch is just what is thrown by Throw: >> n >> Catch[f[1] + f[15]] 11 overflow
>> Catch[f[1] + f[4]] 25
41 CompoundExpression (;) >> Do[Print[{i, j}], {i,1,2}, {j ,3,5}] {1, 3} CompoundExpression[e1, e2, ...] e1; e2; ... {1, 4} evaluates its arguments in turn, returning {1, 5} the last result. {2, 3}
>> a; b; c; d {2, 4} d {2, 5}
If the last argument is omitted, Null is taken: You can use Break[] and Continue[] inside Do: >> a; >> Do[If[i > 10, Break[], If[Mod[i, 2] == 0, Continue[]]; Print[i ]], {i, 5, 20}] Continue 5 7 9 Continue[] continues with the next iteration in a For, While, or Do loop. FixedPoint
>> For[i=1, i<=8, i=i+1, If[Mod[i ,2] == 0, Continue[]]; Print[i]] FixedPoint[f , expr] 1 starting with expr, iteratively applies f until the result no longer changes. 3 FixedPoint[f , expr, n] 5 performs at most n iterations. The same 7 that using $MaxIterations->n$
Do >> FixedPoint[Cos, 1.0] 0.739085
Do[expr,{max}] >> FixedPoint[#+1 &, 1, 20] evaluates expr max times. 21 Do[expr,{i, max}] evaluates expr max times, substituting i in expr with values from 1 to max. FixedPointList Do[expr,{i, min, max}] starts with i = max. Do[expr,{i, min, max, step}] FixedPointList[f , expr] uses a step size of step. starting with expr, iteratively applies f Do[expr,{i,{i1, i2, ...}}] until the result no longer changes, and re- uses values i1, i2, ... for i. turns a list of all intermediate results. Do[expr,{i, imin, imax}, {j, jmin, FixedPointList[f , expr, n] jmax}, ...] performs at most n iterations. evaluates expr for each j from jmin to jmax, for each i from imin to imax, etc. >> FixedPointList[Cos, 1.0, 4] {1., 0.540302, 0.857˜ >> Do[Print[i], {i, 2, 4}] ˜553, 0.65429, 0.79348} 2 3 Observe the convergence of Newton’s method for approximating square roots: 4
42 >> newton[n_] := FixedPointList If [.5(# + n/#)&, 1.]; If[ , , ] >> newton[9] cond pos neg returns pos if cond evaluates to True, and {1., 5., 3.4, 3.02353, 3.00009, 3., 3., 3.} neg if it evaluates to False. Plot the “hailstone” sequence of a number: If[cond, pos, neg, other] returns other if cond evaluates to neither >> collatz[1] := 1; True nor False. If[cond, pos] >> collatz[x_ ? EvenQ] := x / 2; returns Null if cond evaluates to False.
>> collatz[x_] := 3 x + 1; >> If[1<2, a, b]
>> list = FixedPointList[collatz, a 14] If the second branch is not specified, Null is {14, 7, 22, 11, 34, 17, 52, 26, 13, taken: 40, 20, 10, 5, 16, 8, 4, 2, 1, 1} >> If[1<2, a] a >> ListLinePlot[list] >> If[False, a] //FullForm 40 Null 30 You might use comments (inside (* and *)) to make the branches of If more readable: 20 >> If[a, (*then*)b, (*else*)c]; 10 Interrupt 5 10 15 20
Interrupt[] For Interrupt an evaluation and returns $Aborted.
For[ , , , ] start test incr body >> Print["a"]; Interrupt[]; Print[" evaluates start, and then iteratively body b"] and incr as long as test evaluates to True. a For[start, test, incr] evaluates only incr and no body. $Aborted For[start, test] runs the loop without any body. Nest Compute the factorial of 10 using For: >> n := 1 Nest[f , expr, n] starting with expr, iteratively applies f n >> For[i=1, i<=10, i=i+1, n = n * i times and returns the final result. ]
>> Nest[f, x, 3] >> n [ [ ]] 3 628 800 f f f [x]
>> n == 10! >> Nest[(1+#)^ 2 &, x, 2] ( ) True 2 1 + (1 + x)2
43 NestList Return
NestList[f , expr, n] Return[expr] starting with expr, iteratively applies f n aborts a function call and returns expr. times and returns a list of all intermedi-
ate results. >> f[x_] := (If[x < 0, Return[0]]; x) >> NestList[f, x, 3] { [ ] [ [ ]]} x, f [x] , f f [x] , f f f [x] >> f[-1] 0 >> NestList[2 # &, 1, 8] >> Do[If[i > 3, Return[]]; Print[i { } 1, 2, 4, 8, 16, 32, 64, 128, 256 ], {i, 10}] Chaos game rendition of the Sierpinski triangle: 1 >> vertices = {{0,0}, {1,0}, {.5, 2 .5 Sqrt[3]}}; 3 Return only exits from the innermost control >> points = NestList[.5(vertices[[ RandomInteger[{1,3}] ]] + #)&, flow construct. {0.,0.}, 2000]; >> g[x_] := (Do[If[x < 0, Return [0]], {i, {2, 1, 0, -1}}]; x)
>> Graphics[Point[points], ImageSize->Small] >> g[-1] −1
Switch
Switch[expr, pattern1, value1, pattern2, value2, ...] yields the first value for which expr matches the corresponding pattern. NestWhile
>> Switch[2, 1, x, 2, y, 3, z] NestWhile[f , expr, test] y applies a function f repeatedly on an ex- >> Switch[5, 1, x, 2, y] pression expr, until applying test on the [ ] result no longer yields True. Switch 5, 1, x, 2, y NestWhile[f , expr, test, m] supplies the last m results to test (default >> Switch[5, 1, x, 2, a, _, b] value: 1). b NestWhile[f , expr, test, All] >> Switch[2, 1] supplies all results gained so far to test. Switchcalledwith2arguments.Switchmustbecalledwithanoddnumberof arguments. Divide by 2 until the result is no longer an inte- Switch [2, 1] ger: >> NestWhile[#/2&, 10000, IntegerQ] 625 2
44 Throw arguments: >> Which[a, b, c] Throw[‘value‘] Whichcalledwith3arguments. stops evaluation and returns ‘value‘ as Which [a, b, c] the value of the nearest enclosing Catch. Catch[‘value‘, ‘tag‘] is caught only by ‘Catch[expr,form]‘, While where tag matches form.
Using Throw can affect the structure of what is While[test, body] returned by a function: evaluates body as long as test evaluates to True. >> NestList[#^2 + 1 &, 1, 7] While[ ] { test 1, 2, 5, 26, 677, 458 330, runs the loop without any body. 210 066 388 901, 44 127 ˜ } ˜887 745 906 175 987 802 Compute the GCD of two numbers: >> {a, b} = {27, 6}; >> Catch[NestList[If[# > 1000, Throw[#], #^2 + 1] &, 1, 7]] >> While[b != 0, {a, b} = {b, Mod[a 458 330 , b]}];
>> Throw[1] >> a UncaughtHold[Throw[1]]returnedtotoplevel. 3 Hold [Throw [1]]
Which
Which[cond1, expr1, cond2, expr2, ...] yields expr1 if cond1 evaluates to True, expr2 if cond2 evaluates to True, etc.
>> n = 5;
>> Which[n == 3, x, n == 5, y] y
>> f[x_] := Which[x < 0, -x, x == 0, 0, x > 0, x]
>> f[-3] 3 If no test yields True, Which returns Null: >> Which[False, a]
If a test does not evaluate to True or False, eval- uation stops and a Which expression containing the remaining cases is returned: >> Which[False, a, x, b, True, c] Which [x, b, True, c]
Which must be called with an even number of
45 4. Global System Information
Contents
MathicsVersion .... 47 $ScriptCommandLine . 48 $Aborted ...... 46 MemoryAvailable ... 47 Share ...... 48 $ByteOrdering ..... 46 MemoryInUse ..... 47 $SystemID ...... 48 $CommandLine .... 46 Names ...... 47 $SystemMemory ... 48 Environment ..... 46 $Packages ...... 47 $SystemWordLength . 49 $Failed ...... 46 $ParentProcessID ... 48 $UserName ...... 49 GetEnvironment .... 46 $ProcessID ...... 48 $Version ...... 49 $Machine ...... 47 $ProcessorType .... 48 $VersionNumber ... 49 $MachineName .... 47 Run ...... 48
$Aborted Environment
$Aborted Environment[var] is returned by a calculation that has been gives the value of an operating system aborted. environment variable.
>> Environment["HOME"] $ByteOrdering /home/rocky
$ByteOrdering $Failed returns the native ordering of bytes in bi- nary data on your computer system. $Failed is returned by some functions in the event >> $ByteOrdering of an error. −1
$CommandLine GetEnvironment
GetEnvironment["var"] $CommandLine gives the setting corresponding to the is a list of strings passed on the command variable “var” in the operating system line to launch the Mathics session. environment.
>> $CommandLine >> GetEnvironment["HOME"] { docpipeline.py, HOME− > /home/rocky –output, –keep-going}
46 $Machine MemoryInUse
$Machine MemoryInUse[] returns a string describing the type of Returns the amount of memory used by computer system on which the Mathics is the definitions object. being run.
>> MemoryInUse[] >> $Machine 48 linux
Names $MachineName
Names["pattern"] $MachineName returns the list of names matching pattern. is a string that gives the assigned name of the computer on which Mathics is being >> Names["List"] run, if such a name is defined. {List}
>> $MachineName The wildcard * matches any character: muffin >> Names["List*"] {List, ListLinePlot, MathicsVersion ListPlot, ListQ, Listable} The wildcard @ matches only lowercase charac- MathicsVersion ters: this string is the version of Mathics we are >> Names["List@"] running. {Listable}
>> x = 5; >> MathicsVersion 4.0.0 >> Names["Global‘*"] {x}
MemoryAvailable The number of built-in symbols: >> Length[Names["System‘*"]] MemoryAvailable 1 109 Returns the amount of the available physical memory. $Packages
>> MemoryAvailable[] 9 210 286 080 $Packages The relationship between $SystemMemory, returns a list of the contexts correspond- MemoryAvailable, and MemoryInUse: ing to all packages which have been >> $SystemMemory > MemoryAvailable loaded into Mathics. [] > MemoryInUse[] >> $Packages True {ImportExport‘, XML‘, Internal‘, System‘, Global‘}
47 $ParentProcessID >> $ScriptCommandLine {} $ParentProcesID gives the ID assigned to the process which invokes the Mathics by the operat- Share ing system under which it is run. Share[] >> $ParentProcessID Tries to reduce the amount of memory re- 883 272 quired to store definitions, by reducing duplicated definitions. Now it just do nothing. $ProcessID Share[Symbol] Tries to reduce the amount of memory re- quired to store definitions associated to $ProcessID Symbol. gives the ID assigned to the Mathics process by the operating system under which it is run. >> Share[] 0
>> $ProcessID 883 273 $SystemID $ProcessorType $SystemID is a short string that identifies the type of $ProcessorType computer system on which the Mathics is gives a string giving the architecture of being run. the processor on which the Mathics is be- ing run. >> $SystemID linux >> $ProcessorType x86_64 $SystemMemory Run $SystemMemory Returns the total amount of physical Run[command] memory. runs command as an external operating
system command, returning the exit code >> $SystemMemory obtained. 33 691 598 848
>> Run["date"] 0 $SystemWordLength
$ScriptCommandLine $SystemWordLength gives the effective number of bits in raw machine words on the computer system $ScriptCommandLine where Mathics is running. is a list of string arguments when running the kernel is script mode.
48 >> $SystemWordLength 64
$UserName
$UserName returns a string describing the type of computer system on which Mathics is be- ing run.
>> $UserName rocky
$Version
$Version returns a string with the current Math- ics version and the versions of relevant libraries.
>> $Version Mathics 4.0.0 on CPython 3.9.6 (default, Jul 3 2 021, 19:28:34) using SymPy 1.8, mpmath 1.2.1, numpy 1.21.0
$VersionNumber
$VersionNumber is a real number which gives the current Wolfram Language version that Mathics tries to be compatible with.
>> $VersionNumber 10.
49 5. SparseArray Functions
Contents
SparseArray ...... 50
SparseArray
SparseArray[rules] Builds a sparse array acording to the list of rules. SparseArray[rules, dims] Builds a sparse array of dimensions dims acording to the rules. SparseArray[list] Builds a sparse representation of list.
>> SparseArray[{{1, 2} -> 1, {2, 1} -> 1}] [ { } SparseArray Automatic, 2, 2 ,] 0, {{1, 2} − > 1, {2, 1} − > 1}
>> SparseArray[{{1, 2} -> 1, {2, 1} -> 1}, {3, 3}] [ { } SparseArray Automatic, 3, 3 ,] 0, {{1, 2} − > 1, {2, 1} − > 1}
>> M=SparseArray[{{0, a}, {b, 0}}] [ { } SparseArray Automatic, 2, 2 ,] 0, {{1, 2} − > a, {2, 1} − > b}
>> M //Normal {{0, a} , {b, 0}}
50 6. Solving Recurrence Equations
Contents
RSolve ...... 51
RSolve
RSolve[eqn, a[n], n] solves a recurrence equation for the func- tion a[n].
Solve a difference equation: >> RSolve[a[n] == a[n+1], a[n], n] {{a [n] − > C [0]}}
No boundary conditions gives two general para- maters: >> RSolve[{a[n + 2] == a[n]}, a, n] {{ ( [ − { } a > Function ])}}n , ∧ C [0] + C [1] − 1 n
Include one boundary condition: >> RSolve[{a[n + 2] == a[n], a[0] == 1}, a, n] {{ ( [ − { } a > Function n ])}}, ∧ 1 − C [1] + C [1] − 1 n
Geta “pure function” solution for a with two boundary conditions: >> RSolve[{a[n + 2] == a[n], a[0] == 1, a[1] == 4}, a, n] {{ ( [ a− > Function ∧ ])}} 5 3 − 1 n {n} , − 2 2
51 7. Rules and Patterns
The concept of transformation rules for arbitrary Leaves in the beginning of a pattern rather symbolic patterns is key in Mathics. match fewer leaves: » f[a, b, c, d] /. f[start__, Also, functions can get applied or transformed end__] -> {{start}, {end}} = {{a}, {b, c, d}} depending on whether or not functions argu- Optional arguments using Optional: » f[a] /. ments match. f[x_, y_:3] -> {x, y} = {a, 3} Some examples: » a + b + c /. a + b -> t = c + t Options using OptionsPattern and » a + 2 + b + c + x * y /. n_Integer + s__Symbol OptionValue: » f[y, a->3] /. f[x_, + rest_ -> {n, s, rest} = {2, a, b + c + x y} » f[a, b, OptionsPattern[{a->2, b->5}]] -> {x, OptionVa- c, d] /. f[first_, rest___] -> {first, {rest}} = {a, {b, c, lue[a], OptionValue[b]} = {y, 3, 5} d}} The attributes Flat, Orderless, and Tests and Conditions: » f[4] /. f[x_?(# > 0&)] -> OneIdentity affect pattern matching. ∧ ∧ x 2 = 16 » f[4] /. f[x_] /; x > 0 -> x 2 = 16
Contents
Longest ...... 54 Replace ...... 57 Alternatives (|) .... 52 MatchQ ...... 54 ReplaceAll (/.) .... 57 Blank ...... 53 Optional (:) ...... 55 ReplaceList ...... 57 BlankNullSequence .. 53 OptionsPattern .... 55 ReplaceRepeated (//.) 58 BlankSequence .... 53 PatternTest (?) ..... 55 RuleDelayed (:>) 58 Condition (/;) ..... 53 ... Pattern 56 -> Dispatch ...... 53 ...... Rule ( ) ...... 58 .. Except ...... 54 Repeated ( ) ..... 56 Verbatim ...... 58 HoldPattern ...... 54 RepeatedNull (...) .. 56
Alternatives (|) Blank
Blank[] Alternatives[p1, p2, ..., p_i] _ p1 | p2 | ... | p_i is a pattern that matches any of the pat- represents any single expression in a pat- terns ’p1, p2, ...., p_i’. tern. Blank[h] _h >> a+b+c+d/.(a|b)->t represents any expression with head h. c + d + 2t
Alternatives can also be used for string expres- >> MatchQ[a + b, _] sions True >> StringReplace["0123 3210", "1" | "2" -> "X"] Patterns of the form _h can be used to test the types of objects: 0XX3 3XX0 >> MatchQ[42, _Integer] True
52 >> MatchQ[1.0, _Integer] >> MatchQ[f[1, 2.0, 3], f[__Integer False ]] False >> {42, 1.0, x} /. {_Integer -> " integer", _Real -> "real"} // The value captured by a named BlankSequence InputForm pattern is a Sequence object: {"integer", "real", x} >> f[1, 2, 3] /. f[x__] -> x Sequence [1, 2, 3] Blank only matches a single expression: >> MatchQ[f[1, 2], f[_]] False Condition (/;)
BlankNullSequence Condition[pattern, expr] pattern /; expr places an additional constraint on pattern BlankNullSequence[] that only allows it to match if expr evalu- ___ ates to True. represents any sequence of expression leaves in a pattern, including an empty The controlling expression of a Condition can sequence. use variables from the pattern: >> f[3] /. f[x_] /; x>0 -> t BlankNullSequence is like BlankSequence, ex- t cept it can match an empty sequence: >> f[-3] /. f[x_] /; x>0 -> t >> MatchQ[f[], f[___]] − True f [ 3] Condition can be used in an assignment: BlankSequence >> f[x_] := p[x] /; x>0
>> f[3] BlankSequence[] p [3] __ >> f[-3] represents any non-empty sequence of − expression leaves in a pattern. f [ 3] BlankSequence[h] __h represents any sequence of leaves, all of Dispatch which have head h.
Use a BlankSequence pattern to stand for a non- Dispatch[rulelist] empty sequence of arguments: Introduced for compatibility. Currently, >> MatchQ[f[1, 2, 3], f[__]] it just return rulelist. In the fu- ture, it should return an optimized Dis- True patchRules atom, containing an opti- >> MatchQ[f[], f[__]] mized set of rules. False __h will match only if all leaves have head h: >> MatchQ[f[1, 2, 3], f[__Integer]] True
53 Except MatchQ
Except[c] MatchQ[expr, form] represents a pattern object that matches tests whether expr matches form. any expression except those matching c.
Except[c, p] >> MatchQ[123, _Integer] represents a pattern object that matches p True but not c. >> MatchQ[123, _Real] >> Cases[{x, a, b, x, c}, Except[x False ]] >> MatchQ[_Integer][123] {a, b, c} True
>> Cases[{a, 0, b, 1, c, 2, 3}, >> MatchQ[3, Pattern[3]] Except[1, _Integer]] FirstelementinpatternPattern[3]isnotavalidpatternname. {0, 2, 3} False Except can also be used for string expressions: >> StringReplace["Hello world!", Except[LetterCharacter] -> ""] Optional (:) Helloworld Optional[patt, default] patt : default HoldPattern is a pattern which matches patt, which if omitted should be replaced by default. HoldPattern[expr] is equivalent to expr for pattern matching, >> f[x_, y_:1] := {x, y} but maintains it in an unevaluated form. >> f[1, 2]
>> HoldPattern[x + x] {1, 2} HoldPattern [x + x] >> f[a] >> x /. HoldPattern[x] -> t {a, 1} t Note that symb : patt represents a Pattern ob- HoldPattern has attribute HoldAll: ject. However, there is no disambiguity, since >> Attributes[HoldPattern] symb has to be a symbol in this case. {HoldAll, Protected} >> x:_ // FullForm Pattern [x, Blank []]
Longest >> _:d // FullForm Optional [Blank [] , d]
>> StringCases["aabaaab", Longest[" >> x:_+y_:d // FullForm a" ~~__ ~~"b"]] [ [ Pattern x, Plus Blank , {aabaaab} [ [ [] ] ]]] Optional Pattern y, Blank [] , d >> StringCases["aabaaab", Longest[ RegularExpression["a+b"]]] s_. is equivalent to Optional[s_] and repre- { } sents an optional parameter which, if omitted, aab, aaab gets its value from Default.
54 >> FullForm[s_.] PatternTest (?) Optional [Pattern [s, Blank []]]
>> Default[h, k_] := k PatternTest[pattern, test] pattern ? test >> h[a] /. h[x_, y_.] -> {x, y} constrains pattern to match expr only if the {a, 2} evaluation of test[expr] yields True.
>> MatchQ[3, _Integer?(#>0&)] OptionsPattern True
>> MatchQ[-3, _Integer?(#>0&)] OptionsPattern[f ] False is a pattern that stands for a sequence >> MatchQ[3, Pattern[3]] of options given to a function, with de- fault values taken from Options[f ]. The FirstelementinpatternPattern[3]isnotavalidpatternname. options can be of the form opt->value or False opt:>value, and might be in arbitrarily nested lists. OptionsPattern[{opt1->value1, ...}] Pattern takes explicit default values from the given list. The list may also contain symbols f, for which Options[f ] is taken Pattern[symb, patt] into account; it may be arbitrarily nested. symb : patt OptionsPattern[{}] does not use any assigns the name symb to the pattern patt. default values. symb_head is equivalent to symb :_head (accord- The option values can be accessed using ingly with __ and ___). OptionValue. symb : patt : default is a pattern with name symb and default >> f[x_, OptionsPattern[{n->2}]] := Optional[ x ^ OptionValue[n] value default, equivalent to patt : symb, default].
>> f[x] x2 >> FullForm[a_b] Pattern [a, Blank [b]] >> f[x, n->3] x3 >> FullForm[a:_:b] Optional [Pattern [a, Blank []] , b] Delayed rules as options: >> e = f[x, n:>a] Pattern has attribute HoldFirst, so it does not xa evaluate its name: >> x = 2 >> a = 5; 2
>> e >> x_ x5 x_ Options might be given in nested lists: Nested Pattern assign multiple names to the same pattern. Still, the last parameter is the de- >> f[x, {{{n->4}}}] fault value. x4 >> f[y] /. f[a:b,_:d] -> {a, b} [ ] f y
This is equivalent to:
55 >> f[a] /. f[a:_:b] -> {a, b} Replace {a, b}
FullForm: Replace[expr, x -> y]
>> FullForm[a:b:c:d:e] yields the result of replacing expr with y [ if it matches the pattern x. Optional Pattern a, b , [ ] ] Replace[expr, x -> y, levelspec] Optional [Pattern [c, d] , e] replaces only subexpressions at levels specified through levelspec. >> f[] /. f[a:_:b] -> {a, b} Replace[expr,{x -> y, ...}] {b, b} performs replacement with multiple rules, yielding a single result expression. Replace[expr, {{a -> b, ...}, {c -> Repeated (..) d, ...}, ...}] returns a list containing the result of per- forming each set of replacements. Repeated[pattern] matches one or more occurrences of pat- >> Replace[x, {x -> 2}] tern. 2
>> a_Integer.. // FullForm By default, only the top level is searched for [ [ [ ]]] matches Repeated Pattern a, Blank Integer >> Replace[1 + x, {x -> 2}]
>> 0..1//FullForm 1 + x Repeated [0] >> Replace[x, {{x -> 1}, {x -> 2}}]
>> {{}, {a}, {a, b}, {a, a, a}, {a, {1, 2} a, a, a}} /. {Repeated[x : a | b, 3]} -> x Replace stops after the first replacement >> Replace[x, {x -> {}, _List -> y {{} { } { }} , a, a, b , a, a, a, a, a }]
>> f[x, 0, 0, 0] /. f[x, s:0..] -> {} s Replace replaces the deepest levels first Sequence [0, 0, 0] >> Replace[x[1], {x[1] -> y, 1 -> 2}, All] RepeatedNull (...) x [2] By default, heads are not replaced >> Replace[x[x[y]], x -> z, All] RepeatedNull[pattern] [ [ ]] matches zero or more occurrences of pat- x x y tern. Heads can be replaced using the Heads option >> Replace[x[x[y]], x -> z, All, >> a___Integer...//FullForm [ [ Heads -> True] RepeatedNull Pattern[ a, ]]] [ [ ]] BlankNullSequence Integer z z y
>> f[x] /. f[x, 0...] -> t Note that heads are handled at the level of leaves t >> Replace[x[x[y]], x -> z, {1}, Heads -> True] [ [ ]] z x y
You can use Replace as an operator
56 >> Replace[{x_ -> x + 1}][10] ReplaceList 11 ReplaceList[expr, rules] returns a list of all possible results of ap- ReplaceAll (/.) plying rules to expr.
ReplaceAll[expr, x -> y] Get all subsequences of a list: expr /. x -> y >> ReplaceList[{a, b, c}, {___, x__ yields the result of replacing all subex- , ___} -> {x}] pressions of expr matching the pattern x {{a} , {a, b} , {a, b, with y. c} , {b} , {b, c} , {c}} expr /. {x -> y, ...} performs replacement with multiple You can specify the maximum number of items: rules, yielding a single result expression. >> ReplaceList[{a, b, c}, {___, x__ expr /. {{a -> b, ...}, {c -> d, ...}, , ___} -> {x}, 3] ...} returns a list containing the result of per- {{a} , {a, b} , {a, b, c}} forming each set of replacements. >> ReplaceList[{a, b, c}, {___, x__ , ___} -> {x}, 0] >> a+b+c /. c->d {} a + b + d
>> g[a+b+c,a]/.g[x_+y_,x_]->{x,y} If no rule matches, an empty list is returned: {a, b + c} >> ReplaceList[a, b->x] {} If rules is a list of lists, a list of all possible respec- tive replacements is returned: Like in ReplaceAll, rules can be a nested list: >> {a, b} /. {{a->x, b->y}, {a->u, >> ReplaceList[{a, b, c}, {{{___, b->v}} x__, ___} -> {x}}, {{a, b, c} -> t}}, 2] {{x, y} , {u, v}} {{{a} , {a, b}} , {t}} The list can be arbitrarily nested: >> {a, b} /. {{{a->x, b->y}, {a->w, >> ReplaceList[expr, {}, -1] b->z}}, {a->u, b->v}} Non {{{ } { }} { }} −negativeintegerorInfinityexpectedatposition3. x, y , w, z , u, v [ ] ReplaceList expr, {} , − 1 >> {a, b} /. {{{a->x, b->y}, a->w, b->z}, {a->u, b->v}} Possible matches for a sum: Elementso f {{a− > x, b− > y}, a− > w, >> ReplaceList[a + b + c, x_ + y_ b− > z}areamixtureoflistsandnonlists. -> {x, y}] {{a, b} /. {{a− > x, b− > y} , {{a, b + c} , {b, a + c} , {c, a + b} , a− > w, b− > z} , {u, v}} {a + b, c} , {a + c, b} , {b + c, a}}
ReplaceAll also can be used as an operator: >> ReplaceAll[{a -> 1}][{a, b}] ReplaceRepeated (//.) {1, b}
ReplaceAll replaces the shallowest levels first: ReplaceRepeated[expr, x -> y] >> ReplaceAll[x[1], {x[1] -> y, 1 expr //. x -> y -> 2}] repeatedly applies the rule x -> y to expr y until the result no longer changes.
57 >> a+b+c //. c->d Verbatim a + b + d
>> f = ReplaceRepeated[c->d]; Verbatim[expr] prevents pattern constructs in expr from >> f[a+b+c] taking effect, allowing them to match a + b + d themselves.
>> Clear[f]; Create a pattern matching Blank: >> _ /. Verbatim[_]->t Simplification of logarithms: t >> logrules = {Log[x_ * y_] :> Log[
x] + Log[y], Log[x_ ^ y_] :> y * >> x /. Verbatim[_]->t Log[x]}; x
>> Log[a * (b * c)^ d ^ e * f] //. Without Verbatim, Blank has its normal effect: logrules >> x /. _->t [ ] ( ) Log [a] + Log f + Log [b] + Log [c] de t
ReplaceAll just performs a single replacement: >> Log[a * (b * c)^ d ^ e * f] /. logrules [ ] e Log [a] + Log f (bc)d
RuleDelayed (:>)
RuleDelayed[x, y] x :> y represents a rule replacing x with y, with y held unevaluated.
>> Attributes[RuleDelayed] {HoldRest, Protected, SequenceHold}
Rule (->)
Rule[x, y] x -> y represents a rule replacing x with y.
>> a+b+c /. c->d a + b + d
>> {x,x^2,y} /. x->3 {3, 9, y}
58 8. Mathematical Functions
Basic arithmetic functions, including complex number arithmetic. Contents
ExactNumberQ .... 61 Piecewise ...... 64 Abs ...... 59 Factorial (!) ...... 62 PossibleZeroQ ..... 64 Arg ...... 60 Factorial2 (!!) ..... 62 Product ...... 64 Assuming ...... 60 I ...... 62 Rational ...... 65 $Assumptions ..... 60 Im ...... 62 Re ...... 65 Boole ...... 60 InexactNumberQ ... 63 RealNumberQ ..... 65 Complex ...... 60 IntegerQ ...... 63 Real ...... 65 ConditionalExpression 61 Integer ...... 63 Sign ...... 65 Conjugate ...... 61 MachineNumberQ .. 63 Sum ...... 66 DirectedInfinity .... 61 NumberQ ...... 63
Abs Arg
Abs[x] Arg[z, method_option] returns the absolute value of x. returns the argument of a complex value z. >> Abs[-3] 3 • Arg[z] is left unevaluated if z is not a nu- meric quantity. Abs returns the magnitude of complex numbers: >> Abs[3 + I] • Arg[z] gives the phase angle of z in radi- √ ans. 10 • The result from Arg[z] is always be- >> Abs[3.0 + I] tween -Pi and +Pi. 3.16228 • Arg[z] has a branch cut discontinuity >> Plot[Abs[x], {x, -4, 4}] in the complex z plane running from - 4 Infinity to 0. 3 • Arg[0] is 0. 2 >> Arg[-3] 1 Pi Same as above using sympy’s method: −4 −2 2 4 >> Arg[-3, Method->"sympy"] Pi
>> Arg[1-I] − Pi 4
59 Arg evaluate the direction of DirectedInfinity Boole quantities by the Arg of they arguments: >> Arg[DirectedInfinity[1+I]] Boole[expr] Pi returns 1 if expr is True and 0 if expr is 4 False.
>> Arg[DirectedInfinity[]] >> Boole[2 == 2] 1 1 Arg for 0 is assumed to be 0: >> Boole[7 < 5] >> Arg[0] 0 0 >> Boole[a == 7] Boole [a==7] Assuming Complex Assuming[cond, expr] Evaluates expr assuming the conditions cond. Complex is the head of complex numbers.
>> $Assumptions = { x > 0 } Complex[a, b] constructs the complex number a + I b. {x > 0}
>> Assuming[y>0, >> Head[2 + 3*I] ConditionalExpression[y x^2, y Complex >0]//Simplify] >> Complex[1, 2/3] x2y 2I 1 + >> Assuming[Not[y>0], 3 ConditionalExpression[y x^2, y >0]//Simplify] >> Abs[Complex[3, 4]] 5 Undefined
>> ConditionalExpression[y x ^ 2, y > 0]//Simplify ConditionalExpression [ ] ConditionalExpression x2y, y > 0 ConditionalExpression[expr, cond] returns expr if cond evaluates to True, Un- $Assumptions defined if cond evaluates to False.
>> ConditionalExpression[x^2, True] $Assumptions x2 is the default setting for the Assumptions option used in such functions as Simplify, >> ConditionalExpression[x^2, False Refine, and Integrate. ] Undefined
>> f = ConditionalExpression[x^2, x >0] [ ] ConditionalExpression x2, x > 0
60 >> f /. x -> 2 >> DirectedInfinity[1] 4 ∞
>> f /. x -> -2 >> DirectedInfinity[] Undefined ComplexInfinity ConditionalExpression uses assumptions to >> DirectedInfinity[1 + I] evaluate the condition: ( ) √ 1 I >> $Assumptions = x > 0; + 2∞ 2 2
>> ConditionalExpression[x ^ 2, x >> 1 / DirectedInfinity[1 + I] >0]//Simplify 0 x2 >> DirectedInfinity[1] + >> $Assumptions = True; DirectedInfinity[-1]
# » ConditionalExpression[ConditionalExpression[s,x>a], Indeterminateexpression xa, − In f inity + Infinityencountered. x>> DirectedInfinity[0] Conjugate Indeterminateexpression0Infinityencountered. Indeterminate Conjugate[z] returns the complex conjugate of the complex number z. ExactNumberQ
>> Conjugate[3 + 4 I] ExactNumberQ[expr] 3 − 4I returns True if expr is an exact number, and False otherwise. >> Conjugate[3]
3 >> ExactNumberQ[10]
>> Conjugate[a + b * I] True − Conjugate [a] IConjugate [b] >> ExactNumberQ[4.0] False >> Conjugate[{{1, 2 + I 4, a + I b
}, {I}}] >> ExactNumberQ[n] {{1, 2 − 4I, Conjugate [ False − } {− }} a] IConjugate [b] , I ExactNumberQ can be applied to complex num- bers: >> Conjugate[1.5 + 2.5 I] >> ExactNumberQ[1 + I] 1.5 − 2.5I True
>> ExactNumberQ[1 + 1. I] DirectedInfinity False
DirectedInfinity[z] represents an infinite multiple of the com- plex number z. DirectedInfinity[] is the same as ComplexInfinity.
61 Factorial (!) I
I Factorial[n] represents the imaginary number n! Sqrt[-1]. computes the factorial of n.
>> I^2 >> 20! −1 2 432 902 008 176 640 000
>> (3+I)*(3-I) Factorial handles numeric (real and complex) values using the gamma function: 10 >> 10.5! 1.18994 × 107 Im
>> (-3.0+1.5*I)! − 0.0427943 0.00461565I Im[z] returns the imaginary component of the However, the value at poles is ComplexInfinity: complex number z. >> (-1.)! ComplexInfinity >> Im[3+4I] Factorial has the same operator (!) as Not, but 4 with higher precedence: >> Plot[{Sin[a], Im[E^(I a)]}, {a, >> !a! //FullForm 0, 2 Pi}] Not [Factorial [a]] 1.0 Factorial2 (!!) 0.5 1 2 3 4 5 6 Factorial2[n] −0.5 n!! computes the double factorial of n. −1.0 The double factorial or semifactorial of a num- ber n, is the product of all the integers from 1 up InexactNumberQ to n that have the same parity (odd or even) as n. >> 5!! InexactNumberQ[expr] 15. returns True if expr is not an exact num- ber, and False otherwise. >> Factorial2[-3] −1. >> InexactNumberQ[a] Factorial2 accepts Integers, Rationals, Reals, or False Complex Numbers: >> InexactNumberQ[3.0] >> I!! + 1 True 3.71713 + 0.279527I
>> InexactNumberQ[2/3] Irrationals can be handled by using numeric ap- proximation: False >> N[Pi!!, 6] InexactNumberQ can be applied to complex 3.35237 numbers:
62 >> InexactNumberQ[4.0+I] NumberQ True NumberQ[expr] returns True if expr is an explicit number, IntegerQ and False otherwise.
>> NumberQ[3+I] IntegerQ[expr] returns True if expr is an integer, and True False otherwise. >> NumberQ[5!] True >> IntegerQ[3] True >> NumberQ[Pi] False >> IntegerQ[Pi] False Piecewise Integer Piecewise[{{expr1, cond1}, ...}] represents a piecewise function. Integer Piecewise[{{expr1, cond1}, ...}, expr] is the head of integers. represents a piecewise function with de- fault expr.
>> Head[5] Integer Heaviside function >> Piecewise[{{0, x <= 0}}, 1] [ ] Piecewise {{0, x<=0}} , 1 MachineNumberQ >> Integrate[Piecewise[{{1, x <= 0}, {-1, x > 0}}], x] [ ] MachineNumberQ[ ] expr Piecewise {{x, x<=0}} , − x returns True if expr is a machine-
precision real or complex number. >> Integrate[Piecewise[{{1, x <= 0}, {-1, x > 0}}], {x, -1, 2}] = True −1 >> MachineNumberQ [3.14159265358979324] Piecewise defaults to 0 if no other case is match- ing. False >> Piecewise[{{1, False}}] >> MachineNumberQ[1.5 + 2.3 I] 0 True >> Plot[Piecewise[{{Log[x], x > 0}, >> MachineNumberQ {x*-0.5, x < 0}}], {x, -1, 1}] [2.71828182845904524 + 3.14159265358979324 I] 0.5 False −1.0 −0.5 0.5 1.0 −0.5 −1.0 −1.5 −2.0
63 >> Piecewise[{{0 ^ 0, False}}, -1] Product −1 Product[expr,{i, imin, imax}] evaluates the discrete product of expr PossibleZeroQ with i ranging from imin to imax. Product[expr,{i, imax}] same as Product[expr,{i, 1, imax}]. PossibleZeroQ[expr] Product[expr,{i, imin, imax, di}] returns True if basic symbolic and nu- i ranges from imin to imax in steps of di. merical methods suggest that expr has Product[expr,{i, imin, imax}, {j, jmin, value zero, and False otherwise. jmax}, ...] evaluates expr as a multiple product, with Test whether a numeric expression is zero: {i, ...}, {j, ...}, ... being in outermost-to- >> PossibleZeroQ[E^(I Pi/4)- (-1) innermost order. ^(1/4)] True >> Product[k, {k, 1, 10}] 3 628 800 The determination is approximate. Test whether a symbolic expression is likely to >> 10! be identically zero: 3 628 800 >> PossibleZeroQ[(x + 1)(x - 1)- x >> Product[x^k, {k, 2, 20, 2}] ^2 + 1] x110 True >> Product[2 ^ i, {i, 1, n}] >> PossibleZeroQ[(E + Pi)^2 - E^2 - 2 n + n Pi^2 - 2 E Pi] 2 2 2
True >> Product[f[i], {i, 1, 7}] Show that a numeric expression is nonzero: f [1] f [2] f [3] f [4] f [5] f [6] f [7] >> PossibleZeroQ[E^Pi - Pi^E] Symbolic products involving the factorial are False evaluated:
>> PossibleZeroQ[1/x + 1/y - (x + y >> Product[k, {k, 3, n}] )/(x y)] n! True 2 Decide that a numeric expression is zero, based Evaluate the nth primorial: on approximate computations: >> primorial[0] = 1; >> PossibleZeroQ[2^(2 I)- 2^(-2 I)- 2 I Sin[Log[4]]] >> primorial[n_Integer] := Product[ Prime[k], {k, 1, n}]; True
>> primorial[12] >> PossibleZeroQ[Sqrt[x^2] - x] False 7 420 738 134 810
Rational
Rational is the head of rational numbers. Rational[a, b] constructs the rational number a / b.
64 >> Head[1/2] Real Rational Real >> Rational[1, 2] is the head of real (inexact) numbers. 1 2 >> x = 3. ^ -20;
>> InputForm[x] Re ∧ 2.8679719907924413* − 10
Re[z] >> Head[x] returns the real component of the com- Real plex number z.
>> Re[3+4I] Sign 3
>> Plot[{Cos[a], Re[E^(I a)]}, {a, Sign[x] 0, 2 Pi}] return -1, 0, or 1 depending on whether x is negative, zero, or positive. 1.0 0.5 >> Sign[19] 1
1 2 3 4 5 6 >> Sign[-6] −0.5 −1
−1.0 >> Sign[0] 0
>> Sign[{-5, -10, 15, 20, 0}] RealNumberQ {−1, − 1, 1, 1, 0}
>> Sign[3 - 4*I] RealNumberQ[expr] returns True if expr is an explicit number 3 − 4I with no imaginary component. 5 5
>> RealNumberQ[10] True Sum
>> RealNumberQ[4.0] Sum[expr,{i, imin, imax}] True evaluates the discrete sum of expr with i >> RealNumberQ[1+I] ranging from imin to imax. False Sum[expr,{i, imax}] same as Sum[expr,{i, 1, imax}]. >> RealNumberQ[0 * I] Sum[expr,{i, imin, imax, di}] True i ranges from imin to imax in steps of di. Sum[expr,{i, imin, imax}, {j, jmin, >> RealNumberQ[0.0 * I] jmax}, ...] True evaluates expr as a multiple sum, with {i, ...}, {j, ...}, ... being in outermost-to- innermost order.
65 A sum that Gauss in elementary school was asked to do to kill time: >> Sum[k, {k, 1, 10}] 55 The symbolic form he used: >> Sum[k, {k, 1, n}] n (1 + n) 2 A Geometric series with a finite limit: >> Sum[1 / 2 ^ i, {i, 1, k}] − 1 − 2 k
A Geometric series using Infinity: >> Sum[1 / 2 ^ i, {i, 1, Infinity}] 1 Leibniz forumla used in computing Pi: >> Sum[1 / ((-1)^k (2k + 1)), {k, 0, Infinity}] Pi 4 A table of double sums to compute squares: >> Table[ Sum[i * j, {i, 0, n}, {j, 0, n}], {n, 0, 4} ] {0, 1, 9, 36, 100}
Computing Harmonic using a sum >> Sum[1 / k ^ 2, {k, 1, n}] HarmonicNumber [n, 2]
Other symbolic sums: >> Sum[k, {k, n, 2 n}] 3n (1 + n) 2 A sum with Complex-number iteration values >> Sum[k, {k, I, I + 1}] 1 + 2I
>> Sum[f[i], {i, 1, 7}] f [1] + f [2] + f [3] + f [ 4] + f [5] + f [6] + f [7]
Verify algebraic identities: >> Sum[x ^ 2, {x, 1, y}] - y * (y + 1)* (2 * y + 1)/ 6 0
66 9. Functional Programming
Functional programming is a programming paradigm where programs are constructed by applying and composing functions. This is term is often used in contrast to Procedural programming. It is made richer by expressions like f [x] being treating as symbolic data. Contents
Identity ...... 68 SlotSequence ..... 68 Composition ...... 67 Slot ...... 68 Function (&) ...... 68
Composition Function (&)
Composition[f , g] Function[body] returns the composition of two functions body & f and g. represents a pure function with parame- ters #1, #2, etc.
>> Composition[f, g][x] Function[{x1, x2, ...}, body] [ ] represents a pure function with parame- f g x [ ] ters x1, x2, etc. Function[{x1, x2, ...}, body, attr] >> Composition[f, g, h][x, y, z] [ [ [ ]]] assume that the function has the at- f g h x, y, z tributes attr.
>> Composition[] >> f := # ^ 2 & Identity >> f[3] >> Composition[][x] 9 x >> #^3& /@ {1, 2, 3} >> Attributes[Composition] {1, 8, 27} {Flat, OneIdentity, Protected} >> #1+#2&[4, 5] >> Composition[f, Composition[g, h 9 ]] [ ] You can use Function with named parameters: Composition f , g, h >> Function[{x, y}, x * y][2, 3] 6 Parameters are renamed, when necessary, to avoid confusion: >> Function[{x}, Function[{y}, f[x, y]]][y] [ [ ]] Function {y$} , f y, y$
>> Function[{y}, f[x, y]] /. x->y [ [ ]] Function {y} , f y, y
67 >> Function[y, Function[x, y^x]][x SlotSequence ][y] y x ##
>> Function[x, Function[y, x^y]][x is the sequence of arguments supplied to ][y] a pure function. ##n y x starts with the nth argument. Slots in inner functions are not affected by outer function application: >> Plus[##]& [1, 2, 3] >> g[#] & [h[#]] & [5] 6 g h 5 [ [ ]] >> Plus[##2]& [1, 2, 3] 5
Identity >> FullForm[##] SlotSequence [1]
Identity[x] is the identity function, which returns x unchanged.
>> Identity[x] x
>> Identity[x, y] [ ] Identity x, y
Slot
#n represents the nth argument to a pure function. # is short-hand for #1. #0 represents the pure function itself.
>> # #1 Unused arguments are simply ignored: >> {#1, #2, #3}&[1, 2, 3, 4, 5] {1, 2, 3}
Recursive pure functions can be written using #0:
>> If[#1<=1, 1, #1 #0[#1-1]]& [10] 3 628 800
68 10. Code Compilation
Code compilation allows Mathics functions to be run faster. When LLVM and Python libraries are available, compilation produces LLVM code. Contents
CompiledFunction .. 70 Compile ...... 69
Compile >> cf = Compile[{{x, _Real}, {y, _Integer}}, If[x == 0.0 && y <= 0, 0.0, Sin[x ^ y] + 1 / Min[x, Compile[{x1, x2, ...}, expr] 0.5]] + 0.5] Compiles expr assuming each xi is a Real [ number. CompiledFunction {x, Compile[{{x1, t1}{x2, t1} ...}, expr] [ Compiles assuming each xi matches type y} , 0.5 + If x==0.&&y<=0, ti. ] [ ] y 1 Compilation is performed using llvmlite , or 0., Sin x + , Min [x], 0.5] Python’s builtin “compile” function. − − >> cf = Compile[{x, y}, x + 2 y] CompiledCode [ { } CompiledFunction x, y ,] >> cf[3.5, 2] x + 2y, − CompiledCode− 2.18888 >> cf[2.5, 4.3] Loops and variable assignments are supported 11.1 usinv Python builtin “compile” function:
>> cf = Compile[{{x, _Real}}, Sin[x >> Compile[{{a, _Integer}, {b, ]] _Integer}}, While[b != 0, {a, b} [ = {b, Mod[a, b]}]; a] (* GCD of { } CompiledFunction x , ] a, b *) − − [ Sin [x] , CompiledCode { CompiledFunction a, ] >> cf[1.4] b} , a, − PythonizedCode− 0.98545 Compile supports basic flow control: CompiledFunction
’ CompiledFunction[args...] represents compiled code for evaluating a compiled function.
69 >> sqr = Compile[{x}, x x] [ CompiledFunction {x} , ] x2, − CompiledCode−
>> Head[sqr] CompiledFunction
>> sqr[2] 4.
70 11. Options and Default Arguments
Contents
NotOptionQ ...... 71 OptionValue ...... 72 Default ...... 71 OptionQ ...... 72 Options ...... 73 FilterRules ...... 71
Default FilterRules
Default[f ] FilterRules[rules, pattern] gives the default value for an omitted gives those rules that have a left side that paramter of f. matches pattern. Default[f , k] FilterRules[rules,{pattern1, pattern2, gives the default value for a parameter on ...}] the kth position. gives those rules that have a left side that Default[f , k, n] match at least one of pattern1, pattern2, ... gives the default value for the kth param-
eter out of n. >> FilterRules[{x -> 100, y -> 1000}, x] Assign values to Default to specify default val- { − > } ues. x 100 >> Default[f] = 1 >> FilterRules[{x -> 100, y -> 1 1000, z -> 10000}, {a, b, x, z}]
>> f[x_.] := x ^ 2 {x− > 100, z− > 10 000}
>> f[] 1 NotOptionQ Default values are stored in DefaultValues: >> DefaultValues[f] { [ [ ]] } NotOptionQ[expr] HoldPattern Default f :>1 returns True if expr does not have the form of a valid option specification. You can use patterns for k and n: >> Default[h, k_, n_] := {k, n} >> NotOptionQ[x] Note that the position of a parameter is relative True to the pattern, not the matching expression: >> NotOptionQ[2] >> h[] /. h[___, ___, x_., y_., ___ ] -> {x, y} True
{{3, 5} , {4, 5}} >> NotOptionQ["abc"] True
>> NotOptionQ[a -> True] False
71 OptionQ >> f[a->3] /. f[OptionsPattern[{}]] -> {OptionValue[a]} { } OptionQ[expr] 3 returns True if expr has the form of a valid Unavailable options generate a message: option specification. >> f[a->3] /. f[OptionsPattern[{}]] -> {OptionValue[b]} Examples of option specifications: Optionnamebnotfound. >> OptionQ[a -> True] { } True b
>> OptionQ[a :> True] The argument of OptionValue must be a sym- True bol: >> f[a->3] /. f[OptionsPattern[{}]] >> OptionQ[{a -> True}] -> {OptionValue[a+b]} True Argumenta
>> OptionQ[{a :> True}] + batposition1isexpectedtobeasymbol. True {OptionValue [a + b]}
Options lists are flattened when are applyied, so However, it can be evaluated dynamically: >> OptionQ[{a -> True, {b->1, "c >> f[a->5] /. f[OptionsPattern[{}]] "->2}}] -> {OptionValue[Symbol["a"]]} True {5}
>> OptionQ[{a -> True, {b->1, c}}] False Options >> OptionQ[{a -> True, F[b->1,c ->2]}] Options[ ] False f gives a list of optional arguments to f and OptionQ returns False if its argument is not a their default values. valid option specification: >> OptionQ[x] You can assign values to Options to specify op- False tions. >> Options[f] = {n -> 2} {n− > 2} OptionValue >> Options[f] {n:>2} OptionValue[name] gives the value of the option name as >> f[x_, OptionsPattern[f]] := x ^ specified in a call to a function with OptionValue[n] OptionsPattern. OptionValue[f , name] >> f[x] recover the value of the option name asso- x2 ciated to the symbol f. OptionValue[f , optvals, name] >> f[x, n -> 3] recover the value of the option name asso- x3 ciated to the symbol f, extracting the val- ues from optvals if available. Delayed option rules are evaluated just when OptionValue[..., list] the corresponding OptionValue is called: recover the value of the options in list .
72 >> f[a :> Print["value"]] /. f[ OptionsPattern[{}]] :> ( OptionValue[a]; Print["between "]; OptionValue[a]); value between value In contrast to that, normal option rules are eval- uated immediately: >> f[a -> Print["value"]] /. f[ OptionsPattern[{}]] :> ( OptionValue[a]; Print["between "]; OptionValue[a]); value between Options must be rules or delayed rules: >> Options[f] = {a} {a}isnotavalidlistofoptionrules. {a}
A single rule need not be given inside a list: >> Options[f] = a -> b a− > b
>> Options[f] {a:>b}
Options can only be assigned to symbols: >> Options[a + b] = {a -> b} Argumenta + batposition1isexpectedtobeasymbol. {a− > b}
73 12. Attributes of Definitions
While a definition like cube[x_] = x^3 gives a duce. way to specify values of a function, attributes al- The builtin-attributes having a predefined low a way to specify general properties of func- meaning in Mathics which are described below. tions and symbols. This is independent of the However in contrast to Mathematica®, you can parameters they take and the values they pro- set any symbol as an attribute.
Contents
HoldRest ...... 76 Protect ...... 77 Attributes ...... 74 Listable ...... 76 Protected ...... 78 ClearAttributes .... 75 Locked ...... 76 ReadProtected ..... 78 Constant ...... 75 NHoldAll ...... 76 SequenceHold ..... 78 Flat ...... 75 NHoldFirst ...... 76 SetAttributes ..... 78 HoldAll ...... 75 NHoldRest ...... 76 Unprotect ...... 78 HoldAllComplete ... 75 OneIdentity ...... 77 HoldFirst ...... 76 Orderless ...... 77
Attributes >> Attributes[f] = {Flat, Orderless } Attributes[symbol] {Flat, Orderless} returns the attributes of symbol. Attributes["string"] >> f[b, f[a, c]] returns the attributes of Symbol["string"]. f [a, b, c] Attributes[symbol] = {attr1, attr2} sets the attributes of symbol, replacing any Attributes must be symbols: existing attributes. >> Attributes[f] := {a + b} Argumenta
>> Attributes[Plus] + batposition1isexpectedtobeasymbol. {Flat, Listable, NumericFunction, $Failed OneIdentity, Orderless, Protected} Use Symbol to convert strings to symbols:
>> >> Attributes["Plus"] Attributes[f] = Symbol["Listable "] {Flat, Listable, NumericFunction, OneIdentity, Orderless, Protected} Listable
>> Attributes[f] Attributes always considers the head of an ex- { } pression: Listable >> Attributes[a + b + c] {Flat, Listable, NumericFunction, OneIdentity, Orderless, Protected}
You can assign values to Attributes to set at- tributes:
74 ClearAttributes >> f[a, f[b, c]] f [a, b, c] ClearAttributes[symbol, attrib] Flat is taken into account in pattern matching: removes attrib from symbol’s attributes. >> f[a, b, c] /. f[a, b] -> d f [d, c] >> SetAttributes[f, Flat]
>> Attributes[f] {Flat} HoldAll
>> ClearAttributes[f, Flat] HoldAll is an attribute specifying that all argu- >> Attributes[f] {} ments of a function should be left uneval- uated. Attributes that are not even set are simply ig- >> Attributes[Function] nored: { } >> ClearAttributes[{f}, {Flat}] HoldAll, Protected
>> Attributes[f] {} HoldAllComplete
HoldAllComplete Constant is an attribute that includes the effects of HoldAll and SequenceHold, and also Constant protects the function from being affected is an attribute that indicates that a symbol by the upvalues of any arguments. is a constant. HoldAllComplete even prevents upvalues from Mathematical constants like E have attribute being used, and includes SequenceHold. Constant: >> SetAttributes[f, HoldAllComplete >> Attributes[E] ] {Constant, Protected, ReadProtected} >> f[a] ^= 3; Constant symbols cannot be used as variables in Solve and related functions: >> f[a] >> Solve[x + E == 0, E] f [a] Eisnotavalidvariable. >> f[Sequence[a, b]] Solve [E + x==0, E] [ ] f Sequence [a, b]
Flat HoldFirst Flat is an attribute that specifies that nested HoldFirst occurrences of a function should be au- is an attribute specifying that the first ar- tomatically flattened. gument of a function should be left un- evaluated. A symbol with the Flat attribute represents an >> Attributes[Set] associative mathematical operation: { } >> SetAttributes[f, Flat] HoldFirst, Protected, SequenceHold
75 HoldRest >> Attributes[lock] {Flat, Locked} HoldRest However, their values might be modified (as is an attribute specifying that all but the long as they are not Protected too): first argument of a function should be left >> lock = 3 unevaluated. 3
>> Attributes[If] { } HoldRest, Protected NHoldAll
Listable NHoldAll is an attribute that protects all arguments of a function from numeric evaluation. Listable
is an attribute specifying that a function >> N[f[2, 3]] should be automatically applied to each f [2., 3.] element of a list.
>> SetAttributes[f, NHoldAll] >> SetAttributes[f, Listable]
>> N[f[2, 3]] >> f[{1, 2, 3}, {4, 5, 6}] f [2, 3] { f [1, 4] , f [2, 5] , f [3, 6]}
>> f[{1, 2, 3}, 4] NHoldFirst { f [1, 4] , f [2, 4] , f [3, 4]}
>> {{1, 2}, {3, 4}} + {5, 6} NHoldFirst {{6, 7} , {9, 10}} is an attribute that protects the first argu- ment of a function from numeric evalua- tion. Locked
Locked NHoldRest is an attribute that prevents attributes on a symbol from being modified. NHoldRest is an attribute that protects all but the The attributes of Locked symbols cannot be first argument of a function from numeric modified: evaluation. >> Attributes[lock] = {Flat, Locked };
>> SetAttributes[lock, {}] OneIdentity Symbollockislocked. OneIdentity >> ClearAttributes[lock, Flat] is an attribute specifying that f [x] should Symbollockislocked. be treated as equivalent to x in pattern matching. >> Attributes[lock] = {} Symbollockislocked. OneIdentity affects pattern matching: {} >> SetAttributes[f, OneIdentity]
76 >> a /. f[args___] -> {args} >> A {a} {1, 2, 3}
It does not affect evaluation: >> f[a] Protected f [a] Protected is an attribute that prevents values on a Orderless symbol from being modified.
Orderless Values of Protected symbols cannot be modi- is an attribute that can be assigned to a fied: symbol f to indicate that the elements >> Attributes[p] = {Protected}; ei in expressions of the form f [e1, e2,
...] should automatically be sorted into >> p = 2; canonical order. This property is ac- SymbolpisProtected. counted for in pattern matching.
>> f[p] ^= 3; The leaves of an Orderless function are auto- Tagpin f [p]isProtected. matically sorted: >> SetAttributes[f, Orderless] >> Format[p] = "text"; SymbolpisProtected. >> f[c, a, b, a + b, 3, 1.0] f [1., 3, a, b, c, a + b] However, attributes might still be set: >> SetAttributes[p, Flat] A symbol with the Orderless attribute repre- sents a commutative mathematical operation. >> Attributes[p] >> f[a, b] == f[b, a] {Flat, Protected} True Thus, you can easily remove the attribute Orderless affects pattern matching: Protected: >> SetAttributes[f, Flat] >> Attributes[p] = {};
>> f[a, b, c] /. f[a, c] -> d >> p = 2 f [b, d] 2 You can also use Protect or Unprotect, resp. Protect >> Protect[p]
>> Attributes[p] Protect[s1, s2, ...] {Protected} sets the attribute Protected for the sym- bols si. >> Unprotect[p] Protect[str1, str2, ...] protects all symbols whose names textu- If a symbol is Protected and Locked, it can ally match stri. never be changed again: >> SetAttributes[p, {Protected,
>> A = {1, 2, 3}; Locked}]
>> p = 2 >> Protect[A] SymbolpisProtected. >> A[[2]] = 4; 2 SymbolAisProtected.
77 >> Unprotect[p] >> Plus[s] Symbolpislocked. a + b
ReadProtected SetAttributes
ReadProtected SetAttributes[symbol, attrib] is an attribute that prevents values on a adds attrib to the list of symbol’s at- symbol from being read. tributes.
>> SetAttributes[f, Flat] Values associated with ReadProtected symbols cannot be seen in Definition: >> Attributes[f] >> ClearAll[p] {Flat}
>> p = 3; Multiple attributes can be set at the same time using lists: >> Definition[p] >> SetAttributes[{f, g}, {Flat, p = 3 Orderless}]
>> SetAttributes[p, ReadProtected] >> Attributes[g] { } >> Definition[p] Flat, Orderless [ ] Attributes p = {ReadProtected} Unprotect SequenceHold Unprotect[s1, s2, ...] removes the attribute Protected for the SequenceHold symbols si. is an attribute that prevents Sequence ob- Unprotect[str] jects from being spliced into a function’s unprotects symbols whose names textu- arguments. ally match str.
Normally, Sequence will be spliced into a func- tion: >> f[Sequence[a, b]] f [a, b]
It does not for SequenceHold functions: >> SetAttributes[f, SequenceHold]
>> f[Sequence[a, b]] [ ] f Sequence [a, b]
E.g., Set has attribute SequenceHold to allow as- signment of sequences to variables: >> s = Sequence[a, b];
>> s Sequence [a, b]
78 13. Tensors
In mathematics, a tensor is an algebraic object sors), dual vectors, multilinear maps between that describes a (multilinear) relationship be- vector spaces, and even some operations such tween sets of algebraic objects related to a vector as the dot product. Tensors are defined inde- space. Objects that tensors may map between pendent of any basis, although they are often re- include vectors and scalars, and even other ten- ferred to by their components in a basis related sors. to a particular coordinate system. There are many types of tensors, including Mathics represents tensors of vectors and matri- scalars and vectors (which are the simplest ten- ces as lists; tensors of any rank can be handled.
Contents
Dot (.) ...... 80 Outer ...... 81 ArrayDepth ...... 79 IdentityMatrix ..... 80 Transpose ...... 82 ArrayQ ...... 79 Inner ...... 80 VectorQ ...... 82 DiagonalMatrix .... 80 MatrixQ ...... 81 Dimensions ...... 80
ArrayDepth >> ArrayQ[a] False
ArrayDepth[a] >> ArrayQ[{a}] returns the depth of the non-ragged array True a, defined as Length[Dimensions[a]]. >> ArrayQ[{{{a}},{{b,c}}}]
>> ArrayDepth[{{a,b},{c,d}}] False
2 >> ArrayQ[{{a, b}, {c, d}}, 2, SymbolQ] >> ArrayDepth[x] 0 True
ArrayQ DiagonalMatrix
ArrayQ[expr] DiagonalMatrix[list] tests whether expr is a full array. gives a matrix with the values in list on ArrayQ[expr, pattern] its diagonal and zeroes elsewhere. also tests whether the array depth of expr
matches pattern. >> DiagonalMatrix[{1, 2, 3}] ArrayQ[expr, pattern, test] {{1, 0, 0} , {0, 2, 0} , {0, 0, 3}} furthermore tests whether test yields True for all elements of expr. ArrayQ [expr] is equivalent to ArrayQ[ expr, _, True&].
79 >> MatrixForm[%] >> {{a, b}, {c, d}} . {{r, s}, {t, 1 0 0 u}} 0 2 0 {{ar + bt, as + bu} , {cr + dt, cs + du}} 0 0 3 >> a . b a.b Dimensions IdentityMatrix Dimensions[expr] returns a list of the dimensions of the ex- pression expr. IdentityMatrix[n] gives the identity matrix with n rows and A vector of length 3: columns. >> Dimensions[{a, b, c}] >> IdentityMatrix[3] {3} {{1, 0, 0} , {0, 1, 0} , {0, 0, 1}} A 3x2 matrix: >> Dimensions[{{a, b}, {c, d}, {e, f}}] Inner {3, 2} Inner[f , x, y, g] Ragged arrays are not taken into account: computes a generalised inner product of >> Dimensions[{{a, b}, {b, c}, {c, x and y, using a multiplication function f d, e}}] and an addition function g. {3}
>> Inner[f, {a, b}, {x, y}, g] The expression can have any head: [ [ ]] >> Dimensions[f[f[a, b, c]]] g f [a, x] , f b, y {1, 3} Inner can be used to compute a dot product: >> Inner[Times, {a, b}, {c, d}, Plus] == {a, b} . {c, d} Dot (.) True The inner product of two boolean matrices: Dot[x, y] >> Inner[And, {{False, False}, { x . y False, True}}, {{True, False}, { computes the vector dot product or ma- True, True}}, Or] trix product x . y. {{False, False} , {True, True}}
Scalar product of vectors: Inner works with tensors of any depth: >> {a, b, c} . {x, y, z} >> Inner[f, {{{a, b}}, {{c, d}}}, ax + by + cz {{1}, {2}}, g] {{{ [ ]}} g f [a, 1] , f [b, 2] , Product of matrices and vectors: {{ [ ]}}} g f [c, 1] , f [d, 2] >> {{a, b}, {c, d}} . {x, y} {ax + by, cx + dy}
Matrix product:
80 MatrixQ >> Outer[StringJoin, {"", "re", "un "}, {"cover", "draw", "wind"}, {"", "ing", "s"}] // InputForm MatrixQ[m] {{{ } returns True if m is a list of equal-length "cover", "covering", "covers" , lists. {"draw", "drawing", "draws"} , MatrixQ[m, f ] {"wind", "winding", "winds"}} , only returns True if f [x] returns True for {{"recover", "recovering", each element x of the matrix m. "recovers"} , {"redraw", "redrawing", "redraws"} , >> MatrixQ[{{1, 3}, {4.0, 3/2}}, { NumberQ] "rewind", "rewinding", "rewinds"}} , {{"uncover", True "uncovering", "uncovers"} , {"undraw", "undrawing", Outer "undraws"} , {"unwind", "unwinding", "unwinds"}}}
Outer[f , x, y] Compositions of trigonometric functions: computes a generalised outer product of >> trigs = Outer[Composition, {Sin, x and y, using the function f in place of Cos, Tan}, {ArcSin, ArcCos, multiplication. ArcTan}] {{Composition [Sin, ArcSin] , >> Outer[f, {a, b}, {1, 2, 3}] Composition [Sin, ArcCos] , {{ f [a, 1] , f [a, 2] , f [a, 3]} , Composition [Sin, ArcTan]} , { f [b, 1] , f [b, 2] , f [b, 3]}} {Composition [Cos, ArcSin] , Outer product of two matrices: Composition [Cos, ArcCos] , } >> Outer[Times, {{a, b}, {c, d}}, Composition [Cos, ArcTan] , {{1, 2}, {3, 4}}] {Composition [Tan, ArcSin] , {{{{a, 2a} , {3a, 4a}} , {{b, Composition [Tan, ArcCos] , }} 2b} , {3b, 4b}}} , {{{c, 2c} , {3c, Composition [Tan, ArcTan] 4c}} , {{d, 2d} , {3d, 4d}}}} Evaluate at 0: Outer of multiple lists: >> Map[#[0] &, trigs, {2}] >> Outer[f, {a, b}, {x, y, z}, {1, {{0, 1, 0} , {1, 0, 1} , {0, 2}] ComplexInfinity, 0}} {{ { [ { } f [a], x, 1[] , f [a]}, x, 2] , f { a, y, 1 , f }a, y{, 2 , f [a, z, 1] , } { Transpose f [a, z, 2] { ,[ f [b], x, 1[] , f [ } b,]}x, 2] , f b, y, 1 , f b, y}}, 2 , { f [b, z, 1] , f [b, z, 2]} Tranpose[m] transposes rows and columns in the ma- Arrays can be ragged: trix m. >> Outer[Times, {{1, 2}}, {{a, b},
{c, d, e}}] >> Transpose[{{1, 2, 3}, {4, 5, {{{{a, b} , {c, d, e}} , 6}}] {{2a, 2b} , {2c, 2d, 2e}}}} {{1, 4} , {2, 5} , {3, 6}}
Word combinations:
81 >> MatrixForm[%] 1 4 2 5 3 6
VectorQ
VectorQ[v] returns True if v is a list of elements which are not themselves lists. VectorQ[v, f ] returns True if v is a vector and f [x] re- turns True for each element x of v.
>> VectorQ[{a, b, c}] True
82 14. Structural Operations
Contents
Map (/@) ...... 85 Scan ...... 88 Apply (@@) ...... 83 MapAt ...... 86 Sort ...... 88 ApplyLevel (@@@) ... 83 MapIndexed ...... 87 SortBy ...... 88 AtomQ ...... 84 MapThread ...... 87 SymbolName ..... 88 BinarySearch ..... 84 Null ...... 87 SymbolQ ...... 89 ByteCount ...... 84 Operate 87 Depth ...... 84 ...... Symbol ...... 89 Flatten ...... 85 Order ...... 87 Thread ...... 89 FreeQ ...... 85 OrderedQ ...... 87 Through ...... 89 Head ...... 85 PatternsOrderedQ ... 88
Apply ( ) >> Apply[f, {{{{{a}}}}}, {2, -3}] @@ {{ [ [ ]]}} f f {a}
Apply[f , expr] Convert all operations to lists: f @@ expr >> Apply[List, a + b * c ^ e * f[g replaces the head of expr with f. ], {0, Infinity}] Apply[f , expr, levelspec] applies f on the parts specified by level- {a, {b, {g} , {c, e}}} spec.
>> f @@ {1, 2, 3} ApplyLevel (@@@) f [1, 2, 3]
>> Plus @@ {1, 2, 3} ApplyLevel[f , expr] 6 f @@@ expr is equivalent to Apply[f , expr, {1}]. The head of expr need not be List: >> f @@ (a + b + c) >> f @@@ {{a, b}, {c, d}} f [a, b, c] { f [a, b] , f [c, d]} Apply on level 1: >> Apply[f, {a + b, g[c, d, e * f], 3}, {1}] AtomQ { [ ] } f [a, b] , f c, d, e f , 3 AtomQ[x] The default level is 0: is true if x is an atom (an object such as >> Apply[f, {a, b, c}, {0}] a number or string, which cannot be di- f [a, b, c] vided into subexpressions using Part).
Range of levels, including negative level (count- >> AtomQ[x] ing from bottom): True
83 >> AtomQ[1.2] >> CombinatoricaOld‘BinarySearch[{{ True a, 1}, {b, 7}}, 7, #[[2]]&] 2 >> AtomQ[2 + I] True
>> AtomQ[2 / 3] ByteCount True
>> AtomQ[x + y] ByteCount[expr] False gives the internal memory space used by expr, in bytes.
BinarySearch The results may heavily depend on the Python implementation in use.
CombinatoricaOld‘BinarySearch[l, k] searches the list l, which has to be sorted, Depth for key k and returns its index in l. If k does not exist in l, BinarySearch returns (a + b) / 2, where a and b are Depth[expr] the indices between which k would have gives the depth of expr. to be inserted in order to maintain the sorting order in l. Please note that k The depth of an expression is defined as one plus and the elements in l need to be com- the maximum number of Part indices required parable under a strict total order (see to reach any part of expr, except for heads. https://en.wikipedia.org/wiki/Total_order). >> Depth[x] CombinatoricaOld‘BinarySearch[l, k, f ] 1 the index of $k in the elements of l if f is applied to the latter prior to compari- >> Depth[x + y] son. Note that f needs to yield a sorted 2 sequence if applied to the elements of $l. >> Depth[{{{{x}}}}]
>> CombinatoricaOld‘BinarySearch 5 [{3, 4, 10, 100, 123}, 100] Complex numbers are atomic, and hence have 4 depth 1: >> Depth[1 + 2 I] >> CombinatoricaOld‘BinarySearch [{2, 3, 9}, 7] // N 1 2.5 Depth ignores heads: >> Depth[f[a, b][c]] >> CombinatoricaOld‘BinarySearch [{2, 7, 9, 10}, 3] // N 2 1.5
>> CombinatoricaOld‘BinarySearch Flatten [{-10, 5, 8, 10}, -100] // N
0.5 Flatten[expr] flattens out nested lists in expr. >> CombinatoricaOld‘BinarySearch [{-10, 5, 8, 10}, 20] // N Flatten[expr, n] stops flattening at level n. 4.5 Flatten[expr, n, h] flattens expressions with head h instead of List.
84 >> Flatten[{{a, b}, {c, {d}, e}, {f Head , {g, h}}}] {a, b, c, d, e, f , g, h} Head[expr] returns the head of the expression or >> Flatten[{{a, b}, {c, {e}, e}, {f atom expr. , {g, h}}}, 1] { { } { }} a, b, c, e , e, f , g, h >> Head[a * b] Times >> Flatten[f[a, f[b, f[c, d]], e], Infinity, f] >> Head[6] f [a, b, c, d, e] Integer
>> >> Flatten[{{a, b}, {c, d}}, {{2}, Head[x] {1}}] Symbol {{a, c} , {b, d}}
>> Flatten[{{a, b}, {c, d}}, {{1, Map (/@) 2}}] {a, b, c, d} Map[f , expr] or f /@ expr Flatten also works in irregularly shaped arrays applies f to each part on the first level of >> Flatten[{{1, 2, 3}, {4}, {6, 7}, expr. {8, 9, 10}}, {{2}, {1}}] Map[f , expr, levelspec] applies f to each level specified by level- {{ } { } { }} 1, 4, 6, 8 , 2, 7, 9 , 3, 10 spec of expr.
>> f /@ {1, 2, 3} FreeQ { f [1] , f [2] , f [3]}
>> #^2& /@ {1, 2, 3, 4} FreeQ[expr, x] { } returns True if expr does not contain the 1, 4, 9, 16 expression x. Map f on the second level: >> Map[f, {{a, b}, {c, d, e}}, {2}] >> FreeQ[y, x] {{ f [a] , f [b]} , { f [c] , f [d] , f [e]}} True
>> FreeQ[a+b+c, a+b] Include heads: >> Map[f, a + b + c, Heads->True] False [ ] f [Plus] f [a] , f [b] , f [c] >> FreeQ[{1, 2, a^(a+b)}, Plus] False
>> FreeQ[a+b, x_+y_+z_] True
>> FreeQ[a+b+c, x_+y_+z_] False
>> FreeQ[x_+y_+z_][a+b] True
85 MapAt MapIndexed
MapAt[f , expr, n] MapIndexed[f , expr] applies f to the element at position n in applies f to each part on the first level of expr. If n is negative, the position is expr, including the part positions in the counted from the end. call to f. MapAt[f, expr, {i, j ...}] MapIndexed[f , expr, levelspec] applies f to the part of expr at position {i, applies f to each level specified by level- j, ...}. spec of expr. MapAt[f ,pos]
represents an operator form of MapAt >> MapIndexed[f, {a, b, c}] that can be applied to an expression. { [ ] [ ] [ ]} f a, {1} , f b, {2} , f c, {3}
Map f onto the part at position 2: Include heads (index 0): >> MapAt[f, {a, b, c, d}, 2] >> MapIndexed[f, {a, b, c}, Heads-> {a, f [b] , c, d} True] [ ][ [ ] { } { } Map f onto multiple parts: f List[ , 0 ] f[ a, 1 ]] , f b { } f c { } >> MapAt[f, {a, b, c, d}, {{1}, , 2 , , 3 {4}}] Map on levels 0 through 1 (outer expression gets { f [a] , b, c, f [d]} index {}): >> MapIndexed[f, a + b + c * d, {0, Map f onto the at the end: 1}] >> MapAt[f, {a, b, c, d}, -1] [ [ ] [ f f a, {1} + f b, {a, b, c, f [d]} ] [ ] ] {2} + f cd, {3} , {} Map f onto an association: Get the positions of atoms in an expression (con- >> MapAt[f, <|"a" -> 1, "b" -> 2, " c" -> 3, "d" -> 4, "e" -> 5|>, vert operations to List first to disable Listable 3] functions): >> expr = a + b * f[g] * c ^ e; {a− > 1, b− > 2, c− > f [
3] , d− > 4, e− > 5} >> listified = Apply[List, expr, {0, Infinity}]; Use negative position in an association: >> MapAt[f, <|"a" -> 1, "b" -> 2, " >> MapIndexed[#2 &, listified, c" -> 3, "d" -> 4|>, -3] {-1}] {a− > 1, b− > f [2] , c− > 3, d− > 4} {{1} , {{2, 1} , {{2, 2, 1}} , {{2, 3, 1} , {2, 3, 2}}}} Use the operator form of MapAt: >> MapAt[f, 1][{a, b, c, d}] Replace the heads with their positions, too: { f [a] , b, c, d} >> MapIndexed[#2 &, listified, {-1}, Heads -> True] [ [ { } { } { } { } 0 1 , [ 2, 0 2], 1 , { } { } { 2[, 2, 0 2, 2, 1 , ]]]2, 3, 0} {2, 3, 1} , {2, 3, 2}
The positions are given in the same format as used by Extract. Thus, mapping Extract on the indices given by MapIndexed re-constructs the original expression:
86 >> MapIndexed[Extract[expr, #2] &, The default value of n is 1: listified, {-1}, Heads -> True] >> Operate[p, f[a, b], 1] [ ] [ ] a + b f g ce p f [a, b]
With n=0, Operate acts like Apply: >> Operate[p, f[a][b][c], 0] MapThread [ ] p f [a][b][c]
’MapThread[f, {{a1, a2, ...}, {b1, b2, ...}, ...}] returns {f [a1, b1, ...], f [a2, Order b2, ...], ...}. MapThread[f ,{expr1, expr2, ...}, n] applies f at level n. Order[x, y] returns a number indicating the canoni-
>> MapThread[f, {{a, b, c}, {1, 2, cal ordering of x and y. 1 indicates that x 3}}] is before y, -1 that y is before x. 0 indicates that there is no specific ordering. Uses the { } f [a, 1] , f [b, 2] , f [c, 3] same order as Sort.
>> MapThread[f, {{{a, b}, {c, d}}, {{e, f}, {g, h}}}, 2] >> Order[7, 11] {{ [ ]} 1 {f [a[, e] ,]f b, f }}, f c, g , f [d, h] >> Order[100, 10] −1
>> Order[x, z] Null 1
>> Order[x, x] Null 0 is the implicit result of expressions that do not yield a result. OrderedQ >> FullForm[a:=b] Null OrderedQ[a, b] It is not displayed in StandardForm, is True if a sorts before b according to >> a:=b canonical ordering. in contrast to the empty string: >> OrderedQ[a, b] >> "" True
>> OrderedQ[b, a] Operate False
Operate[p, expr] PatternsOrderedQ applies p to the head of expr. Operate[p, expr, n] PatternsOrderedQ[ , ] applies p to the nth head of expr. patt1 patt2 returns True if pattern patt1 would be ap- plied before patt2 according to canonical >> Operate[p, f[a, b]] [ ] pattern ordering. p f [a, b]
87 >> PatternsOrderedQ[x__, x_] >> Sort[{2+c_, 1+b__}, False PatternsOrderedQ] {2 + c_, 1 + b__} >> PatternsOrderedQ[x_, x__]
True >> Sort[{x_ + n_*y_, x_ + y_}, PatternsOrderedQ] >> PatternsOrderedQ[b, a] True {x_ + n_y_, x_ + y_}
Scan SortBy
Scan[ , ] f expr SortBy[list, f ] applies f to each element of expr and re- sorts list (or the leaves of any other ex- Null. turns pression) according to canonical ordering ’Scan[f, expr, levelspec] of the keys that are extracted from the applies f to each level specified by level- list’s elements using $f. Chunks of leaves spec of expr. that appear the same under $f are sorted according to their natural order (without >> Scan[Print, {1, 2, 3}] applying $f). 1 SortBy[f ] 2 creates an operator function that, when 3 applied, sorts by $f.
>> SortBy[{{5, 1}, {10, -1}}, Last] Sort {{10, − 1} , {5, 1}}
>> SortBy[Total][{{5, 1}, {10, Sort[list] -9}}] sorts list (or the leaves of any other ex- pression) according to canonical order- {{10, − 9} , {5, 1}} ing. Sort[list, p] sorts using p to determine the order of SymbolName two elements.
>> Sort[{4, 1.0, a, 3+I}] SymbolName[s] {1., 3 + I, 4, a} returns the name of the symbol s (without any leading context name). Sort uses OrderedQ to determine ordering by de- fault. You can sort patterns according to their >> SymbolName[x] // InputForm precedence using PatternsOrderedQ: "x" >> Sort[{items___, item_, OptionsPattern[], item_symbol, item_?test}, PatternsOrderedQ] SymbolQ {item_symbol, item_? test, item_, items___, OptionsPattern []} SymbolQ[x] When sorting patterns, values of atoms do not is True if x is a symbol, or False other- matter: wise. >> Sort[{a, b/;t}, PatternsOrderedQ ] >> SymbolQ[a] {b/;t, a} True
88 >> SymbolQ[1] >> Through[f[g][x]] [ ] False f g [x]
>> SymbolQ[a + b] >> Through[p[f, g][x]] [ ] False p f [x] , g [x]
Symbol
Symbol is the head of symbols.
>> Head[x] Symbol
You can use Symbol to create symbols from strings: >> Symbol["x"] + Symbol["x"] 2x
Thread
Thread[f [args]] threads f over any lists that appear in args. Thread[f [args], h] threads over any parts with head h.
>> Thread[f[{a, b, c}]] { f [a] , f [b] , f [c]}
>> Thread[f[{a, b, c}, t]] { f [a, t] , f [b, t] , f [c, t]}
>> Thread[f[a + b + c], Plus] f [a] + f [b] + f [c]
Functions with attribute Listable are automati- cally threaded over lists: >> {a, b, c} + {d, e, f} + g {a + d + g, b + e + g, c + f + g}
Through
Through[p[f ][x]] gives p[f [x]].
89 15. Drawing Graphics
Contents
Graphics ...... 95 Show ...... 100 AbsoluteThickness .. 90 Large ...... 96 Small ...... 100 Arrow ...... 91 Line ...... 96 Text ...... 100 Arrowheads ...... 92 Medium ...... 96 Thick ...... 100 Circle ...... 93 Point ...... 97 Thickness ...... 101 Disk ...... 94 PointSize ...... 97 Thin ...... 101 EdgeForm ...... 94 Polygon ...... 98 Tiny ...... 101 FilledCurve ...... 94 Rectangle ...... 99 FontColor ...... 95 RegularPolygon .... 99
AbsoluteThickness Arrow
AbsoluteThickness[p] Arrow[{p1, p2}] sets the line thickness for subsequent represents a line from p1 to p2 that ends graphics primitives to p points. with an arrow at p2. Arrow[{p1, p2}, s]
>> Graphics[Table[{ represents a line with arrow that keeps a AbsoluteThickness[t], Line[{{20 distance of s from p1 and p2. t, 10}, {20 t, 80}}], Text[ Arrow[{point_1, point_2}, {s1, s2}] ToString[t]<>"pt", {20 t, 0}]}, represents a line with arrow that keeps a {t, 0, 10}]] distance of s1 from p1 and a distance of s2 from p2. Arrow[{point_1, point_2}, {s1, s2}] represents a line with arrow that keeps a distance of s1 from p1 and a distance of s2 from p2.
>> Graphics[Arrow[{{0,0}, {1,1}}]] 0pt 1pt 2pt 3pt 4pt 5pt 6pt 7pt 8pt 9pt10pt
90 >> Graphics[{Circle[], Arrow[{{2, >> Table[Graphics[{Circle[], Arrow[ 1}, {0, 0}}, 1]}] Table[{Cos[phi],Sin[phi]},{phi ,0,2*Pi,Pi/2}],{d, d}]}],{d ,0,2,0.5}] Arrows can also be drawn in 3D by giving poing , , , , in three dimensions: >> Graphics3D[Arrow[{{1, 1, -1}, {2, 2, 0}, {3, 3, -1}, {4, 4, 0}}]]
Keeping distances may happen across multiple segments:
91 Arrowheads >> Graphics[{Circle[], Arrowheads [{{0.04, 1, Graphics[{Red, Disk []}]}}], Arrow[{{0, 0}, {Cos[Pi Arrowheads[ ] s /3],Sin[Pi/3]}}]}] specifies that Arrow[] draws one arrow of size s (relative to width of image, defaults to 0.04). Arrowheads[{spec1, spec2, ..., specn}] specifies that Arrow[] draws n arrows as defined by spec1, spec2, ... specn. Arrowheads[{{s}}] specifies that one arrow of size s should be drawn. Arrowheads[{{s, pos}}] specifies that one arrow of size s should be drawn at position pos (for the arrow to be on the line, pos has to be between 0, i.e. the start for the line, and 1, i.e. the end of the line). Arrowheads[{{s, pos, g}}] specifies that one arrow of size s should >> Graphics[{Arrowheads[Table be drawn at position pos using Graphics [{0.04, i/10, Graphics[Disk g. []]},{i,1,10}]], Arrow[{{0, 0}, {6, 5}, {1, -3}, {-2, 2}}]}]
Arrows on both ends can be achieved using neg- ative sizes: >> Graphics[{Circle[],Arrowheads [{-0.04, 0.04}], Arrow[{{0, 0}, {2, 2}}, {1,1}]}]
Circle
Circle[{cx, cy}, r] draws a circle with center (cx, cy) and You may also specify our own arrow shapes: radius r. Circle[{cx, cy}, {rx, ry}] draws an ellipse. Circle[{cx, cy}] chooses radius 1. Circle[] chooses center (0, 0) and radius 1.
92 >> Graphics[{Red, Circle[{0, 0}, Disk {2, 1}]}] Disk[{cx, cy}, r] fills a circle with center (cx, cy) and ra- dius r. Disk[{cx, cy}, {rx, ry}] fills an ellipse. Disk[{cx, cy}] chooses radius 1. Disk[] chooses center (0, 0) and radius 1. >> Graphics[{Circle[], Disk[{0, 0}, Disk[{x, y}, ..., {t1, t2}] {1, 1}, {0, 2.1}]}] is a sector from angle t1 to t2.
>> Graphics[{Blue, Disk[{0, 0}, {2, 1}]}]
The outer border can be drawn using EdgeForm: >> Graphics[{EdgeForm[Black], Red, Target practice: Disk[]}] >> Graphics[Circle[], Axes-> True] 1.0
0.5
−1.0 −0.5 0.5 1.0
−0.5
−1.0 Disk can also draw sectors of circles and ellipses
93 >> Graphics[Disk[{0, 0}, 1, {Pi / >> Graphics[{Style[Disk[],EdgeForm 3, 2 Pi / 3}]] [{Thick,Red}]], Circle[{1,1}]}]
>> Graphics[{Blue, Disk[{0, 0}, {1, 2}, {Pi / 3, 5 Pi / 3}]}] FilledCurve
FilledCurve[{segment1, segment2 ...}] represents a filled curve.
>> Graphics[FilledCurve[{Line[{{0, 0}, {1, 1}, {2, 0}}]}]]
EdgeForm >> Graphics[FilledCurve[{ BezierCurve[{{0, 0}, {1, 1}, {2, >> Graphics[{EdgeForm[{Thick, Green 0}}], Line[{{3, 0}, {0, 2}}]}]] }], Disk[]}]
94 FontColor >> Graphics[{Rectangle[{1, 1}]}, Axes -> True, PlotRange -> {{-2, 1.5}, {-1, 1.5}}] FontColor is an option for Style to set the font color. 1.5 1.0 Graphics 0.5
Graphics[primitives, options] −2.0−1.5−1.0−0.5 0.5 1.0 1.5 represents a graphic. −0.5
Options include: −1.0 • Axes >> Graphics[{Rectangle[],Red,Disk • TicksStyle [{1,0}]},PlotRange • AxesStyle ->{{0,1},{0,1}}] • LabelStyle • AspectRatio • PlotRange • PlotRangePadding • ImageSize • Background
>> Graphics[{Blue, Line[{{0,0}, {1,1}}]}]
Graphics produces GraphicsBox boxes: >> Graphics[Rectangle[]] // ToBoxes // Head GraphicsBox
In TeXForm, Graphics produces Asymptote fig- ures: >> Graphics[Circle[]] // TeXForm Graphics supports PlotRange: \begin{asy} usepackage("amsmath"); size(5.8556cm, 5.8333cm); draw(ellipse((175,175),175,175), rgb(0, 0, 0)+linewidth(0.66667)); clip(box((-0.33333,0.33333), (350.33,349.67))); \end{asy}
95 Large Medium
ImageSize -> Large ImageSize -> Medium produces a large image. produces a medium-sized image.
Line Point
Line[{point_1, point_2 ...}] Point[{point_1, point_2 ...}] represents the line primitive. represents the point primitive. Line[{{p_11, p_12, ...}, {p_21, p_22, Point[{{p_11, p_12, ...}, {p_21, p_22, ...}, ...}] ...}, ...}] represents a number of line primitives. represents a number of point primitives.
>> Graphics[Line Points are rendered if possible as circular re- [{{0,1},{0,0},{1,0},{1,1}}]] gions. Their diameters can be specified using PointSize. Points can be specified as {x, y}: >> Graphics[Point[{0, 0}]]
>> Graphics[Point[Table[{Sin[t], Cos[t]}, {t, 0, 2. Pi, Pi / 15.}]]]
>> Graphics3D[Line [{{0,0,0},{0,1,1},{1,0,0}}]]
or as {x, y, z}:
96 >> Graphics3D[{Orange, PointSize >> Table[Graphics3D[{PointSize[r], [0.05], Point[Table[{Sin[t], Cos Point[{0, 0, 0}]}], {r, {0.05, [t], 0}, {t, 0, 2 Pi, Pi / 0.1, 0.8}}] 15.}]]}] , , PointSize PointSize[t] sets the diameter of points to t, which is relative to the overall width. PointSize can be used for both two- and three- dimensional graphics. The initial default point- size is 0.008 for two-dimensional graphics and 0.01 for three-dimensional graphics. >> Table[Graphics[{PointSize[r], Point[{0, 0}]}], {r, {0.02, 0.05, 0.1, 0.3}}] Polygon Polygon[{point_1, point_2 ...}] , , , represents the filled polygon primitive. Polygon[{{p_11, p_12, ...}, {p_21, p_22, ...}, ...}] represents a number of filled polygon primitives.
A Right Triangle:
97 >> Graphics[Polygon >> Graphics3D[Polygon [{{1,0},{0,0},{0,1}}]] [{{0,0,0},{0,1,1},{1,0,0}}]]
Notice that there is a line connecting from the last point to the first one. A point is an element of the polygon if a ray from the point in any direction in the plane crosses Rectangle the boundary line segments an odd number of times. >> Graphics[Polygon Rectangle[{xmin, ymin}] [{{150,0},{121,90},{198,35},{102,35},{179,90}}]]represents a unit square with bottom-left corner at {xmin, ymin}. ’Rectangle[{xmin, ymin}, {xmax, ymax}] is a rectange extending from {xmin, ymin} to {xmax, ymax}.
>> Graphics[Rectangle[]]
98 >> Graphics[{Blue, Rectangle[{0.5, >> Graphics[{Yellow, Rectangle[], 0}], Orange, Rectangle[{0, Orange, RegularPolygon[{1, 1}, 0.5}]}] {0.25, 0}, 3]}]
RegularPolygon Show
RegularPolygon[n] Show[graphics, options] gives the regular polygon with n edges. shows a list of graphics with the specified RegularPolygon[r, n] options added. gives the regular polygon with n edges and radius r. RegularPolygon[{r, phi}, n] gives the regular polygon with radius r with one vertex drawn at angle phi. RegularPolygon[{$x, $y}, r, n] gives the regular polygon centered at the position {$x, $y}.
>> Graphics[RegularPolygon[5]]
99 >> Show[{Plot[x, {x, 0, 10}], Small ListPlot[{1,2,3}]}] ImageSize Small 3.0 -> 10 produces a small image. 8 2.5 6 2.0 Text 4 1.5 2 Text[" ", { , }] text x y 2 4 6 8 10 draws1.5 text centered2.0 2 on.5 position3.0{x, y}. , , $OptionSyntax >> Graphics[{Text["First", {0, 0}], Text["Second", {1, 1}]}, Axes-> True, PlotRange->{{-2, 2}, {-2, 2}}] 2 1 Second − > Ignore, AspectRatio − > Automatic, Axes − > False, AxesStyle First − − − > {} , Background 2 1 1 2 − > Automatic, ImageSize − − > Automatic, LabelStyle 1 − > {} , PlotRange − > Automatic, PlotRangePadding −2 Thick Thick sets the line width for subsequent graph- ics primitives to 2pt. − − {} > Automatic, TicksStyle > Thickness Thickness[t] sets the line thickness for subsequent graphics primitives to t times the size of the plot area.
100 >> Graphics[{Thickness[0.2], Line [{{0, 0}, {0, 5}}]}, Axes->True, PlotRange->{{-5, 5}, {-5, 5}}]
4
2
−4 −2 2 4 −2
−4
Thin
Thin sets the line width for subsequent graph- ics primitives to 0.5pt.
Tiny
ImageSize -> Tiny produces a tiny image.
101 16. Strings and Characters - Miscellaneous
Contents
StringContainsQ ... 103 ToExpression ..... 104 Alphabet ...... 102 StringQ ...... 104 ToString ...... 105 $CharacterEncoding .. 102 StringRepeat ...... 104 Transliterate ...... 105 HexidecimalCharacter . 102 String ...... 104 Whitespace ...... 105 LetterNumber ..... 103 NumberString ..... 103 $SystemCharacterEn- coding ...... 104 RemoveDiacritics ... 103
Alphabet >> StringMatchQ[#, HexidecimalCharacter] & /@ {"a", "1", "A", "x", "H", " ", "."} Alphabet[] { gives the list of lowercase letters a-z in the True, True, True, False, } English alphabet . False, False, False Alphabet[type] gives the alphabet for the language or class type. LetterNumber
>> Alphabet[] LetterNumber[c] {a, b, c, d, e, f, g, h, i, j, k, l, m, returns the position of the character c in n, o, p, q, r, s, t, u, v, w, x, y, z} the English alphabet. LetterNumber[‘‘string’]’ >> Alphabet["German"] returns a list of the positions of characters {a, b, c, d, e, f, g, h, i, j, k, l, m, in string. n, o, p, q, r, s, t, u, v, w, x, y, z} LetterNumber[‘‘string’,’ alpha] returns a list of the positions of characters in string, regarding the alphabet alpha. $CharacterEncoding >> LetterNumber["b"] 2 CharacterEncoding LetterNumber also works with uppercase char- specifies the default character encoding acters to use if no other encoding is specified. >> LetterNumber["B"] 2 HexidecimalCharacter >> LetterNumber["ss2!"] {19, 19, 0, 0}
HexidecimalCharacter Get positions of each of the letters in a string: represents the characters 0-9, a-f and A-F. >> LetterNumber[Characters["Peccary "]] {16, 5, 3, 3, 1, 18, 25}
102 >> LetterNumber[{"P", "Pe", "P1", " StringContainsQ eck"}] { { } { } { }} 16, 16, 5 , 16, 0 , 5, 3, 11 StringContainsQ["string", patt] returns True if any part of string matches >> LetterNumber["\[Beta]", "Greek"] patt, and returns False otherwise. 2 StringContainsQ[{‘‘s1’, “s2”, ...}, patt]’ returns the list of results for each element NumberString of string list. StringContainsQ[patt] represents an operator form of String- NumberString ContainsQ that can be applied to an ex- represents the characters in a number. pression.
>> StringMatchQ["1234", >> StringContainsQ["mathics", "m" ~ NumberString] ~__ ~~"s"] True True >> StringMatchQ["1234.5", >> StringContainsQ["mathics", "a" ~ NumberString] ~__ ~~"m"] True False >> StringMatchQ["1.2‘20", >> StringContainsQ["Mathics", "MA" NumberString] , IgnoreCase -> True] False True
>> StringContainsQ[{"g", "a", "laxy RemoveDiacritics ", "universe", "sun"}, "u"] {False, False, False, True, True} RemoveDiacritics[s] >> StringContainsQ["e" ~~___ ~~"u"] returns a version of s with all diacritics re- /@ {"The Sun", "Mercury", " moved. Venus", "Earth", "Mars", " Jupiter", "Saturn", "Uranus", " >> RemoveDiacritics["en prononçant Neptune"} pêcher et pécher"] {True, True, True, False, False, en prononcant pecher et pecher False, False, False, True}
>> RemoveDiacritics["piñata"] pinata StringQ
StringQ[expr] returns True if expr is a String, or False otherwise.
>> StringQ["abc"] True
>> StringQ[1.5] False
103 >> Select[{"12", 1, 3, 5, "yz", x, ToExpression y}, StringQ] { } 12, yz ToExpression[input] inteprets a given string as Mathics input. ToExpression[input, form] StringRepeat reads the given input in the specified form. ToExpression[input, form, h] StringRepeat["string", n] applies the head h to the expression be- gives string repeated n times. fore evaluating it. StringRepeat["string", n, max] gives string repeated n times, but not >> ToExpression["1 + 2"] more than max characters. 3
>> StringRepeat["abc", 3] >> ToExpression["{2, 3, 1}", abcabcabc InputForm, Max] 3 >> StringRepeat["abc", 10, 7]
abcabca >> ToExpression["2 3", InputForm] 6 String Note that newlines are like semicolons, not blanks. So so the return value is the second-line value. String >> ToExpression["2\[NewLine]3"] is the head of strings. 3
>> Head["abc"] String ToString
>> "abc" abc ToString[expr] returns a string representation of expr. Use InputForm to display quotes around strings: ToString[expr, form] >> InputForm["abc"] returns a string representation of expr in "abc" the form form. FullForm also displays quotes: >> ToString[2] >> FullForm["abc" + 2] Plus [2, "abc"] 2
>> ToString[2] // InputForm "2" $SystemCharacterEncoding >> ToString[a+b] a + b $SystemCharacterEncoding >> "U" <> 2 Stringexpected. U<>2
>> "U" <> ToString[2] U2
104 >> ToString[Integrate[f[x],x], TeXForm] \int f\left[x\right] \, dx
Transliterate
Transliterate[s] transliterates a text in some script into an ASCII string.
ASCII translateration examples can be found in: • https://en.wikipedia.org/wiki/ Iliad, • https://en.wikipedia.org/wiki/ Russian_language, and • https://en.wikipedia.org/wiki/ Hiragana
Whitespace
Whitespace represents a sequence of whitespace char- acters.
>> StringMatchQ["\r \n", Whitespace ] True
>> StringSplit["a \n b \r\n c d", Whitespace] {a, b, c, d}
>> StringReplace[" this has leading and trailing whitespace \n ", ( StartOfString ~~Whitespace)| ( Whitespace ~~EndOfString)-> ""] <> " removed" // FullForm "this has leading and trailing whitespace removed"
105 17. Mathematical Optimization
Mathematical optimization is the selection of a nomics, and the development of solution meth- best element, with regard to some criterion, from ods has been of interest in mathematics for cen- some set of available alternatives. turies. Optimization problems of sorts arise in all quan- We intend to provide local and global optimiza- titative disciplines from computer science and tion techniques, both numeric and symbolic. engineering to operations research and eco-
Contents
Minimize ...... 106 Maximize ...... 106
Maximize
Maximize[f , x] compute the maximum of f respect x that change between a and b
>> Maximize[-2 x^2 - 3 x + 5, x] {{ { }}} 49 3 , x− > − 8 4
∧ #» Maximize[1 - (x y - 3) 2, {x, y}] = {{1, {x -> 3, y -> 1}}} ∧ ∧ #» Maximize[{x - 2 y, x 2 + y 2 <= 1}, {x, y}] = {{Sqrt[5], {x -> Sqrt[5] / 5, y -> -2 Sqrt[5] / 5}}}
Minimize
Minimize[f , x] compute the minimum of f respect x that change between a and b
>> Minimize[2 x^2 - 3 x + 5, x] {{ { }}} 31 3 , x− > 8 4
∧ #» Minimize[(x y - 3) 2 + 1, {x, y}] = {{1, {x -> 3, y -> 1}}} ∧ ∧ #» Minimize[{x - 2 y, x 2 + y 2 <= 1}, {x, y}] = {{-Sqrt[5], {x -> -Sqrt[5] / 5, y -> 2 Sqrt[5] / 5}}}
106 18. Drawing Options and Option Values
The various common Plot and Graphics options, along with the meaning of specific option values are described here. Contents
ChartLegends ..... 108 Mesh ...... 110 Automatic ...... 107 Filling ...... 108 PlotPoints ...... 110 Axes ...... 107 Full ...... 108 PlotRange ...... 110 Axis ...... 108 ImageSize ...... 108 TicksStyle ...... 111 Bottom ...... 108 Joined ...... 109 Top ...... 111 ChartLabels ...... 108 MaxRecursion ..... 109
Automatic >> Graphics[Circle[], Axes -> True] 1.0 Automatic is used to specify an automatically com- puted option value. 0.5
Automatic is the default for PlotRange, ImageSize, and other graphical options: −1.0 −0.5 0.5 1.0 >> Cases[Options[Plot], HoldPattern [_ :> Automatic]] −0.5 {Background:>Automatic, Exclusions:>Automatic, − ImageSize:>Automatic, 1.0 MaxRecursion:>Automatic, PlotRange:>Automatic, PlotRangePadding:>Automatic} Axis
Axis Axes is a possible value for the Filling option.
Axes >> ListLinePlot[Table[Sin[x], {x, -5, 5, 0.2}], Filling->Axis] is an option for charting and graph- ics functions that specifies whether axes 1.0 should be drawn. 0.5 • Axes->True draws all axes. • Axes->False draws no axes. 10 20 30 40 50 • Axes->{False,True} draws an axis y but −0.5 no x axis in two dimensions. −1.0
107 Bottom Filling
Bottom Filling Top |Bottom|Axis is a possible value for the Filling option. is a an option to Plot to specify what fill- ing to add under point, curves, and sur- >> ListLinePlot[Table[Sin[x], {x, faces -5, 5, 0.2}], Filling->Bottom]
>> ListLinePlot[Table[Sin[x], {x, 1.0 -5, 5, 0.2}], Filling->Axis] 0.5 1.0
10 20 30 40 50 0.5 −0.5 10 20 30 40 50 −1.0 −0.5 −1.0 ChartLabels
ChartLabels Full is a charting option that specifies what la- bels should be used for chart elements. Full is a possible value for the Mesh and >> PieChart[{30, 20, 10}, PlotRange options. ChartLabels -> {Dogs, Cats, Fish }] ImageSize
Dogs ImageSize is an option that specifies the overall size of an image to display.
Specifications for both width and height can be Fish any of the following: Cats Automatic determined by location or other dimen- sion (default) Tiny, Small, Medium, Large pre defined absolute sizes ChartLegends >> Plot[Sin[x], {x, 0, 10}, ImageSize -> Small] ChartLegends 1.0 is a charting option. 0.5 −0.5 2 4 6 8 10 −1.0
108 Joined >> Plot[Sin[Cos[x^2]],{x,-4,4},Mesh ->All] Joined boolean is an option for Plot that gives whether to join points to make lines. 0.5
>> ListPlot[Table[n ^ 2, {n, 10}], Joined->True] −4 −2 2 4 − 100 0.5 80
60 >> Plot[Sin[x], {x,0,4 Pi}, Mesh-> 40 Full] 20 1.0
4 6 8 10 0.5
2 4 6 8 10 12 MaxRecursion −0.5 −1.0 MaxRecursion
is an option for functions like NIntegrate >> DensityPlot[Sin[x y], {x, -2, and Plot that specifies how many recur- 2}, {y, -2, 2}, Mesh->Full] sive subdivisions can be made.
>> NIntegrate[Exp[-10^8 x^2], {x, -1, 1}, MaxRecursion -> 10] − 1.97519 × 10 207
Mesh
Mesh is a charting option, such as for Plot, BarChart, PieChart, etc. that specifies the mesh to be drawn. The default is Mesh->None.
109 >> Plot3D[Sin[x y], {x, -2, 2}, {y, >> Plot[Sin[Cos[x^2]],{x,-4,4}, -2, 2}, Mesh->Full] PlotRange -> All]
0.5
−4 −2 2 4 −0.5
>> Graphics[Disk[], PlotRange -> {{-.5, .5}, {0, 1.5}}]
PlotPoints
PlotPoints n A number specifies how many initial sample points to use.
>> Plot[Sin[Cos[x^2]],{x,-4,4}, PlotPoints->22] TicksStyle
0.5 TicksStyle is an option for graphics functions which specifies how ticks should be rendered. −4 −2 2 4 − 0.5 • TicksStyle gives styles for both tick marks and tick labels. • TicksStyle can be used in both two and three-dimensional graphics. • TicksStyle->list specifies the colors of each PlotRange of the axes.
PlotRange is a charting option, such as for Plot, BarChart, PieChart, etc. that gives the range of coordinates to include in a plot.
• All all points are included. • Automatic - outlying points are dropped. • max - explicit limit for each function. • {min, max} - explicit limits for y (2D), z (3D), or array values. • {{x_min, x_max}, {{$y_min}, {$y_max}} - ex- plit limits for x and y.
110 >> Graphics[Circle[], Axes-> True, TicksStyle -> {Blue, Red}] 1.0
0.5
−1.0 −0.5 0.5 1.0
−0.5
−1.0
Top
Top is a possible value for the Filling option.
>> ListLinePlot[Table[Sin[x], {x, -5, 5, 0.2}], Filling->Axis|Top| Bottom] 1.0 0.5
10 20 30 40 50 −0.5 −1.0
111 19. Physical and Chemical data
Contents
ElementData ...... 113
ElementData Some data is missing: >> ElementData["Tc", "SpecificHeat "] ElementData["name‘‘,”property"] gives the value of the property for the Missing [NotAvailable] chemical specified by name. ElementData[n,"property"] All the known properties: gives the value of the property for the nth >> ElementData["Properties"] chemical element. {Abbreviation, AbsoluteBoilingPoint, >> ElementData[74] AbsoluteMeltingPoint, Tungsten AtomicNumber, AtomicRadius,
>> ElementData["He", " AtomicWeight, Block, BoilingPoint, AbsoluteBoilingPoint"] BrinellHardness, BulkModulus, 4.22 CovalentRadius, CrustAbundance, Density, DiscoveryYear, >> ElementData["Carbon", " ElectroNegativity, ElectronAffinity, IonizationEnergies"] ElectronConfiguration, { 1 086.5, 2 352.6, 4 620.5 ElectronConfigurationString, } , 6 222.7, 37 831, 47 277. ElectronShellConfiguration,
>> ElementData[16, " FusionHeat, Group, ElectronConfigurationString"] IonizationEnergies, LiquidDensity, [Ne] 3s2 3p4 MeltingPoint, MohsHardness, Name, Period, PoissonRatio, >> ElementData[73, " Series, ShearModulus, ElectronConfiguration"] SpecificHeat, StandardName, {{2} , {2, 6} , {2, 6, 10} , {2, ThermalConductivity, 6, 10, 14} , {2, 6, 3} , {2}} VanDerWaalsRadius, VaporizationHeat, The number of known elements: VickersHardness, YoungModulus} >> Length[ElementData[All]] 118 Some properties are not appropriate for certain elements: >> ElementData["He", " ElectroNegativity"] [ ] Missing NotApplicable
112 >> ListPlot[Table[ElementData[z, " AtomicWeight"], {z, 118}]] 300 250 200 150 100 50
20 40 60 80 100 120
113 20. List Functions - Miscellaneous
Contents
IntersectingQ ..... 117 Position ...... 121 All ...... 114 Join ...... 117 Quartiles ...... 121 ByteArray ...... 114 Key ...... 117 RankedMax ...... 121 CentralMoment .... 114 LeafCount ...... 118 RankedMin ...... 121 ClusteringComponents 115 Level ...... 118 Split ...... 121 ContainsOnly ..... 115 LevelQ ...... 118 SplitBy ...... 122 Delete ...... 116 List ...... 119 SubsetQ ...... 122 DisjointQ ...... 116 ListQ ...... 119 TakeLargest ...... 122 Failure ...... 116 Nearest ...... 119 TakeLargestBy ..... 122 FindClusters ...... 117 None ...... 119 TakeSmallest ..... 122 Fold ...... 117 NotListQ ...... 119 TakeSmallestBy .... 123 FoldList ...... 117 PadLeft ...... 120 UnitVector ...... 123 Insert ...... 117 PadRight ...... 120
All >> ToString[A] ByteArray["ARkD"] All >> ByteArray["ARkD"] is a possible option value for Span, Quiet, Part and related functions. All ByteArray ["ARkD"] specifies all parts at a particular level. >> B=ByteArray["asy"] ThefirstargumentinBytearray[asy]shouldbeaB64encondedstringoravectorofintegers. ByteArray $Failed
ByteArray[{b_1, b_2, ...}] CentralMoment Represents a sequence of Bytes b_1, b_2, ... CentralMoment[list, r] ByteArray[‘‘string’]’ gives the the rth central moment (i.e. the Constructs a byte array where bytes rth moment about the mean) of list. comes from decode a b64 encoded String
>> CentralMoment[{1.1, 1.2, 1.4, >> A=ByteArray[{1, 25, 3}] 2.1, 2.4}, 4] ByteArray ["ARkD"] 0.100845
>> A[[2]] 25
>> Normal[A] {1, 25, 3}
114 ClusteringComponents Delete
ClusteringComponents[list] Delete[expr, i] forms clusters from list and returns a list deletes the element at position i in expr. of cluster indices, in which each element The position is counted from the end if i shows the index of the cluster in which is negative. the corresponding element in list ended Delete[expr,{m, n, ...}] up. deletes the element at position {m, n, ...}. ClusteringComponents[list, k] Delete[expr, {{m1, n1, ...}, {m2, forms k clusters from list and returns a list n2, ...}, ...}] of cluster indices, in which each element deletes the elements at several positions. shows the index of the cluster in which the corresponding element in list ended Delete the element at position 3: up. >> Delete[{a, b, c, d}, 3] {a, b, d} For more detailed documentation regarding op- tions and behavior, see FindClusters[]. Delete at position 2 from the end: >> ClusteringComponents[{1, 2, 3, >> Delete[{a, b, c, d}, -2] 1, 2, 10, 100}] {a, b, d} {1, 1, 1, 1, 1, 1, 2} Delete at positions 1 and 3:
>> ClusteringComponents[{10, 100, >> Delete[{a, b, c, d}, {{1}, {3}}] 20}, Method -> "KMeans"] {b, d} {1, 0, 1} Delete in a 2D array: >> Delete[{{a, b}, {c, d}}, {2, 1}] {{ } { }} ContainsOnly a, b , d Deleting the head of a whole expression gives a Sequence object: ContainsOnly[list1, list2] >> Delete[{a, b, c}, 0] yields True if list1 contains only elements that appear in list2. Sequence [a, b, c] Delete in an expression with any head: >> ContainsOnly[{b, a, a}, {a, b, c >> Delete[f[a, b, c, d], 3] }] f [a, b, d] True Delete a head to splice in its arguments: The first list contains elements not present in the >> Delete[f[a, b, u + v, c], {3, second list: 0}] >> ContainsOnly[{b, a, d}, {a, b, c }] f [a, b, u, v, c]
False >> Delete[{a, b, c}, 0]
>> ContainsOnly[{}, {a, b, c}] Sequence [a, b, c]
True Delete without the position: Use Equal as the comparison function to have >> Delete[{a, b, c, d}] numerical tolerance: Deletecalledwith1argument; 2argumentsareexpected. [ ] >> ContainsOnly[{a, 1.0}, {1, a, b Delete {a, b, c, d} }, {SameTest -> Equal}] True Delete with many arguments:
115 >> Delete[{a, b, c, d}, 1, 2] >> FindClusters[{25, 100, 17, 20}] Deletecalledwith3arguments; 2argumentsareexpected. {{25, 17, 20} , {100}} [ ] Delete {a, b, c, d} , 1, 2 >> FindClusters[{3, 6, 1, 100, 20, 5, 25, 17, -10, 2}] Delete the element out of range: {{ − } >> Delete[{a, b, c, d}, 5] 3, 6, 1, 5, 10, 2 , { } { }} Part{5}o f {a, b, c, d}doesnotexist. 100 , 20, 25, 17 [ ] { } Delete a, b, c, d , 5 >> FindClusters[{1, 2, 10, 11, 20, 21}] Delete the position not integer: {{1, 2} , {10, 11} , {20, 21}} >> Delete[{a, b, c, d}, {1, n}] { Positionspecificationnin a, >> FindClusters[{1, 2, 10, 11, 20, b, c, d}isnotamachine 21}, 2] − sizedintegeroralistofmachine {{1, 2, 10, 11} , {20, 21}} − sizedintegers. [ ] { } { } >> FindClusters[{1 -> a, 2 -> b, 10 Delete a, b, c, d , 1, n -> c}] {{a, b} , {c}}
DisjointQ >> FindClusters[{1, 2, 5} -> {a, b, c}] {{ } { }} DisjointQ[a, b] a, b , c gives True if $a and $b are disjoint, or >> FindClusters[{1, 2, 3, 1, 2, 10, False if $a and $b have any common el- 100}, Method -> "Agglomerate"] ements. {{1, 2, 3, 1, 2, 10} , {100}}
>> FindClusters[{1, 2, 3, 10, 17, Failure 18}, Method -> "Agglomerate"] {{1, 2, 3} , {10} , {17, 18}} Failure[tag, assoc] represents a failure of a type indicated by >> FindClusters[{{1}, {5, 6}, {7}, tag, with details given by the association {2, 4}}, DistanceFunction -> ( assoc. Abs[Length[#1] - Length[#2]]&)] {{{1} , {7}} , {{5, 6} , {2, 4}}}
>> FindClusters[{"meep", "heap", " FindClusters deep", "weep", "sheep", "leap", "keep"}, 3] FindClusters[list] {{meep, deep, weep, keep} , returns a list of clusters formed from the {heap, leap} , {sheep}} elements of list. The number of cluster is determined automatically. FindClusters’ automatic distance function detec- FindClusters[list, k] tion supports scalars, numeric tensors, boolean returns a list of k clusters formed from the vectors and strings. elements of list. The Method option must be either “Agglomer- ate” or “Optimize”. If not specified, it defaults to >> FindClusters[{1, 2, 20, 10, 11, “Optimize”. Note that the Agglomerate and Op- 40, 19, 42}] timize methods usually produce different clus- {{1, 2, 20, 10, 11, 19} , {40, 42}} terings. The runtime of the Agglomerate method is
116 quadratic in the number of clustered points n, >> Insert[{a,b,c,d,e}, x, 3] builds the clustering from the bottom up, and is {a, b, x, c, d, e} exact (no element of randomness). The Optimize method’s runtime is linear in n, Optimize builds >> Insert[{a,b,c,d,e}, x, -2] the clustering from top down, and uses random {a, b, c, d, x, e} sampling.
Fold IntersectingQ
Fold[f , x, list] IntersectingQ[a, b] returns the result of iteratively applying gives True if there are any common ele- the binary operator f to each element of ments in $a and $b, or False if $a and $b list, starting with x. are disjoint. Fold[f , list] is equivalent to Fold[f , First[list], Rest[list]]. Join
>> Fold[Plus, 5, {1, 1, 1}] 8 Join[l1, l2] concatenates the lists l1 and l2. >> Fold[f, 5, {1, 2, 3}] [ [ ] ] f f f [5, 1] , 2 , 3 Join concatenates lists: >> Join[{a, b}, {c, d, e}] {a, b, c, d, e} FoldList >> Join[{{a, b}, {c, d}}, {{1, 2}, {3, 4}}] FoldList[f , x, list] {{ } { } { } { }} returns a list starting with x, where each a, b , c, d , 1, 2 , 3, 4 element is the result of applying the bi- The concatenated expressions may have any nary operator f to the previous result and head: the next element of list. >> Join[a + b, c + d, e + f] FoldList[f , list] is equivalent to FoldList[f , First[ a + b + c + d + e + f list], Rest[list]]. However, it must be the same for all expressions: >> Join[a + b, c * d] >> FoldList[f, x, {1, 2, 3}] { [ HeadsPlusandTimesareexpectedtobethesame. x, f [x, 1] , f f [x, 1] , ] [ [ ] ]} Join [a + b, cd] 2 , f f f [x, 1] , 2 , 3
>> FoldList[Times, {1, 2, 3}] {1, 2, 6} Key
Key[key] Insert represents a key used to access a value in an association. Key[key][assoc] Insert[list, elem, n] inserts elem at position n in list. When n is negative, the position is counted from the end.
117 LeafCount >> Level[{{{{a}}}}, -5] {} LeafCount[expr] >> Level[h0[h1[h2[h3[a]]]], {0, returns the total number of indivisible -1}] subexpressions in expr. {a, h3 [a] , h2 [h3 [a]] , h1 [h2 [ } >> LeafCount[1 + x + y^a] h3 [a]]] , h0 [h1 [h2 [h3 [a]]]]
6 Use the option Heads -> True to include heads:
>> LeafCount[f[x, y]] >> Level[{{{{a}}}}, 3, Heads -> True] 3 {List, List, List, {a} , {{a}} , {{{a}}}} >> LeafCount[{1 / 3, 1 + I}]
7 >> Level[x^2 + y^3, 3, Heads -> True] >> LeafCount[Sqrt[2]] { } 5 Plus, Power, x, 2, x2, Power, y, 3, y3
>> LeafCount[100!] >> Level[a ^ 2 + 2 * b, {-1}, Heads 1 -> True] {Plus, Power, a, 2, Times, 2, b} Level >> Level[f[g[h]][x], {-1}, Heads -> True] Level[expr, levelspec] { f , g, h, x} gives a list of all subexpressions of expr at
the level(s) specified by levelspec. >> Level[f[g[h]][x], {-2, -1}, Heads -> True] { [ ] } Level uses standard level specifications: f , g, h, g [h] , x, f g [h] [x] n levels 1 through n Infinity LevelQ all levels from level 1 {n} level n only LevelQ[expr] {m, n} tests whether expr is a valid level specifi- levels m through n cation.
>> LevelQ[2] Level 0 corresponds to the whole expression. A negative level -n consists of parts with depth True n. >> LevelQ[{2, 4}] Level -1 is the set of atoms in an expression: True >> Level[a + b ^ 3 * f[2 x ^ 2], {-1}] >> LevelQ[Infinity] {a, b, 3, 2, x, 2} True
>> LevelQ[a + b] >> Level[{{{{a}}}}, 3] False {{a} , {{a}} , {{{a}}}}
>> Level[{{{{a}}}}, -4] {{{{a}}}}
118 List >> Nearest[{5, 2.5, 10, 11, 15, 8.5, 14}, 12] List[e1, e2, ..., ei] {11} {e1, e2, ..., ei} represents a list containing the elements Return all items within a distance of 5: e1...ei. >> Nearest[{5, 2.5, 10, 11, 15, 8.5, 14}, 12, {All, 5}] List is the head of lists: {11, 10, 14} >> Head[{1, 2, 3}] >> Nearest[{Blue -> "blue", White List -> "white", Red -> "red", Green Lists can be nested: -> "green"}, {Orange, Gray}] >> {{a, b, {c, d}}} {{red} , {white}} {{a, b, {c, d}}} >> Nearest[{{0, 1}, {1, 2}, {2, 3}} -> {a, b, c}, {1.1, 2}] ListQ {b}
ListQ[expr] tests whether expr is a List. None
>> ListQ[{1, 2, 3}] None True is a possible value for Span and Quiet.
>> ListQ[{{1, 2}, {3, 4}}] True NotListQ >> ListQ[x] False NotListQ[expr] returns true if expr is not a list. Nearest
Nearest[list, x] returns the one item in list that is nearest to x. Nearest[list, x, n] returns the n nearest items. Nearest[list, x,{n, r}] returns up to n nearest items that are not farther from x than r. Nearest[{p1 -> q1, p2 -> q2, ...}, x] returns q1, q2, ... but measures the dis- tances using p1, p2, ... Nearest[{p1, p2, ...} -> {q1, q2, ...}, x] returns q1, q2, ... but measures the dis- tances using p1, p2, ...
119 PadLeft PadRight
PadLeft[list, n] PadRight[list, n] pads list to length n by adding 0 on the pads list to length n by adding 0 on the left. right. PadLeft[list, n, x] PadRight[list, n, x] pads list to length n by adding x on the pads list to length n by adding x on the left. right. PadLeft[list,{n1, $n2, ...}, x] PadRight[list,{n1, $n2, ...}, x] pads list to lengths n1, n2 at levels 1, 2, ... pads list to lengths n1, n2 at levels 1, 2, ... respectively by adding x on the left. respectively by adding x on the right. PadLeft[list, n, x, m] PadRight[list, n, x, m] pads list to length n by adding x on the pads list to length n by adding x on the left and adding a margin of m on the left and adding a margin of m on the left. right. PadRight[list, n, x,{m1, m2, ...}] PadLeft[list, n, x,{m1, m2, ...}] pads list to length n by adding x on the pads list to length n by adding x on the right and adding margins of m1, m2, ... left and adding margins of m1, m2, ... on on levels 1, 2, ... on the left. levels 1, 2, ... on the right. PadRight[list] PadLeft[list] turns the ragged list list into a regular list turns the ragged list list into a regular list by adding 0 on the right. by adding 0 on the left.
>> PadRight[{1, 2, 3}, 5] >> PadLeft[{1, 2, 3}, 5] {1, 2, 3, 0, 0} {0, 0, 1, 2, 3} >> PadRight[x[a, b, c], 5] >> PadLeft[x[a, b, c], 5] x [a, b, c, 0, 0] x [0, 0, a, b, c] >> PadRight[{1, 2, 3}, 2] >> PadLeft[{1, 2, 3}, 2] {1, 2} {2, 3}
>> PadRight[{{}, {1, 2}, {1, 2, >> PadLeft[{{}, {1, 2}, {1, 2, 3}}] 3}}] {{0, 0, 0} , {0, 1, 2} , {1, 2, 3}} {{0, 0, 0} , {1, 2, 0} , {1, 2, 3}}
>> PadLeft[{1, 2, 3}, 10, {a, b, c }, 2] >> PadRight[{1, 2, 3}, 10, {a, b, c }, 2] {b, c, a, b, c, 1, 2, 3, a, b} {b, c, 1, 2, 3, a, b, c, a, b}
>> PadLeft[{{1, 2, 3}}, {5, 2}, x, 1] >> PadRight[{{1, 2, 3}}, {5, 2}, x, 1] {{x, x} , {x, x} , {x, {{x, x} , {x, 1} , {x, x} , {3, x} , {x, x}} x} , {x, x} , {x, x}}
120 Position >> RankedMax[{482, 17, 181, -12}, 2] Position[expr, patt] 181 returns the list of positions for which expr matches patt. Position[expr, patt, ls] RankedMin returns the positions on levels specified by levelspec ls. RankedMin[list, n] returns the nth smallest element of list >> Position[{1, 2, 2, 1, 2, 3, 2}, (with n = 1 yielding the smallest element, 2] n = 2 yielding the second smallest ele- {{2} , {3} , {5} , {7}} ment, and so on).
Find positions upto 3 levels deep >> RankedMin[{482, 17, 181, -12}, >> Position[{1 + Sin[x], x, (Tan[x] 2] - y)^2}, x, 3] 17 {{1, 2, 1} , {2}} Find all powers of x Split >> Position[{1 + x^2, x y ^ 2, 4 y, x ^ z}, x^_] {{1, 2} , {4}} Split[list] splits list into collections of consecutive Use Position as an operator identical elements. >> Position[_Integer][{1.5, 2, Split[list, test] 2.5}] splits list based on whether the function test yields True on consecutive elements. {{2}}
>> Split[{x, x, x, y, x, y, y, z}] Quartiles {{x, x, x} , {y} , {x} , {y, y} , {z}} Split into increasing or decreasing runs of ele- Quartiles[list] ments returns the 1/4, 1/2, and 3/4 quantiles of >> Split[{1, 5, 6, 3, 6, 1, 6, 3, list. 4, 5, 4}, Less] {{1, 5, 6} , {3, 6} , {1, >> Quartiles[Range[25]] { } 6} , {3, 4, 5} , {4}} 27 77 , 13, 4 4 >> Split[{1, 5, 6, 3, 6, 1, 6, 3, 4, 5, 4}, Greater] {{1} , {5} , {6, 3} , {6, RankedMax 1} , {6, 3} , {4} , {5, 4}}
Split based on first element RankedMax[ , ] list n >> Split[{x -> a, x -> y, 2 -> a, z returns the nth largest element of list -> c, z -> a}, First[#1] === (with n = 1 yielding the largest element, First[#2] &] n = 2 yielding the second largest element, {{ − − } and so on). x > a, x > y , {2− > a} , {z− > c, z− > a}}
121 SplitBy >> TakeLargest[{-8, 150, Missing[ abc]}, 2] { − } SplitBy[list, f ] 150, 8 splits list into collections of consecutive You may specify which items are ignored using elements that give the same result when f the option ExcludedForms: is applied. >> TakeLargest[{-8, 150, Missing[ abc]}, 2, ExcludedForms -> {}] >> SplitBy[Range[1, 3, 1/3], Round] {{ } { } { }} {Missing [abc] , 150} 4 5 7 8 1, , , 2, , , 3 3 3 3 3
>> SplitBy[{1, 2, 1, 1.2}, {Round, TakeLargestBy Identity}] {{{ }} {{ }} {{ } { }}} 1 , 2 , 1 , 1.2 TakeLargestBy[list, f , n] returns the a sorted list of the n largest items in list using f to retrieve the items’ SubsetQ keys to compare them.
For details on how to use the ExcludedForms SubsetQ[list1, list2] option, see TakeLargest[]. returns True if list2 is a subset of list1, and >> TakeLargestBy[{{1, -1}, {10, False otherwise. 100}, {23, 7, 8}, {5, 1}}, Total , 2] >> SubsetQ[{1, 2, 3}, {3, 1}] {{ } { }} True 10, 100 , 23, 7, 8
The empty list is a subset of every list: >> TakeLargestBy[{"abc", "ab", "x >> SubsetQ[{}, {}] "}, StringLength, 1] True {abc}
>> SubsetQ[{1, 2, 3}, {}] True TakeSmallest Every list is a subset of itself: >> SubsetQ[{1, 2, 3}, {1, 2, 3}] TakeSmallest[list, f , n] True returns the a sorted list of the n smallest items in list.
TakeLargest For details on how to use the ExcludedForms option, see TakeLargest[]. >> TakeSmallest[{100, -1, 50, 10}, TakeLargest[list, f , n] 2] returns the a sorted list of the n largest items in list. {−1, 10}
>> TakeLargest[{100, -1, 50, 10}, 2] {100, 50}
None, Null, Indeterminate and expressions with head Missing are ignored by default:
122 TakeSmallestBy
TakeSmallestBy[list, f , n] returns the a sorted list of the n smallest items in list using f to retrieve the items’ keys to compare them.
For details on how to use the ExcludedForms option, see TakeLargest[]. >> TakeSmallestBy[{{1, -1}, {10, 100}, {23, 7, 8}, {5, 1}}, Total , 2] {{1, − 1} , {5, 1}}
>> TakeSmallestBy[{"abc", "ab", "x "}, StringLength, 1] {x}
UnitVector
UnitVector[n, k] returns the n-dimensional unit vector with a 1 in position k. UnitVector[k] is equivalent to UnitVector[2, k].
>> UnitVector[2] {0, 1}
>> UnitVector[4, 3] {0, 0, 1, 0}
123 21. Numeric Evaluation and Precision
Support for numeric evaluation with arbitrary precision is just a proof-of-concept. Precision is not “guarded” through the evaluation process. Only integer precision is supported. How- ever, things like N[Pi, 100] should work as expected. Contents
$MachinePrecision .. 125 NumericQ ...... 127 Chop ...... 124 $MaxPrecision ..... 125 Precision ...... 128 Hash ...... 124 $MinPrecision ..... 126 Rationalize ...... 128 IntegerDigits ..... 125 N ...... 127 RealDigits ...... 128 $MachineEpsilon ... 125 NIntegrate ...... 127 Round ...... 129 MachinePrecision ... 125
Chop Hash
Chop[expr] Hash[expr] replaces floating point numbers close to 0 returns an integer hash for the given expr. by 0. Hash[expr, type] Chop[expr, delta] returns an integer hash of the specified uses a tolerance of delta. The default tol- type for the given expr. erance is 10^-10. The types supported are “MD5”, “Adler32”, “CRC32”, “SHA”, “SHA224”, “SHA256”, “SHA384”, and “SHA512”. >> Chop[10.0 ^ -16] Hash[expr, type, format] 0 Returns the hash in the specified format.
>> Chop[10.0 ^ -9] − 1. × 10 9 > Hash[“The Adventures of Huckleberry Finn”] = 213425047836523694663619736686226550816 >> Chop[10 ^ -11 I] > Hash[“The Adventures of Huckleberry Finn”, I “SHA256”] = 95092649594590384288057183408609254918934351811669818342876362244564858646638 100 000 000 000 > Hash[1/3] = 56073172797010645108327809727054836008 > Hash[{a, b, {c, {d, e, f}}}] = 135682164776235407777080772547528225284 >> Chop[0. + 10 ^ -11 I] > Hash[SomeHead[3.1415]] = 58042316473471877315442015469706095084 0 >> Hash[{a, b, c}, "xyzstr"] [ ] Hash {a, b, c} , xyzstr, Integer
124 IntegerDigits MachinePrecision
IntegerDigits[n] MachinePrecision returns a list of the base-10 digits in the represents the precision of machine pre- integer n. cision numbers. IntegerDigits[n, base] returns a list of the base-base digits in n. >> N[MachinePrecision] IntegerDigits[n, base, length] 15.9546 returns a list of length length, truncating >> N[MachinePrecision, 30] or padding with zeroes on the left as nec- essary. 15.9545897701910033463281614204
>> IntegerDigits[76543] $MachinePrecision {7, 6, 5, 4, 3}
The sign of n is discarded: $MachinePrecision >> IntegerDigits[-76543] is the number of decimal digits of preci- {7, 6, 5, 4, 3} sion for machine-precision numbers.
>> IntegerDigits[15, 16] >> $MachinePrecision {15} 15.9546
>> IntegerDigits[1234, 16] {4, 13, 2} $MaxPrecision
>> IntegerDigits[1234, 10, 5] $MaxPrecision {0, 1, 2, 3, 4} represents the maximum number of dig- its of precision permitted in abitrary- precision numbers. $MachineEpsilon
>> $MaxPrecision ∞ $MachineEpsilon
is the distance between 1.0 and the next >> $MaxPrecision = 10; nearest representable machine-precision number. >> N[Pi, 11] Requestedprecision11islargerthan$MaxPrecision.Usingcurrent$MaxPrecisionof 10.instead.$MaxPrecision >> $MachineEpsilon − 2.22045 × 10 16 = Infinityspecifiesthatanyprecisionshouldbeallowed. 3.141592654 >> x = 1.0 + {0.4, 0.5, 0.6} $MachineEpsilon;
>> x{ - 1 } $MinPrecision − 0., 0., 2.22045 × 10 16 $MinPrecision represents the minimum number of dig- its of precision permitted in abitrary- precision numbers.
>> $MinPrecision 0
125 >> $MinPrecision = 10; >> N[c, p_?(#>10&)] := p
>> N[Pi, 9] >> N[c, 3] Requestedprecision9issmallerthan$MinPrecision.Usingcurrentc $MinPrecisionof 10.instead.
3.141592654 >> N[c, 11] 11.000000000 N You can also use UpSet or TagSet to specify val- ues for N: >> N[d] ^= 5; N[expr, prec] evaluates expr numerically with a preci- However, the value will not be stored in sion of prec digits. UpValues, but in NValues (as for Set): >> UpValues[d]
>> N[Pi, 50] {} 3.141592653589793238462643˜ >> NValues[d] ˜3832795028841971693993751 {HoldPattern [N [d, >> N[1/7] MachinePrecision]] :>5} 0.142857 >> e /: N[e] = 6; >> N[1/7, 5]
0.14286 >> N[e] You can manually assign numerical values to 6. symbols. When you do not specify a precision, Values for N[expr] must be associated with the MachinePrecision is taken. head of expr: >> N[a] = 10.9 >> f /: N[e[f]] = 7; 10.9 Tagfnotfoundortoodeepforanassignedrule. >> a a You can use Condition: >> N[g[x_, y_], p_] := x + y * Pi N automatically threads over expressions, ex- /; x + y > 3 cept when a symbol has attributes NHoldAll,
NHoldFirst, or NHoldRest. >> SetAttributes[g, NHoldRest] >> N[a + b] 10.9 + b >> N[g[1, 1]] g [1., 1] >> N[a, 20] a >> N[g[2, 2]] // InputForm >> N[a, 20] = 11; 8.283185307179586
>> N[a + b, 20] The precision of the result is no higher than the precision of the input 11.000000000000000000 + b >> N[Exp[0.1], 100] >> N[f[a, b]] 1.10517 f [10.9, b] >> % // Precision >> SetAttributes[f, NHoldAll] MachinePrecision
>> N[f[a, b]] f [a, b]
The precision can be a pattern:
126 >> N[Exp[1/10], 100] >> NIntegrate[1 / z, {z, -1 - I, 1 1.105170918075647624811707˜ - I, 1 + I, -1 + I, -1 - I}, Tolerance->1.*^-4] ˜826490246668224547194737˜ Integrationoveracomplexdomainisnotimplementedyet ˜518718792863289440967966˜ [ ˜747654302989143318970748654 1 NIntegrate , {z, − 1 − I, z >> % // Precision − − − − } 100. 1 I, 1 + I, 1 + I, ] 1 I , − > >> N[Exp[1.0‘20], 100] Tolerance 0.0001 2.7182818284590452354 Integrate singularities with weak divergences: >> % // Precision >> Table[ NIntegrate[x^(1./k-1.), { 20. x,0,1.}, Tolerance->1*^-6], {k ,1,7.} ] NIntegrate {1., 2., 3., 4., 5., 6., 7.} Mutiple Integrals : >> NIntegrate[x * y,{x, 0, 1}, {y, NIntegrate[expr, interval] 0, 1}] returns a numeric approximation to the definite integral of expr with limits inter- 0.25 val and with a precision of prec digits. NIntegrate[expr, interval1, interval2, ...] returns a numeric approximation to the NumericQ multiple integral of expr with limits inter- val1, interval2 and with a precision of prec digits. NumericQ[expr] tests whether expr represents a numeric quantity. >> NIntegrate[Exp[-x],{x,0,Infinity },Tolerance->1*^-6] >> NumericQ[2] 1. True >> NIntegrate[Exp[x],{x,-Infinity, 0},Tolerance->1*^-6] >> NumericQ[Sqrt[Pi]] True 1.
>> NumberQ[Sqrt[Pi]] >> NIntegrate[Exp[-x^2/2.],{x,- Infinity, Infinity},Tolerance False ->1*^-6] 2.50663 Precision >> Table[1./NIntegrate[x^k,{x,0,1}, Tolerance->1*^-6], {k,0,6}] Precision[expr] Thespecifiedmethodfailedtoreturnanumber.Fallingbackintotheinternalevaluatorexamines the number of. significant digits {1., 2., 3., 4., 5., 6., 7.} of expr. This is rather a proof-of-concept than a full im-
plementation. Precision of compound expres- sion is not supported yet. >> Precision[1] ∞
127 >> Precision[1/2] >> RealDigits[19 / 7] ∞ {{2, {7, 1, 4, 2, 8, 5}} , 1}
>> Precision[0.5] The 10000th digit of is an 8: MachinePrecision >> RealDigits[Pi, 10, 1, -10000] {{8} , − 9 999} Rationalize ∧ 20 digits starting with the coefficient of 10 -5: >> RealDigits[Pi, 10, 20, -5] Rationalize[x] {{9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, converts a real number x to a nearby ra- 2, 3, 8, 4, 6, 2, 6, 4, 3} , − 4} tional number. Rationalize[x, dx] RealDigits gives Indeterminate if more digits finds the rational number within dx of x than the precision are requested: with the smallest denominator. >> RealDigits[123.45, 10, 18] {{1, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, >> Rationalize[2.2] 11 0, 0, 0, 0, 0, Indeterminate, } } 5 Indeterminate , 3 Not all numbers can be well approximated. Return 25 digits of in base 10: >> Rationalize[N[Pi]] >> RealDigits[Pi, 10, 25] 3.14159 {{3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, } } Find the exact rational representation of N[Pi] 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3 , 1 >> Rationalize[N[Pi], 0] 245 850 922 78 256 779 Round
Round[expr] RealDigits rounds expr to the nearest integer. Round[expr, k] rounds expr to the closest multiple of k. RealDigits[n] returns the decimal representation of the >> Round[10.6] real number n as list of digits, together with the number of digits that are to the 11
left of the decimal point. >> Round[0.06, 0.1] RealDigits[n, b] 0.1 returns a list of base_b representation of the real number n. >> Round[0.04, 0.1] RealDigits[n, b, len] 0. returns a list of len digits. RealDigits[n, b, len, p] Constants can be rounded too return len digits starting with the coeffi- >> Round[Pi, .5] ∧ cient of b p 3.
>> Round[Pi^2] Return the list of digits and exponent: 10 >> RealDigits[123.55555] {{1, 2, 3, 5, 5, 5, 5, 5, Round to exact value >> Round[2.6, 1/3] 0, 0, 0, 0, 0, 0, 0, 0} , 3} 8 Return an explicit recurring decimal form: 3
128 >> Round[10, Pi] 3Pi Round complex numbers >> Round[6/(2 + 3 I)] 1 − I
>> Round[1 + 2 I, 2 I] 2I Round Negative numbers too >> Round[-1.4] −1
Expressions other than numbers remain uneval- uated: >> Round[x] Round [x]
>> Round[1.5, k] Round [1.5, k]
129 22. Arithmetic Functions
Arithmetic Functions are functions that work on individual numbers, lists, and arrays: in either sym- bolic or algebraic forms. Contents
Plus (+) ...... 131 Sums, Simple Statistics 133 Basic Arithmetic .... 130 Power (^) ..... 132 Accumulate .... 133 CubeRoot ..... 130 Sqrt ...... 132 Mean ...... 133 Divide (/) ..... 130 Subtract (-) .... 132 Total ...... 133 - Minus ( ) ..... 131 Times (*) ..... 133
Basic Arithmetic >> Pi / 4.0 0.785398 Basic Arithmetic >> 1 / 8 The functions here are the basic arithmetic oper- ations that you might find on a calculator. >> N[%] 0.125 CubeRoot Nested divisions: >> a / b / c CubeRoot[n] a finds the real-valued cube root of the given n. bc
>> a / (b / c)
>> CubeRoot[16] ac 1 b 22 3 >> a / b / (c / (d / e)) ad Divide (/) bce
>> a / (b ^ 2 * c ^ 3 / e) Divide[ , ] a b ae a / b b2c3 represents the division of a by b.
>> 30 / 5 Minus (-) 6
>> 1 / 8 Minus[expr] is the negation of expr. >> Pi / 4 Pi >> -a //FullForm 4 Times [ − 1, a] Use N or a decimal point to force numeric evalu- Minus automatically distributes: ation:
130 >> -(x - 2/3) >> 2 Graphics[{Red,Disk[]}] + 3 2 Graphics[{Red,Disk[]}] − x 3 Minus threads over lists: >> -Range[10] {−1, − 2, − 3, − 4, − 5, − 6, − 7, − 8, − 9, − 10}
Plus (+)
Plus[a, b, ...] a + b + ... represents the sum of the terms a, b, ... 5
>> 1 + 2 3 Power (^) Plus performs basic simplification of terms: >> a + b + a Power[a, b] 2a + b a ^ b represents a raised to the power of b. >> a + a + 3 * a 5a >> 4 ^ (1/2) >> a + b + 4.5 + a + b + a + 2 + 2 1.5 b >> 4 ^ (1/3) 6.5 + 3a + 3.5b 2 2 3 Apply Plus on a list to sum up its elements: >> 3^123 >> Plus @@ {2, 4, 6} 48 519 278 097 689 642 681 ˜ 12 ˜155 855 396 759 336 072 ˜ The sum of the first 1000 integers: ˜749 841 943 521 979 872 827 >> Plus @@ Range[1000] >> (y ^ 2)^ (1/2) 500 500 √ 2 Plus has default value 0: y >> DefaultValues[Plus] >> (y ^ 2)^ 3 {HoldPattern [Default [Plus]] :>0} y6 >> a /. n_. + x_ :> {n, x} {0, a}
The sum of 2 red circles and 3 red circles is...
131 >> Plot[Evaluate[Table[x^y, {y, 1, Complex numbers: 5}]], {x, -1.5, 1.5}, >> Sqrt[-4] AspectRatio -> 1] 2I
>> I == Sqrt[-1] 3 True
2 >> Plot[Sqrt[a^2], {a, -2, 2}] 1 2.0 1.5 −1.5−1.0−0.5 0.5 1.0 1.5 − 1 1.0 −2 0.5 −3 −2 −1 1 2 Use a decimal point to force numeric evaluation: >> 4.0 ^ (1/3) 1.5874 Subtract (-) Power has default value 1 for its second argu- ment: Subtract[a, b] >> DefaultValues[Power] a - b { } HoldPattern [Default [Power, 2]] :>1 represents the subtraction of b from a.
>> a /. x_ ^ n_. :> {x, n} >> 5 - 3 {a, 1} 2
Power can be used with complex numbers: >> a - b // FullForm >> (1.5 + 1.0 I)^ 3.5 Plus [a, Times [ − 1, b]] −3.68294 + 6.95139I >> a - b - c >> (1.5 + 1.0 I)^ (3.5 + 1.5 I) a − b − c −3.19182 + 0.645659I >> a - (b - c) a − b + c Sqrt Times (*) Sqrt[expr] returns the square root of expr. Times[a, b, ...]
>> Sqrt[4] a * b * ... a b ... 2 represents the product of the terms a, b, ... >> Sqrt[5] √ 5 >> 10 * 2 20 >> Sqrt[5] // N >> 10 2 2.23607 20
>> Sqrt[a]^2 >> a * a a a2
132 >> x ^ 10 * x ^ -2 Total x8 Total[list] >> {1, 2, 3} * 4 adds all values in list. {4, 8, 12} Total[list, n] adds all values up to level n. >> Times @@ {1, 2, 3, 4} Total[list,{n}] 24 totals only the values at level {n}. Total[list,{n_1, n_2}] >> IntegerLength[Times@@Range [5000]] totals at levels {n_1, n_2}. 16 326 >> Total[{1, 2, 3}] Times has default value 1: 6 >> DefaultValues[Times] >> Total[{{1, 2, 3}, {4, 5, 6}, {7, { } HoldPattern [Default [Times]] :>1 8 ,9}}]
>> a /. n_. * x_ :> {n, x} {12, 15, 18} {1, a} Total over rows and columns >> Total[{{1, 2, 3}, {4, 5, 6}, {7, 8 ,9}}, 2] Sums, Simple Statistics 45 Sums, Simple Statistics Total over rows instead of columns These functions perform a simple arithmetic >> Total[{{1, 2, 3}, {4, 5, 6}, {7, computation over a list. 8 ,9}}, {2}] {6, 15, 24} Accumulate
Accumulate[list] accumulates the values of list, returning a new list.
>> Accumulate[{1, 2, 3}] {1, 3, 6}
Mean
Mean[list] returns the statistical mean of list.
>> Mean[{26, 64, 36}] 42
>> Mean[{1, 1, 2, 3, 5, 8}] 10 3
>> Mean[{a, b}] a + b 2
133 23. Colors
Programmatic support for symbolic colors. Contents
Darker ...... 137 LightGreen .... 144 Color Directives .... 134 DominantColors . 138 LightMagenta .. 144 CMYKColor ... 134 Lighter ...... 138 LightOrange ... 145 ColorDistance .. 135 Named Colors ..... 138 LightPink ..... 145 GrayLevel .... 135 Black ...... 139 LightPurple .... 146 Hue ...... 135 Blue ...... 139 LightRed ..... 146 LABColor ..... 135 Brown ...... 140 LightYellow ... 147 LCHColor .... 135 Cyan ...... 140 Magenta ..... 147 LUVColor .... 135 Gray ...... 141 Orange ...... 148 RGBColor ..... 136 Green ...... 141 Pink ...... 148 XYZColor ..... 136 LightBlue ..... 142 Purple ...... 148 Color Operations ... 136 LightBrown .... 142 Red ...... 149 Blend ...... 136 LightCyan .... 143 White ...... 149 ColorConvert ... 136 LightGray .... 143 Yellow ...... 150 ColorNegate ... 137
Color Directives ColorDistance
Color Directives ColorDistance[c1, c2] There are many different way to specify color; returns a measure of color distance be- we support all of the color formats below and tween the colors c1 and c2. will convert between the different color formats. ColorDistance[list, c2] returns a list of color distances between CMYKColor the colors in list and c2.
The option DistanceFunction specifies the CMYKColor[c, m, y, k] method used to measure the color distance. represents a color with the specified cyan, Available options are: magenta, yellow and black components. • CIE76: Euclidean distance in the LAB- Color space >> Graphics[MapIndexed[{CMYKColor @@ #1, Disk[2*#2 ~Join~{0}]} &, • CIE94: Euclidean distance in the LCH- IdentityMatrix[4]], ImageSize-> Color space Small] • CIE2000 or CIEDE2000: CIE94 distance with corrections • CMC: Color Measurement Committee metric (1984) • DeltaL: difference in the L component of LCHColor • DeltaC: difference in the C component of LCHColor
134 • DeltaH: difference in the H component of >> Graphics[Table[{EdgeForm[{ LCHColor GrayLevel[0, 0.5]}], Hue[(-11+q It is also possible to specify a custom distance. +10r)/72, 1, 1, 0.6], Disk[(8-r) {Cos[2Pi q/12], Sin[2Pi q/12]}, >> ColorDistance[Magenta, Green] (8-r)/3]}, {r, 6}, {q, 12}]] 2.2507
>> ColorDistance[{Red, Blue}, { Green, Yellow}, DistanceFunction -> {"CMC", "Perceptibility"}] {1.0495, 1.27455}
GrayLevel
GrayLevel[g] represents a shade of gray specified by g, ranging from 0 (black) to 1 (white). GrayLevel[g, a] represents a shade of gray specified by g with opacity a. LABColor
Hue LABColor[l, a, b] represents a color with the specified light- Hue[h, s, l, a] ness, red/green and yellow/blue compo- represents the color with hue h, satura- nents in the CIE 1976 L*a*b* (CIELAB) tion s, lightness l and opacity a. color space. Hue[h, s, l] is equivalent to Hue[h, s, l, 1]. Hue[h, s] LCHColor is equivalent to Hue[h, s, 1, 1]. Hue[h] LCHColor[l, c, h] is equivalent to Hue[h, 1, 1, 1]. represents a color with the specified light- ness, chroma and hue components in the >> Graphics[Table[{EdgeForm[Gray], CIELCh CIELab cube color space. Hue[h, s], Disk[{12h, 8s}]}, {h, 0, 1, 1/6}, {s, 0, 1, 1/4}]] LUVColor
LCHColor[l, u, v] represents a color with the specified com- ponents in the CIE 1976 L*u*v* (CIELUV) color space.
RGBColor
RGBColor[r, g, b] represents a color with the specified red, green and blue components.
135 >> Graphics[MapIndexed[{RGBColor @@ Blend #1, Disk[2*#2 ~Join~{0}]} &, IdentityMatrix[3]], ImageSize-> Blend[{c1, c2}] Small] represents the color between c1 and c2. Blend[{c1, c2}, x] represents the color formed by blending c1 and c2 with factors 1 - x and x respec- tively. >> RGBColor[0, 1, 0] Blend[{c1, c2, ..., cn}, x] blends between the colors c1 to cn accord- ing to the factor x. >> RGBColor[0, 1, 0] // ToBoxes [ [ StyleBox GraphicsBox { >> Blend[{Red, Blue}] EdgeForm [RGBColor [ 0, 0, 0]] , RGBColor[ [0,]}1, 0] , RectangleBox {0, 0} , >> Blend[{Red, Blue}, 0.3] $OptionSyntax− > Ignore, − AspectRatio > Automatic, >> Blend[{Red, Blue, Green}, 0.75] Axes− > False, AxesStyle− > {} , Background− > Automatic, >> Graphics[Table[{Blend[{Red, ImageSize− > 16, Green, Blue}, x], Rectangle[{10 − > {} LabelStyle , x, 0}]}, {x, 0, 1, 1/10}]] PlotRange− > Automatic, − PlotRangePadding] > Automatic, − {} TicksStyle > , ] >> Graphics[Table[{Blend[{RGBColor ImageSizeMultipliers− > {1, 1} [1, 0.5, 0, 0.5], RGBColor[0, 0, 1, 0.5]}, x], Disk[{5x, 0}]}, { x, 0, 1, 1/10}]] XYZColor
XYZColor[x, y, z] represents a color with the specified com- ponents in the CIE 1931 XYZ color space.
Color Operations ColorConvert
Color Operations ColorConvert[c, colspace] Functions for manipulating colors and color im- returns the representation of c in the color ages. space colspace. c may be a color or an im- age.
Valid values for colspace are: CMYK: convert to CMYKColor Grayscale: con- vert to GrayLevel HSB: convert to Hue LAB: concert to LABColor LCH: convert to LCHColor LUV: convert to LUVColor RGB: convert to RG- BColor XYZ: convert to XYZColor
136 ColorNegate >> Graphics3D[{Darker[Green], Sphere[]}]
- ColorNegate[image]
- returns the negative of image in which colors have been negated.
- ColorNegate[color]
- returns the nega- tive of a color. Yellow is RGBColor[1.0, 1.0, 0.0] >> ColorNegate[Yellow]
Darker
Darker[c, f ] is equivalent to Blend[{c, Black}, f ]. Darker[c] is equivalent to Darker[c, 1/3]. >> Graphics[Table[{Darker[Yellow, x ], Disk[{12x, 0}]}, {x, 0, 1, >> Graphics[{Darker[Red], Disk[]}] 1/6}]]
DominantColors
DominantColors[image] gives a list of colors which are dominant in the given image. DominantColors[image, n] returns at most n colors. DominantColors[image, n, prop] returns the given property prop, which may be “Color” (return RGB col- ors), “LABColor” (return LAB colors), “Count” (return the number of pixels a dominant color covers), “Coverage” (re- turn the fraction of the image a dominant color covers), or “CoverageImage” (re- turn a black and white image indicating with white the parts that are covered by a dominant color).
The option “ColorCoverage” specifies the min- imum amount of coverage needed to include a dominant color in the result. The option “MinColorDistance” specifies the distance (in LAB color space) up to which col- ors are merged and thus regarded as belonging to the same dominant color.
137 >> img = Import["ExampleData/lena. >> Graphics[{Lighter[Orange, 1/4], tif"] Disk[]}] −Image−
>> DominantColors[img] { , , , , , }
>> DominantColors[img, 3] { , , }
>> DominantColors[img, 3, "Coverage "] { } 28 579 751 23 841 , , 131 072 4 096 131 072
>> DominantColors[img, 3, " CoverageImage"] >> Graphics[Table[{Lighter[Orange, {−Image−, − Image−, − Image−} x], Disk[{12x, 0}]}, {x, 0, 1, 1/6}]] >> DominantColors[img, 3, "Count"] {57 158, 48 064, 47 682}
>> DominantColors[img, 2, "LABColor "] { , } Named Colors
>> DominantColors[img, Named Colors MinColorDistance -> 0.5] Mathics has definitions for the most common { , } color names which can be used in a graphics or style specification.
>> DominantColors[img, ColorCoverage -> 0.15] Black { , , } Black represents the color black in graphics. Lighter
>> Graphics[{EdgeForm[Black], Black Lighter[c, f ] , Disk[]}, ImageSize->Small] is equivalent to Blend[{c, White}, f ]. Lighter[c] is equivalent to Lighter[c, 1/3].
>> Lighter[Orange, 1/4]
138 >> Black // ToBoxes >> Blue // ToBoxes [ [ [ [ StyleBox{ GraphicsBox StyleBox{ GraphicsBox EdgeForm [RGBColor [ EdgeForm [RGBColor [ 0, 0, 0]] , RGBColor[ [0,]}0, 0] , 0, 0, 0]] , RGBColor[ [0,]}0, 1] , RectangleBox {0, 0} , RectangleBox {0, 0} , $OptionSyntax− > Ignore, $OptionSyntax− > Ignore, AspectRatio− > Automatic, AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Axes− > False, AxesStyle− > {} , Background− > Automatic, Background− > Automatic, ImageSize− > 16, ImageSize− > 16, LabelStyle− > {} , LabelStyle− > {} , PlotRange− > Automatic, PlotRange− > Automatic, − − PlotRangePadding] > Automatic, PlotRangePadding] > Automatic, − {} − {} TicksStyle > , ] TicksStyle > , ] ImageSizeMultipliers− > {1, 1} ImageSizeMultipliers− > {1, 1}
>> Black >> Blue
Blue Brown
Blue Brown represents the color blue in graphics. represents the color brown in graphics.
>> Graphics[{EdgeForm[Black], Blue, >> Graphics[{EdgeForm[Black], Brown Disk[]}, ImageSize->Small] , Disk[]}, ImageSize->Small]
139 >> Brown // ToBoxes >> Cyan // ToBoxes [ [ [ [ StyleBox{ GraphicsBox StyleBox{ GraphicsBox EdgeForm [RGBColor [ EdgeForm [RGBColor [ 0, 0, 0]] , RGBColor [0.6, 0.4]}, 0, 0, 0]] , RGBColor[ [0,]}1, 1] , 0.2] , RectangleBox {0, 0} , RectangleBox {0, 0} , $OptionSyntax− > Ignore, $OptionSyntax− > Ignore, AspectRatio− > Automatic, AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Axes− > False, AxesStyle− > {} , Background− > Automatic, Background− > Automatic, ImageSize− > 16, ImageSize− > 16, LabelStyle− > {} , LabelStyle− > {} , PlotRange− > Automatic, PlotRange− > Automatic, − > − PlotRangePadding] Automatic, PlotRangePadding] > Automatic, − > {} − {} TicksStyle , ] TicksStyle > , ] ImageSizeMultipliers− > {1, 1} ImageSizeMultipliers− > {1, 1}
>> Brown >> Cyan
Cyan Gray
Cyan Gray represents the color cyan in graphics. represents the color gray in graphics.
>> Graphics[{EdgeForm[Black], Cyan, >> Graphics[{EdgeForm[Black], Gray, Disk[]}, ImageSize->Small] Disk[]}, ImageSize->Small]
140 >> Gray // ToBoxes >> Green // ToBoxes [ [ [ [ StyleBox{ GraphicsBox StyleBox{ GraphicsBox EdgeForm [RGBColor [0, 0, 0]][ , EdgeForm [RGBColor [ { GrayLevel]} [0.5] , RectangleBox 0, 0, 0, 0]] , RGBColor[ [0,]}1, 0] , 0} , $OptionSyntax− > Ignore, RectangleBox {0, 0} , AspectRatio− > Automatic, $OptionSyntax− > Ignore, Axes− > False, AxesStyle− > {} , AspectRatio− > Automatic, Background− > Automatic, Axes− > False, AxesStyle− > {} , ImageSize− > 16, Background− > Automatic, LabelStyle− > {} , ImageSize− > 16, PlotRange− > Automatic, LabelStyle− > {} , − − > PlotRangePadding] > Automatic, PlotRange Automatic, − {} − > TicksStyle > , ] PlotRangePadding] Automatic, − {} ImageSizeMultipliers− > {1, 1} TicksStyle > , ] ImageSizeMultipliers− > {1, 1} >> Gray >> Green
Green LightBlue Green represents the color green in graphics. LightBlue represents the color light blue in graph-
>> Graphics[{EdgeForm[Black], Green ics. , Disk[]}, ImageSize->Small] >> Graphics[{EdgeForm[Black], LightBlue, Disk[]}, ImageSize-> Small]
141 >> LightBlue // ToBoxes >> Graphics[{EdgeForm[Black], [ [ LightBrown, Disk[]}, ImageSize-> StyleBox GraphicsBox { Small] EdgeForm [RGBColor [0, 0, 0]] , RGBColor [[0.87, 0.94]}, 1] , RectangleBox {0, 0} , $OptionSyntax− > Ignore, AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Background− > Automatic, ImageSize− > 16, LabelStyle− > {} , >> LightBrown // ToBoxes PlotRange− > Automatic, [ [ StyleBox GraphicsBox PlotRangePadding− > Automatic, { ] EdgeForm [RGBColor [0, 0, TicksStyle− > {} , ] 0]] , RGBColor [0.94, 0.91, 0.88 ImageSizeMultipliers− > {1, 1} [ ]} ] , RectangleBox {0, 0} , − >> Graphics[{LightBlue, EdgeForm[ $OptionSyntax > Ignore, Black], Disk[]}] AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Background− > Automatic, ImageSize− > 16, LabelStyle− > {} , PlotRange− > Automatic, − PlotRangePadding] > Automatic, − {} TicksStyle > , ] ImageSizeMultipliers− > {1, 1}
LightCyan
LightCyan
>> Plot[Sin[x], {x, 0, 2 Pi}, represents the color light cyan in graph- Background -> LightBlue] ics.
1.0 >> Graphics[{EdgeForm[Black], LightCyan, Disk[]}, ImageSize-> 0.5 Small]
1 2 3 4 5 6 −0.5 −1.0
LightBrown
LightBrown represents the color light brown in graph- ics.
142 >> LightCyan // ToBoxes >> LightGray // ToBoxes [ [ [ [ StyleBox{ GraphicsBox StyleBox{ GraphicsBox EdgeForm [RGBColor [ EdgeForm [RGBColor [0, 0, 0, 0]] , RGBColor[[0.9, 1.,]} 0, 0]] , GrayLevel [0[.666667]}, 1.] , RectangleBox {0, 0} , 1.] , RectangleBox {0, 0} , $OptionSyntax− > Ignore, $OptionSyntax− > Ignore, AspectRatio− > Automatic, AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Axes− > False, AxesStyle− > {} , Background− > Automatic, Background− > Automatic, ImageSize− > 16, ImageSize− > 16, LabelStyle− > {} , LabelStyle− > {} , PlotRange− > Automatic, PlotRange− > Automatic, − − PlotRangePadding] > Automatic, PlotRangePadding] > Automatic, − {} − {} TicksStyle > , ] TicksStyle > , ] ImageSizeMultipliers− > {1, 1} ImageSizeMultipliers− > {1, 1}
LightGray LightGreen
LightGray LightGreen represents the color light gray in graph- represents the color light green in graph- ics. ics.
>> Graphics[{EdgeForm[Black], >> Graphics[{EdgeForm[Black], LightGray, Disk[]}, ImageSize-> LightGreen, Disk[]}, ImageSize-> Small] Small]
143 >> LightGreen // ToBoxes >> LightMagenta // ToBoxes [ [ [ [ StyleBox{ GraphicsBox StyleBox{ GraphicsBox EdgeForm [RGBColor [0, 0, EdgeForm [RGBColor [0, 0, 0]] , RGBColor [0[.88, 1., 0]}.88 0]] , RGBColor [1.,[0.333333]}, ] , RectangleBox {0, 0} , 1.] , RectangleBox {0, 0} , $OptionSyntax− > Ignore, $OptionSyntax− > Ignore, AspectRatio− > Automatic, AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Axes− > False, AxesStyle− > {} , Background− > Automatic, Background− > Automatic, ImageSize− > 16, ImageSize− > 16, LabelStyle− > {} , LabelStyle− > {} , PlotRange− > Automatic, PlotRange− > Automatic, − − PlotRangePadding] > Automatic, PlotRangePadding] > Automatic, − {} − {} TicksStyle > , ] TicksStyle > , ] ImageSizeMultipliers− > {1, 1} ImageSizeMultipliers− > {1, 1}
LightMagenta LightOrange
LightMagenta LightOrange represents the color light magenta in represents the color light orange in graphics. graphics.
>> Graphics[{EdgeForm[Black], >> Graphics[{EdgeForm[Black], LightMagenta, Disk[]}, ImageSize LightOrange, Disk[]}, ImageSize ->Small] ->Small]
144 >> LightOrange // ToBoxes >> LightPink // ToBoxes [ [ [ [ StyleBox{ GraphicsBox StyleBox{ GraphicsBox EdgeForm [RGBColor [0, EdgeForm [RGBColor [0, 0, 0, 0]] , RGBColor[ [1, 0.]}9, 0.8] , 0]] , RGBColor [1[., 0.925]}, 0.925 RectangleBox {0, 0} , ] , RectangleBox {0, 0} , $OptionSyntax− > Ignore, $OptionSyntax− > Ignore, AspectRatio− > Automatic, AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Axes− > False, AxesStyle− > {} , Background− > Automatic, Background− > Automatic, ImageSize− > 16, ImageSize− > 16, LabelStyle− > {} , LabelStyle− > {} , PlotRange− > Automatic, PlotRange− > Automatic, − − PlotRangePadding] > Automatic, PlotRangePadding] > Automatic, − {} − {} TicksStyle > , ] TicksStyle > , ] ImageSizeMultipliers− > {1, 1} ImageSizeMultipliers− > {1, 1}
LightPink LightPurple
LightPink LightPurple represents the color light pink in graph- represents the color light purple in graph- ics. ics.
>> Graphics[{EdgeForm[Black], >> Graphics[{EdgeForm[Black], LightPink, Disk[]}, ImageSize-> LightPurple, Disk[]}, ImageSize Small] ->Small]
145 >> LightPurple // ToBoxes >> LightRed // ToBoxes [ [ [ [ StyleBox{ GraphicsBox StyleBox{ GraphicsBox EdgeForm [RGBColor [0, 0, EdgeForm [RGBColor [0, 0, 0]] , RGBColor [0[.94, 0.88]}, 0.94 0]] , RGBColor [1[., 0.85, 0]}.85 ] , RectangleBox {0, 0} , ] , RectangleBox {0, 0} , $OptionSyntax− > Ignore, $OptionSyntax− > Ignore, AspectRatio− > Automatic, AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Axes− > False, AxesStyle− > {} , Background− > Automatic, Background− > Automatic, ImageSize− > 16, ImageSize− > 16, LabelStyle− > {} , LabelStyle− > {} , PlotRange− > Automatic, PlotRange− > Automatic, − − PlotRangePadding] > Automatic, PlotRangePadding] > Automatic, − {} − {} TicksStyle > , ] TicksStyle > , ] ImageSizeMultipliers− > {1, 1} ImageSizeMultipliers− > {1, 1}
LightRed LightYellow
LightRed LightYellow represents the color light red in graphics. represents the color light yellow in graphics.
>> Graphics[{EdgeForm[Black], LightRed, Disk[]}, ImageSize-> >> Graphics[{EdgeForm[Black], Small] LightYellow, Disk[]}, ImageSize ->Small]
146 >> LightYellow // ToBoxes >> Magenta // ToBoxes [ [ [ [ StyleBox{ GraphicsBox StyleBox{ GraphicsBox EdgeForm [RGBColor [0, 0, EdgeForm [RGBColor [ 0]] , RGBColor [1[., 1., 0.333333]} 0, 0, 0]] , RGBColor[ [1,]}0, 1] , ] , RectangleBox {0, 0} , RectangleBox {0, 0} , $OptionSyntax− > Ignore, $OptionSyntax− > Ignore, AspectRatio− > Automatic, AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Axes− > False, AxesStyle− > {} , Background− > Automatic, Background− > Automatic, ImageSize− > 16, ImageSize− > 16, LabelStyle− > {} , LabelStyle− > {} , PlotRange− > Automatic, PlotRange− > Automatic, − − PlotRangePadding] > Automatic, PlotRangePadding] > Automatic, − {} − {} TicksStyle > , ] TicksStyle > , ] ImageSizeMultipliers− > {1, 1} ImageSizeMultipliers− > {1, 1}
>> Magenta Magenta
Magenta Orange represents the color magenta in graphics.
Orange >> Graphics[{EdgeForm[Black], Magenta, Disk[]}, ImageSize-> represents the color orange in graphics. Small] >> Graphics[{EdgeForm[Black], Orange, Disk[]}, ImageSize-> Small]
147 >> Orange // ToBoxes Purple [ [ StyleBox{ GraphicsBox EdgeForm [RGBColor [ Purple represents the color purple in graphics. 0, 0, 0]] , RGBColor[ [1, 0.5]}, 0] , RectangleBox {0, 0} , >> Graphics[{EdgeForm[Black], $OptionSyntax− > Ignore, Purple, Disk[]}, ImageSize-> − > AspectRatio Automatic, Small] Axes− > False, AxesStyle− > {} , Background− > Automatic, ImageSize− > 16, LabelStyle− > {} , PlotRange− > Automatic, − PlotRangePadding] > Automatic, − {} TicksStyle > , ] ImageSizeMultipliers− > {1, 1}
>> Purple // ToBoxes [ [ Pink StyleBox{ GraphicsBox EdgeForm [RGBColor [0, Pink 0, 0]] , RGBColor[ [0.5,]}0, 0.5] , { } represents the color pink in graphics. RectangleBox 0, 0 , $OptionSyntax− > Ignore, − >> Graphics[{EdgeForm[Black], Pink, AspectRatio > Automatic, Disk[]}, ImageSize->Small] Axes− > False, AxesStyle− > {} , Background− > Automatic, ImageSize− > 16, LabelStyle− > {} , PlotRange− > Automatic, − PlotRangePadding] > Automatic, − {} TicksStyle > , ] ImageSizeMultipliers− > {1, 1}
>> Pink // ToBoxes [ [ StyleBox{ GraphicsBox Red EdgeForm [RGBColor [ Red 0, 0, 0]] , RGBColor [1., 0.5,]} represents the color red in graphics. 0.5] , RectangleBox {0, 0} , $OptionSyntax− > Ignore, >> Graphics[{EdgeForm[Black], Red, AspectRatio− > Automatic, Disk[]}, ImageSize->Small] Axes− > False, AxesStyle− > {} , Background− > Automatic, ImageSize− > 16, LabelStyle− > {} , PlotRange− > Automatic, − PlotRangePadding] > Automatic, − {} TicksStyle > , ] ImageSizeMultipliers− > {1, 1}
148 >> Red // ToBoxes >> White // ToBoxes [ [ [ [ StyleBox{ GraphicsBox StyleBox{ GraphicsBox EdgeForm [RGBColor [ EdgeForm [RGBColor [0, 0,[0]] , { 0, 0, 0]] , RGBColor[ [1,]}0, 0] , GrayLevel]} [1] , RectangleBox 0, RectangleBox {0, 0} , 0} , $OptionSyntax− > Ignore, $OptionSyntax− > Ignore, AspectRatio− > Automatic, AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Axes− > False, AxesStyle− > {} , Background− > Automatic, Background− > Automatic, ImageSize− > 16, ImageSize− > 16, LabelStyle− > {} , LabelStyle− > {} , PlotRange− > Automatic, − − PlotRange > Automatic, PlotRangePadding] > Automatic, − − {} PlotRangePadding] > Automatic, TicksStyle > , ] − {} − { } TicksStyle > , ] ImageSizeMultipliers > 1, 1 ImageSizeMultipliers− > {1, 1} >> White
>> Red
Yellow White Yellow White represents the color yellow in graphics. represents the color white in graphics.
>> Graphics[{EdgeForm[Black],
>> Graphics[{EdgeForm[Black], White Yellow, Disk[]}, ImageSize-> , Disk[]}, ImageSize->Small] Small]
149 >> Yellow // ToBoxes [ [ StyleBox{ GraphicsBox EdgeForm [RGBColor [ 0, 0, 0]] , RGBColor[ [1,]}1, 0] , RectangleBox {0, 0} , $OptionSyntax− > Ignore, AspectRatio− > Automatic, Axes− > False, AxesStyle− > {} , Background− > Automatic, ImageSize− > 16, LabelStyle− > {} , PlotRange− > Automatic, − PlotRangePadding] > Automatic, − {} TicksStyle > , ] ImageSizeMultipliers− > {1, 1}
>> Yellow
150 24. Distance and Similarity Measures
Different measures of distance or similarity for different types of analysis. Contents
String Distances and EditDistance ... 152 Similarity HammingDistance 152 Measures ..... 151 DamerauLeven- shteinDis- tance ... 151
String Distances and Similarity The IgnoreCase option makes DamerauLeven- Measures shteinDistance ignore the case of letters: >> DamerauLevenshteinDistance["time ", "Thyme"] String Distances and Similarity Measure 3
DamerauLevenshteinDistance >> DamerauLevenshteinDistance["time ", "Thyme", IgnoreCase -> True] DamerauLevenshteinDistance[a, b] 2 returns the Damerau-Levenshtein dis- tance of a and b, which is defined as DamerauLevenshteinDistance also works on the minimum number of transpositions, lists: insertions, deletions and substitutions >> DamerauLevenshteinDistance[{1, E needed to transform one into the other. In , 2, Pi}, {1, E, Pi, 2}] contrast to EditDistance, DamerauLeven- 1 shteinDistance counts transposition of adjacent items (e.g. “ab” into “ba”) as one operation of change. EditDistance
>> DamerauLevenshteinDistance[" EditDistance[a, b] kitten", "kitchen"] returns the Levenshtein distance of a and 2 b, which is defined as the minimum num- ber of insertions, deletions and substi- >> DamerauLevenshteinDistance["abc tutions on the constituents of a and b ", "ac"] needed to transform one into the other. 1 >> EditDistance["kitten", "kitchen >> DamerauLevenshteinDistance["abc "] ", "acb"] 2 1 >> EditDistance["abc", "ac"] >> DamerauLevenshteinDistance["azbc 1 ", "abxyc"] 3 >> EditDistance["abc", "acb"] 2
151 >> EditDistance["azbc", "abxyc"] 3 The IgnoreCase option makes EditDistance ig- nore the case of letters: >> EditDistance["time", "Thyme"] 3
>> EditDistance["time", "Thyme", IgnoreCase -> True] 2 EditDistance also works on lists: >> EditDistance[{1, E, 2, Pi}, {1, E, Pi, 2}] 2
HammingDistance
HammingDistance[u, v] returns the Hamming distance between u and v, i.e. the number of different el- ements. u and v may be lists or strings.
>> HammingDistance[{1, 0, 1, 0}, {1, 0, 0, 1}] 2
>> HammingDistance["time", "dime"] 1
>> HammingDistance["TIME", "dime", IgnoreCase -> True] 1
152 25. Graphics, Drawing, and Images
Functions like Plot and ListPlot can be used to >> ListPlot[ Table[Prime[n], {n, draw graphs of functions and data. 20} ]] Graphics is implemented as a collection of graph- ics primitives. Primatives are objects like Point, Line, and Polygon and become elements of a 60 graphics object. A graphics object can have directives as well 40 such as RGBColor, and Thickness. There are several kinds of graphics objects; each 20 kind has a head which identifies its type.
5 10 15 20
» Head[%] = Graphics » Graphics3D[Sphere[]] = -Graphics3D- » Head[%] = Graphics3D »
Contents
ImageConvolve . 157 WordCloud .... 161 Image[] and image Three-Dimensional related functions. 154 ImageData .... 157 Graphics ..... 161 Binarize ...... 154 ImageDimensions 157 Cuboid ...... 162 BinaryImageQ .. 154 ImageImport ... 157 Cylinder ..... 162 Blur ...... 154 ImageMultiply .. 158 Graphics3D .... 163 BoxMatrix .... 154 ImagePartition .. 158 Sphere ...... 164 Closing ...... 154 ImageQ ...... 158 Plotting Data ..... 164 ColorCombine .. 155 ImageReflect ... 158 BarChart ..... 165 ColorQuantize .. 155 ImageResize ... 159 ColorData .... 165 ColorSeparate .. 155 ImageRotate ... 159 DensityPlot .... 166 Colorize ..... 155 ImageSubtract .. 159 Histogram .... 167 DiamondMatrix . 155 ImageTake .... 159 ListLinePlot ... 167 Dilation ...... 155 ImageType .... 160 ListPlot ...... 167 DiskMatrix .... 155 MaxFilter ..... 160 ParametricPlot .. 168 EdgeDetect .... 156 MedianFilter ... 160 PieChart ..... 170 Erosion ...... 156 MinFilter ..... 160 Plot ...... 171 GaussianFilter .. 156 Opening ..... 160 Plot3D ...... 172 ImageAdd .... 156 PixelValue .... 160 PolarPlot ..... 172 ImageAdjust ... 156 PixelValuePositions 160 Splines ...... 173 ImageAspectRatio 156 RandomImage .. 161 BernsteinBasis .. 173 Image ...... 157 Sharpen ...... 161 BezierCurve ... 173 ImageChannels .. 157 TextRecognize .. 161 BezierFunction 173 ImageColorSpace . 157 Threshold ..... 161 ..
153 Image[] and image related Blur functions. Blur[image] Image[] and image related functions. gives a blurred version of image. Note that you (currently) need scikit-image in- Blur[image, r] stalled in order for this module to work. blurs image with a kernel of size r.
Binarize >> lena = Import["ExampleData/lena. tif"];
Binarize[image] >> Blur[lena] gives a binarized version of image, in −Image− which each pixel is either 0 or 1. Binarize[image, t] >> Blur[lena, 5] map values x > t to 1, and values x <= t to −Image− 0. Binarize[image,{t1, t2}] map t1 < x < t2 to 1, and all other values BoxMatrix to 0. BoxMatrix[$s] >> img = Import["ExampleData/lena. Gives a box shaped kernel of size 2 s + 1. tif"];
>> Binarize[img] >> BoxMatrix[3] −Image− {{1, 1, 1, 1, 1, 1, 1} , {1, 1, 1, 1, 1, 1, 1} , {1, 1, 1, 1, 1, 1, 1} , {1, 1, 1, >> Binarize[img, 0.7] 1, 1, 1, 1} , {1, 1, 1, 1, 1, 1, 1} , {1, − − Image 1, 1, 1, 1, 1, 1} , {1, 1, 1, 1, 1, 1, 1}}
>> Binarize[img, {0.2, 0.6}] − − Image Closing
BinaryImageQ Closing[image, ker] Gives the morphological closing of image with respect to structuring element ker. BinaryImageQ[$image] returns True if the pixels of $image are bi- >> ein = Import["ExampleData/ nary bit values, and False otherwise. Einstein.jpg"];
>> img = Import["ExampleData/lena. >> Closing[ein, 2.5] tif"]; −Image−
>> BinaryImageQ[img] False ColorCombine
>> BinaryImageQ[Binarize[img]] True ColorCombine[channels, colorspace] Gives an image with colorspace and the respective components described by the given channels.
154 >> ColorCombine[{{{1, 0}, {0, DiamondMatrix 0.75}}, {{0, 1}, {0, 0.25}}, {{0, 0}, {1, 0.5}}}, "RGB"] DiamondMatrix[$s] −Image− Gives a diamond shaped kernel of size 2 s + 1.
ColorQuantize >> DiamondMatrix[3] {{0, 0, 0, 1, 0, 0, 0} , {0, 0, 1, 1, 1, } { } { ColorQuantize[image, n] 0, 0 , 0, 1, 1, 1, 1, 1, 0 , 1, 1, 1, gives a version of image using only n col- 1, 1, 1, 1} , {0, 1, 1, 1, 1, 1, 0} , {0, ors. 0, 1, 1, 1, 0, 0} , {0, 0, 0, 1, 0, 0, 0}}
>> img = Import["ExampleData/lena. tif"]; Dilation
>> ColorQuantize[img, 6] Dilation[ , ] − − image ker Image Gives the morphological dilation of image with respect to structuring element ker. ColorSeparate >> ein = Import["ExampleData/ Einstein.jpg"]; ColorSeparate[image] Gives each channel of image as a separate >> Dilation[ein, 2.5] grayscale image. −Image−
Colorize DiskMatrix
DiskMatrix[$s] Colorize[values] Gives a disk shaped kernel of size 2 s + 1. returns an image where each number in the rectangular matrix values is a pixel and each occurence of the same number >> DiskMatrix[3] is displayed in the same unique color, {{0, 0, 1, 1, 1, 0, 0} , {0, 1, 1, 1, 1, which is different from the colors of all 1, 0} , {1, 1, 1, 1, 1, 1, 1} , {1, 1, 1, non-identical numbers. 1, 1, 1, 1} , {1, 1, 1, 1, 1, 1, 1} , {0, Colorize[image] 1, 1, 1, 1, 1, 0} , {0, 0, 1, 1, 1, 0, 0}} gives a colorized version of image.
>> Colorize[{{1.3, 2.1, 1.5}, {1.3, EdgeDetect 1.3, 2.1}, {1.3, 2.1, 1.5}}] −Image− EdgeDetect[image]
>> Colorize[{{1, 2}, {2, 2}, {2, returns an image showing the edges in 3}}, ColorFunction -> (Blend[{ image. White, Blue}, #]&)] >> lena = Import["ExampleData/lena. −Image− tif"];
>> EdgeDetect[lena] −Image−
155 >> EdgeDetect[lena, 5] >> noise = RandomImage[{-0.1, 0.1}, −Image− ImageDimensions[ein]];
>> EdgeDetect[lena, 4, 0.5] >> ImageAdd[noise, ein] − − −Image− Image
>> lena = Import["ExampleData/lena. tif"]; Erosion
>> noise = RandomImage[{-0.2, 0.2}, Erosion[image, ker] ImageDimensions[lena], Gives the morphological erosion of image ColorSpace -> "RGB"]; with respect to structuring element ker. >> ImageAdd[noise, lena] − − >> ein = Import["ExampleData/ Image Einstein.jpg"];
>> Erosion[ein, 2.5] ImageAdjust −Image− ImageAdjust[image] adjusts the levels in image. GaussianFilter ImageAdjust[image, c] adjusts the contrast in image by c. GaussianFilter[image, r] ImageAdjust[image,{c, b}] blurs image using a Gaussian blur filter of adjusts the contrast c, and brightness b in radius r. image. ImageAdjust[image,{c, b, g}]
>> lena = Import["ExampleData/lena. adjusts the contrast c, brightness b, and tif"]; gamma g in image.
>> GaussianFilter[lena, 2.5] >> lena = Import["ExampleData/lena. −Image− tif"];
>> ImageAdjust[lena] ImageAdd −Image−
ImageAdd[image, expr_1, expr_2, ...] adds all expr_i to image where each expr_i ImageAspectRatio must be an image or a real number. ImageAspectRatio[image] >> i = Image[{{0, 0.5, 0.2, 0.1, gives the aspect ratio of image. 0.9}, {1.0, 0.1, 0.3, 0.8,
0.6}}]; >> img = Import["ExampleData/lena. tif"]; >> ImageAdd[i, 0.5]
−Image− >> ImageAspectRatio[img] 1 >> ImageAdd[i, i] −Image− >> ImageAspectRatio[Image[{{0, 1}, {1, 0}, {1, 1}}]] >> ein = Import["ExampleData/ 3 Einstein.jpg"]; 2
156 Image ImageData ImageChannels ImageData[image] gives a list of all color values of image as a ImageChannels[image] matrix. gives the number of channels in image. ImageData[image, stype] gives a list of color values in type stype.
>> ImageChannels[Image[{{0, 1}, {1,
0}}]] >> img = Image[{{0.2, 0.4}, {0.9, 1 0.6}, {0.5, 0.8}}];
>> img = Import["ExampleData/lena. >> ImageData[img] tif"]; {{0.2, 0.4} , {0.9, 0.6} , {0.5, 0.8}}
>> ImageChannels[img] >> ImageData[img, "Byte"] 3 {{51, 102} , {229, 153} , {127, 204}}
>> ImageData[Image[{{0, 1}, {1, 0}, ImageColorSpace {1, 1}}], "Bit"] {{0, 1} , {1, 0} , {1, 1}} ImageColorSpace[image] gives image’s color space, e.g. “RGB” or “CMYK”. ImageDimensions
>> img = Import["ExampleData/lena. tif"]; ImageDimensions[image] Returns the dimensions of image in pixels.
>> ImageColorSpace[img] RGB >> lena = Import["ExampleData/lena. tif"];
ImageConvolve >> ImageDimensions[lena] {512, 512} ImageConvolve[image, kernel] >> ImageDimensions[RandomImage[1, Computes the convolution of image using {50, 70}]] kernel. {50, 70}
>> img = Import["ExampleData/lena. tif"]; ImageImport >> ImageConvolve[img, DiamondMatrix [5] / 61] >> Import["ExampleData/Einstein.jpg "] −Image− −Image− >> ImageConvolve[img, DiskMatrix[5] / 97] >> Import["ExampleData/MadTeaParty. gif"] −Image− −Image− >> ImageConvolve[img, BoxMatrix[5] / 121] >> Import["ExampleData/moon.tif"] − − −Image− Image
157 ImageMultiply ImageQ
ImageMultiply[image, expr_1, expr_2, ImageQ[Image[$pixels]] ...] returns True if $pixels has dimensions multiplies all expr_i with image where from which an Image can be constructed, each expr_i must be an image or a real and False otherwise. number. >> ImageQ[Image[{{0, 1}, {1, 0}}]] >> i = Image[{{0, 0.5, 0.2, 0.1, True 0.9}, {1.0, 0.1, 0.3, 0.8, 0.6}}]; >> ImageQ[Image[{{{0, 0, 0}, {0, 1, 0}}, {{0, 1, 0}, {0, 1, 1}}}]] >> ImageMultiply[i, 0.2] True −Image− >> ImageQ[Image[{{{0, 0, 0}, {0,
>> ImageMultiply[i, i] 1}}, {{0, 1, 0}, {0, 1, 1}}}]] −Image− False
>> ein = Import["ExampleData/ >> ImageQ[Image[{1, 0, 1}]] Einstein.jpg"]; False
>> noise = RandomImage[{0.7, 1.3}, >> ImageQ["abc"] ImageDimensions[ein]]; False
>> ImageMultiply[noise, ein] −Image− ImageReflect
ImageReflect[image] ImagePartition Flips image top to bottom. ImageReflect[image, side] ImagePartition[image, s] Flips image so that side is interchanged Partitions an image into an array of s x s with its opposite. pixel subimages. ImageReflect[image, side_1 -> side_2] ImagePartition[image,{w, h}] Flips image so that side_1 is interchanged Partitions an image into an array of w x h with side_2. pixel subimages. >> ein = Import["ExampleData/ Einstein.jpg"]; >> lena = Import["ExampleData/lena. tif"]; >> ImageReflect[ein] − − >> ImageDimensions[lena] Image {512, 512} >> ImageReflect[ein, Left] − − >> ImagePartition[lena, 256] Image {{− − − −} Image , Image , >> ImageReflect[ein, Left -> Top] {− − − −}} Image , Image −Image−
>> ImagePartition[lena, {512, 128}] {{−Image−} , {−Image−} , {−Image−} , {−Image−}}
158 ImageResize >> ImageRotate[ein, Pi / 2] −Image− ImageResize[image, width] ImageResize[image,{width, height}] ImageSubtract
>> ein = Import["ExampleData/ Einstein.jpg"]; ImageSubtract[image, expr_1, expr_2, ...] >> ImageDimensions[ein] subtracts all expr_i from image where each {615, 768} expr_i must be an image or a real number.
>> ImageResize[ein, {400, 600}] >> i = Image[{{0, 0.5, 0.2, 0.1, −Image− 0.9}, {1.0, 0.1, 0.3, 0.8, 0.6}}]; >> ImageResize[ein, 256]
−Image− >> ImageSubtract[i, 0.2] −Image− >> ImageDimensions[%]
{256, 320} >> ImageSubtract[i, i] −Image− The default sampling method is Bicubic >> ImageResize[ein, 256, Resampling -> "Bicubic"] ImageTake −Image−
>> ImageResize[ein, 256, Resampling ImageTake[image, n] -> "Nearest"] gives the first n rows of image. ImageTake[image,-n] −Image− gives the last n rows of image. ImageTake[image,{r1, r2}] >> ImageResize[ein, 256, Resampling -> "Gaussian"] gives rows r1, ..., r2 of image. ImageTake[image,{r1, r2}, {c1, c2}] − − Image gives a cropped version of image.
ImageRotate ImageType
ImageRotate[image] Rotates image 90 degrees counterclock- ImageType[image] wise. gives the interval storage type of image, ImageRotate[image, theta] e.g. “Real”, “Bit32”, or “Bit”. Rotates image by a given angle theta >> img = Import["ExampleData/lena.
>> ein = Import["ExampleData/ tif"]; Einstein.jpg"]; >> ImageType[img]
>> ImageRotate[ein] Byte −Image− >> ImageType[Image[{{0, 1}, {1,
>> ImageRotate[ein, 45 Degree] 0}}]] −Image− Real
159 >> ImageType[Binarize[img]] >> ein = Import["ExampleData/ Bit Einstein.jpg"];
>> Opening[ein, 2.5] MaxFilter −Image−
MaxFilter[image, r] gives image with a maximum filter of ra- PixelValue dius r applied on it. This always picks the largest value in the filter’s area. PixelValue[image,{x, y}] gives the value of the pixel at position {x,
>> lena = Import["ExampleData/lena. y} in image. tif"];
>> lena = Import["ExampleData/lena. >> MaxFilter[lena, 5] tif"]; −Image− >> PixelValue[lena, {1, 1}] {0.321569, 0.0862745, 0.223529} MedianFilter
MedianFilter[image, r] PixelValuePositions gives image with a median filter of radius r applied on it. This always picks the me- PixelValuePositions[image, val] dian value in the filter’s area. gives the positions of all pixels in image that have value val. >> lena = Import["ExampleData/lena.
tif"]; >> PixelValuePositions[Image[{{0, 1}, {1, 0}, {1, 1}}], 1] >> MedianFilter[lena, 5] {{1, 1} , {1, 2} , {2, 1} , {2, 3}} −Image−
>> PixelValuePositions[Image[{{0.2, 0.4}, {0.9, 0.6}, {0.3, 0.8}}], MinFilter 0.5, 0.15] {{2, 2} , {2, 3}} MinFilter[image, r]
gives image with a minimum filter of ra- >> img = Import["ExampleData/lena. dius r applied on it. This always picks tif"]; the smallest value in the filter’s area. >> PixelValuePositions[img, 3 / >> lena = Import["ExampleData/lena. 255, 0.5 / 255] tif"]; {{180, 192, 2} , {181, 192, 2} , { } { } >> MinFilter[lena, 5] 181, 193, 2 , 188, 204, 2 , { } { } { −Image− 265, 314, 2 , 364, 77, 2 , 365, 72, 2} , {365, 73, 2} , {365, 77, 2} , {366, 70, 2} , {367, 65, 2}} Opening >> PixelValue[img, {180, 192}] {0.25098, 0.0117647, 0.215686} Opening[image, ker] Gives the morphological opening of im- age with respect to structuring element ker.
160 RandomImage >> Threshold[img] 0.456739 RandomImage[max] >> Binarize[img, %] creates an image of random pixels with − − values 0 to max. Image RandomImage[{min, max}] >> Threshold[img, Method -> "Mean"] creates an image of random pixels with values min to max. 0.486458 RandomImage[..., ] size >> Threshold[img, Method -> "Median creates an image of the given size. "] 0.504726 >> RandomImage[1, {100, 100}] −Image− WordCloud
Sharpen WordCloud[{word1, word2, ...}] Gives a word cloud with the given list of Sharpen[image] words. gives a sharpened version of image. WordCloud[{weight1 -> word1, weight2 -> Sharpen[image, r] word2, ...}] sharpens image with a kernel of size r. Gives a word cloud with the words weighted using the given weights. WordCloud[{weight1, weight2, ...} -> { >> lena = Import["ExampleData/lena. word1, word2, ...}] tif"]; Also gives a word cloud with the words weighted using the given weights. >> Sharpen[lena] WordCloud[{{word1, weight1}, {word2, − − Image weight2}, ...}] Gives a word cloud with the words >> Sharpen[lena, 5] weighted using the given weights. −Image−
>> WordCloud[StringSplit[Import[" ExampleData/EinsteinSzilLetter. TextRecognize txt"]]] −Image− TextRecognize[{image}] Recognizes text in image and returns it as >> WordCloud[Range[50] -> ToString string. /@ Range[50]] −Image−
Threshold Three-Dimensional Graphics Threshold[image] gives a value suitable for binarizing im- Three-Dimensional Graphic age.
The option “Method” may be “Cluster” (use Otsu’s threshold), “Median”, or “Mean”. >> img = Import["ExampleData/lena. tif"];
161 Cuboid Cylinder
Cuboid[{xmin, ymin, zmin}] Cylinder[{{x1, y1, z1}, {x2, y2, z2}}] is a unit cube. represents a cylinder of radius 1. Cuboid[{xmin, ymin, zmin}, {xmax, Cylinder[{{x1, y1, z1}, {x2, y2, z2}}, ymax, zmax}] r] represents a cuboid extending from is a cylinder of radius r starting at (x1, y1, {xmin, ymin, zmin} to {xmax, ymax, zmax}. z1) and ending at (x2, y2, z2). Cylinder[{{x1, y1, z1}, {x2, y2, z2},
>> Graphics3D[Cuboid[{0, 0, 1}]] ... }, r] is a collection cylinders of radius r
>> Graphics3D[Cylinder[{{0, 0, 0}, {1, 1, 1}}, 1]]
>> Graphics3D[{Red, Cuboid[{0, 0, 0}, {1, 1, 0.5}], Blue, Cuboid [{0.25, 0.25, 0.5}, {0.75, 0.75, 1}]}]
>> Graphics3D[{Yellow, Cylinder [{{-1, 0, 0}, {1, 0, 0}, {0, 0, Sqrt[3]}, {1, 1, Sqrt[3]}}, 1]}]
162 Graphics3D >> Graphics3D[Sphere[]] // TeXForm
\begin{asy} Graphics3D[primitives, options] import three; represents a three-dimensional graphic. See also the Section “Plotting” for a list of Plot import solids; options. size(6.6667cm, 6.6667cm); currentprojection=perspective(2.6,-4.8,4.0);
>> Graphics3D[Polygon[{{0,0,0}, currentlight=light(rgb(0.5,0.5,1), {0,1,1}, {1,0,0}}]] specular=red, (2,0,2), (2,2,2), (0,2,2)); // Sphere3DBox draw(surface(sphere((0, 0, 0), 1)), rgb(1,1,1)); draw(((-1,-1,-1)–(1,-1,-1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); draw(((-1,1,-1)–(1,1,-1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); draw(((-1,-1,1)–(1,-1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); draw(((-1,1,1)–(1,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); draw(((-1,-1,-1)–(-1,1,-1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); draw(((1,-1,-1)–(1,1,-1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); In TeXForm, Graphics3D creates Asymptote fig- draw(((-1,-1,1)–(-1,1,1)), rgb(0.4, 0.4, ures: 0.4)+linewidth(1)); draw(((1,-1,1)–(1,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); draw(((-1,-1,-1)–(-1,-1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); draw(((1,-1,-1)–(1,-1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); draw(((-1,1,-1)–(-1,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); draw(((1,1,-1)–(1,1,1)), rgb(0.4, 0.4, 0.4)+linewidth(1)); \end{asy}
163 Sphere Plotting Data
Plotting Data Sphere[{x, y, z}] is a sphere of radius 1 centered at the Plotting functions take a function as a parameter point {x, y, z}. and data, often a range of points, as another pa- Sphere[{x, y, z}, r] rameter, and plot or show the function applied is a sphere of radius r centered at the to the data. point {x, y, z}. Sphere[{{x1, y1, z1}, {x2, y2, z2}, ... BarChart }, r] is a collection spheres of radius r centered BarChart[{b1, b2 ...}] x1 y2 z2 x2 y2 z2 at the points { , , }, { , , }, ... makes a bar chart with lengths b1, b2, .... Drawing options include - Charting: >> Graphics3D[Sphere[{0, 0, 0}, 1]] • Mesh • PlotRange • ChartLabels • ChartLegends • ChartStyle BarChart specific: • Axes (default {False, True}) • AspectRatio: (default 1 / GoldenRatio) A bar chart of a list of heights: >> BarChart[{1, 4, 2}] 4
3
2 >> Graphics3D[{Yellow, Sphere[{{-1, 0, 0}, {1, 0, 0}, {0, 0, Sqrt 1 [3.]}}, 1]}]
>> BarChart[{1, 4, 2}, ChartStyle -> {Red, Green, Blue}] 4
3
2
1
164 >> BarChart[{{1, 2, 3}, {2, 3, 4}}] Compare it to the default color function, 4 LakeColors: >> {DensityPlot[x + y, {x, -1, 1}, 3 {y, -1, 1}], DensityPlot[x + y, {x, -1, 1}, {y, -1, 1}, ColorFunction->"test"]} 2 1 Chart several datasets with categorical labels: >> BarChart[{{1, 2, 3}, {2, 3, 4}}, ChartLabels -> {"a", "b", "c"}] 4 3 2 , 1 a b c a b c >> BarChart[{{1, 5}, {3, 4}}, ChartStyle -> {{EdgeForm[Thin], White}, {EdgeForm[Thick], White }}] 5 4 3 2 DensityPlot 1 DensityPlot[f ,{x, xmin, xmax}, {y, ymin, ymax}] plots a density plot of f with x ranging from xmin to xmax and y ranging from ColorData ymin to ymax.
ColorData["name"] returns a color function with the given name.
Define a user-defined color function: >> Unprotect[ColorData]; ColorData ["test"] := ColorDataFunction[" test", "Gradients", {0, 1}, Blend[{Red, Green, Blue}, #1] &]; Protect[ColorData]
165 >> DensityPlot[x ^ 2 + 1 / y, {x, >> DensityPlot[1/(x^2 + y^2 + 1), { -1, 1}, {y, 1, 4}] x, -1, 1}, {y, -2,2}, Mesh->Full ]
>> DensityPlot[1 / x, {x, 0, 1}, {y , 0, 1}] >> DensityPlot[x^2 y, {x, -1, 1}, { y, -1, 1}, Mesh->All]
>> DensityPlot[Sqrt[x * y], {x, -1, 1}, {y, -1, 1}] Histogram
Histogram[{x1, x2 ...}] plots a histogram using the values x1, x2, ....
166 >> Histogram[{3, 8, 10, 100, 1000, >> ListLinePlot[{{-2, -1}, {-1, 500, 300, 200, 10, 20, 200, 100, -1}}] 200, 300, 500}] 12 −1.8 −1.6 −1.4 −1.2 −1.0 − 10 0.5 8 −1.0 6 4 −1.5 2 −2.0 200 400 600 800 1000
>> Histogram[{{1, 2, 10, 5, 50, ListPlot 20}, {90, 100, 101, 120, 80}}] 5 ListPlot[{y_1, y_2, ...}] plots a list of y-values, assuming integer 4 x-values 1, 2, 3, ... ListPlot[{{x_1, y_1}, {x_2, y_2}, 3 ...}] 2 plots a list of x, y pairs. ListPlot[{list_1, list_2, ...}] 1 plots several lists of points.
20 40 60 80 100 120 ListPlot accepts a superset of the Graphics op- tions. >> ListPlot[Table[n ^ 2, {n, 10}]] ListLinePlot 100 ListLinePlot[{y_1, y_2, ...}] 80 plots a line through a list of y-values, as- 60 suming integer x-values 1, 2, 3, ... ListLinePlot[{{x_1, y_1}, {x_2, y_2}, 40 ...}] plots a line through a list of x, y pairs. 20 ListLinePlot[{list_1, list_2, ...}] plots several lines. 4 6 8 10
ListPlot accepts a superset of the Graphics op- tions. >> ListLinePlot[Table[{n, n ^ 0.5}, {n, 10}]]
3.0 2.5 2.0 1.5
4 6 8 10
167 ParametricPlot >> ParametricPlot[{{Sin[u], Cos[u ]},{0.6 Sin[u], 0.6 Cos[u]}, ParametricPlot[{f_x, f_y}, {u, umin, {0.2 Sin[u], 0.2 Cos[u]}}, {u, umax}] 0, 2 Pi}, PlotRange->1, plots a parametric function f with the pa- AspectRatio->1] rameter u ranging from umin to umax. 1.0 ParametricPlot[{{f_x, f_y}, {g_x, g_y}, ...}, {u, umin, umax}] plots several parametric functions f, g, ... 0.5 ParametricPlot[{f_x, f_y}, {u, umin, umax}, {v, vmin, vmax}] plots a parametric area. ParametricPlot[{{f_x, f_y}, {g_x, g_y}, −1.0 −0.5 0.5 1.0 ...}, {u, umin, umax}, {v, vmin, vmax}] −0.5 plots several parametric areas.
>> ParametricPlot[{Sin[u], Cos[3 u −1.0 ]}, {u, 0, 2 Pi}]
1.0 PieChart 0.5 PieChart[{a1, a2 ...}] draws a pie chart with sector angles pro- −1.0 −0.5 0.5 1.0 portional to a1, a2, .... −0.5 Drawing options include - Charting: −1.0 • Mesh • PlotRange
>> ParametricPlot[{Cos[u] / u, Sin[ • ChartLabels u] / u}, {u, 0, 50}, PlotRange • ChartLegends ->0.5] • ChartStyle PieChart specific: 0.4 • Axes (default: False, False) • AspectRatio (default 1) 0.2 • SectorOrigin: (default {Automatic, 0}) • SectorSpacing" (default Automatic) −0.4 −0.2 0.2 0.4 A hypothetical comparsion between types of −0.2 pets owned: −0.4
168 >> PieChart[{30, 20, 10}, Same as the above, but without gaps between ChartLabels -> {Dogs, Cats, Fish the groups of data: }] >> PieChart[{{10, 20, 30}, {15, 22, 30}}, SectorSpacing -> None]
Dogs
Fish Cats
A doughnut chart for a list of values: >> PieChart[{8, 16, 2}, The doughnut chart above with labels on each of SectorOrigin -> {Automatic, the 3 pieces: 1.5}] >> PieChart[{{10, 20, 30}, {15, 22, 30}}, ChartLabels -> {A, B, C}]
B A A B
C
C
A Pie chart with multple datasets: >> PieChart[{{10, 20, 30}, {15, 22, Negative values are removed, the data below is 30}}] the same as {1, 3}:
169 >> PieChart[{1, -1, 3}] >> Plot[Tan[x], {x, -6, 6}, Mesh-> Full] 15 10 5
−6 −4 −2 2 4 6 −5 −10 −15
>> Plot[x^2, {x, -1, 1}, MaxRecursion->5, Mesh->All]
Plot 0.8 0.6 Plot[f ,{x, xmin, xmax}] plots f with x ranging from xmin to xmax. 0.4 Plot[{f1, f2, ...}, {x, xmin, xmax}] 0.2 plots several functions f1, f2, ... −1.0 −0.5 0.5 1.0 >> Plot[{Sin[x], Cos[x], x / 3}, {x , -Pi, Pi}] >> Plot[Log[x], {x, 0, 5}, MaxRecursion->0] 1.0 1.5 0.5 1.0 0.5 −3 −2 −1 1 2 3 − 0.5 1 2 3 4 5 −0.5 − 1.0 −1.0
>> Plot[Sin[x], {x, 0, 4 Pi}, >> Plot[Tan[x], {x, 0, 6}, Mesh-> PlotRange->{{0, 4 Pi}, {0, All, PlotRange->{{-1, 5}, {0, 1.5}}] 15}}, MaxRecursion->10] 1.5 15
1.0 10
0.5 5
2 4 6 8 10 12 −1 1 2 3 4 5
A constant function:
170 >> Plot[3, {x, 0, 1}] >> Plot3D[Sin[y + Sin[3 x]], {x, 6 -2, 2}, {y, -2, 2}, PlotPoints ->20] 5 4 3 2 1
0.2 0.4 0.6 0.8 1.0
Plot3D
Plot3D[f ,{x, xmin, xmax}, {y, ymin, ymax}] creates a three-dimensional plot of f with >> Plot3D[x / (x ^ 2 + y ^ 2 + 1), x ranging from xmin to xmax and y rang- {x, -2, 2}, {y, -2, 2}, Mesh-> ing from ymin to ymax. None]
Plot3D has the same options as Graphics3D, in particular: • Mesh • PlotPoints • MaxRecursion >> Plot3D[x ^ 2 + 1 / y, {x, -1, 1}, {y, 1, 4}]
>> Plot3D[Sin[x y] /(x y), {x, -3, 3}, {y, -3, 3}, Mesh->All]
171 >> Plot3D[Log[x + y^2], {x, -1, 1}, >> PolarPlot[Abs[Cos[5t]], {t, 0, {y, -1, 1}] Pi}] 1.0
0.8
0.6
0.4
0.2
−1.0 −0.5 0.5 1.0
Coils around a ring: PolarPlot >> PolarPlot[{1, 1 + Sin[20 t] / 5}, {t, 0, 2 Pi}]
PolarPlot[r,{t, t_min, t_max}] creates a polar plot of curve with radius 1.0 r as a function of angle t ranging from t_min to t_max. 0.5 In a Polar Plot, a polar coordinate system is used. A polar coordinate system is a two-dimensional − − coordinate system in which each point on a 1.0 0.5 0.5 1.0 plane is determined by a distance from a refer- −0.5 ence point and an angle from a reference direc- tion. Here is a 5-blade propeller, or maybe a flower, −1.0 using PolarPlot: >> PolarPlot[Cos[5t], {t, 0, Pi}] A spring having 16 turns: 1.0 >> PolarPlot[Sqrt[t], {t, 0, 16 Pi }] 0.5
5 −0.5 0.5 1.0
−0.5 −5 5
−1.0 −5 The number of blades and be change by adjust- ing the t multiplier. A slight change adding Abs turns this a clump of grass:
172 Splines >> Graphics[{BezierCurve[pts], Green, Line[pts], Red, Point[pts Splines ]}] Splines are used both in graphics and computa- tions.
BernsteinBasis
BernsteinBasis[d,n,x] returns the nth Bernstein basis of degree d at x.
A Bernstein polynomial is a polynomial that is a = linear combination of Bernstein basis polynomi- als. With the advent of computer graphics, Bernstein BezierFunction polynomials, restricted to the interval [0, 1], be- came important in the form of Bézier curves. BezierFunction[{pt_1, pt_2, ...}] BernsteinBasis[d,n,x] equals Binomial[d, n returns a Bézier function for the curve ] x^n (1-x)^(d-n) in the interval [0, 1] and defined by points pt_i. The embed- zero elsewhere. ding dimension for the curve represented >> BernsteinBasis[4, 3, 0.5] by BezierFunction[{pt_1,pt_2,...}] is 0.25 given by the length of the lists pt_i.
>> f = BezierFunction[{{0, 0}, {1, BezierCurve 1}, {2, 0}, {3, 2}}]; = BezierCurve[{pt_1, pt_2 ...}] >> f[.5] represents a Bézier curve with control { } points p_i. 1.5, 0.625 = Option: Plotting the Bézier Function accoss a Bézier • SplineDegree->d specifies that the under- curve: lying polynomial basis should have maxi- >> Module[{p={{0, 0},{1, 1},{2, mal degree d. -1},{4, 0}}}, Graphics[{ Set up some points... BezierCurve[p], Red, Point[Table >> pts = {{0, 0}, {1, 1}, {2, -1}, [BezierFunction[p][x], {x, 0, 1, {3, 0}, {5, 2}, {6, -1}, {7, 0.1}]]}]] 3}};
= A composite Bézier curve and its control points:
173 26. Input/Output, Files, and Filesystem
Contents
CopyFile ..... 182 ResetDirectory .. 187 File and Stream CreateDirectory 182 Operations .... 175 . $RootDirectory .. 188 CreateFile ..... 182 SetDirectory 188 BinaryRead .... 175 ... CreateTemporary . 182 BinaryWrite .... 176 SetFileDate .... 188 DeleteDirectory .. 182 Byte ...... 176 $TemporaryDirec- DeleteFile ..... 183 tory .... 188 Character ..... 176 Directory ..... 183 ToFileName ... 188 Close ...... 176 DirectoryName .. 183 URLSave ..... 188 EndOfFile .... 176 DirectoryQ .... 183 $UserBaseDirectory 188 Expression .... 176 DirectoryStack .. 183 Importing and Exporting 188 FilePrint ..... 176 ExpandFileName . 183 B64Decode .... 188 Find ...... 177 FileBaseName .. 183 B64Encode .... 189 Get (<<) ...... 177 FileByteCount .. 183 RemoveLin- $Input ...... 177 FileDate ...... 184 earSyntax . 189 $InputFileName . 177 FileExistsQ .... 184 $extensionMap- InputStream ... 177 FileExtension ... 184 pings ... 189 Number ..... 177 FileHash ..... 184 $formatMappings 189 OpenAppend ... 177 FileInformation .. 185 Export ...... 189 OpenRead .... 178 FileNameDepth . 185 $ExportFormats . 189 OpenWrite .... 178 FileNameJoin ... 185 ExportString ... 190 OutputStream .. 178 FileNameSplit .. 185 FileFormat .... 190 Put (>>) ...... 178 FileNameTake .. 185 Import ...... 190 PutAppend (>>>) . 178 FileNames .... 186 $ImportFormats . 190 Read ...... 179 FileType ..... 186 ImportString ... 191 ReadList ..... 179 FindFile ...... 186 RegisterExport .. 191 Record ...... 180 FindList ...... 186 RegisterImport .. 192 SetStreamPosition 180 $HomeDirectory . 186 URLFetch ..... 192 Skip ...... 180 $InitialDirectory . 186 The Main Loop .... 193 StreamPosition .. 180 $InstallationDirec- $HistoryLength .. 193 Streams ...... 181 tory .... 187 $Post ...... 193 StringToStream .. 181 Needs ...... 187 $Pre ...... 193 Word ...... 181 $OperatingSystem 187 $PrePrint ..... 193 Write ...... 181 ParentDirectory . 187 $PreRead ..... 193 WriteString .... 181 $Path ...... 187 $SyntaxHandler . 193 Filesystem Operations 182 $PathnameSepara- In ...... 194 AbsoluteFileName 182 tor ..... 187 $Line ...... 194 $BaseDirectory .. 182 RenameDirectory . 187 Out ...... 194 CopyDirectory .. 182 RenameFile .... 187
174 File and Stream Operations BinaryWrite
File and Stream Operation BinaryWrite[channel, b] writes a single byte given as an integer BinaryRead from 0 to 255. BinaryWrite[channel, {b1, b2, ...}] writes a sequence of byte. BinaryRead[stream] BinaryWrite[channel, ‘‘string’]’ reads one byte from the stream as an in- writes the raw characters in a string. teger from 0 to 255. BinaryWrite[channel, x, type] BinaryRead[stream, type] writes x as the specified type. reads one object of specified type from BinaryWrite[channel,{x1, x2, ...}, the stream. type] BinaryRead[stream,{type1, type2, ...}] writes a sequence of objects as the speci- reads a sequence of objects of specified fied type. types. BinaryWrite[channel,{x1, x2, ...}, { type1, type2, ...}] >> strm = OpenWrite[BinaryFormat -> writes a sequence of objects using a se- True] [ quence of specified types. OutputStream ] /tmp/tmpgcvj97kh, 153 >> strm = OpenWrite[BinaryFormat -> True] >> BinaryWrite[strm, {97, 98, 99}] [ >> BinaryWrite[strm, {39, 4, 122}] OutputStream ] [ /tmp/tmpgcvj97kh, 153 OutputStream ] /tmp/tmpaqi9yveh, 273 >> Close[strm] /tmp/tmpgcvj97kh >> Close[strm]
>> strm = OpenRead[%, BinaryFormat >> strm = OpenRead[%, BinaryFormat -> True] -> True] [ InputStream ] >> BinaryRead[strm] /tmp/tmpgcvj97kh, 154 39
>> BinaryRead[strm, {"Character8", >> BinaryRead[strm, "Byte"] "Character8", "Character8"}] 4 {a, b, c} >> BinaryRead[strm, "Character8"] z >> Close[strm];
>> Close[strm];
Write a String >> strm = OpenWrite[BinaryFormat -> True]
>> BinaryWrite[strm, "abc123"] [ OutputStream ] /tmp/tmpnmfc1ofe, 275
>> Close[%]
Read as Bytes
175 >> strm = OpenRead[%, BinaryFormat Close -> True] Close[stream] >> BinaryRead[strm, {"Character8", closes an input or output stream. "Character8", "Character8", " Character8", "Character8", " Character8", "Character8"}] >> Close[StringToStream["123abc"]] String {a, b, c, 1, 2, 3, EndOfFile}
>> Close[OpenWrite[]] >> Close[strm] /tmp/tmpu73w24xh Read as Characters >> strm = OpenRead[%, BinaryFormat -> True] EndOfFile
>> BinaryRead[strm, {"Byte", "Byte EndOfFile ", "Byte", "Byte", "Byte", "Byte is returned by Read when the end of an ", "Byte"}] input stream is reached. {97, 98, 99, 49, 50, 51, EndOfFile}
>> Close[strm] Expression Write Type >> strm = OpenWrite[BinaryFormat -> Expression True] is a data type for Read.
>> BinaryWrite[strm, 97, "Byte"] [ OutputStream ] FilePrint /tmp/tmpbgwzsftj, 278
>> BinaryWrite[strm, {97, 98, 99}, FilePrint[file] {"Byte", "Byte", "Byte"}] prints the raw contents of file. [ OutputStream ] /tmp/tmpbgwzsftj, 278 Find >> Close[%] Find[stream, text] find the first line in stream that contains Byte text.
>> stream = OpenRead["ExampleData/ Byte EinsteinSzilLetter.txt"]; is a data type for Read.
>> Find[stream, "uranium"]
Character >> Find[stream, "uranium"]
>> Close[stream] Character Read. is a data type for >> stream = OpenRead["ExampleData/ EinsteinSzilLetter.txt"];
>> Find[stream, {"energy", "power"} ]
176 >> Find[stream, {"energy", "power"} InputStream ] InputStream[name, n] >> Close[stream] represents an input stream.
Get (<<) >> stream = StringToStream["Mathics is cool!"] [ ] <> Close[stream] sion, returning only the last one. Get[name, Trace->True] String Runs Get tracing each line before it is evaluated. Number
>> filename = $TemporaryDirectory <> "/example_file"; Number is a data type for Read. >> Put[x + y, filename]
>> Get[filename] OpenAppend >> filename = $TemporaryDirectory <> "/example_file"; OpenAppend[‘‘file’]’ opens a file and returns an OutputStream >> Put[x + y, 2x^2 + 4z!, Cos[x] + to which writes are appended. I Sin[x], filename]
>> Get[filename] >> OpenAppend[] [ OutputStream ] >> DeleteFile[filename] /tmp/tmp788p0opa, 297
$Input OpenRead
$Input OpenRead[‘‘file’]’ is the name of the stream from which in- opens a file and returns an InputStream. put is currently being read.
>> OpenRead["ExampleData/ >> $Input EinsteinSzilLetter.txt"] [ InputStream ExampleData/EinsteinSzilLetter.txt, $InputFileName ] 301
$InputFileName >> OpenRead["https://raw. is the name of the file from which input is githubusercontent.com/mathics/ currently being read. Mathics/master/README.rst"] [ InputStream While in interactive mode, $InputFileName is https://raw.githubusercontent.com/mathics/Mathics/master/README.rst] , “”. 302 >> $InputFileName
177 >> Close[%]; >> Get[filename] 815 915 283 247 897 734 345 611 ˜ ˜269 596 115 894 272 000 000 000 OpenWrite >> DeleteFile[filename]
OpenWrite[‘‘file’]’ >> filename = $TemporaryDirectory opens a file and returns an Output- <> "/fiftyfactorial"; Stream. >> Put[10!, 20!, 30!, filename]
>> OpenWrite[] [ >> FilePrint[filename] OutputStream ] /tmp/tmpucjb9hco, 305 >> DeleteFile[filename]
= OutputStream >> filename = $TemporaryDirectory <> "/example_file";
OutputStream[name, n] >> Put[x + y, 2x^2 + 4z!, Cos[x] + represents an output stream. I Sin[x], filename]
>> OpenWrite[] >> FilePrint[filename] [ OutputStream ] >> DeleteFile[filename] /tmp/tmp48v0lhqm, 307
>> Close[%] PutAppend (>>>) /tmp/tmp48v0lhqm
expr >>> filename Put (>>) append expr to a file. PutAppend[expr1, expr2, ..., $‘‘ filename’$]’ expr >> filename write a sequence of expressions to a file. write expr to a file. Put[expr1, expr2, ..., filename] >> Put[50!, "factorials"] write a sequence of expressions to a file.
>> FilePrint["factorials"] >> Put[40!, fortyfactorial] fortyfactorialisnotstring, >> PutAppend[10!, 20!, 30!, " InputStream[], orOutputStream[] factorials"]
815 915 283 247 897 734 345 ˜ >> FilePrint["factorials"] ˜611 269 596 115 894 272 ˜ ˜000 000 000»fortyfactorial >> 60! >>> "factorials"
>> filename = $TemporaryDirectory >> FilePrint["factorials"] <> "/fortyfactorial"; >> "string" >>> factorials
>> Put[40!, filename] >> FilePrint["factorials"]
>> FilePrint[filename]
178 Read >> Read[stream, Expression] 5 Read[stream] >> Close[stream]; reads the input stream and returns one expression. Reading a comment however will return the Read[stream, type] empy list: reads the input stream and returns an ob- >> stream = StringToStream["(* :: ject of the given type. Package:: *)"]; Read[stream, type] reads the input stream and returns an ob- >> Read[stream, Hold[Expression]] ject of the given type. Read[stream, Hold[Expression]] >> Close[stream]; reads the input stream for an Expression Hold. and puts it inside >> stream = StringToStream["123 abc type is one of: "];
• Byte >> Read[stream, {Number, Word}] • Character {123, abc} • Expression • HoldExpression Multiple lines: • Number >> stream = StringToStream["\"Tengo una\nvaca lechera.\""]; Read[ • Real stream] • Record • String Tengo una • Word vaca lechera. >> stream = StringToStream["abc123 "]; ReadList
>> Read[stream, String] abc123 ReadList["file"] Reads all the expressions until the end of >> stream = StringToStream["abc file. 123"]; ReadList["file", type] Reads objects of a specified type until the >> Read[stream, Word] end of file. ReadList["file", {type1, type2, ...}] >> Read[stream, Word] Reads a sequence of specified types until the end of file. >> stream = StringToStream["123, 4"]; >> ReadList[StringToStream["a 1 b
>> Read[stream, Number] 2"], {Word, Number}] {{a, 1} , {b, 2}} >> Read[stream, Number]
>> stream = StringToStream["\" >> stream = StringToStream["2+2\n2 abc123\""]; +3"];
>> ReadList[stream] Read Hold[Expression] with a returns the ex- {abc123} pression it reads unevaluated so it can be later inspected and evaluated: >> InputForm[%] >> Read[stream, Hold[Expression]] {"abc123"}
179 Record StreamPosition
Record StreamPosition[stream] is a data type for Read. returns the current position in a stream as an integer.
SetStreamPosition >> stream = StringToStream["Mathics is cool!"] [ ] SetStreamPosition[stream, n] InputStream String, 358 sets the current position in a stream. >> Read[stream, Word]
>> stream = StringToStream["Mathics Mathics is cool!"] [ ] >> StreamPosition[stream] InputStream String, 352 7
>> SetStreamPosition[stream, 8] 8 Streams
>> Read[stream, Word] Streams[] is returns a list of all open streams.
>> SetStreamPosition[stream, Infinity] 16
Skip
Skip[stream, type] skips ahead in an input steream by one object of the specified type. Skip[stream, type, n] skips ahead in an input steream by n ob- jects of the specified type.
>> stream = StringToStream["a b c d "];
>> Read[stream, Word]
>> Skip[stream, Word]
>> Read[stream, Word]
>> stream = StringToStream["a b c d "];
>> Read[stream, Word]
>> Skip[stream, Word, 2]
>> Read[stream, Word]
180 >> Streams[] { Write InputStream [stdin, 0] , OutputStream [stdout, 1] , Write[channel, expr1, expr2, ...] OutputStream [stderr, 2] , writes the expressions to the output chan- [ nel followed by a newline. OutputStream] /tmp/tmp788p0opa[ , 297 , InputStream >> stream = OpenWrite[] /src/external-vcs/github/mathics/Mathics/mathics/data/ExampleData/EinsteinSzilLetter.txt] [ [ , 301 , OutputStream OutputStream ] /tmp/tmp5y9m8m8l, 364 /tmp/tmpucjb9hco] [, 305 , InputStream ] [ >> Write[stream, 10 x + 15 y ^ 2] String, 326] , InputStream [ String, 338] , InputStream [ >> Write[stream, 3 Sin[z]] String, 339] , InputStream [ >> Close[stream] String, 340] , InputStream [ /tmp/tmp5y9m8m8l String, 341] , InputStream [ String, 344] , InputStream [ >> stream = OpenRead[%]; String, 345] , InputStream [ >> ReadList[stream] String, 346] , InputStream [ { } 2 String, 348] , InputStream [ 10x + 15y , 3Sin [z] String, 349] , InputStream [ String, 350] , InputStream [ String, 351] , InputStream [ WriteString String, 352] , InputStream [ String, 355] , InputStream [ WriteString[stream, $str1, str2, ... ] String, 356] , InputStream [ writes the strings to the output stream. String, 357] , InputStream [ String, 358 , OutputStream]} >> stream = OpenWrite[]; /tmp/tmpxcye7a9x, 359 >> WriteString[stream, "This is a >> Streams["stdout"] test 1"] {OutputStream [stdout, 1]} >> WriteString[stream, "This is also a test 2"] StringToStream >> Close[stream]
StringToStream[string] >> FilePrint[%] converts a string to an open input stream. >> stream = OpenWrite[];
>> strm = StringToStream["abc 123"] [ ] >> WriteString[stream, "This is a InputStream String, 361 test 1", "This is also a test 2"]
Word >> Close[stream]
>> FilePrint[%] Word is a data type for Read.
181 Filesystem Operations CreateDirectory
Filesystem Operation CreateDirectory["dir"] creates a directory called dir. AbsoluteFileName CreateDirectory[] creates a temporary directory. AbsoluteFileName["name"] returns the absolute version of the given >> dir = CreateDirectory[] filename. /tmp/mmri3vxqv
>> AbsoluteFileName["ExampleData/ sunflowers.jpg"] CreateFile /src/external-vcs/github/mathics/Mathics/mathics/data/ExampleData/sunflowers.jpg CreateFile[‘‘filename’]’ Creates a file named “filename” tempo- $BaseDirectory rary file, but do not open it. CreateFile[] $UserBaseDirectory Creates a temporary file, but do not open it. returns the folder where user configura- tions are stored.
>> $RootDirectory CreateTemporary / CreateTemporary[] Creates a temporary file, but do not open CopyDirectory it.
CopyDirectory["dir1‘‘,”dir2"] copies directory dir1 to dir2. DeleteDirectory
DeleteDirectory["dir"] CopyFile deletes a directory called dir.
CopyFile["file1‘‘,”file2"] >> dir = CreateDirectory[] copies file1 to file2. /tmp/mh055p76q
>> DeleteDirectory[dir] >> CopyFile["ExampleData/sunflowers .jpg", "MathicsSunflowers.jpg"] >> DirectoryQ[dir] MathicsSunflowers.jpg False
>> DeleteFile["MathicsSunflowers. jpg"] DeleteFile
Delete["file"] deletes file. Delete[{"file1‘‘,”file2", ...}] deletes a list of files.
182 >> CopyFile["ExampleData/sunflowers DirectoryStack .jpg", "MathicsSunflowers.jpg"]; DirectoryStack[] >> DeleteFile["MathicsSunflowers. jpg"] returns the directory stack.
>> CopyFile["ExampleData/sunflowers >> DirectoryStack[] .jpg", "MathicsSunflowers1.jpg {/src/external-vcs/github/mathics/Mathics/mathics} "];
>> CopyFile["ExampleData/sunflowers .jpg", "MathicsSunflowers2.jpg ExpandFileName "]; ExpandFileName["name"] >> DeleteFile[{"MathicsSunflowers1. expands name to an absolute filename for jpg", "MathicsSunflowers2.jpg"}] your system.
>> ExpandFileName["ExampleData/ Directory sunflowers.jpg"] /src/external-vcs/github/mathics/Mathics/mathics/ExampleData/sunflowers.jpg Directory[] returns the current working directory. FileBaseName >> Directory[] /src/external-vcs/github/mathics/Mathics/mathicsFileBaseName["file"] gives the base name for the specified file name. DirectoryName >> FileBaseName["file.txt"] DirectoryName["name"] file extracts the directory name from a file- >> FileBaseName["file.tar.gz"] name. file.tar
>> DirectoryName["a/b/c"] a/b FileByteCount
>> DirectoryName["a/b/c", 2] a FileByteCount[file] returns the number of bytes in file. DirectoryQ >> FileByteCount["ExampleData/ sunflowers.jpg"] DirectoryQ["name"] 142 286 returns True if the directory called name exists and False otherwise. FileDate >> DirectoryQ["ExampleData/"] True FileDate[file, types] returns the time and date at which the file >> DirectoryQ["ExampleData/ MythicalSubdir/"] was last modified. False
183 >> FileDate["ExampleData/sunflowers >> FileExtension["file.txt"] .jpg"] txt { } 2 120, 9, 7, 7, 16, 33.2822 >> FileExtension["file.tar.gz"] gz >> FileDate["ExampleData/sunflowers .jpg", "Access"] {2 121, 7, 31, 23, 35, 32.6415} FileHash
>> FileDate["ExampleData/sunflowers .jpg", "Creation"] FileHash[file] [ ] returns an integer hash for the given file. Missing NotApplicable FileHash[file, type] returns an integer hash of the specified >> FileDate["ExampleData/sunflowers type for the given file. .jpg", "Change"] The types supported are “MD5”, {2 120, 9, 7, 7, 16, 33.2822} “Adler32”, “CRC32”, “SHA”, “SHA224”, “SHA256”, “SHA384”, and “SHA512”. >> FileDate["ExampleData/sunflowers FileHash[file, type, format] .jpg", "Modification"] gives a hash code in the specified format. {2 120, 9, 7, 7, 16, 33.2822} >> FileHash["ExampleData/sunflowers >> FileDate["ExampleData/sunflowers .jpg"] .jpg", "Rules"] { 109 937 059 621 979 839 ˜ − { Access > 2 121, 7, 31, 23, 35, [ ˜952 736 809 235 486 742 106 } − 32.6415 , Creation] > Missing >> FileHash["ExampleData/sunflowers − > { NotApplicable , Change .jpg", "MD5"] 2 120, 9, 7, 7, 16, 33.282˜ } − { 109 937 059 621 979 839 ˜ ˜2 , Modification > } ˜952 736 809 235 486 742 106 2 120, 9, 7, 7, 16, 33.2822} >> FileHash["ExampleData/sunflowers .jpg", "Adler32"] FileExistsQ 1 607 049 478
>> FileHash["ExampleData/sunflowers FileExistsQ[" "] file .jpg", "SHA256"] returns True if file exists and False other- wise. 111 619 807 552 579 450 300 684 600 ˜ ˜241 129 773 909 359 865 098 672 ˜ >> FileExistsQ["ExampleData/ ˜286 468 229 443 390 003 894 913 065 sunflowers.jpg"] True FileInformation >> FileExistsQ["ExampleData/ sunflowers.png"] FileInformation["file"] False returns information about file.
This function is totally undocumented in MMA! FileExtension
FileExtension["file"] gives the extension for the specified file name.
184 >> FileInformation["ExampleData/ FileNameSplit sunflowers.jpg"] { File FileNameSplit["filenames"] splits a filename into a list of parts. − > /src/external-vcs/github/mathics/Mathics/mathics/ExampleData/sunflowers.jpg, FileType− > File, ByteCount− > } >> FileNameSplit["example/path/file 142 286, Date− > 6.96413 × 109 .txt"] {example, path, file.txt}
FileNameDepth FileNameTake FileNameDepth["name"] gives the number of path parts in the FileNameTake["file"] given filename. returns the last path element in the file name name. FileNameTake["file", n] >> FileNameDepth["a/b/c"] returns the first n path elements in the file 3 name name.
>> FileNameDepth["a/b/c/"] FileNameTake["file", $-n$] n 3 returns the last path elements in the file name name.
FileNameJoin FileNames FileNameJoin[{"dir_1‘‘,”dir_2", ...}] joins the dir_i together into one path. FileNames[] FileNameJoin[..., OperatingSystem->‘‘ Returns a list with the filenames in the os’]’ current working folder. yields a file name in the format for FileNames[form] the specified operating system. Possible Returns a list with the filenames in the choices are “Windows”, “MacOSX”, and current working folder that matches with “Unix”. form. FileNames[{form_1, form_2, ...}] >> FileNameJoin[{"dir1", "dir2", " Returns a list with the filenames in the dir3"}] current working folder that matches with one of form_1, form_2, .... dir1/dir2/dir3 FileNames[{form_1, form_2, ...},{dir_1, >> FileNameJoin[{"dir1", "dir2", " dir_2, ...}] dir3"}, OperatingSystem -> "Unix Looks into the directories dir_1, dir_2, .... "] FileNames[{form_1, form_2, ...},{dir_1, dir_2, ...}] dir1/dir2/dir3 Looks into the directories dir_1, dir_2, ....
>> FileNameJoin[{"dir1", "dir2", " FileNames[{forms, dirs, n] dir3"}, OperatingSystem -> " Look for files up to the level n. Windows"] dir1\dir2\dir3 >> SetDirectory[ $InstallationDirectory <> "/ autoload"];
>> FileNames["*.m", "formats"]// Length 0
185 >> FileNames["*.m", "formats", 3]// FindList Length 15 FindList[file, text] returns a list of all lines in file that contain >> FileNames["*.m", "formats", text. Infinity]//Length FindList[file,{text1, text2, ...}] 15 returns a list of all lines in file that contain any of the specified string. FindList[{file1, file2, ...}, ...] FileType returns a list of all lines in any of the filei that contain the specified strings. FileType["file"] gives the type of a file, a string. This is >> stream = FindList["ExampleData/ typically File, Directory or None. EinsteinSzilLetter.txt", " uranium"];
>> FileType["ExampleData/sunflowers >> FindList["ExampleData/ .jpg"] EinsteinSzilLetter.txt", " File uranium", 1] { >> FileType["ExampleData"] in manuscript, leads me Directory to expect that the element uranium may be turned into} >> FileType["ExampleData/ nonexistant"] None $HomeDirectory
$HomeDirectory FindFile returns the users HOME directory.
FindFile[name] >> $HomeDirectory searches $Path for the given filename. /home/rocky
>> FindFile["ExampleData/sunflowers .jpg"] $InitialDirectory /src/external-vcs/github/mathics/Mathics/mathics/data/ExampleData/sunflowers.jpg
>> FindFile["VectorAnalysis‘"] $InitialDirectory /src/external-vcs/github/mathics/Mathics/mathics/packages/VectorAnalysis/Kernel/init.mreturns the directory from which Mathics was started.
>> FindFile["VectorAnalysis‘ VectorAnalysis‘"] >> $InitialDirectory /src/external-vcs/github/mathics/Mathics/mathics/packages/VectorAnalysis/VectorAnalysis.m/src/external-vcs/github/mathics/Mathics/mathics
$InstallationDirectory
$InstallationDirectory returns the top-level directory in which Mathics was installed.
186 >> $InstallationDirectory $PathnameSeparator /src/external-vcs/github/mathics/Mathics/mathics $PathnameSeparator returns a string for the seperator in paths. Needs
>> $PathnameSeparator Needs["context‘"] / loads the specified context if not already in $Packages. RenameDirectory >> Needs["VectorAnalysis‘"] RenameDirectory["dir1‘‘,”dir2"] renames directory dir1 to dir2. $OperatingSystem
$OperatingSystem RenameFile gives the type of operating system run- ning Mathics. RenameFile["file1‘‘,”file2"] renames file1 to file2. >> $OperatingSystem Unix >> CopyFile["ExampleData/sunflowers .jpg", "MathicsSunflowers.jpg"] ParentDirectory MathicsSunflowers.jpg
>> RenameFile["MathicsSunflowers. ParentDirectory[] jpg", "MathicsSunnyFlowers.jpg"] returns the parent of the current working directory. MathicsSunnyFlowers.jpg ParentDirectory["dir"] >> DeleteFile["MathicsSunnyFlowers. returns the parent dir. jpg"]
>> ParentDirectory[] /src/external-vcs/github/mathics/Mathics/mathicsResetDirectory
ResetDirectory[] $Path pops a directory from the directory stack and returns it. $Path
returns the list of directories to search >> ResetDirectory[] when looking for a file. /src/external-vcs/github/mathics/Mathics/mathics/autoload
>> $Path {., /home/rocky, $RootDirectory /src/external-vcs/github/mathics/Mathics/mathics/data, } /src/external-vcs/github/mathics/Mathics/mathics/packages$RootDirectory returns the system root directory.
>> $RootDirectory /
187 SetDirectory FileNameJoin.
>> ToFileName[{"dir1", "dir2"}, " file"] SetDirectory[dir] sets the current working directory to dir. dir1/dir2/file
>> ToFileName["dir1", "file"] >> SetDirectory[] dir1/file /home/rocky >> ToFileName[{"dir1", "dir2", " dir3"}] SetFileDate dir1/dir2/dir3
SetFileDate["file"] set the file access and modification dates URLSave of file to the current date. SetFileDate["file", date] URLSave[‘‘url’]’ set the file access and modification dates Save “url” in a temporary file. of file to the specified date list. URLSave[‘‘url’,’ filename] SetFileDate["file", date,"type"] Save “url” in filename. set the file date of file to the specified date list. The "type“ can be one of ”Access“, ”Creation“, ”Modification", or All. $UserBaseDirectory Create a temporary file (for example purposes) >> tmpfilename = $UserBaseDirectory $TemporaryDirectory <> "/tmp0"; returns the folder where user configura- tions are stored. >> Close[OpenWrite[tmpfilename]];
>> $RootDirectory >> SetFileDate[tmpfilename, {2002, 1, 1, 0, 0, 0.}, "Access"]; /
>> FileDate[tmpfilename, "Access"] {2 002, 1, 1, 0, 0, 0.} Importing and Exporting
Importing and Exporting $TemporaryDirectory B64Decode $TemporaryDirectory returns the directory used for temporary System‘Convert‘B64Dump‘B64Decode[ files. string] Decode string in Base64 coding to an ex- pression. >> $TemporaryDirectory /tmp >> System‘Convert‘B64Dump‘B64Decode ["R!="] ToFileName String”R! = ”isnotavalidb64encodedstring. ToFileName[{"dir_1‘‘,”dir_2", ...}] $Failed joins the dir_i together into one path.
ToFileName has been superseded by
188 B64Encode Export
System‘Convert‘B64Dump‘B64Encode[expr] Export["file.ext", expr] Encodes expr in Base64 coding exports expr to a file, using the extension ext to determine the format. >> System‘Convert‘B64Dump‘B64Encode Export["file", expr,"format"] ["Hello world"] exports expr to a file in the specified for- mat. SGVsbG8gd29ybGQ= Export["file", exprs, elems]
>> System‘Convert‘B64Dump‘B64Decode exports exprs to a file as elements speci- [%] fied by elems.
>> System‘Convert‘B64Dump‘B64Encode [Integrate[f[x],{x,0,2}]] $ExportFormats SW50ZWdyYXRlW2ZbeF0sIHt4LCAwLCAyfV0=
>> System‘Convert‘B64Dump‘B64Decode $ExportFormats [%] returns a list of file formats supported by Export.
RemoveLinearSyntax >> $ExportFormats {BMP, Base64, CSV, GIF, JPEG, System‘Convert‘CommonDump‘ JPEG2 000, PBM, PCX, PGM, RemoveLinearSyntax[something] PNG, PPM, SVG, TIFF, Text, asy} Keine anung... Undocumented in wma
ExportString $extensionMappings ExportString[expr, form] exports expr to a string, in the format $extensionMappings form. Returns a list of associations between file Export["file", exprs, elems] extensions and file types. exports exprs to a string as elements spec- ified by elems.
$formatMappings >> ExportString [{{1,2,3,4},{3},{2},{4}}, "CSV"] $formatMappings 1,2,3,4 Returns a list of associations between file 3, extensions and file types. 2, 4,
>> ExportString[{1,2,3,4}, "CSV"] 1, 2, 3, 4,
>> ExportString[Integrate[f[x],{x ,0,2}], "SVG"]//Head String
189 FileFormat >> Import["ExampleData/colors.json "] FileFormat["name"] {colorsArray attempts to determine what format − > {{colorName− > black, Import should use to import specified rgbValue− > (0, 0, 0), file. hexValue− > #000 000} , { − >> FileFormat["ExampleData/ colorName > red, sunflowers.jpg"] rgbValue− > (255, 0, 0), − } JPEG hexValue > #FF0 000 , {colorName− > green, >> FileFormat["ExampleData/ rgbValue− > (0, 255, 0), EinsteinSzilLetter.txt"] hexValue− > #00FF00} , Text {colorName− > blue, − >> FileFormat["ExampleData/lena.tif rgbValue > (0, 0, 255), "] hexValue− > #0 000FF} , TIFF {colorName− > yellow, rgbValue− > (255, 255, 0), hexValue− > #FFFF00} , Import {colorName− > cyan, rgbValue− > (0, 255, 255), Import["file"] hexValue− > #00FFFF} , imports data from a file. {colorName− > magenta, Import["file", elements] rgbValue− > (255, 0, 255), imports the specified elements from a file. − } Import["http://url", ...] and Import[" hexValue > #FF00FF , ftp://url", ...] {colorName− > white, imports from a URL. rgbValue− > (255, 255, 255), hexValue− > #FFFFFF}}} >> Import["ExampleData/ExampleData. txt", "Elements"] {Data, Lines, Plaintext, String, Words} $ImportFormats
>> Import["ExampleData/ExampleData. $ImportFormats txt", "Lines"] returns a list of file formats supported by {Example File Format, Created Import. by Angus, 0.629452 0.586355, 0.711009 0.687453, 0.246540 >> $ImportFormats 0.433973, 0.926871 0.887255, {BMP, Base64, CSV, 0.825141 0.940900, 0.847035 ExpressionJSON, GIF, HTML, 0.127464, 0.054348 0.296494, ICO, JPEG, JPEG2 000, JSON, 0.838545 0.247025, 0.838697 PBM, PCX, PGM, PNG, PPM, 0.436220, 0.309496 0.833591} Package, TGA, TIFF, Text, XML}
190 ImportString >> ExampleExporter2[filename_, data_, opts___] := Module[{strm = OpenWrite[filename], char}, (* ImportString["data‘‘,”format"] TODO: Check data *)char = imports data in the specified format from FromCharacterCode[Mod[ a string. ToCharacterCode[data] - 84, 26] ImportString["file", elements] + 97]; WriteString[strm, char]; imports the specified elements from a Close[strm]] string. ImportString["data"] >> ImportExport‘RegisterExport[" attempts to determine the format of the ExampleFormat2", string from its content. ExampleExporter2]
>> str = "Hello!\n This is a >> Export["sample.txt", " testing text\n"; encodethisstring", " ExampleFormat2"]; >> ImportString[str, "Elements"] {Data, Lines, Plaintext, String, Words} >> FilePrint["sample.txt"]
>> ImportString[str, "Lines"] {Hello!, This is a testing text} RegisterImport
RegisterImport["format", defaultFunction] RegisterExport register defaultFunction as the default function used when importing from a file RegisterExport["format", func] of type "format". register func as the default function used RegisterImport["format", {"elem1" :> when exporting from a file of type " conditionalFunction1,"elem2" :> conditional- format". Function2, ..., defaultFunction}] registers multiple elements (elem1, ...) and their corresponding converter func- Simple text exporter tions (conditionalFunction1, ...) in addition >> ExampleExporter1[filename_, to the defaultFunction. data_, opts___] := Module[{strm RegisterImport["format", {" = OpenWrite[filename], char = conditionalFunctions, defaultFunction, data}, WriteString[strm, char]; "elem3" :> postFunction3,"elem4" :> Close[strm]] postFunction4, ...}] also registers additional elements (elem3, >> ImportExport‘RegisterExport[" ...) whose converters (postFunction3, ...) ExampleFormat1", act on output from the low-level fun- ExampleExporter1] cions.
>> Export["sample.txt", "Encode this string!", "ExampleFormat1 First, define the default function used to import "]; the data. >> ExampleFormat1Import[
>> FilePrint["sample.txt"] filename_String] := Module[{ stream, head, data}, stream = Very basic encrypted text exporter OpenRead[filename]; head = ReadList[stream, String, 2]; data = Partition[ReadList[stream , Number], 2]; Close[stream]; {" Header" -> head, "Data" -> data }]
191 RegisterImport is then used to register the >> Import["ExampleData/ExampleData. above function to a new data format. txt", {"ExampleFormat2", " >> ImportExport‘RegisterImport[" Elements"}] ExampleFormat1", {Data, Header} ExampleFormat1Import]
>> Import["ExampleData/ExampleData. >> FilePrint["ExampleData/ txt", {"ExampleFormat2", "Header ExampleData.txt"] "}] ExampleFileFormat {Example File Format, CreatedbyAngus Created by Angus} 0.6294520.586355 >> Import["ExampleData/ExampleData. 0.7110090.687453 txt", {"ExampleFormat2", "Data 0.2465400.433973 "}] // Grid 0.9268710.887255 0.8251410.940900 0.629452 0.586355 0.8470350.127464 0.711009 0.687453 0.24654 0.433973 0.0543480.296494 0.926871 0.887255 0.8385450.247025 0.825141 0.9409 0.8386970.436220 0.847035 0.127464 0.3094960.833591 0.054348 0.296494
>> Import["ExampleData/ExampleData. 0.838545 0.247025 txt", {"ExampleFormat1", " 0.838697 0.43622 Elements"}] 0.309496 0.833591 {Data, Header}
>> Import["ExampleData/ExampleData. URLFetch txt", {"ExampleFormat1", "Header "}] URLFetch[URL] Returns the content of URL as a string. {Example File Format, Created by Angus} # = ...
Conditional Importer: >> ExampleFormat2DefaultImport[ filename_String] := Module[{ The Main Loop stream, head}, stream = OpenRead [filename]; head = ReadList[ The Main Loop stream, String, 2]; Close[stream An interactive session operates a loop, called the ]; {"Header" -> head}] “main loop” in this way: • read input >> ExampleFormat2DataImport[ • process input filename_String] := Module[{ • format and print results stream, data}, stream = OpenRead • repeat [filename]; Skip[stream, String, 2]; data = Partition[ReadList[ As part of this loop, various global objects in this stream, Number], 2]; Close[ section are consulted. stream]; {"Data" -> data}] There are a variety of “hooks” that allow you to insert functions to be applied to the expresssions
>> ImportExport‘RegisterImport[" at various stages in the main loop. ExampleFormat2", {"Data" :> If you assign a function to the global variable ExampleFormat2DataImport, $PreRead it will be applied with the input that ExampleFormat2DefaultImport}] is read in the first step listed above.
192 Similarly, if you assign a function to global vari- >> $Post := (Print["[Storing result able $Pre, it will be applied with the input be- ...]"]; #1)& fore processing the input, the second step listed [Processinginput...] above. [Storingresult...]
$HistoryLength >> $PrePrint := (Print["The result is:"]; {TimeUsed[], #1})& $HistoryLength [Processinginput...] specifies the maximum number of In and [Storingresult...] Out entries. >> 2 + 2 >> $HistoryLength >> $Pre = .; $Post = .; $PrePrint = 100 .; $EnlapsedTime = .; >> $HistoryLength = 1; [Processinginput...]
>> 42 >> 2 + 2
>> %
>> %% $PrePrint %3 $PrePrint >> $HistoryLength = 0; is a global variable whose value, if set, is ap- plied to every output expression before it is >> 42 printed.
>> %
$PreRead $Post $PreRead $Post is a global variable whose value, if set, is ap- is a global variable whose value, if set, is ap- plied to the text or box form of every input plied to every output expression. expression before it is fed to the parser. (Not implemented yet)
$Pre $SyntaxHandler $Pre is a global variable whose value, if set, is ap- $SyntaxHandler plied to every input expression. is a global variable whose value, if set, is ap- plied to any input string that is found to con- Set Timing as the $Pre function, stores the en- tain a syntax error. lapsed time in a variable, stores just the result in (Not implemented yet) Out[$Line] and print a formated version show- ing the enlapsed time >> $Pre := (Print["[Processing In input...]"];#1)&
In[k] gives the kth line of input.
193 >> x = 1 >> 42 1 42
>> x = x + 1 >> % 2 >> 43; >> Do[In[2], {3}]
>> % >> x
5 >> 44
>> In[-1] 44
5 >> %1
>> Definition[In] 42
Attributes [In] = {Listable, Protected} >> %% In [6] = Definition [In] 44 In [5] = In [ − 1] >> Hold[Out[-1]] In [4] = x [ ] In [3] = Do In [2] , {3} Hold [%]
In [2] = x = x + 1 >> Hold[%4] In [1] = x = 1 Hold [%4]
>> Out[0] $Line Out [0]
$Line holds the current input line number.
>> $Line
>> $Line
>> $Line = 12;
>> 2 * 5 10
>> Out[13] 10
>> $Line = -1; Non − negativeintegerexpected.
Out
Out[k] %k gives the result of the kth input line. %, %%, etc. gives the result of the previous input line, of the line before the previous input line, etc.
194 27. Integer Functions
Integer Functions can work on integers of any size. Contents
SokalSneathDis- PowerMod .... 199 Combinatorial Functions 195 similarity . 197 PrimeQ ...... 199 Binomial ..... 195 Subsets ...... 197 DiceDissimilarity . 195 Quotient ..... 199 YuleDissimilarity . 197 JaccardDissimilarity 196 QuotientRemainder 199 Division-Related MatchingDissimi- Recurrence and Sum Functions ..... 197 larity ... 196 Functions ..... 199 CoprimeQ .... 198 Multinomial ... 196 Fibonacci ..... 199 EvenQ ...... 198 RogersTanimo- HarmonicNumber 200 GCD ...... 198 toDissimi- StirlingS1 ..... 200 LCM ...... 198 larity ... 196 StirlingS2 ..... 200 RussellRaoDissim- Mod ...... 198 ilarity ... 196 OddQ ...... 198
Combinatorial Functions >> Binomial[-10.5, -3.5] 0. Combinatorial Functions Combinatorics is an area of mathematics primar- ily concerned with counting, both as a means DiceDissimilarity and an end in obtaining results, and certain properties of finite structures. DiceDissimilarity[u, v] It is closely related to many other areas of mathe- returns the Dice dissimilarity between matics and has many applications ranging from the two boolean 1-D lists u and v, which logic to statistical physics, from evolutionary bi- is defined as (c_tf + c_ft) / (2 * c_tt + ology to computer science, etc. c_ft + c_tf), where n is len(u) and c_ij is the number of occurrences of u[k]=i and Binomial v[k]=j for kBinomial[n, k] >> DiceDissimilarity[{1, 0, 1, 1, gives the binomial coefficient n choose k. 0, 1, 1}, {0, 1, 1, 0, 0, 0, 1}] 1 >> Binomial[5, 3] 2 10 Binomial supports inexact numbers: >> Binomial[10.5,3.2] 165.286 Some special cases: >> Binomial[10, -2] 0
195 JaccardDissimilarity >> Multinomial[2, 3] 10 JaccardDissimilarity[u, v] returns the Jaccard-Needham dissimilar- ity between the two boolean 1-D lists u RogersTanimotoDissimilarity and v, which is defined as (c_tf + c_ft) / (c_tt + c_ft + c_tf), where n is len(u) and RogersTanimotoDissimilarity[u, v] c_ij is the number of occurrences of u[k]=i returns the Rogers-Tanimoto dissimilar- and v[k]=j for k>> JaccardDissimilarity[{1, 0, 1, + R) where n is len(u), c_ij is the num- 1, 0, 1, 1}, {0, 1, 1, 0, 0, 0, ber of occurrences of u[k]=i and v[k]=j for 1}] k> RogersTanimotoDissimilarity[{1, 3 0, 1, 1, 0, 1, 1}, {0, 1, 1, 0, 0, 0, 1}] MatchingDissimilarity 8 11 MatchingDissimilarity[u, v] returns the Matching dissimilarity be- tween the two boolean 1-D lists u and v, RussellRaoDissimilarity which is defined as (c_tf + c_ft) / n, where n is len(u) and c_ij is the number of occur- RussellRaoDissimilarity[u, v] rences of u[k]=i and v[k]=j for k>> MatchingDissimilarity[{1, 0, 1, which is defined as (n - c_tt) / c_tt where 1, 0, 1, 1}, {0, 1, 1, 0, 0, 0, n is len(u) and c_ij is the number of occur- 1}] rences of u[k]=i and v[k]=j for k> RussellRaoDissimilarity[{1, 0, 7 1, 1, 0, 1, 1}, {0, 1, 1, 0, 0, 0, 1}] Multinomial 5 7 Multinomial[n1, n2, ...] gives the multinomial coefficient (n1+ n2+...)!/(n1!n2!...). SokalSneathDissimilarity
>> Multinomial[2, 3, 4, 5] SokalSneathDissimilarity[u, v] 2 522 520 returns the Sokal-Sneath dissimilarity be- tween the two boolean 1-D lists u and v, >> Multinomial[] which is defined as R / (c_tt + R) where n 1 is len(u), c_ij is the number of occurrences of u[k]=i and v[k]=j for k> Multinomial[a, b, c] Binomial [a, a] Binomial [ a + b, b] Binomial [a + b + c, c]
Multinomial[n-k, k] is equivalent to Binomial [n, k].
196 >> SokalSneathDissimilarity[{1, 0, >> Subsets[{a, b, c, d, e}, {0, 5, 1, 1, 0, 1, 1}, {0, 1, 1, 0, 0, 2}] 0, 1}] {{} , {a, b} , {a, c} , {a, d} , {a, e} , 4 {b, c} , {b, d} , {b, e} , {c, d} , {c, 5 e} , {d, e} , {a, b, c, d} , {a, b, c, e} , {a, b, d, e} , {a, c, d, e} , {b, c, d, e}}
Subsets The 25th subset: >> Subsets[Range[5], All, {25}] Subsets[ ] list {{2, 4, 5}} finds a list of all possible subsets of list. Subsets[list, n] The odd-numbered subsets of {a,b,c,d} in reverse finds a list of all possible subsets contain- order: ing at most n elements. >> Subsets[{a, b, c, d}, All, {15, Subsets[list,{n}] 1, -2}] finds a list of all possible subsets contain- {{ } { } { } ing exactly n elements. b, c, d , a, b, d , c, d , Subsets[list,{min, max}] {b, c} , {a, c} , {d} , {b} , {}} finds a list of all possible subsets contain- ing between min and max elements. Subsets[list, spec, n] YuleDissimilarity finds a list of the first n possible subsets. Subsets[list, spec,{n}] YuleDissimilarity[u, v] finds the nth possible subset. returns the Yule dissimilarity between the two boolean 1-D lists u and v, which is All possible subsets (power set): defined as R / (c_tt * c_ff + R / 2) where n >> Subsets[{a, b, c}] is len(u), c_ij is the number of occurrences {{} , {a} , {b} , {c} , {a, of u[k]=i and v[k]=j for kAll possible subsets containing up to 2 elements: >> YuleDissimilarity[{1, 0, 1, 1, >> Subsets[{a, b, c, d}, 2] 0, 1, 1}, {0, 1, 1, 0, 0, 0, 1}] {{} , {a} , {b} , {c} , {d} , 6 {a, b} , {a, c} , {a, d} , 5 {b, c} , {b, d} , {c, d}} Subsets containing exactly 2 elements: Division-Related Functions >> Subsets[{a, b, c, d}, {2}] {{a, b} , {a, c} , {a, d} , Division-Related Function {b, c} , {b, d} , {c, d}} CoprimeQ The first 5 subsets containing 3 elements: >> Subsets[{a, b, c, d, e}, {3}, 5] CoprimeQ[x, y] {{a, b, c} , {a, b, d} , {a, tests whether x and y are coprime by } { } { }} b, e , a, c, d , a, c, e computing their greatest common divi- sor. All subsets with even length:
>> CoprimeQ[7, 9] True
>> CoprimeQ[-4, 9] True
197 >> CoprimeQ[12, 15] LCM False LCM[n1, n2, ...] CoprimeQ also works for complex numbers computes the least common multiple of >> CoprimeQ[1+2I, 1-I] the given integers. True
>> LCM[15, 20] >> CoprimeQ[4+2I, 6+3I] True 60
>> LCM[20, 30, 40, 50] >> CoprimeQ[2, 3, 5] 600 True
>> CoprimeQ[2, 4, 5] False Mod
Mod[x, m] EvenQ returns x modulo m.
EvenQ[x] >> Mod[14, 6] returns True if x is even, and False oth- 2 erwise. >> Mod[-3, 4] 1 >> EvenQ[4] True >> Mod[-3, -4] −3 >> EvenQ[-3] False >> Mod[5, 0] Theargument0shouldbenonzero. >> EvenQ[n] False Mod [5, 0]
GCD OddQ
GCD[n1, n2, ...] OddQ[x] computes the greatest common divisor of returns True if x is odd, and False other- the given integers. wise.
>> OddQ[-3] >> GCD[20, 30] 10 True
>> OddQ[0] >> GCD[10, y] [ ] False GCD 10, y
GCD is Listable: PowerMod >> GCD[4, {10, 11, 12, 13, 14}] {2, 1, 4, 1, 2} PowerMod[x, y, m] ∧ GCD does not work for rational numbers and computes x y modulo m. Gaussian integers yet. >> PowerMod[2, 10000000, 3] 1
198 >> PowerMod[3, -2, 10] Quotient 9 Quotient[m, n] >> PowerMod[0, -1, 2] computes the integer quotient of m and n. 0isnotinvertiblemodulo2. PowerMod [0, − 1, 2] >> Quotient[23, 7]
>> PowerMod[5, 2, 0] 3 Theargument0shouldbenonzero. PowerMod [5, 2, 0] QuotientRemainder PowerMod does not support rational coefficients (roots) yet. QuotientRemainder[m, n] computes a list of the quotient and re- PrimeQ mainder from division of m by n.
>> QuotientRemainder[23, 7] PrimeQ[ ] n { } returns True if n is a prime number. 3, 2
For very large numbers, PrimeQ uses proba- bilistic prime testing, so it might be wrong Recurrence and Sum Functions sometimes (a number might be composite even though PrimeQ says it is prime). The algorithm Recurrence and Sum Functions might be changed in the future. A recurrence relation is an equation that recur- >> PrimeQ[2] sively defines a sequence or multidimensional array of values, once one or more initial terms True are given; each further term of the sequence or >> PrimeQ[-3] array is defined as a function of the preceding True terms.
>> PrimeQ[137] Fibonacci True
>> PrimeQ[2 ^ 127 - 1] Fibonacci[n] True computes the nth Fibonacci number. All prime numbers between 1 and 100: >> Fibonacci[0] >> Select[Range[100], PrimeQ] 0 {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, >> Fibonacci[1] 61, 67, 71, 73, 79, 83, 89, 97} 1
>> Fibonacci[10] PrimeQ Listable: has attribute 55 >> PrimeQ[Range[20]] >> Fibonacci[200] {False, True, True, False, True, 280 571 172 992 510 140 037 ˜ False, True, False, False, False, ˜611 932 413 038 677 189 525 True, False, True, False, False, False, True, False, True, False} HarmonicNumber
HarmonicNumber[n] returns the nth harmonic number.
199 >> Table[HarmonicNumber[n], {n, 8}] { } 3 11 25 137 49 363 761 1, , , , , , , 2 6 12 60 20 140 280
>> HarmonicNumber[3.8] 2.03806
StirlingS1
StirlingS1[n, m] gives the Stirling number of the first kind ∧ $ _n m$.
Integer mathematical function, suitable for both symbolic and numerical manipulation. gives the number of permutations of n elements that con- tain exactly m cycles. >> StirlingS1[50, 1] −608 281 864 034 267 560 872 ˜ ˜252 163 321 295 376 887 552 ˜ ˜831 379 210 240 000 000 000
StirlingS2
StirlingS2[n, m] gives the Stirling number of the second ∧ kind _n m. returns the number of ways of partitioning a set of n elements into m non empty subsets. >> Table[StirlingS2[10, m], {m, 10}] {1, 511, 9 330, 34 105, 42 525 , 22 827, 5 880, 750, 45, 1}
200 28. List Functions
S-Expressions make up a core part of Mathics. The parsed and internal representation of an an S- Expression is nothing more than a list with possibliy nested elements. As a result, there about a hundred list functions. Contents
Cases ...... 206 Span (;;) ..... 210 Associations ...... 201 Count ...... 206 Take ...... 211 Association .... 201 DeleteCases .... 206 Rearranging and AssociationQ ... 202 Drop ...... 206 Restructuring Lists 211 Keys ...... 202 Extract ...... 206 Catenate ..... 211 Lookup ...... 202 First 206 Complement ... 211 Values ...... 202 ...... DeleteDuplicates . 211 Constructing Lists ... 202 FirstCase ..... 207 Gather ...... 212 Array ...... 203 FirstPosition ... 207 GatherBy ..... 212 ConstantArray .. 203 Last ...... 207 Intersection .... 212 Normal ...... 203 Length ...... 207 Join ...... 212 Permutations ... 203 MemberQ ..... 208 Range ...... 203 Most ...... 208 Partition ..... 212 Reap ...... 204 Part ...... 209 Reverse ...... 213 Sow ...... 204 Pick ...... 209 Riffle ...... 213 Table ...... 204 Prepend ..... 209 RotateLeft .... 213 Tuples ...... 205 PrependTo .... 209 RotateRight .... 214 Elements of Lists ... 205 ReplacePart .... 210 Tally ...... 214 Append ...... 205 Rest ...... 210 Union ...... 214 AppendTo .... 205 Select ...... 210
Associations >> Head[<|a -> x, b -> y, c -> z|>] Association Associations An Association maps keys to values and is sim- >> <|a -> x, b -> y|> ilar to a dictionary in Python; it is often sparse <|a− > x, b− > y|> in that their key space is much larger than the number of actual keys found in the collection. >> Association[{a -> x, b -> y}] <|a− > x, b− > y|> Association Associations can be nested: >> <|a -> x, b -> y, <|a -> z, d -> Association[key1 -> val1, key2 -> val2, t|>|> ...] <|key1 -> val1, key2 -> val2, ...|> <|a− > z, b− > y, d− > t|> represents an association between keys and values.
Association is the head of associations:
201 AssociationQ Values
AssociationQ[expr] Values[<|key1 -> val1, key2 -> val2, return True if expr is a valid Association ...|>] object, and False otherwise. return a list of the values vali in an asso- ciation. Values[{key1 -> val1, key2 -> val2, >> AssociationQ[<|a -> 1, b :> 2|>] ...}] True return a list of the vali in a list of rules.
>> AssociationQ[<|a, b|>] False >> Values[<|a -> x, b -> y|>] {x, y}
Keys >> Values[{a -> x, b -> y}] {x, y} Keys[<|key1 -> val1, key2 -> val2, Values automatically threads over lists: ...|>] >> Values[{<|a -> x, b -> y|>, {c return a list of the keys keyi in an associa- -> z, {}}}] tion. Keys[{key1 -> val1, key2 -> val2, ...}] {{x, y} , {z, {}}} return a list of the keyi in a list of rules. Values are listed in the order of their appearance: >> Values[{c -> z, b -> y, a -> x}] >> Keys[<|a -> x, b -> y|>] { } {a, b} z, y, x
>> Keys[{a -> x, b -> y}] {a, b} Constructing Lists
Keys automatically threads over lists: Constructing Lists >> Keys[{<|a -> x, b -> y|>, {w -> Functions for constructing lists of various sizes z, {}}}] and structure. {{a, b} , {w, {}}} Array Keys are listed in the order of their appearance: >> Keys[{c -> z, b -> y, a -> x}] Array[f , n] {c, b, a} returns the n-element list {f [1], ..., f [n]}. Array[f , n, a] Lookup returns the n-element list {f [a], ..., f [ a + n]}. Lookup[assoc, key] Array[f ,{n, m}, {a, b}] looks up the value associated with returns an n-by-m matrix created by ap- key in the association assoc, or Miss- plying f to indices ranging from (a, b) ing[KeyAbsent]. to (a + n, b + m). Array[f , dims, origins, h] returns an expression with the specified dimensions and index origins, with head h (instead of List).
>> Array[f, 4] { f [1] , f [2] , f [3] , f [4]}
202 >> Array[f, {2, 3}] Elements are differentiated by their position in {{ f [1, 1] , f [1, 2] , f [1, 3]} , list, not their value. >> Permutations[{a, b, b}] { f [2, 1] , f [2, 2] , f [2, 3]}} {{a, b, b} , {a, b, b} , {b, a, b} , >> Array[f, {2, 3}, 3] {b, b, a} , {b, a, b} , {b, b, a}} {{ f [3, 3] , f [3, 4] , f [3, 5]} , >> Permutations[{1, 2, 3}, 2] { f [4, 3] , f [4, 4] , f [4, 5]}} {{} , {1} , {2} , {3} , {1, 2} , {1, >> Array[f, {2, 3}, {4, 6}] 3} , {2, 1} , {2, 3} , {3, 1} , {3, 2}} {{ f [4, 6] , f [4, 7] , f [4, 8]} , >> Permutations[{1, 2, 3}, {2}] { f [5, 6] , f [5, 7] , f [5, 8]}} {{1, 2} , {1, 3} , {2, 1} , >> Array[f, {2, 3}, 1, Plus] {2, 3} , {3, 1} , {3, 2}} f [1, 1] + f [1, 2] + f [1, 3] + f [2, 1] + f [2, 2] + f [2, 3] Range
ConstantArray Range[n] returns a list of integers from 1 to n. Range[ , ] ConstantArray[expr, n] a b returns a list of n copies of expr. returns a list of integers from a to b.
>> Range[5] >> ConstantArray[a, 3] { } {a, a, a} 1, 2, 3, 4, 5
>> Range[-3, 2] >> ConstantArray[a, {2, 3}] {− − − } {{a, a, a} , {a, a, a}} 3, 2, 1, 0, 1, 2
>> Range[0, 2, 1/3] { } 1 2 4 5 Normal 0, , , 1, , , 2 3 3 3 3 Normal[expr_] Brings especial expressions to a normal Reap expression from different especial forms.
Reap[expr] gives the result of evaluating expr, to- Permutations gether with all values sown during this evaluation. Values sown with different Permutations[list] tags are given in different lists. gives all possible orderings of the items Reap[expr, pattern] in list. only yields values sown with a tag Permutations[list, n] matching pattern. Reap[expr] is equiva- gives permutations up to length n. lent to Reap[expr, _]. Permutations[list,{n}] Reap[expr,{pattern1, pattern2, ...}] gives permutations of length n. uses multiple patterns. Reap[expr, pattern, f ]
>> Permutations[{y, 1, x}] applies f on each tag and the cor- responding values sown in the form {{y, 1, x} , {y, x, 1} , {1, y, x} , f [tag, {e1, e2, ...}]. {1, x, y} , {x, y, 1} , {x, 1, y}}
203 >> Reap[Sow[3]; Sow[1]] Table {1, {{3, 1}}} Table[expr, n] >> Reap[Sow[2, {x, x, x}]; Sow[3, x generates a list of n copies of expr. ]; Sow[4, y]; Sow[4, 1], { Table[expr,{i, n}] _Symbol, _Integer, x}, f] generates a list of the values of expr when { {{ [ ] [ 4, f x, {2, 2, 2, 3} , f i runs from 1 to n. ]} { [ ]} Table[expr,{i, start, stop, step}] y, {4} , f 1, {4} , { [ ]}}} evaluates expr with i ranging from start to { } f x, 2, 2, 2, 3 stop, incrementing by step. Table[expr,{i,{e1, e2, ..., ei}}] Find the unique elements of a list, keeping their evaluates expr with i taking on the values order: e1, e2, ..., ei. >> Reap[Sow[Null, {a, a, b, d, c, a }], _, # &][[2]] >> Table[x, 3] { } a, b, d, c {x, x, x}
Sown values are reaped by the innermost match- >> n = 0; Table[n = n + 1, {5}] ing Reap: {1, 2, 3, 4, 5} >> Reap[Reap[Sow[a, x]; Sow[b, 1], _Symbol, Print["Inner: ", >> Table[i, {i, 4}] #1]&];, _, f] {1, 2, 3, 4} {Inner : {x [ ]}} Null, f 1, {b} >> Table[i, {i, 2, 5}] {2, 3, 4, 5} When no value is sown, an empty list is re- turned: >> Table[i, {i, 2, 6, 2}] >> Reap[x] {2, 4, 6} {x, {}} >> Table[i, {i, Pi, 2 Pi, Pi / 2}] { } 3Pi Pi, , 2Pi Sow 2
>> Table[x^2, {x, {a, b, c}}] Sow[e] { } 2 2 2 sends the value e to the innermost Reap. a , b , c Sow[e, tag] sows e using tag. Sow[e] is equivalent to Table supports multi-dimensional tables: Sow[e, Null]. >> Table[{i, j}, {i, {a, b}}, {j, Sow[e,{tag1, tag2, ...}] 1, 2}] uses multiple tags. {{{a, 1} , {a, 2}} , {{b, 1} , {b, 2}}}
Tuples
Tuples[list, n] returns a list of all n-tuples of elements in list. Tuples[{list1, list2, ...}] returns a list of tuples with elements from the given lists.
204 >> Tuples[{a, b, c}, 2] AppendTo {{a, a} , {a, b} , {a, c} , {b, a} , {b, b} , {b, c} , {c, a} , {c, b} , {c, c}} AppendTo[s, item] append item to value of s and sets s to the >> Tuples[{}, 2] result. {}
>> s = {}; >> Tuples[{a, b, c}, 0] {{}} >> AppendTo[s, 1] {1} >> Tuples[{{a, b}, {1, 2, 3}}] >> s {{a, 1} , {a, 2} , {a, 3} , {1} {b, 1} , {b, 2} , {b, 3}} Append works on expressions with heads other The head of list need not be List: than List: >> Tuples[f[a, b, c], 2] >> y = f[]; { f [a, a] , f [a, b] , f [a, c] , f [b, a] , f [b, b] , f [b, c] , >> AppendTo[y, x] f [c, a] , f [c, b] , f [c, c]} f [x]
However, when specifying multiple expres- >> y sions, List is always used: f [x] >> Tuples[{f[a, b], g[c, d]}] {{a, c} , {a, d} , {b, c} , {b, d}} Cases
Elements of Lists Cases[list, pattern] returns the elements of list that match pat- Elements of Lists tern. Functions for accessing elements of lists using Cases[list, pattern, ls] either indices, positions, or patterns of criteria. returns the elements matching at level- spec ls. Cases[list, pattern, Heads->bool] Append Match including the head of the expres- sion in the search. Append[expr, elem] returns expr with elem appended. >> Cases[{a, 1, 2.5, "string"}, _Integer|_Real]
>> Append[{1, 2, 3}, 4] {1, 2.5} {1, 2, 3, 4} >> Cases[_Complex][{1, 2I, 3, 4-I, 5}] Append works on expressions with heads other than List: {2I, 4 − I} >> Append[f[a, b], c] Find symbols among the elements of an expres- f [a, b, c] sion: Unlike Join, Append does not flatten lists in >> Cases[{b, 6, \[Pi]}, _Symbol] item: {b, Pi} >> Append[{a, b}, {c, d}] Also include the head of the expression in the {a, b, {c, d}} previous search:
205 >> Cases[{b, 6, \[Pi]}, _Symbol, >> Drop[{a, b, c, d}, 3] Heads -> True] {d} {List, b, Pi} >> Drop[{a, b, c, d}, -2] {a, b} Count >> Drop[{a, b, c, d, e}, {2, -2}] { } Count[list, pattern] a, e returns the number of times pattern ap- Drop a submatrix: pears in list. >> A = Table[i*10 + j, {i, 4}, {j, Count[list, pattern, ls] 4}] counts the elements matching at level- spec ls. {{11, 12, 13, 14} , {21, 22, 23, 24} , {31, 32, 33, 34} , {41, 42, 43, 44}}
>> Count[{3, 7, 10, 7, 5, 3, 7, 10}, 3] >> Drop[A, {2, 3}, {2, 3}] {{ } { }} 2 11, 14 , 41, 44
>> Count[{{a, a}, {a, a, a}, a}, a, {2}] Extract 5 Extract[expr, list] extracts parts of expr specified by list. DeleteCases Extract[expr,{list1, list2, ...}] extracts a list of parts. DeleteCases[list, pattern] returns the elements of list that do not Extract[expr, i, j, ...] is equivalent to Part match pattern. [expr,{i, j, ...}]. DeleteCases[ , , ] list pattern levelspec >> Extract[a + b + c, {2}] removes all parts of $list on levels spec- b ified by levelspec that match pattern (not fully implemented). >> Extract[{{a, b}, {c, d}}, {{1}, DeleteCases[list, pattern, levelspec, n] {2, 2}}] removes the first n parts of list that match {{a, b} , d} pattern.
>> DeleteCases[{a, 1, 2.5, "string First "}, _Integer|_Real] { } a, string First[expr] returns the first element in expr. >> DeleteCases[{a, b, 1, c, 2, 3}, _Symbol] First[expr] is equivalent to expr[[1]]. {1, 2, 3} >> First[{a, b, c}] a
Drop >> First[a + b + c] a
Drop[expr, n] >> First[x] returns expr with the first n leaves re- Nonatomicexpressionexpected. moved. First [x]
206 FirstCase Last
FirstCase[{e1, e2, ...}, pattern] Last[expr] gives the first ei to match pattern, or returns the last element in expr. $Missing[“NotFound”]$ if none match- ing pattern is found. Last[expr] is equivalent to expr[[-1]]. FirstCase[{e1,e2, ...}, pattern -> rhs] >> Last[{a, b, c}] gives the value of rhs corresponding to c the first ei to match pattern. FirstCase[expr, pattern, default] >> Last[x] gives default if no element matching pat- Nonatomicexpressionexpected. tern is found. Last [x] FirstCase[expr, pattern, default, levelspec] finds only objects that appear on levels specified by levelspec. Length FirstCase[pattern] represents an operator form of FirstCase that can be applied to an expression. Length[expr] returns the number of leaves in expr.
FirstPosition Length of a list: >> Length[{1, 2, 3}] FirstPosition[expr, pattern] 3 gives the position of the first element Length operates on the FullForm of expressions: in expr that matches pattern, or Miss- >> Length[Exp[x]] ing[“NotFound”] if no such element is found. 2 FirstPosition[ , , ] expr pattern default >> FullForm[Exp[x]] gives default if no element matching pat- Power [E, x] tern is found. FirstPosition[expr, pattern, default, The length of atoms is 0: levelspec] >> Length[a] finds only objects that appear on levels specified by levelspec. 0 Note that rational and complex numbers are >> FirstPosition[{a, b, a, a, b, c, atoms, although their FullForm might suggest b}, b] the opposite: >> Length[1/3] {2} 0 >> FirstPosition[{{a, a, b}, {b, a, a}, {a, b, a}}, b] >> FullForm[1/3] Rational [1, 3] {1, 3}
>> FirstPosition[{x, y, z}, b] MemberQ Missing [NotFound]
∧ Find the first position at which x 2 to appears: MemberQ[list, pattern] >> FirstPosition[{1 + x^2, 5, x^4, returns True if pattern matches any ele- a + (1 + x^2)^2}, x^2] ment of list, or False otherwise. {1, 2} >> MemberQ[{a, b, c}, b] True
207 >> MemberQ[{a, b, c}, d] >> M = {{a, b}, {c, d}}; False >> M[[1, 2]] >> MemberQ[{"a", b, f[x]}, _? b NumericQ] You can use Span to specify a range of parts: False >> {1, 2, 3, 4}[[2;;4]] >> MemberQ[_List][{{}}] {2, 3, 4} True >> {1, 2, 3, 4}[[2;;-1]] {2, 3, 4} Most A list of parts extracts elements at certain in- Most[expr] dices: returns expr with the last element re- >> {a, b, c, d}[[{1, 3, 3}]] moved. {a, c, c}
Most[expr] is equivalent to expr[[;;-2]]. Get a certain column of a matrix: >> >> Most[{a, b, c}] B = {{a, b, c}, {d, e, f}, {g, h , i}}; {a, b}
>> B[[;;, 2]] >> Most[a + b + c] { } a + b b, e, h
>> Most[x] Extract a submatrix of 1st and 3rd row and the Nonatomicexpressionexpected. two last columns: >> B = {{1, 2, 3}, {4, 5, 6}, {7, Most [x] 8, 9}};
>> B[[{1, 3}, -2;;-1]] Part {{2, 3} , {8, 9}}
Part[expr, i] The 3d column of a matrix: returns part i of expr. >> {{a, b, c}, {d, e, f}, {g, h, i }}[[All, 3]] Extract an element from a list: {c, f , i} >> A = {a, b, c, d}; Further examples: >> A[[3]] >> (a+b+c+d)[[-1;;-2]] c 0 Negative indices count from the end: >> x[[2]] >> {a, b, c}[[-2]] Partspecificationislongerthandepthofobject. b x [[2]] Part can be applied on any expression, not nec- essarily lists. Assignments to parts are possible: >> >> (a + b + c)[[2]] B[[;;, 2]] = {10, 11, 12} b {10, 11, 12} expr[[0]] gives the head of expr: >> B >> (a + b + c)[[0]] Plus >> B[[;;, 3]] = 13 13 Parts of nested lists:
208 >> B Prepend
>> B[[1;;-2]] = t; Prepend[expr, item] returns expr with item prepended to its >> B leaves. Prepend[ ] >> F = Table[i*j*k, {i, 1, 3}, {j, expr 1, 3}, {k, 1, 3}]; Prepend[elem][expr] is equivalent to Prepend[expr,elem].
>> F[[;; All, 2 ;; 3, 2]] = t; Prepend is similar to Append, but adds item to >> F the beginning of expr: >> Prepend[{2, 3, 4}, 1] >> F[[;; All, 1 ;; 2, 3 ;; 3]] = k; {1, 2, 3, 4}
>> F Prepend works on expressions with heads other Of course, part specifications have precedence than List: over most arithmetic operations: >> Prepend[f[b, c], a] >> A[[1]] + B[[2]] + C[[3]] // Hold f [a, b, c] // FullForm Unlike Join, Prepend does not flatten lists in Hold [Plus [Part [A, 1] , item: Part [B, 2] , Part [C, 3]]] >> Prepend[{c, d}, {a, b}] {{a, b} , c, d} Pick PrependTo Pick[list, sel] returns those items in list that are True in sel. PrependTo[s, item] Pick[list, sel, patt] prepends item to value of s and sets s to returns those items in list that match patt the result. in sel. Assign s to a list >> Pick[{a, b, c}, {False, True, >> s = {1, 2, 4, 9} False}] {1, 2, 4, 9} {b} Add a new value at the beginning of the list: >> Pick[f[g[1, 2], h[3, 4]], {{True >> PrependTo[s, 0] , False}, {False, True}}] { } [ ] 0, 1, 2, 4, 9 f g [1] , h [4] The value assigned to s has changed:
>> Pick[{a, b, c, d, e}, {1, 2, >> s 3.5, 4, 5.5}, _Integer] {0, 1, 2, 4, 9} { } a, b, d PrependTo works with a head other than List: >> y = f[a, b, c];
>> PrependTo[y, x] f [x, a, b, c]
>> y f [x, a, b, c]
209 ReplacePart Rest[expr] is equivalent to expr[[2;;]]. >> Rest[{a, b, c}] ReplacePart[expr, i -> new] {b, c} replaces part i in expr with new. ReplacePart[expr, {{i, j} -> e1,{k, >> Rest[a + b + c] l} -> e2}] b + c replaces parts i and j with e1, and parts k >> Rest[x] and l with e2. Nonatomicexpressionexpected.
>> ReplacePart[{a, b, c}, 1 -> t] Rest [x] {t, b, c}
>> ReplacePart[{{a, b}, {c, d}}, Select {2, 1} -> t] Select[{ , , ...}, ] {{a, b} , {t, d}} e1 e2 f returns a list of the elements ei for which
>> ReplacePart[{{a, b}, {c, d}}, f [ei] returns True. {{2, 1} -> t, {1, 1} -> t}] {{t, b} , {t, d}} Find numbers greater than zero: >> Select[{-3, 0, 1, 3, a}, #>0&] >> ReplacePart[{a, b, c}, {{1}, {1, 3} {2}} -> t] Select {t, t, c} works on an expression with any head: >> Select[f[a, 2, 3], NumberQ] Delayed rules are evaluated once for each re- f [2, 3] placement: >> n = 1; >> Select[a, True] Nonatomicexpressionexpected. >> ReplacePart[{a, b, c, d}, {{1}, Select [a, True] {3}} :> n++] {1, b, 2, d} Span (;;) Non-existing parts are simply ignored: >> ReplacePart[{a, b, c}, 4 -> t] { } Span a, b, c is the head of span ranges like 1;;3. You can replace heads by replacing part 0: >> >> ReplacePart[{a, b, c}, 0 -> ;; // FullForm Times] Span [1, All] abc >> 1;;4;;2 // FullForm (This is equivalent to Apply.) Span [1, 4, 2] Negative part numbers count from the end: >> 2;;-2 // FullForm >> ReplacePart[{a, b, c}, -1 -> t] Span [2, − 2] {a, b, t}
>> ;;3 // FullForm Span 1, 3 Rest [ ]
Rest[expr] returns expr with the first element re- moved.
210 Take The sets all, e1, etc can have any head, which must all match. The returned expression has the Take[expr, n] same head as the input expressions. The expres- returns expr with all but the first n leaves sion will be sorted and each element will only removed. occur once. >> Complement[{a, b, c}, {a, c}]
>> Take[{a, b, c, d}, 3] {b} {a, b, c} >> Complement[{a, b, c}, {a, c}, {b
>> Take[{a, b, c, d}, -2] }] {c, d} {}
>> Take[{a, b, c, d, e}, {2, -2}] >> Complement[f[z, y, x, w], f[x], { } f[x, z]] b, c, d [ ] f w, y Take a submatrix:
>> A = {{a, b, c}, {d, e, f}}; >> Complement[{c, b, a}] {a, b, c} >> Take[A, 2, 2] {{a, b} , {d, e}}
Take a single column: DeleteDuplicates >> Take[A, All, {2}] {{b} , {e}} DeleteDuplicates[list] deletes duplicates from list. DeleteDuplicates[list, test] Rearranging and Restructuring deletes elements from list based on whether the function test yields True on Lists pairs of elements. DeleteDuplicates does not change the order of Rearranging and Restructuring Lists the remaining elements. These functions reorder and rearrange lists.
>> DeleteDuplicates[{1, 7, 8, 4, 3, Catenate 4, 1, 9, 9, 2, 1}] {1, 7, 8, 4, 3, 9, 2} Catenate[{l1, l2, ...}] concatenates the lists l1, l2, ... >> DeleteDuplicates[{3,2,1,2,3,4}, Less]
>> Catenate[{{1, 2, 3}, {4, 5}}] {3, 2, 1} {1, 2, 3, 4, 5} Gather Complement Gather[list, test] list Complement[all, e1, e2, ...] gathers leaves of into sub lists of items that are the same according to test. returns an expression containing the ele- Gather[list] ments in the set all that are not in any of gathers leaves of list into sub lists of items e1, e2, etc. Complement[all, e1, e2, ..., SameTest-> that are the same. test] applies test to the elements in all and each The order of the items inside the sub lists is the of the ei to determine equality. same as in the original list.
211 >> Gather[{1, 7, 3, 7, 2, 3, 9}] >> Intersection[{{a, b}, {x, y}}, {{1} , {7, 7} , {3, 3} , {2} , {9}} {{x, x}, {x, y}, {x, z}}] {{x, y}} >> Gather[{1/3, 2/6, 1/9}] {{ } { }} 1 1 1 >> Intersection[{c, b, a}] , , 3 3 9 {a, b, c}
>> Intersection[{1, 2, 3}, {2, 3, GatherBy 4}, SameTest->Less] {3} GatherBy[list, f ] gathers leaves of list into sub lists of items whose image under $f identical. Join GatherBy[list,{f , g, ...}] gathers leaves of list into sub lists of items Join[l1, l2] whose image under $f identical. Then, concatenates the lists l1 and l2. gathers these sub lists again into sub sub lists, that are identical under $g. Join concatenates lists: >> Join[{a, b}, {c, d, e}] >> GatherBy[{{1, 3}, {2, 2}, {1, {a, b, c, d, e} 1}}, Total] >> Join[{{a, b}, {c, d}}, {{1, 2}, {{{1, 3} , {2, 2}} , {{1, 1}}} {3, 4}}] >> GatherBy[{"xy", "abc", "ab"}, {{a, b} , {c, d} , {1, 2} , {3, 4}} StringLength] {{xy, ab} , {abc}} The concatenated expressions may have any head:
>> GatherBy[{{2, 0}, {1, 5}, {1, >> Join[a + b, c + d, e + f] 0}}, Last] a + b + c + d + e + f {{{2, 0} , {1, 0}} , {{1, 5}}} However, it must be the same for all expressions:
>> GatherBy[{{1, 2}, {2, 1}, {3, >> Join[a + b, c * d] 5}, {5, 1}, {2, 2, 2}}, {Total, HeadsPlusandTimesareexpectedtobethesame. Length}] Join [a + b, cd] {{{{1, 2} , {2, 1}}} , {{{3, 5}}} , {{{5, 1}} , {{2, 2, 2}}}} Partition
Intersection Partition[list, n] partitions list into sublists of length n. Intersection[a, b, ...] Parition[list, n, d] gives the intersection of the sets. The re- partitions list into sublists of length n sulting list will be sorted and each ele- which overlap d indicies. ment will only occur once. >> Partition[{a, b, c, d, e, f}, 2]
>> Intersection[{1000, 100, 10, 1}, {{a, b} , {c, d} , {e, f }} {1, 5, 10, 15}] >> Partition[{a, b, c, d, e, f}, 3, { } 1, 10 1] {{a, b, c} , {b, c, d} , {c, d, e} , {d, e, f }}
212 Reverse RotateLeft
Reverse[expr] RotateLeft[expr] reverses the order of expr’s items (on the rotates the items of expr’ by one item to top level) the left. Reverse[expr, n] RotateLeft[expr, n] reverses the order of items in expr on level rotates the items of expr’ by n items to the n left. Reverse[expr,{n1, n2, ...}] RotateLeft[expr,{n1, n2, ...}] reverses the order of items in expr on lev- rotates the items of expr’ by n1 items to els n1, n2, ... the left at the first level, by n2 items to the left at the second level, and so on.
>> Reverse[{1, 2, 3}] {3, 2, 1} >> RotateLeft[{1, 2, 3}] {2, 3, 1} >> Reverse[x[a, b, c]] x [c, b, a] >> RotateLeft[Range[10], 3] {4, 5, 6, 7, 8, 9, 10, 1, 2, 3} >> Reverse[{{1, 2}, {3, 4}}, 1] {{3, 4} , {1, 2}} >> RotateLeft[x[a, b, c], 2] x [c, a, b] >> Reverse[{{1, 2}, {3, 4}}, 2] {{2, 1} , {4, 3}} >> RotateLeft[{{a, b, c}, {d, e, f }, {g, h, i}}, {1, 2}] >> Reverse[{{1, 2}, {3, 4}}, {1, {{ f , d, e} , {i, g, h} , {c, a, b}} 2}] {{4, 3} , {2, 1}} RotateRight Riffle RotateRight[expr] rotates the items of expr’ by one item to Riffle[list, x] the right. inserts a copy of x between each element RotateRight[expr, n] of list. rotates the items of expr’ by n items to the Riffle[{a1, a2, ...}, {b1, b2, ...}] right. interleaves the elements of both lists, re- RotateRight[expr,{n1, n2, ...}] turning {a1, b1, a2, b2, ...}. rotates the items of expr’ by n1 items to the right at the first level, by n2 items to >> Riffle[{a, b, c}, x] the right at the second level, and so on. {a, x, b, x, c} >> RotateRight[{1, 2, 3}] >> Riffle[{a, b, c}, {x, y, z}] {3, 1, 2} {a, x, b, y, c, z} >> RotateRight[Range[10], 3] >> Riffle[{a, b, c, d, e, f}, {x, y {8, 9, 10, 1, 2, 3, 4, 5, 6, 7} , z}] {a, x, b, y, c, z, d, x, e, y, f } >> RotateRight[x[a, b, c], 2] x [b, c, a]
>> RotateRight[{{a, b, c}, {d, e, f }, {g, h, i}}, {1, 2}] {{h, i, g} , {b, c, a} , {e, f , d}}
213 Tally
Tally[list] counts and returns the number of oc- curences of objects and returns the result as a list of pairs {object, count}. Tally[list, test] counts the number of occurences of ob- jects and uses $test to determine if two objects should be counted in the same bin.
>> Tally[{a, b, c, b, a}] {{a, 2} , {b, 2} , {c, 1}}
Tally always returns items in the order as they first appear in list: >> Tally[{b, b, a, a, a, d, d, d, d , c}] {{b, 2} , {a, 3} , {d, 4} , {c, 1}}
Union
Union[a, b, ...] gives the union of the given set or sets. The resulting list will be sorted and each element will only occur once.
>> Union[{5, 1, 3, 7, 1, 8, 3}] {1, 3, 5, 7, 8}
>> Union[{a, b, c}, {c, d, e}] {a, b, c, d, e}
>> Union[{c, b, a}] {a, b, c}
>> Union[{{a, 1}, {b, 2}}, {{c, 1}, {d, 3}}, SameTest->(SameQ[Last [#1],Last[#2]]&)] {{b, 2} , {c, 1} , {d, 3}}
>> Union[{1, 2, 3}, {2, 3, 4}, SameTest->Less] {1, 2, 2, 3, 4}
214 29. Statistics, Moments, and Generating Functions
Moments or combinations of moments are used to summarize a distribution or data. Mean is used to in- dicate a center location, variance and standard deviation are used to indicate dispersion and covariance, and correlation to indicate dependence. Contents
Special Moments ... 215 Skewness ..... 216 Basic statistics ..... 215 Correlation .... 215 StandardDeviation 216 Median ...... 215 Covariance .... 216 Variance ..... 216 Quantile ..... 215 Kurtosis ..... 216
Basic statistics >> Quantile[Range[11], 1/3] 4 Basic statistic >> Quantile[Range[16], 1/4] Median 5
Median[list] Special Moments returns the median of list. Special Moment >> Median[{26, 64, 36}] 36 Correlation For lists with an even number of elements, Me- dian returns the mean of the two middle values: Correlation[a, b] >> Median[{-11, 38, 501, 1183}] computes Pearson’s correlation of two 539 equal-sized vectors a and b. 2 Passing a matrix returns the medians of the re- An example from Wikipedia: spective columns: >> Correlation[{10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5}, {8.04, >> Median[{{100, 1, 10, 50}, {-1, 1, -2, 2}}] 6.95, 7.58, 8.81, 8.33, 9.96, { } 7.24, 4.26, 10.84, 4.82, 5.68}] 99 , 1, 4, 26 0.816421 2
Covariance Quantile Covariance[a, b] Quantile[list, q] computes the covariance between the returns the qth quantile of list. equal-sized vectors a and b.
215 >> Covariance[{0.2, 0.3, 0.1}, >> StandardDeviation[{{1, 10}, {-1, {0.3, 0.3, -0.2}] 20}}] {√ √ } 0.025 2, 5 2
Kurtosis Variance Kurtosis[list] gives the Pearson measure of kurtosis for Variance[list] list (a measure of existing outliers). computes the variance of $list. list may consist of numerical values or symbols. Numerical values may be real or com- >> Kurtosis[{1.1, 1.2, 1.4, 2.1, 2.4}] plex. Variance[{{a1, a2, ...}, {b1, b2, ...}, ...}] will yield 1.42098 {Variance[{a1, b1, ...}, Variance[{a2, b2, ...}], ...}.
Skewness >> Variance[{1, 2, 3}] 1
Skewness[list] >> Variance[{7, -5, 101, 3}] gives Pearson’s moment coefficient of 7 475 skewness for list (a measure for estimat- 3 ing the symmetry of a distribution). >> Variance[{1 + 2I, 3 - 10I}]
>> Skewness[{1.1, 1.2, 1.4, 2.1, 74 2.4}] >> Variance[{a, a}] 0.407041 0
>> Variance[{{1, 3, 5}, {4, 10, 100}}] StandardDeviation { } 9 49 9 025 , , StandardDeviation[list] 2 2 2 computes the standard deviation of $list. list may consist of numerical values or symbols. Numerical values may be real or complex. StandardDeviation[{{a1, a2, ...}, {b1, b2, ...}, ...}] will yield {StandardDeviation[{a1, b1, ...}, StandardDeviation[{a2, b2, ...}], ...}.
>> StandardDeviation[{1, 2, 3}] 1
>> StandardDeviation[{7, -5, 101, 100}] √ 13 297 2
>> StandardDeviation[{a, a}] 0
216 30. Integer and Number-Theoretical Functions
Contents
Integers ...... 228 LogisticSigmoid . 236 Algebraic Manipulation 218 Integrate ..... 228 Sec ...... 236 Apart ...... 218 Limit ...... 229 Sech ...... 236 Cancel ...... 218 O ...... 229 Sin ...... 236 Coefficient .... 219 Reals ...... 229 Sinh ...... 236 CoefficientArrays . 219 Root ...... 229 Tan ...... 236 CoefficientList .. 220 Series ...... 229 Tanh ...... 236 Collect ...... 220 SeriesData .... 229 Integer Functions ... 236 Denominator ... 220 Solve ...... 230 BitLength ..... 237 Expand ...... 221 Differential Equations 230 Ceiling ...... 237 ExpandAll .... 221 C ...... 231 DigitCount .... 237 ExpandDenomi- DSolve ...... 231 nator ... 221 Floor ...... 237 Exponential, Exponent ..... 222 FromDigits .... 238 Trigonometric IntegerDigits ... 238 Factor ...... 222 and Hyperbolic IntegerLength .. 239 FactorTermsList . 222 Functions ..... 231 IntegerReverse .. 239 FullSimplify ... 222 AnglePath .... 232 IntegerString ... 239 MinimalPolynomial 223 AngleVector ... 232 Linear algebra ..... 239 Numerator .... 223 ArcCos ...... 232 BrayCurtisDistance 239 PolynomialQ ... 223 ArcCosh ..... 232 CanberraDistance 240 PowerExpand .. 223 ArcCot ...... 232 ChessboardDistance 240 Simplify ..... 223 ArcCoth ..... 233 CosineDistance 240 Together ..... 224 ArcCsc ...... 233 .. Variables ..... 224 ArcCsch ..... 233 Cross ...... 240 Mathematical Constants 224 ArcSec ...... 233 DesignMatrix ... 240 Catalan ...... 224 ArcSech ...... 233 Det ...... 240 ComplexInfinity . 224 ArcSin ...... 233 Eigensystem ... 241 Degree ...... 224 ArcSinh ...... 233 Eigenvalues ... 241 E ...... 224 ArcTan ...... 234 Eigenvectors ... 241 EulerGamma ... 225 ArcTanh ..... 234 EuclideanDistance 242 Glaisher ..... 225 Cos ...... 234 Inverse ...... 242 GoldenRatio ... 225 Cosh ...... 234 LeastSquares ... 242 Indeterminate .. 225 Cot ...... 234 LinearModelFit .. 242 Infinity ...... 225 Coth ...... 234 LinearSolve .... 243 Khinchin ..... 225 Csc ...... 234 ManhattanDistance 243 Pi ...... 225 Csch ...... 234 MatrixExp .... 243 Calculus ...... 226 Exp ...... 235 MatrixPower ... 243 Complexes .... 226 Haversine .... 235 MatrixRank .... 243 D ...... 226 InverseHaversine . 235 Norm ...... 244 Derivative (’) ... 227 Log ...... 235 Normalize .... 244 DiscreteLimit ... 227 Log10 ...... 235 NullSpace .... 244 FindRoot ..... 228 Log2 ...... 235 PseudoInverse .. 244
217 QRDecomposition 244 FactorInteger ... 246 RandomPrime .. 248 RowReduce .... 245 FractionalPart .. 246 Random number SingularValueDe- FromContinued- generation .... 248 composition 245 Fraction .. 246 Random ..... 248 SquaredEuclide- IntegerExponent . 246 RandomChoice .. 249 anDistance 245 MantissaExponent 247 RandomComplex . 249 Tr ...... 245 NextPrime .... 247 RandomInteger .. 249 VectorAngle ... 245 PartitionsP .... 247 RandomReal ... 250 Number theoretic Prime ...... 247 RandomSample . 250 functions ..... 245 PrimePi ...... 247 $RandomState .. 250 ContinuedFraction 245 PrimePowerQ .. 247 SeedRandom ... 251 Divisors ..... 246
Algebraic Manipulation Cancel
Algebraic Manipulation Cancel[expr] cancels out common factors in numera- Apart tors and denominators.
>> Cancel[x / x ^ 2] Apart[expr] 1 writes expr as a sum of individual frac- tions. x Apart[expr, var] Cancel threads over sums: treats var as the main variable. >> Cancel[x / x ^ 2 + y / y ^ 2] 1 1 >> Apart[1 / (x^2 + 5x + 6)] + x y 1 − 1 2 + x 3 + x >> Cancel[f[x] / x + x * f[x] / x ^ 2] When several variables are involved, the results can be different depending on the main variable: 2 f [x] >> Apart[1 / (x^2 - y^2), x] x − ( 1 ) ( 1 ) + − 2y x + y 2y x y Coefficient
>> Apart[1 / (x^2 - y^2), y] Coefficient[expr, form] ( 1 ) ( 1 ) + − returns the coefficient of form in the poly- 2x x + y 2x x y nomial expr. Coefficient[expr, form, n] Apart is Listable: ∧ return the coefficient of form n in expr. >> Apart[{1 / (x^2 + 5x + 6)}] { } 1 1 − >> Coefficient[(x + y)^4, (x^2)* (y 2 + x 3 + x ^2)] But it does not touch other expressions: 6 >> Sin[1 / (x ^ 2 - y ^ 2)] // >> Coefficient[a x^2 + b y^3 + c x Apart [ ] + d y + 5, x] 1 c Sin x2 − y2 >> Coefficient[(x + 3 y)^5, x] 405y4
218 >> Coefficient[(x + 3 y)^5, x * y >> CoefficientArrays[(x+y+Sin[z]) ^4] ^3, {x,y}] { { 405 Sin [z]3 , 3Sin [z]2 , 3Sin [ } >> Coefficient[(x + 2)/(y - 3)+ (x 2 {{ } + 3)/(y - 2), x] z] , 3Sin [z] , 6Sin [z] , { }} {{{ } 1 1 0, 3Sin [z] , 1, 3 , } + −3 + y −2 + y {0, 3}} , {{0, 0} , {0, 1}}}
>> Coefficient[x*Cos[x + 3] + 6*y, >> CoefficientArrays[(x + y + Sin[z x] ])^3, {x, z}] Cos [3 + x] (x+y+Sin[z])3isnotapolynomialin{x, z} [ >> Coefficient[(x + 1)^3, x, 2] CoefficientArrays 3 ( ) ] 3 x + y + Sin [z] , {x, z} >> Coefficient[a x^2 + b y^3 + c x + d y + 5, y, 3] b CoefficientList Find the free term in a polynomial: >> Coefficient[(x + 2)^3 + (x + 3) CoefficientList[poly, var] ^2, x, 0] returns a list of coefficients of powers of 17 var in poly, starting with power 0. CoefficientList[poly, {var1, var2, >> Coefficient[(x + 2)^3 + (x + 3) ...}] ^2, y, 0] returns an array of coefficients of the vari. (2 + x)3 + (3 + x)2 >> CoefficientList[(x + 3)^5, x] >> Coefficient[a x^2 + b y^3 + c x {243, 405, 270, 90, 15, 1} + d y + 5, x, 0] >> CoefficientList[(x + y)^4, x] 5 + by3 + dy { } y4, 4y3, 6y2, 4y, 1
CoefficientArrays >> CoefficientList[a x^2 + b y^3 + c x + d y + 5, x] { } CoefficientArrays[polys, vars] 5 + by3 + dy, c, a returns a list of arrays of coefficients of the variables vars in the polynomial poly. >> CoefficientList[(x + 2)/(y - 3)+ x/(y - 2), x] >> CoefficientArrays[1 + x^3, x] { } 2 1 1 {1, {0} , {{0}} , {{{1}}}} , + −3 + y −3 + y −2 + y
>> CoefficientArrays[1 + x y+ x^3, >> CoefficientList[(x + y)^3, z] {x, y}] {( ) } 3 {1, {0, 0} , {{0, 1} , {0, 0}} , {{{1, x + y 0} , {0, 0}} , {{0, 0} , {0, 0}}}} >> CoefficientList[a x^2 + b y^3 +
>> CoefficientArrays[{1 + x^2, x y c x + d y + 5, {x, y}] }, {x, y}] {{5, d, 0, b} , {c, 0, 0, 0} , {a, 0, 0, 0}} {{1, 0} , {{0, 0} , {0, 0}} , {{{1, 0} , {0, 0}} , {{0, 1} , {0, 0}}}}
219 >> CoefficientList[(x - 2 y + 3 z) Denominator ^3, {x, y, z}] {{{0, 0, 0, 27} , {0, 0, − 54, 0} , Denominator[expr] {0, 36, 0, 0} , {−8, 0, 0, 0}} , {{0, gives the denominator in expr. 0, 27, 0} , {0, − 36, 0, 0} , {12, >> Denominator[a / b] 0, 0, 0} , {0, 0, 0, 0}} , {{0, 9, 0, b 0} , {−6, 0, 0, 0} , {0, 0, 0, 0} , {0, 0, 0, 0}} , {{1, 0, 0, 0} , {0, 0, >> Denominator[2 / 3] 0, 0} , {0, 0, 0, 0} , {0, 0, 0, 0}}} 3
>> Denominator[a + b] 1 Collect
Collect[expr, x] Expand Expands expr and collect together terms having the same power of x. Expand[expr] Collect[expr,{x_1, x_2, ...}] expands out positive integer powers and Expands expr and collect together terms products of sums in expr, as well as having the same powers of x_1, x_2, .... trigonometric identities. Collect[expr,{x_1, x_2, ...}, filter] Expand[expr, target] After collect the terms, applies filter to just expands those parts involving target. each coefficient.
>> Expand[(x + y)^ 3] >> Collect[(x+y)^3, y] 3 2 2 3 x3 + 3x2y + 3xy2 + y3 x + 3x y + 3xy + y
>> Expand[(a + b)(a + c + d)] >> Collect[2 Sin[x z] (x+2 y^2 + Sin[y] x), y] a2 + ab + ac + ad + bc + bd 2xSin [xz] + 2xSin [ [ ] >> Expand[(a + b)(a + c + d)(e + f) 2 xz] Sin y + 4y Sin [xz] + e a a] 2 2 >> Collect[3 x y+2 Sin[x z] (x+2 y 2a e + a f + abe + ab f + ace + ac f ^2 + x)+ (x+y)^3, y] + ade + ad f + bce + bc f + bde + bd f 4xSin [ ( ) >> Expand[(a + b)^ 2 * (c + d)] xz]+x3 +y 3x+3x2 +y2 (3x+4Sin [ a2c + a2d + 2abc + 2abd + b2c + b2d xz]) + y3 >> Expand[(x + y)^ 2 + x y] >> Collect[3 x y+2 Sin[x z] (x+2 y x2 + 3xy + y2 ^2 + x)+ (x+y)^3, {x,y}] 3 2 2 >> Expand[((a + b)(c + d))^ 2 + b 4xSin [xz]+ x +3xy +3x y +4y Sin [ (1 + a)] xz] + 3xy2 + y3 a2c2 + 2a2cd + a2d2 + b + ab + 2abc2 >> Collect[3 x y+2 Sin[x z] (x+2 y + 4abcd + 2abd2 + b2c2 + 2b2cd + b2d2 ^2 + x)+ (x+y)^3, {x,y}, h] Expand expands items in lists and rules: 3 xh [4Sin [xz]] + x h [1] + xyh [ >> Expand[{4 (x + y), 2 (x + y)-> 4 3] + x2yh [3] + y2h [4Sin [ (x + y)}] 2 3 xz]] + xy h [3] + y h [1] {4x + 4y, 2x + 2y− > 4x + 4y}
Expand expands trigonometric identities
220 >> Expand[Sin[x + y], Trig -> True] >> ExpandAll[Sin[(x+y)^2]] [ ] [ ] [ ] Cos [x] Sin y + Cos y Sin [x] Sin x2 + 2xy + y2
>> Expand[Tanh[x + y], Trig -> True >> ExpandAll[Sin[(x+y)^2], Trig-> ] [ ] True] [ ] [ ] [ Cosh[[x]] Sinh y [ ] −Sin x2 Sin 2xy Sin Cosh [x] Cosh y [+]Sinh [x] Sinh y ] [ ] [ ] [ Cosh y Sinh [x] y2 + Cos x2 Cos 2xy Sin + [ ] [ ] ] [ ] [ ] Cosh [x] Cosh y + Sinh [x] Sinh y [ y2 + Cos x2 Cos y2 Sin ] [ ] [ ] [ ] Expand does not change any other expression. 2xy + Cos 2xy Cos y2 Sin x2 >> Expand[Sin[x (1 + y)]] [ ( )] Sin x 1 + y ExpandAll also expands heads >> ExpandAll[((1 + x)(1 + y))[x]] Using the second argument, the expression only ( ) expands those subexpressions containing pat: 1 + x + y + xy [x] >> Expand[(x+a)^2+(y+a)^2+(x+y)(x+a ExpandAll can also work in finite fields ), y] >> ExpandAll[(1 + a)^ 6 / (x + y) a2 +2ay + x (a + x)+ y (a + x)+ y2 +(a + x)2 ^3, Modulus -> 3] 3 6 Expand also works in Galois fields 1 + 2a + a 3 3 >> Expand[(1 + a)^12, Modulus -> 3] x + y 1 + a3 + a9 + a12
>> Expand[(1 + a)^12, Modulus -> 4] ExpandDenominator 1 + 2a2 + 3a4 + 3a8 + 2a10 + a12 ExpandDenominator[expr] expands out negative integer powers and ExpandAll products of sums in expr.
ExpandAll[expr] >> ExpandDenominator[(a + b)^ 2 / expands out negative integer powers and ((c + d)^2 (e + f))] products of sums in expr. (a + b)2 ExpandAll[expr, target] c2e + c2 f + 2cde + 2cd f + d2e + d2 f just expands those parts involving target.
>> ExpandAll[(a + b)^ 2 / (c + d) Exponent ^2] a2 2ab + Exponent[expr, form] c2 + 2cd + d2 c2 + 2cd + d2 returns the maximum power with which b2 form appears in the expanded form of + c2 + 2cd + d2 expr. Exponent[expr, form, h] ExpandAll descends into sub expressions applies h to the set of exponents with >> ExpandAll[(a + Sin[x (1 + y)]) which form appears in expr. ^2] [ ] [ ] 2 2 2aSin x + xy + a + Sin x + xy >> Exponent[5 x^2 - 3 x + 7, x] 2
221 >> Exponent[(x^3 + 1)^2 + 1, x] >> FactorTermsList[2 x^2 - 2] { } 6 2, − 1 + x2
>> Exponent[x^(n + 1)+ Sqrt[x] + 1, >> FactorTermsList[x^2 - 2 x + 1] x] { } [ ] 1 1, 1 − 2x + x2 Max , 1 + n 2 >> f = 3 (-1 + 2 x)(-1 + y)(1 - a) ( ) >> Exponent[x / y, y] 3 (−1 + 2x) −1 + y (1 − a) −1 >> FactorTermsList[f] >> Exponent[(x^2 + 1)^3 - 1, x, Min {− − − − ] 3, 1 + a 2ax ay + 2x + y − 2xy + 2axy} 2
>> FactorTermsList[f, x] >> Exponent[0, x] −∞ {−3, 1 − a − y + ay, − 1 + 2x}
>> Exponent[1, x] 0 FullSimplify
Factor FullSimplify[expr] simplifies expr using an extended set of simplification rules. Factor[expr] FullSimplify[expr, assump] factors the polynomial expression expr. simplifies expr assuming assump instead of Assumptions. >> Factor[x ^ 2 + 2 x + 1] TODO: implement the extension. By now, this (1 + x)2 does the same than Simplify... >> Factor[1 / (x^2+2x+1)+ 1 / (x >> FullSimplify[2*Sin[x]^2 + 2*Cos[ ^4+2x^2+1)] x]^2] 2 + 2x + 3x2 + x4 2 ( ) 2 (1 + x)2 1 + x2 MinimalPolynomial FactorTermsList MinimalPolynomial[s, x] gives the minimal polynomial in x for FactorTermsList[poly] which the algebraic number s is a root. returns a list of 2 elements. The first ele- ment is the numerical factor in poly. The second one is the remaining of the poly- >> MinimalPolynomial[7, x] nomial with numerical factor removed −7 + x FactorTermsList[poly, {x1, x2, ...}] returns a list of factors in poly. The first >> MinimalPolynomial[Sqrt[2] + Sqrt element is the numerical factor in poly. [3], x] The next ones are factors that are inde- 1 − 10x2 + x4 pendent of variables lists which are cre- ated by removing each variable xi from >> MinimalPolynomial[Sqrt[1 + Sqrt right to left. The last one is the remain- [3]], x] ing of polynomial after dividing poly to −2 − 2x2 + x4 all previous factors
222 >> MinimalPolynomial[Sqrt[I + Sqrt PowerExpand [6]], x] 49 − 10x4 + x8 PowerExpand[expr] expands out powers of the form (x^y)^z and (x*y)^z in expr. Numerator
>> PowerExpand[(a ^ b)^ c] Numerator[expr] abc gives the numerator in expr. >> PowerExpand[(a * b)^ c] c c >> Numerator[a / b] a b a PowerExpand is not correct without certain as- >> Numerator[2 / 3] sumptions: 2 >> PowerExpand[(x ^ 2)^ (1/2)] x >> Numerator[a + b] a + b Simplify PolynomialQ Simplify[expr] simplifies expr. PolynomialQ[expr, var] Simplify[expr, assump] returns True if expr is a polynomial in var, simplifies expr assuming assump instead and returns False otherwise. of Assumptions. PolynomialQ[expr, {var1, ...}] tests whether expr is a polynomial in the vari. >> Simplify[2*Sin[x]^2 + 2*Cos[x ]^2]
>> PolynomialQ[x^3 - 2 x/y + 3xz, x 2 ] >> Simplify[x] True x
>> PolynomialQ[x^3 - 2 x/y + 3xz, y >> Simplify[f[x]] ] f [x] False Simplify over conditional expressions uses >> PolynomialQ[f[a] + f[a]^2, f[a]] $Assumptions, or assump to evaluate the True condition: # TODO: enable this once the logic for conditional expression # be restau- >> PolynomialQ[x^2 + axy^2 - bSin[c ], {x, y}] red. # » $Assumptions={a <= 0}; # » Sim- plify[ConditionalExpression[1, a > 0]] # = Unde- True fined # » Simplify[ConditionalExpression[1, a > 0], { a > 0 }] # = 1 >> PolynomialQ[x^2 + axy^2 - bSin[c ], {a, b, c}] False Together
Together[expr] writes sums of fractions in expr together.
223 >> Together[a / c + b / c] ComplexInfinity a + b c ComplexInfinity represents an infinite complex quantity of Together operates on lists: undetermined direction. >> Together[{x / (y+1)+ x / (y+1) ^2}] >> 1 / ComplexInfinity { ( ) } x 2 + y 0 ( ) 2 1 + y >> ComplexInfinity * Infinity ComplexInfinity But it does not touch other functions: >> Together[f[a / c + b / c]] [ ] >> FullForm[ComplexInfinity] a b DirectedInfinity [] f + c c
Degree Variables Degree Variables[expr] is the number of radians in one degree. It gives a list of the variables that appear in has a numerical value of π / 180. the polynomial expr.
>> Cos[60 Degree] >> Variables[a x^2 + b x + c] 1 {a, b, c, x} 2
>> Variables[{a + b x, c y^2 + x Degree has the value of Pi / 180 /2}] >> Degree == Pi / 180 {a, b, c, x, y} True
>> N[\[Degree]] == N[Degree] >> Variables[x + Sin[y]] { [ ]} True x, Sin y
E Mathematical Constants E Mathematical Constants is the constant e with numerical value ≃ Numeric, Arithmetic, or Symbolic constants like 2.71828. Pi, E, or Infinity. >> N[E] Catalan 2.71828
>> N[E, 50] Catalan 2.718281828459045235360287˜ is Catalan’s constant with numerical ˜4713526624977572470937000 value ≃ 0.915966.
>> Catalan // N EulerGamma 0.915965594177219
>> N[Catalan, 20] EulerGamma γ 0.91596559417721901505 is Euler’s constant with numerial value ≃ 0.577216.
224 >> EulerGamma // N >> 1 / Infinity 0.577216 0
>> N[EulerGamma, 40] >> Infinity + 100 0.577215664901532860˜ ∞ ˜6065120900824024310422 Use Infinity in sum and limit calculations: >> Sum[1/x^2, {x, 1, Infinity}] Glaisher Pi2 6 Glaisher is Glaisher’s constant, with numerical value ≃ 1.28243. Khinchin
>> N[Glaisher] Khinchin 1.28242712910062 is Khinchin’s constant, with numerical value ≃ 2.68545. >> N[Glaisher, 50]
1.282427129100622636875342˜ >> N[Khinchin] ˜5688697917277676889273250 2.68545200106531
# 1.2824271291006219541941391071304678916931152343750>> N[Khinchin, 50] 2.685452001065306445309714˜ GoldenRatio ˜8354817956938203822939945
GoldenRatio # = 2.6854520010653075701156922150403261184692382812500 is the golden ratio, = (1+Sqrt[5])/2. Pi
>> GoldenRatio // N 1.61803398874989 Pi is the constant π. >> N[GoldenRatio, 40]
1.618033988749894848˜ >> N[Pi] ˜204586834365638117720 3.14159 Pi to a numeric precision of 20 digits: Indeterminate >> N[Pi, 20] 3.1415926535897932385 Indeterminate Note that the above is not the same thing as represents an indeterminate result. the number of digits after the decimal point. This may differ from similar concepts from other >> 0^0 mathematical libraries, including those which Indeterminateexpression00encountered. Mathics uses! Indeterminate Use numpy to compute Pi to 20 digits: >> N[Pi, 20, Method->"numpy"] >> Tan[Indeterminate] 3.1415926535897930000 Indeterminate “sympy” is the default method. >> Attributes[Pi] Infinity {Constant, Protected, ReadProtected}
Infinity represents an infinite real quantity.
225 Calculus Derivatives of unknown functions are repre- sented using Derivative: Calculu >> D[f[x], x] ′ f [x] Complexes >> D[f[x, x], x] (0,1) (1,0) Complexes f [x, x] + f [x, x] is the set of complex numbers. >> D[f[x, x], x] // InputForm [ ] Derivative [0, 1] f [x,]x] D + Derivative [1, 0] f [x, x] Chain rule: D[f , x] >> D[f[2x+1, 2y, x+y], x] gives the partial derivative of f with re- [ 2 f (1,0,0) 1 + 2x, 2y, spect to x. ] [ ] D[f , x, y, ...] x + y + f (0,0,1) 1 + 2x, 2y, x + y differentiates successively with respect to x, y, etc. >> D[f[x^2, x, 2y], {x,2}, y] // D[ ,{ , }] Expand f x n [ ] [ gives the multiple derivative of order n. 8x f (1,1,1) x2, x, 2y + 8x2 f (2,0,1) D[f , {{x1, x2, ...}}] ] [ gives the vector derivative of f with re- x2, x, 2y + 2 f (0,2,1) x2, x, spect to x1, x2, etc. ] [ ] 2y + 4 f (1,0,1) x2, x, 2y First-order derivative of a polynomial: >> D[x^3 + x^2, x] Compute the gradient vector of a function: 2 >> D[x ^ 3 * Cos[y], {{x, y}}] 2x + 3x { [ ] [ ]} 3x2Cos y , − x3Sin y Second-order derivative: >> D[x^3 + x^2, {x, 2}] Hesse matrix: 2 + 6x >> D[Sin[x] * Cos[y], {{x,y}, 2}] {{ [ ] Trigonometric derivatives: − − Cos[ y]}Sin{ [x] , Cos [ [ >> D[Sin[Cos[x]], x] x] Sin y , −Cos [x] Sin − ] [ ] }} Cos [Cos [x]] Sin [x] y , − Cos y Sin [x]
>> D[Sin[x], {x, 2}] −Sin x [ ] Derivative (’)
>> D[Cos[t], {t, 2}] − Cos [t] Derivative[n][f ] represents the nth derivative of the func- Unknown variables are treated as constant: tion f. >> D[y, x] Derivative[n1, n2, ...][f ] 0 represents a multivariate derivative.
>> D[x, x] >> Derivative[1][Sin] 1 Cos [#1] & >> D[x + y, x] 1 >> Derivative[3][Sin] −Cos [#1] &
226 >> Derivative[2][# ^ 3&] >> DiscreteLimit[n/(n + 1), n -> 6#1& Infinity] Derivative can be entered using ’: 1
>> Sin’[x] >> DiscreteLimit[f[n], n -> Cos [x] Infinity] ∞ >> (# ^ 4&)’’ f [ ] 12#12&
>> f’[x] // InputForm FindRoot [ ] Derivative [1] f [x] FindRoot[f ,{x, x0}] >> Derivative[1][#2 Sin[#1]+Cos searches for a numerical root of f, starting [#2]&] from x=x0. FindRoot[lhs == rhs,{x, x0}] Cos [#1] #2& tries to solve the equation lhs == rhs.
>> Derivative[1,2][#2^3 Sin[#1]+Cos [#2]&] FindRoot by default uses Newton’s method, 6Cos [#1] #2& so the function of interest should have a first derivative. Deriving with respect to an unknown parameter >> FindRoot[Cos[x], {x, 1}] yields 0: {x− > 1.5708} >> Derivative[1,2,1][#2^3 Sin[#1]+
Cos[#2]&] >> FindRoot[Sin[x] + Exp[x],{x, 0}] 0& {x− > −0.588533}
The 0th derivative of any expression is the ex- >> FindRoot[Sin[x] + Exp[x] == Pi,{ pression itself: x, 0}] >> Derivative[0,0,0][a+b+c] {x− > 0.866815} a + b + c FindRoot has attribute HoldAll and effectively You can calculate the derivative of custom func- uses Block to localize x. However, in the result x tions: will eventually still be replaced by its value. >> f[x_] := x ^ 2 >> x = "I am the result!";
>> f’[x] >> FindRoot[Tan[x] + Sin[x] == Pi, 2x {x, 1}] Unknown derivatives: {I am the result!− > 1.14911} >> Derivative[2, 1][h] >> Clear[x] h(2,1)
>> Derivative[2, 0, 1, 0][h[g]] FindRoot stops after 100 iterations: [ ] >> FindRoot[x^2 + x + 1, {x, 1}] h g (2,0,1,0) Themaximumnumberofiterationswasexceeded.Theresultmightbeinaccurate. {x− > −1.} DiscreteLimit Find complex roots: >> FindRoot[x ^ 2 + x + 1, {x, -I}] DiscreteLimit[ , ->Infinity] f k { − − − } gives the limit of the sequence f as k tends x > 0.5 0.866025I to infinity. The function has to return numerical values:
227 >> FindRoot[f[x] == 0, {x, 0}] Definite integrals: Thefunctionvalueisnotanumberatx = 0.. >> Integrate[x ^ 2 + x, {x, 1, 3}] [ ] FindRoot f [x] − 0, {x, 0} 38 3 The derivative must not be 0: >> Integrate[Sin[x], {x, 0, Pi/2}] >> FindRoot[Sin[x] == x, {x, 0}] 1 Encounteredasingularderivativeatthepointx = 0.. [ ] Some other integrals: FindRoot Sin [x] − x, {x, 0} >> Integrate[1 / (1 - 4 x + x^2), x ] ( [ ] [ ]) >> FindRoot[x^2 - 2, {x, 1,3}, √ √ √ − − − − Method->"Secant"] 3 Log 2 3 + x Log 2 + 3 + x {x− > 1.41421} 6
>> Integrate[4 Sin[x] Cos[x], x] 2 Integers 2Sin [x] Integration in TeX: Integers >> Integrate[f[x], {x, a, b}] // is the set of integer numbers. TeXForm ∧ \int_a b f\left[x\right] \, dx Limit a solution to integer numbers: >> Solve[-4 - 4 x + x^4 + x^5 == 0, Sometimes there is a loss of precision during in- x, Integers] tegration. You can check the precision of your re- sult with the following sequence of commands. {{x− > −1}} >> Integrate[Abs[Sin[phi]], {phi,
>> Solve[x^4 == 4, x, Integers] 0, 2Pi}] // N {} 4.
>> % // Precision MachinePrecision Integrate >> Integrate[ArcSin[x / 3], x] [ ] √ x Integrate[f , x] xArcSin + 9 − x2 integrates f with respect to x. The result 3
does not contain the additive integration >> Integrate[f’[x], {x, a, b}] constant. − Integrate[f ,{x, a, b}] f [b] f [a] computes the definite integral of f with respect to x from a to b. Limit Integrate a polynomial: Limit[expr, x->x0] >> Integrate[6 x ^ 2 + 3 x ^ 2 - 4 x + 10, x] gives the limit of expr as x approaches x0. ( ) Limit[expr, x->x0, Direction->1] x 10 − 2x + 3x2 approaches x0 from smaller values. Limit[expr, x->x0, Direction->-1] Integrate trigonometric functions: approaches x0 from larger values. >> Integrate[Sin[x] ^ 5, x] >> Limit[x, x->2] Cos [x]5 2Cos [x]3 −Cos [x] − + 2 5 3
228 >> Limit[Sin[x] / x, x->0] Series 1 Series[f ,{x, x0, n}] >> Limit[1/x, x->0, Direction->-1] ∞ Represents the series expansion around x=x0 up to order n. >> Limit[1/x, x->0, Direction->1] −∞ >> Series[Exp[x],{x,0,2}] 1 1 + x + x2 + O [x]3 O 2 >> Series[Exp[x^2],{x,0,2}] O[x]^n 2 3 ∧ 1 + x + O [x] Represents a term of order $x n$. ∧ O[x] n is generated to represent omitted higher order terms in power series. SeriesData
>> Series[1/(1-x),{x,0,2}] SeriesData[...] 1 + x + x2 + O [x]3 Represents a series expansion
TODO: - Implement sum, product and composi- Reals tion of series
Reals Solve is the set of real numbers.
Limit a solution to real numbers: Solve[equation, vars] attempts to solve equation for the vari- >> Solve[x^3 == 1, x, Reals] {{ − }} ables vars. x > 1 Solve[equation, vars, domain] restricts variables to domain, which can be Complexes or Reals or Integers. Root
>> Solve[x ^ 2 - 3 x == 4, x] Root[ , ] f i {{x− > −1} , {x− > 4}} represents the i-th complex root of the
polynomial f >> Solve[4 y - 8 == 0, y] {{y− > 2}} >> Root[#1 ^ 2 - 1&, 1] −1 Apply the solution: >> sol = Solve[2 x^2 - 10 x - 12 == >> Root[#1 ^ 2 - 1&, 2] 0, x] 1 {{x− > −1} , {x− > 6}} Roots that can’t be represented by radicals: >> x /. sol >> Root[#1 ^ 5 + 2 #1 + 1&, 2] [ ] {−1, 6} Root #15 + 2#1 + 1&, 2 Contradiction: >> Solve[x + 1 == x, x] {}
Tautology:
229 >> Solve[x ^ 2 == x ^ 2, x] >> sol = Solve[eqs, {x, y}] // {{}} Simplify Rational equations: {x− > 0, y− > 0} , {x− > 1, >> Solve[x / (x ^ 2 + 1)== 1, x] {{ √ } − 1 − I { √ x > 3 , 1 I { 2 2 }} y− > 1} , x− > − + 3, √ 2 2 − 1 I √ } x > + 3 1 I 2 2 y− > − − 3 , 2 2 ( √ ) >> Solve[(x^2 + 3 x + 2)/(4 x - 2) − 2 == 0, x] 1 I 3 x− > , {{x− > −2} , {x− > −1}} 4 Transcendental equations: √ − − 1 I >> Solve[Cos[x] == 0, x] y > + 3 {{ } { }} 2 2 Pi 3Pi x− > , x− > 2 2 >> eqs /. sol // Simplify Solve can only solve equations with respect to {{True, True} , {True, True} , symbols or functions: {True, True} , {True, True}} >> Solve[f[x + y] == 3, f[x + y]] {{ [ ] }} f x + y − > 3 An underdetermined system: >> Solve[x^2 == 1 && z^2 == -1, {x,
>> Solve[a + b == 2, a + b] y, z}] a + bisnotavalidvariable. Equationsmaynotgivesolutionsforall”solve”variables. Solve [a + b==2, a + b] {{x− > −1, z− > −I} , { − − − } { − This happens when solving with respect to an x > 1, z > I , x > 1, assigned symbol: z− > −I} , {x− > 1, z− > I}} >> x = 3; Domain specification:
>> >> Solve[x == 2, x] Solve[x^2 == -1, x, Reals] {} 3isnotavalidvariable. Solve [False, 3] >> Solve[x^2 == 1, x, Reals]
>> Clear[x] {{x− > −1} , {x− > 1}}
>> Solve[a < b, a] >> Solve[x^2 == -1, x, Complexes] a < bisnotawell − formedequation. {{x− > −I} , {x− > I}} Solve [a < b, a] >> Solve[4 - 4 * x^2 - x^4 + x^6 == 0, x, Integers] Solve a system of equations: >> eqs = {3 x ^ 2 - 3 y == 0, 3 y ^ {{x− > −1} , {x− > 1}} 2 - 3 x == 0};
Differential Equations
Differential Equation
230 C simplification rules are not implemented yet.
C[n] AnglePath represents the nth constant in a solution to a differential equation. AnglePath[{phi1, phi2, ...}] returns the points formed by a turtle starting at {0, 0} and angled at 0 degrees DSolve going through the turns given by angles phi1, phi2, ... and using distance 1 for each DSolve[eq, y[x], x] step. solves a differential equation for the func- AnglePath[{{r1, phi1}, {r2, phi2}, ...}] tion y[x]. instead of using 1 as distance, use r1, r2, ... as distances for the respective steps. AngleVector[phi0,{phi1, phi2, ...}] >> DSolve[y’’[x] == 0, y[x], x] returns the points on a path formed by a {{y [x] − > xC [2] + C [1]}} turtle starting with direction phi0 instead of 0. >> DSolve[y’’[x] == y[x], y[x], x] {{ }} AngleVector[{x, y}, {phi1, phi2, ...}] − y [x] − > C [1] E x + C [2] Ex returns the points on a path formed by a turtle starting at {$x, $y} instead of {0, 0}. >> DSolve[y’’[x] == y[x], y, x] AngleVector[{{ , }, }, { , , {{ ( [ x y phi0 phi1 phi2 − > { } ...}] y Function ])}}x , − specifies initial position {x, y} and initial C E x C Ex [1] + [2] direction phi0. AngleVector[{{x, y}, {dx, dy}}, {phi1, DSolve can also solve basic PDE phi2, ...}] >> DSolve[D[f[x, y], x] / f[x, y] + specifies initial position {x, y} and a slope 3 D[f[x, y], y] / f[x, y] == 2, {dx, dy} that is understood to be the initial f, {x, y}] {{ ( [ direction of the turtle. f − > Function {x, y} , [ ]])}} >> AnglePath[{90 Degree, 90 Degree, x + 3y E 5 5 C [1] 3x − y 90 Degree, 90 Degree}] {{0, 0} , {0, 1} , {−1, >> DSolve[D[f[x, y], x] x + D[f[x, 1} , {−1, 0} , {0, 0}} y], y] y == 2, f[x, y], {x, y}] {{ [ ] [ ]}} y >> AnglePath[{{1, 1}, 90 Degree}, f x, y − > 2Log [x] + C [1] x {{1, 90 Degree}, {2, 90 Degree}, {1, 90 Degree}, {2, 90 Degree >> DSolve[D[y[x, t], t] + 2 D[y[x, }}] t], x] == 0, y[x, t], {x, t}] {{1, 1} , {0, 1} , {0, {{y [x, t] − > C [1][x − 2t]}} − 1} , {1, − 1} , {1, 1}}
>> AnglePath[{a, b}] Exponential, Trigonometric and {{0, 0} , {Cos [a] , Sin [a]} , {Cos [ Hyperbolic Functions a] + Cos [a + b] , Sin [a] + Sin [a + b]}}
Exponential, Trigonometric and Hyperbolic >> Precision[Part[AnglePath[{N[1/3, Functions 100], N[2/3, 100]}], 2, 1]] Mathics basically supports all important trigono- 100. metric and hyperbolic functions. Numerical values and derivatives can be com- puted; however, most special exact values and
231 >> Graphics[Line[AnglePath[Table >> AngleVector[{1, 10}, a] [1.7, {50}]]]] {1 + Cos [a] , 10 + Sin [a]}
ArcCos
ArcCos[z] returns the inverse cosine of z.
>> ArcCos[1] 0
>> ArcCos[0] Pi 2
>> Integrate[ArcCos[x], {x, -1, 1}] >> Graphics[Line[AnglePath[ Pi RandomReal[{-1, 1}, {100}]]]]
ArcCosh
ArcCosh[z] returns the inverse hyperbolic cosine of z.
>> ArcCosh[0] I Pi 2
>> ArcCosh[0.] 0. + 1.5708I
>> ArcCosh [0.00000000000000000000000000000000000000]
AngleVector 1.570796326794896619˜ ˜2313216916397514421I AngleVector[phi] returns the point at angle phi on the unit circle. ArcCot AngleVector[{r, phi}] returns the point at angle phi on a circle of ArcCot[z] radius r. returns the inverse cotangent of z. AngleVector[{x, y}, phi]
returns the point at angle phi on a circle of >> ArcCot[0] radius 1 centered at {x, y}. Pi AngleVector[{x, y}, {r, phi}] 2 returns point at angle phi on a circle of ra-
dius r centered at {x, y}. >> ArcCot[1] Pi >> AngleVector[90 Degree] 4 {0, 1}
232 ArcCoth >> ArcSec[-1] Pi ArcCoth[z] returns the inverse hyperbolic cotangent of z. ArcSech
>> ArcCoth[0] ArcSech[z] I returns the inverse hyperbolic secant of z. Pi 2 >> ArcSech[0] >> ArcCoth[1] ∞ ∞
>> ArcSech[1] >> ArcCoth[0.0] 0 0. + 1.5708I >> ArcSech[0.5] >> ArcCoth[0.5] 1.31696 0.549306 − 1.5708I
ArcSin ArcCsc ArcSin[z] ArcCsc[z] returns the inverse sine of z. returns the inverse cosecant of z.
>> ArcSin[0] >> ArcCsc[1] 0 Pi 2 >> ArcSin[1] Pi >> ArcCsc[-1] 2 − Pi 2 ArcSinh
ArcCsch ArcSinh[z] returns the inverse hyperbolic sine of z. ArcCsch[z] returns the inverse hyperbolic cosecant of >> ArcSinh[0] z. 0
>> ArcCsch[0] >> ArcSinh[0.] ComplexInfinity 0.
>> ArcSinh[1.0] >> ArcCsch[1.0] 0.881374 0.881374
ArcSec ArcTan
ArcTan[ ] ArcSec[z] z returns the inverse secant of z. returns the inverse tangent of z.
>> ArcSec[1] 0
233 >> ArcTan[1] Cot Pi 4 Cot[z] returns the cotangent of z. >> ArcTan[1.0] 0.785398 >> Cot[0] >> ArcTan[-1.0] ComplexInfinity −0.785398 >> Cot[1.] >> ArcTan[1, 1] 0.642093 Pi 4 Coth
ArcTanh Coth[z] returns the hyperbolic cotangent of z. ArcTanh[z]
returns the inverse hyperbolic tangent of >> Coth[0] z. ComplexInfinity
>> ArcTanh[0] Csc >> ArcTanh[1] ∞ Csc[z] >> ArcTanh[0] returns the cosecant of z.
>> ArcTanh[.5 + 2 I] >> Csc[0] 0.0964156 + 1.12656I ComplexInfinity >> ArcTanh[2 + I] >> Csc[1] (* Csc[1] in Mathematica ArcTanh [2 + I] *) 1 Cos Sin [1]
>> Csc[1.] Cos[z] returns the cosine of z. 1.1884
>> Cos[3 Pi] Csch −1 Csch[z] Cosh returns the hyperbolic cosecant of z.
>> Csch[0] Cosh[z] returns the hyperbolic cosine of z. ComplexInfinity
>> Cosh[0] Exp 1
Exp[z] returns the exponential function of z.
234 >> Exp[1] >> Log[{0, 1, E, E * E, E ^ 3, E ^ x}] E { [ ]} −∞, 0, 1, 2, 3, Log Ex >> Exp[10.0]
22 026.5 >> Log[0.]
>> Exp[x] //FullForm Indeterminate
Power [E, x] >> Plot[Log[x], {x, 0, 5}]
>> Plot[Exp[x], {x, 0, 3}] 1.5 1.0 15 0.5
10 1 2 3 4 5 −0.5 5 −1.0
0.5 1.0 1.5 2.0 2.5 3.0 Log10
Haversine Log10[z] returns the base-10 logarithm of z. Haversine[z] returns the haversine function of z. >> Log10[1000] 3 >> Haversine[1.5] 0.464631 >> Log10[{2., 5.}] {0.30103, 0.69897} >> Haversine[0.5 + 2I] − 1.15082 + 0.869405I >> Log10[E ^ 3] 3 InverseHaversine Log [10]
InverseHaversine[z] Log2 returns the inverse haversine function of z. Log2[z]
>> InverseHaversine[0.5] returns the base-2 logarithm of z. 1.5708 >> Log2[4 ^ 8] >> InverseHaversine[1 + 2.5 I] 1.76459 + 2.33097I 16
>> Log2[5.6] Log 2.48543 >> Log2[E ^ 2] Log[z] 2 returns the natural logarithm of z. Log [2]
235 LogisticSigmoid >> Sin[3 Pi] 0
LogisticSigmoid[z] >> Sin[1.0 + I] returns the logistic sigmoid of z. 1.29846 + 0.634964I
>> Plot[Sin[x], {x, -Pi, Pi}] >> LogisticSigmoid[0.5] 0.622459 1.0 >> LogisticSigmoid[0.5 + 2.3 I] 0.5 1.06475 + 0.808177I
>> LogisticSigmoid[{-0.2, 0.1, −3 −2 −1 1 2 3 0.3}] −0.5 {0.450166, 0.524979, 0.574443} −1.0 Sec Sinh Sec[z] returns the secant of z. Sinh[z] returns the hyperbolic sine of z. >> Sec[0] 1 >> Sinh[0] >> Sec[1] (* Sec[1] in Mathematica 0 *) 1 Cos [1] Tan
>> Sec[1.] Tan[z] 1.85082 returns the tangent of z.
Sech >> Tan[0] 0
Sech[z] >> Tan[Pi / 2] returns the hyperbolic secant of z. ComplexInfinity
>> Sech[0] 1 Tanh
Tanh[z] Sin returns the hyperbolic tangent of z.
Sin[z] >> Tanh[0] returns the sine of z. 0
>> Sin[0] 0 Integer Functions
>> Sin[0.5] 0.479426 Integer Function
236 BitLength >> DigitCount[Floor[Pi * 10^100]] {8, 12, 12, 10, 8, 9, 8, 12, 14, 8} BitLength[x] gives the number of bits needed to repre- >> DigitCount[1022, 2] sent the integer x. x’s sign is ignored. {9, 1}
>> DigitCount[1022, 2, 1] >> BitLength[1023] 9 10
>> BitLength[100] Floor 7
>> BitLength[-5] Floor[x] 3 gives the smallest integer less than or equal to x. >> BitLength[0] Floor[x, a] 0 gives the smallest multiple of a less than or equal to x. Ceiling >> Floor[10.4] 10 Ceiling[x] gives the first integer greater than x. >> Floor[10/3] 3
>> Ceiling[1.2] >> Floor[10] 2 10
>> Ceiling[3/2] >> Floor[21, 2] 2 20
For complex x, take the ceiling of real an imagi- >> Floor[2.6, 0.5] nary parts. 2.5 >> Ceiling[1.3 + 0.7 I] >> Floor[-10.4] I 2 + −11
For complex x, take the floor of real an imagi- DigitCount nary parts. >> Floor[1.5 + 2.7 I] DigitCount[n, b, d] 1 + 2I returns the number of times digit d occurs For negative a, the smallest multiple of a greater in the base b representation of n. than or equal to x is returned. DigitCount[n, b] >> Floor[10.4, -1] returns a list indicating the number of times each digit occurs in the base b rep- 11
resentation of n. >> Floor[-10.4, -1] DigitCount[n, b] −10 returns a list indicating the number of times each digit occurs in the decimal representation of n.
>> DigitCount[1022] {1, 2, 0, 0, 0, 0, 0, 0, 0, 1}
237 FromDigits IntegerDigits
FromDigits[l] IntegerDigits[n] returns the integer corresponding to the returns the decimal representation of in- decimal representation given by l. l can teger x as list of digits. x’s sign is ignored. be a list of digits or a string. IntegerDigits[n, b] FromDigits[l, b] returns the base b representation of inte- returns the integer corresponding to the ger x as list of digits. x’s sign is ignored. base b representation given by l. l can be IntegerDigits[n, b, length] a list of digits or a string. returns a list of length length. If the num- ber is too short, the list gets padded with 0 on the left. If the number is too long, the >> FromDigits["123"] length least significant digits are returned. 123
>> FromDigits[{1, 2, 3}] >> IntegerDigits[12345] 123 {1, 2, 3, 4, 5}
>> FromDigits[{1, 0, 1}, 1000] >> IntegerDigits[-500] 1 000 001 {5, 0, 0} FromDigits can handle symbolic input: >> IntegerDigits[12345, 10, 8] >> FromDigits[{a, b, c}, 5] {0, 0, 0, 1, 2, 3, 4, 5} c + 5 (5a + b)
>> IntegerDigits[12345, 10, 3] Note that FromDigits does not automatically de- tect if you are providing a non-decimal represen- {3, 4, 5} tation: >> IntegerDigits[11, 2] >> FromDigits["a0"] { } 100 1, 0, 1, 1
>> FromDigits["a0", 16] >> IntegerDigits[123, 8] 160 {1, 7, 3}
FromDigits on empty lists or strings returns 0: >> IntegerDigits[98765, 20] >> FromDigits[{}] {12, 6, 18, 5} 0
>> FromDigits[""] IntegerLength 0
IntegerLength[x] gives the number of digits in the base-10 representation of x. IntegerLength[x, b] gives the number of base-b digits in x.
>> IntegerLength[123456] 6
>> IntegerLength[10^10000] 10 001
>> IntegerLength[-10^1000] 1 001
238 IntegerLength with base 2: For bases > 10, alphabetic characters a, b, ... are >> IntegerLength[8, 2] used to represent digits 11, 12, ... . Note that base 4 must be an integer in the range from 2 to 36. >> IntegerString[12345] IntegerLength Check that is correct for the first 12 345 100 powers of 10: >> IntegerLength /@ (10 ^ Range >> IntegerString[-500] [100])== Range[2, 101] 500 True >> IntegerString[12345, 10, 8] The base must be greater than 1: 00 012 345 >> IntegerLength[3, -2] >> IntegerString[12345, 10, 3] Base − 2isnotanintegergreaterthan1. 345 IntegerLength [3, − 2] >> IntegerString[11, 2] 0 is a special case: 1 011 >> IntegerLength[0] >> IntegerString[123, 8] 0 173
>> IntegerString[32767, 16] IntegerReverse 7fff
IntegerReverse[n] >> IntegerString[98765, 20] returns the integer that has the reverse c6i5 decimal representation of x without sign. IntegerReverse[n, b] returns the integer that has the reverse Linear algebra base b represenation of x without sign. Linear algebra >> IntegerReverse[1234] 4 321 BrayCurtisDistance
>> IntegerReverse[1022, 2] 511 BrayCurtisDistance[u, v] returns the Bray Curtis distance between >> IntegerReverse[-123] u and v. 321 >> BrayCurtisDistance[-7, 5] 6 IntegerString >> BrayCurtisDistance[{-1, -1}, {10, 10}] IntegerString[n] returns the decimal representation of in- 11 teger x as string. x’s sign is ignored. 9 IntegerString[n, b] returns the base b representation of inte- ger x as string. x’s sign is ignored. CanberraDistance IntegerString[n, b, length] returns a string of length length. If CanberraDistance[u, v] the number is too short, the string gets returns the canberra distance between u padded with 0 on the left. If the number and v, which is a weighted version of the is too long, the length least significant dig- Manhattan distance. its are returned.
239 >> CanberraDistance[-7, 5] >> Cross[{x, y}] 1 {−y, x}
>> CanberraDistance[{-1, -1}, {1, >> Cross[{1, 2}, {3, 4, 5}] 1}] Theargumentsareexpectedtobevectorsofequallength, 2 andthenumberof argumentsisexpectedtobe1lessthantheirlength. [ ] Cross {1, 2} , {3, 4, 5} ChessboardDistance
ChessboardDistance[u, v] DesignMatrix returns the chessboard distance (also known as Chebyshev distance) between DesignMatrix[m, f , x] u and v, which is the number of moves returns the design matrix. a king on a chessboard needs to get from square u to square v. >> DesignMatrix[{{2, 1}, {3, 4}, {5, 3}, {7, 6}}, x, x] >> ChessboardDistance[-7, 5] {{1, 2} , {1, 3} , {1, 5} , {1, 7}} 12
>> ChessboardDistance[{-1, -1}, {1, >> DesignMatrix[{{2, 1}, {3, 4}, 1}] {5, 3}, {7, 6}}, f[x], x] 2 {{1, f [2]} , {1, f [3]} , {1, f [5]} , {1, f [7]}} CosineDistance Det CosineDistance[u, v] returns the cosine distance between u and Det[m] v. computes the determinant of the matrix m. >> N[CosineDistance[{7, 9}, {71,
89}]] >> Det[{{1, 1, 0}, {1, 0, 1}, {0, 0.0000759646 1, 1}}] −2 >> CosineDistance[{a, b}, {c, d}] 1 Symbolic determinant: −ac − bd + √ √ >> Det[{{a, b, c}, {d, e, f}, {g, h Abs [a]2 + Abs [b]2 Abs [c]2 + Abs [d]2 , i}}] aei − a f h − bdi + b f g + cdh − ceg
Cross Eigensystem Cross[a, b] computes the vector cross product of a Eigensystem[m] and b. returns the list {Eigenvalues[m], Eigenvectors[m]}. >> Cross[{x1, y1, z1}, {x2, y2, z2 }] {y1z2 − y2z1, − x1z2 + x2z1, x1y2 − x2y1}
240 >> Eigensystem[{{1, 1, 0}, {1, 0, >> Eigenvectors[{{2, 0, 0}, {0, -1, 1}, {0, 1, 1}}] 0}, {0, 0, 0}}] {{2, − 1, 1} , {{1, 1, 1} , {{1, 0, 0} , {0, 1, 0} , {0, 0, 1}} {1, − 2, 1} , {−1, 0, 1}}} >> Eigenvectors[{{0.1, 0.2}, {0.8, 0.5}}] Eigenvalues {{−0.355518216481267016676297˜ ˜559501705929896062805897153˜ Eigenvalues[m] ˜500209120909839738411406528˜ computes the eigenvalues of the matrix ˜939551208168268203735351562˜ m. By default Sympy’s routine is used. ˜500000000000000000000000000˜ Sometimes this is slow and less good than ˜000000000000000000000000000˜ the corresponding mpmath routine. Use ˜000000000000000000000000000˜ option Method->“mpmath” if you want − to use mpmath’s routine instead. ˜0000000000000, 1.150481115˜ ˜772866118834236549972506478˜ Numeric eigenvalues are sorted in order of de- ˜611688789589714534394707980˜ creasing absolute value: ˜136107750013252370990812778˜ >> Eigenvalues[{{1, 1, 0}, {1, 0, ˜472900390625000000000000000˜ 1}, {0, 1, 1}}] ˜000000000000000000000000000˜ {2, − 1, 1} ˜000000000000000000000000000˜ ˜000000000000000000000000000} , Symbolic eigenvalues: {−0.628960169645094045731745˜ >> Eigenvalues[{{Cos[theta],Sin[ ˜684302104224901929314653543˜ theta],0},{-Sin[theta],Cos[theta ˜850901708147770746704097177˜ ],0},{0,0,1}}] // Sort { ˜826042752712965011596679687˜ 1, Cos [theta] ˜500000000000000000000000000˜ √ + (−1 + Cos [theta])(1 + Cos [theta]), ˜000000000000000000000000000˜ ˜000000000000000000000000000˜ Cos [theta] } √ ˜0000000000000, 0.777437524821˜ − (−1 + Cos [theta])(1 + Cos [theta]) ˜136041447958386087174831147˜ ˜822934682708885214954348721˜ >> Eigenvalues[{{7, 1}, {-4, 3}}] ˜189125726027668861206620931˜ >> Eigenvalues[{{7, 1}, {-4, 3}}] ˜625366210937500000000000000˜ ˜000000000000000000000000000˜ ˜000000000000000000000000000˜ Eigenvectors ˜0000000000000000000000000}}
Eigenvectors[m] computes the eigenvectors of the matrix EuclideanDistance m. EuclideanDistance[u, v] >> Eigenvectors[{{1, 1, 0}, {1, 0, returns the euclidean distance between u 1}, {0, 1, 1}}] and v. {{1, 1, 1} , {1, − 2, 1} , {−1, 0, 1}} >> EuclideanDistance[-7, 5] >> Eigenvectors[{{1, 0, 0}, {0, 1, 12 0}, {0, 0, 0}}] {{0, 1, 0} , {1, 0, 0} , {0, 0, 1}}
241 >> EuclideanDistance[{-1, -1}, {1, >> LeastSquares[{{1, 1, 1}, {1, 1, 1}] 2}}, {1, 3}] √ Solvingforunderdeterminedsystemnotimplemented. 2 2 [ LeastSquares {{1, 1, >> EuclideanDistance[{a, b}, {c, d ] } { }} { } }] 1 , 1, 1, 2 , 1, 3 √ Abs [a − c]2 + Abs [b − d]2 LinearModelFit
Inverse LinearModelFit[m, f , x] returns the design matrix. Inverse[m] computes the inverse of the matrix m. >> m = LinearModelFit[{{2, 1}, {3, 4}, {5, 3}, {7, 6}}, x, x];
>> Inverse[{{1, 2, 0}, {2, 3, 0}, {3, 4, 1}}] >> m["BasisFunctions"]
{{−3, 2, 0} , {2, − 1, 0} , {1, − 2, 1}} >> m["BestFit"] 0.186441 + 0.779661x >> Inverse[{{1, 0}, {0, 0}}] Thematrix{{1, 0}, {0, 0}}issingular. >> m["BestFitParameters"] [ ] {0.186441, 0.779661} Inverse {{1, 0} , {0, 0}}
>> m["DesignMatrix"] >> Inverse[{{1, 0, 0}, {0, Sqrt {{ } { } { } { }} [3]/2, 1/2}, {0,-1 / 2, Sqrt 1, 2 , 1, 3 , 1, 5 , 1, 7 [3]/2}}] { { √ >> m["Function"] { } 3 1, 0, 0 , 0, , >> m["Response"] 2 } { √ }} {1, 4, 3, 6} 1 1 3 − , 0, , 2 2 2 >> m["FitResiduals"]
>> m = LinearModelFit[{{2, 2, 1}, {3, 2, 4}, {5, 6, 3}, {7, 9, LeastSquares 6}}, {Sin[x], Cos[y]}, {x, y}];
LeastSquares[m, b] >> m["BasisFunctions"] computes the least squares solution to m x = b, finding an x that solves for b opti- >> m["Function"] mally. >> m = LinearModelFit[{{{1, 4}, {1, 5}, {1, 7}}, {1, 2, 3}}]; >> LeastSquares[{{1, 2}, {2, 3},
{5, 6}}, {1, 5, 3}] >> m["BasisFunctions"] { } − 28 31 , >> m["FitResiduals"] 13 13
>> Simplify[LeastSquares[{{1, 2}, {2, 3}, {5, 6}}, {1, x, 3}]] { } 12 8x 4 7x − , − + 13 13 13 13
242 LinearSolve >> MatrixExp[{{0, 2}, {0, 1}}] {{1, − 2 + 2E} , {0, E}} LinearSolve[matrix, right] solves the linear equation system matrix >> MatrixExp[{{1.5, 0.5}, {0.5, . x = right and returns one correspond- 2.0}}] ing solution x. {{5.16266, 3.02952} , {3.02952, 8.19218}} >> LinearSolve[{{1, 1, 0}, {1, 0, 1}, {0, 1, 1}}, {1, 2, 3}] {0, 1, 2} MatrixPower
Test the solution: MatrixPower[m, n] >> {{1, 1, 0}, {1, 0, 1}, {0, 1, computes the nth power of a matrix m. 1}} . {0, 1, 2} { } 1, 2, 3 >> MatrixPower[{{1, 2}, {1, 1}}, 10] If there are several solutions, one arbitrary solu- {{ } { }} tion is returned: 3 363, 4 756 , 2 378, 3 363 >> LinearSolve[{{1, 2, 3}, {4, 5, >> MatrixPower[{{1, 2}, {2, 5}}, 6}, {7, 8, 9}}, {1, 1, 1}] -3] {−1, 1, 0} {{169, − 70} , {−70, 29}} Infeasible systems are reported: >> LinearSolve[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}, {1, -2, 3}] MatrixRank Linearequationencounteredthathasnosolution. [ MatrixRank[matrix] {{ } { LinearSolve 1, 2, 3 , 4, ] returns the rank of matrix. 5, 6} , {7, 8, 9}} , {1, − 2, 3} >> MatrixRank[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}] ManhattanDistance 2
>> MatrixRank[{{1, 1, 0}, {1, 0, ManhattanDistance[u, v] 1}, {0, 1, 1}}] returns the Manhattan distance between u and v, which is the number of horizon- 3 tal or vertical moves in the gridlike Man- >> MatrixRank[{{a, b}, {3 a, 3 b}}] hattan city layout to get from u to v. 1
>> ManhattanDistance[-7, 5] 12 Norm
>> ManhattanDistance[{-1, -1}, {1, 1}] Norm[m, l] computes the l-norm of matrix m (cur- 4 rently only works for vectors!). Norm[m] MatrixExp computes the 2-norm of matrix m (cur- rently only works for vectors!).
MatrixExp[m] >> Norm[{1, 2, 3, 4}, 2] computes the exponential of the matrix √ m. 30
243 >> Norm[{10, 100, 200}, 1] PseudoInverse 310 PseudoInverse[m] >> Norm[{a, b, c}] √ computes the Moore-Penrose pseudoin- Abs [a]2 + Abs [b]2 + Abs [c]2 verse of the matrix m. If m is invertible, the pseudoinverse equals the inverse.
>> Norm[{-100, 2, 3, 4}, Infinity] 100 >> PseudoInverse[{{1, 2}, {2, 3}, {3, 4}}] >> Norm[1 + I] {{ } { }} √ 11 1 7 4 1 2 − , − , , , , − 2 6 3 6 3 3 3
>> PseudoInverse[{{1, 2, 0}, {2, 3, Normalize 0}, {3, 4, 1}}] {{−3, 2, 0} , {2, − 1, 0} , {1, − 2, 1}} Normalize[v]
calculates the normalized vector v. >> PseudoInverse[{{1.0, 2.5}, {2.5, Normalize[z] 1.0}}] calculates the normalized complex num- {{−0.190476, 0.47619} , ber z. {0.47619, − 0.190476}}
>> Normalize[{1, 1, 1, 1}] { } 1 1 1 1 , , , QRDecomposition 2 2 2 2
>> Normalize[1 + I] QRDecomposition[m] ( ) √ 1 I computes the QR decomposition of the + 2 2 2 matrix m.
>> QRDecomposition[{{1, 2}, {3, 4}, NullSpace {5, 6}}] {{{ √ √ √ } 35 3 35 35 , , , NullSpace[matrix] 35 35 7 { returns a list of vectors that span the √ √ 13 210 2 210 nullspace of matrix. , , 210 105 √ }} {{ √ >> NullSpace[{{1, 2, 3}, {4, 5, 6}, 210 − , 35, {7, 8, 9}}] 42 } { }}} {{ − }} √ √ 1, 2, 1 44 35 2 210 , 0, >> A = {{1, 1, 0}, {1, 0, 1}, {0, 35 35 1, 1}};
>> NullSpace[A] RowReduce {} RowReduce[matrix] >> MatrixRank[A] returns the reduced row-echelon form of 3 matrix.
244 >> RowReduce[{{1, 0, a}, {1, 1, b Symbolic trace: }}] >> Tr[{{a, b, c}, {d, e, f}, {g, h, {{1, 0, a} , {0, 1, − a + b}} i}}] a + e + i >> RowReduce[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}] // MatrixForm 1 0 −1 VectorAngle 0 1 2 0 0 0 VectorAngle[u, v] gives the angles between vectors u and v
SingularValueDecomposition >> VectorAngle[{1, 0}, {0, 1}] Pi SingularValueDecomposition[m] 2 calculates the singular value decomposi- tion for the matrix m. >> VectorAngle[{1, 2}, {3, 1}] Pi SingularValueDecomposition returns u, s, w 4 such that m=u s v, uu=1, vv=1, and s is diago- nal. >> VectorAngle[{1, 1, 0}, {1, 0, 1}] >> SingularValueDecomposition [{{1.5, 2.0}, {2.5, 3.0}}] Pi {{{0.538954, 0.842335} , {0.842335 3 , − 0.538954}} , {{4.63555, 0.} , { }} {{ 0., 0.107862 , 0.628678, 0.777˜ Number theoretic functions ˜666} , {−0.777666, 0.628678}}} Number theoretic function SquaredEuclideanDistance ContinuedFraction
SquaredEuclideanDistance[u, v] ContinuedFraction[x, n] returns squared the euclidean distance generate the first n terms in the continued between u and v. fraction reprentation of x. ContinuedFraction[x] >> SquaredEuclideanDistance[-7, 5] the complete continued fraction repre- 144 sentation for a rational or quadradic irra- tional number. >> SquaredEuclideanDistance[{-1, -1}, {1, 1}] >> ContinuedFraction[Pi, 10] 8 {3, 7, 15, 1, 292, 1, 1, 1, 2, 1}
>> ContinuedFraction[(1 + 2 Sqrt Tr [3])/5] { { }} Tr[m] 0, 1, 8, 3, 34, 3 computes the trace of the matrix m. >> ContinuedFraction[Sqrt[70]] {8, {2, 1, 2, 1, 2, 16}} >> Tr[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}] 15
245 Divisors FromContinuedFraction
Divisors[n] FromContinuedFraction[list] returns a list of the integers that divide n. reconstructs a number from the list of its continued fraction terms.
>> Divisors[96] >> FromContinuedFraction[{3, 7, 15, {1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96} 1, 292, 1, 1, 1, 2, 1}] >> Divisors[704] 1 146 408 {1, 2, 4, 8, 11, 16, 22, 32, 364 913 44, 64, 88, 176, 352, 704} >> FromContinuedFraction[Range[5]]
>> Divisors[{87, 106, 202, 305}] 225 {{1, 3, 29, 87} , {1, 2, 53, 106} , 157 {1, 2, 101, 202} , {1, 5, 61, 305}} IntegerExponent FactorInteger IntegerExponent[n, b] gives the highest exponent of b that di- FactorInteger[n] vides n. returns the factorization of n as a list of factors and exponents. >> IntegerExponent[16, 2] 4 >> factors = FactorInteger[2010] {{2, 1} , {3, 1} , {5, 1} , {67, 1}} >> IntegerExponent[-510000] 4 To get back the original number: >> >> Times @@ Power @@@ factors IntegerExponent[10, b] 2 010 IntegerExponent [10, b] FactorInteger factors rationals using negative exponents: MantissaExponent >> FactorInteger[2010 / 2011] {{2, 1} , {3, 1} , {5, 1} , { } { − }} MantissaExponent[n] 67, 1 , 2 011, 1 finds a list containing the mantissa and exponent of a given number n. MantissaExponent[n, b] FractionalPart finds the base b mantissa and exponent of n. FractionalPart[n] finds the fractional part of n. >> MantissaExponent[2.5*10^20] {0.25, 21} >> FractionalPart[4.1] 0.1 >> MantissaExponent[125.24] {0.12524, 3} >> FractionalPart[-5.25] − 0.25 >> MantissaExponent[125., 2] {0.976563, 7}
>> MantissaExponent[10, b] MantissaExponent [10, b]
246 NextPrime When given a list of integers, a list is returned: >> Prime[{5, 10, 15}] NextPrime[n] {11, 29, 47} gives the next prime after n. NextPrime[n,k] 1.2 isn’t an integer gives the kth prime after n. >> Prime[1.2] Prime [1.2]
>> NextPrime[10000] Since 0 is less than 1, like 1.2 it is invalid. 10 007 >> Prime[{0, 1, 1.2, 3}] >> NextPrime[100, -5] {Prime [0] , 2, Prime [1.2] , 5} 73
>> NextPrime[10, -5] PrimePi −2
>> NextPrime[100, 5] PrimePi[x] 113 gives the number of primes less than or equal to x. >> NextPrime[5.5, 100] 563 PrimePi is the inverse of Prime: >> NextPrime[5, 10.5] >> PrimePi[2] NextPrime [5, 10.5] 1
>> PrimePi[100] PartitionsP 25 >> PrimePi[-1] PartitionsP[n] 0 return the number p(n) of unrestricted >> PrimePi[3.5] partitions of the integer n. 2
>> PrimePi[E] >> Table[PartitionsP[k], {k, -2, 12}] 1 {0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77} PrimePowerQ
PrimePowerQ[n] Prime returns True if n is a power of a prime number. Prime[n]
Prime[{n0, n1, ...}] >> PrimePowerQ[9] returns the nth prime number where n is True an positive Integer. If given a list of inte- gers, the return value is a list with Prime >> PrimePowerQ[52142] applied to each. False
>> PrimePowerQ[-8] Note that the first prime is 2, not 1: True >> Prime[1]
2 >> PrimePowerQ[371293] True >> Prime[167] 991
247 RandomPrime RandomChoice
RandomPrime[{imin, $imax}] RandomChoice[items] gives a random prime between imin and randomly picks one item from items. imax. RandomChoice[items, n] RandomPrime[imax] randomly picks n items from items. Each gives a random prime between 2 and pick in the n picks happens from the imax. given set of items, so each item can be RandomPrime[range, n] picked any number of times. gives a list of n random primes in range. RandomChoice[items,{n1, n2, ...}] randomly picks items from items and ar-
>> RandomPrime[{14, 17}] ranges the picked items in the nested list structure described by {n1, n2, ...}. 17 RandomChoice[weights -> items, n] >> RandomPrime[{14, 16}, 1] randomly picks n items from items and Therearenoprimesinthespecifiedinterval. uses the corresponding numeric values in [ ] weights to determine how probable it is { } RandomPrime 14, 16 , 1 for each item in items to get picked (in the long run, items with higher weights >> RandomPrime[{8,12}, 3] will get picked more often than ones with {11, 11, 11} lower weight). RandomChoice[weights -> items] >> RandomPrime[{10,30}, {2,5}] randomly picks one items from items us- {{19, 19, 19, 19, 19} , ing weights weights. {19, 19, 19, 19, 19}} RandomChoice[weights -> items,{n1, n2, ...}] randomly picks a structured list of items Random number generation from items using weights weights.
Random number generation Note: SeedRandom is used below so we get re- Random numbers are generated using the peatable “random” numbers that we can test. Mersenne Twister. >> SeedRandom[42]
>> RandomChoice[{a, b, c}] Random {c} Legacy function. Superseded by RandomReal, RandomInteger and RandomComplex. >> SeedRandom[42] (* Set for repeatable randomness *)
>> RandomChoice[{a, b, c}, 20] {c, a, c, c, a, a, c, b, c, c, c, c, a, c, b, a, b, b, b, b}
>> SeedRandom[42]
>> RandomChoice[{"a", {1, 2}, x, {}}, 10] {x, {} , a, x, x, {} , a, a, x, {1, 2}}
>> SeedRandom[42]
>> RandomChoice[{a, b, c}, {5, 2}] {{c, a} , {c, c} , {a, a} , {c, b} , {c, c}}
248 >> SeedRandom[42] RandomInteger
>> RandomChoice[{1, 100, 5} -> {a, RandomInteger[{ , }] b, c}, 20] min max yields a pseudorandom integer in the {b, b, b, b, b, b, b, b, b, b, range from min to max inclusive. b, c, b, b, b, b, b, b, b, b} RandomInteger[max] yields a pseudorandom integer in the range from 0 to max inclusive. RandomComplex RandomInteger[] gives 0 or 1. RandomInteger[range, n] RandomComplex[{z_min, z_max}] gives a list of n pseudorandom integers. yields a pseudorandom complex num- RandomInteger[range,{n1, n2, ...}] ber in the rectangle with complex corners gives a nested list of pseudorandom inte- z_min and z_max. gers. RandomComplex[z_max] yields a pseudorandom complex number >> RandomInteger[{1, 5}] in the rectangle with corners at the origin and at z_max. 4 RandomComplex[] >> RandomInteger[100, {2, 3}] // yields a pseudorandom complex number TableForm with real and imaginary parts from 0 to 1. RandomComplex[range, n] 75 97 20 gives a list of n pseudorandom complex 34 61 73 numbers. RandomComplex[range,{n1, n2, ...}] Calling RandomInteger changes $RandomState: gives a nested list of pseudorandom com- >> previousState = $RandomState; plex numbers. >> RandomInteger[]
>> RandomComplex[] 0
0.581769 + 0.685436I >> $RandomState != previousState
>> RandomComplex[{1+I, 5+5I}] True 2.86092 + 1.87268I
>> RandomComplex[1+I, 5] RandomReal {0.539603 + 0.550787I, 0.289˜ RandomReal[{ , }] ˜271 + 0.725075I, 0.683522 + min max yields a pseudorandom real number in 0.617513I, 0.492286 + 0.164˜ the range from min to max. } ˜871I, 0.593449 + 0.363578I RandomReal[max] yields a pseudorandom real number in >> RandomComplex[{1+I, 2+2I}, {2, the range from 0 to max. 2}] RandomReal[] {{1.30849 + 1.41458I, 1.191˜ yields a pseudorandom real number in ˜59 + 1.29931I} , {1.25355 + the range from 0 to 1. 1.02239I, 1.97414 + 1.07719I}} RandomReal[range, n] gives a list of n pseudorandom real num- bers. RandomReal[range,{n1, n2, ...}] gives a nested list of pseudorandom real numbers.
>> RandomReal[] 0.164393
249 >> RandomReal[{1, 5}] >> RandomSample[{"a", {1, 2}, x, 1.84723 {}}, 3] {{1, 2} , {} , a}
RandomSample >> SeedRandom[42]
>> RandomSample[Range[100], {2, 3}] RandomSample[items] randomly picks one item from items. {{84, 54, 71} , {46, 45, 40}} RandomSample[items, n] >> SeedRandom[42] randomly picks n items from items. Each pick in the n picks happens after the pre- >> RandomSample[Range[100] -> Range vious items picked have been removed [100], 5] from items, so each item can be picked at most once. {62, 98, 86, 78, 40} RandomSample[items,{n1, n2, ...}] randomly picks items from items and ar- ranges the picked items in the nested list $RandomState structure described by {n1, n2, ...}. Each item gets picked at most once. $RandomState RandomSample[weights -> items, n] is a long number representing the inter- randomly picks n items from items and nal state of the pseudorandom number uses the corresponding numeric values in generator. weights to determine how probable it is for each item in items to get picked (in the long run, items with higher weights >> Mod[$RandomState, 10^100] will get picked more often than ones with 4 655 454 733 528 649 727 215 205 ˜ lower weight). Each item gets picked at ˜217 452 230 466 834 005 504 017 ˜ most once. ˜054 442 808 272 607 407 752 631 ˜ RandomSample[weights -> items] ˜449 491 946 049 683 375 216 956 462 randomly picks one items from items us- ing weights weights. Each item gets >> IntegerLength[$RandomState] picked at most once. 6 440 RandomSample[weights -> items,{n1, n2, ...}] So far, it is not possible to assign values to randomly picks a structured list of items $RandomState. from items using weights weights. Each >> $RandomState = 42 item gets picked at most once. Itisnotpossibletochangetherandomstate. 42 >> SeedRandom[42] Not even to its own value: >> RandomSample[{a, b, c}] >> $RandomState = $RandomState; {a} Itisnotpossibletochangetherandomstate.
>> SeedRandom[42] SeedRandom >> RandomSample[{a, b, c, d, e, f, g, h}, 7] SeedRandom[n] { } b, f , a, h, c, e, d resets the pseudorandom generator with seed n. >> SeedRandom[42] SeedRandom[] uses the current date and time as the seed.
250 SeedRandom can be used to get reproducible ran- dom numbers: >> SeedRandom[42]
>> RandomInteger[100]
>> RandomInteger[100]
>> SeedRandom[42]
>> RandomInteger[100]
>> RandomInteger[100]
String seeds are supported as well: >> SeedRandom["Mathics"]
>> RandomInteger[100]
Calling SeedRandom without arguments will seed the random number generator to a random state: >> SeedRandom[]
>> RandomInteger[100]
251 31. Special Functions
There are a number of functions found in math- for arbitrary complex values of their arguments. ematical physics and found in standard hand- However defining relations may apply only for books. some special choices of arguments. Here, the One thing to note is that the technical liter- full function corresponds to an extension or “an- ature often contains several conflicting defini- alytic continuation” of the defining relation. tions. So beware and check for conformance For example, integral representations of func- with the Mathics documentation. tions are only valid when the integral exists, but A number of special functions can be evaluated the functions can usually be defined b by ana- lytic continuation.
Contents
KelvinKer .... 256 Pochhammer ... 259 Bessel and Related StruveH 256 Functions ..... 252 ..... Orthogonal Polynomials 259 StruveL ...... 256 AiryAi ...... 253 ChebyshevT ... 259 WeberE ...... 257 AiryAiPrime ... 253 ChebyshevU ... 259 Error Function and AiryAiZero .... 253 GegenbauerC ... 260 Related Functions 257 AiryBi ...... 253 HermiteH ..... 260 Erf ...... 257 AiryBiPrime ... 253 JacobiP ...... 260 Erfc ...... 257 AiryBiZero .... 253 LaguerreL .... 260 FresnelC ..... 257 AngerJ ...... 254 LegendreP .... 260 FresnelS ..... 258 BesselI ...... 254 LegendreQ .... 261 InverseErf .... 258 BesselJ ...... 254 SphericalHarmon- InverseErfc .... 258 BesselJZero .... 254 icY .... 261 Exponential Integral BesselK ...... 254 Exponential Integral and Special and Special BesselY ...... 255 Functions ..... 258 Functions ..... 261 BesselYZero ... 255 ExpIntegralE ... 258 LerchPhi ..... 261 HankelH1 .... 255 ExpIntegralEi ... 258 Zeta ...... 261 HankelH2 .... 255 ProductLog .... 258 KelvinBei ..... 255 Gamma and Related KelvinBer ..... 255 Functions ..... 258 KelvinKei ..... 256 Gamma ...... 259
Bessel and Related Functions Exact values: >> AiryAi[0] Bessel and Related Function 1 3 3 [ ] 3Gamma 2 AiryAi 3 AiryAi can be evaluated numerically: AiryAi[x] >> AiryAi[0.5] returns the Airy function Ai(x). 0.231694
252 >> AiryAi[0.5 + I] >> AiryBi[0] 0.157118 − 0.24104I 5 3 6 [ ] 2 >> Plot[AiryAi[x], {x, -10, 10}] 3Gamma 3
Numeric evaluation: 0.4 >> AiryBi[0.5] 0.2 0.854277
>> AiryBi[0.5 + I] −10 −5 5 10 0.688145 + 0.370815I − 0.2 >> Plot[AiryBi[x], {x, -10, 2}] −0.4 1.5 1.0 AiryAiPrime 0.5 AiryAiPrime[x] returns the derivative of the Airy func- −10 −8 −6 −4 −2 2 tion AiryAi[x]. −0.5 Exact values: >> AiryAiPrime[0] 2 AiryBiPrime − 3 3 [ ] 1 3Gamma 3 AiryBiPrime[x] returns the derivative of the Airy func- Numeric evaluation: tion of the second kind AiryBi[x]. >> AiryAiPrime[0.5] −0.224911 Exact values: >> AiryBiPrime[0] 1 AiryAiZero 3 6 [ ] 1 Gamma 3 AiryAiZero[k] returns the kth zero of the Airy function Numeric evaluation: Ai(z). >> AiryBiPrime[0.5] 0.544573
>> N[AiryAiZero[1]] − 2.33811 AiryBiZero
AiryBi AiryBiZero[k] returns the kth zero of the Airy function Bi(z). AiryBi[x] returns the Airy function of the second kind Bi(x). >> N[AiryBiZero[1]] −1.17371 Exact values:
253 AngerJ >> D[BesselJ[n, z], z] BesselJ [1 + n, z] BesselJ [ − 1 + n, z] − + AngerJ[n, z] 2 2 returns the Anger function J_n(z). >> Plot[BesselJ[0, x], {x, 0, 10}]
>> AngerJ[1.5, 3.5] 0.8 0.294479 0.6 0.4 >> Plot[AngerJ[1, x], {x, -10, 10}] 0.2 0.6 0.4 −0.2 2 4 6 8 10 − 0.2 0.4 − − 10 5 − 5 10 0.2 BesselJZero −0.4 −0.6 BesselJZero[n, k] returns the kth zero of the Bessel function of the first kind J_n(z). BesselI >> N[BesselJZero[0, 1]] BesselI[n, z] 2.40483 returns the modified Bessel function of the first kind I_n(z). BesselK
>> BesselI[1.5, 4] BesselK[n, z] 8.17263 returns the modified Bessel function of
>> Plot[BesselI[0, x], {x, 0, 5}] the second kind K_n(z). 20 >> BesselK[1.5, 4] 15 0.014347
>> Plot[BesselK[0, x], {x, 0, 5}] 10 1.2 5 1.0 0.8 1 2 3 4 5 0.6 0.4 BesselJ 0.2 1 2 3 4 5 BesselJ[n, z] returns the Bessel function of the first kind J_n(z). BesselY
>> BesselJ[0, 5.2] BesselY[n, z] − 0.11029 returns the Bessel function of the second kind Y_n(z).
254 >> BesselY[1.5, 4] >> KelvinBei[0.5] 0.367112 0.0624932
>> Plot[BesselY[0, x], {x, 0, 10}] >> KelvinBei[1.5 + I] 0.326323 + 0.755606I
0.4 >> KelvinBei[0.5, 0.25] 0.2 0.370153
>> Plot[KelvinBei[x], {x, 0, 10}] 2 4 6 8 10 −0.2 10 −0.4 2 4 6 8 10 −10 BesselYZero −20 −30 BesselYZero[n, k] returns the kth zero of the Bessel function of the second kind Y_n(z). KelvinBer >> N[BesselYZero[0, 1]] 0.893577 KelvinBer[z] returns the Kelvin function ber(z). KelvinBer[n, z] HankelH1 returns the Kelvin function ber_n(z).
HankelH1[n, z] >> KelvinBer[0.5] returns the Hankel function of the first ∧ 0.999023 kind H_n 1 (z). >> KelvinBer[1.5 + I] 1.1162 − 0.117944I >> HankelH1[1.5, 4]
0.185286 + 0.367112I >> KelvinBer[0.5, 0.25] 0.148824
HankelH2 >> Plot[KelvinBer[x], {x, 0, 10}] 80 HankelH2[n, z] returns the Hankel function of the second ∧ 60 kind H_n 2 (z). 40 >> HankelH2[1.5, 4] 20 0.185286 − 0.367112I 2 4 6 8 10 KelvinBei
KelvinBei[z] returns the Kelvin function bei(z). KelvinBei[n, z] returns the Kelvin function bei_n(z).
255 KelvinKei StruveH
KelvinKei[z] StruveH[n, z] returns the Kelvin function kei(z). returns the Struve function H_n(z). KelvinKei[n, z]
returns the Kelvin function kei_n(z). >> StruveH[1.5, 3.5] 1.13192 >> KelvinKei[0.5] >> Plot[StruveH[0, x], {x, 0, 20}] −0.671582
>> KelvinKei[1.5 + I] 0.6 − 0.248994 + 0.303326I 0.4 >> KelvinKei[0.5, 0.25] 0.2 −2.0517
>> Plot[KelvinKei[x], {x, 0, 10}] 5 10 15 20 −0.2 2 4 6 8 10 −0.1 −0.2 StruveL −0.3 StruveL[n, z] −0.4 returns the modified Struve function −0.5 L_n(z).
>> StruveL[1.5, 3.5] KelvinKer 4.41126
>> Plot[StruveL[0, x], {x, 0, 5}] KelvinKer[z] returns the Kelvin function ker(z). 20 KelvinKer[n, z] returns the Kelvin function ker_n(z). 15 10 >> KelvinKer[0.5] 0.855906 5
>> KelvinKer[1.5 + I] − − 0.167162 0.184404I 1 2 3 4 5
>> KelvinKer[0.5, 0.25] 0.450023 WeberE >> Plot[KelvinKer[x], {x, 0, 10}] WeberE[n, z] 0.5 returns the Weber function E_n(z). 0.4
0.3 >> WeberE[1.5, 3.5] 0.2 −0.397256 0.1
−0.1 2 4 6 8 10
256 >> Plot[WeberE[1, x], {x, -10, 10}] Erfc
0.6 Erfc[z] 0.4 returns the complementary error func- tion of z. 0.2
>> Erfc[-x] / 2 −10 −5 5 10 −0.2 2 − Erfc [x] 2 −0.4 >> Erfc[1.0] 0.157299
>> Erfc[0] Error Function and Related 1 Functions >> Plot[Erfc[x], {x, -2, 2}] Error Function and Related Function 2.0
Erf 1.5 1.0 Erf[z] returns the error function of z. 0.5 Erf[z0, z1] returns the result of Erf[z1] - Erf[z0]. −2 −1 1 2 Erf[x] is an odd function: >> Erf[-x] −Erf [x] FresnelC
>> Erf[1.0] FresnelC[z] 0.842701 is the Fresnel C integral C(z).
>> Erf[0] >> FresnelC[{0, Infinity}] 0 { } 1 >> {Erf[0, x], Erf[x, 0]} 0, 2 {Erf [x] , − Erf [x]}
>> Integrate[Cos[x^2 Pi/2], {x, 0, >> Plot[Erf[x], {x, -2, 2}] z}] 1.0 FresnelC [z] 0.5 FresnelS −2 −1 1 2 − FresnelS[z] 0.5 is the Fresnel S integral S(z). −1.0 >> FresnelS[{0, Infinity}] { } 1 0, 2
257 >> Integrate[Sin[x^2 Pi/2], {x, 0, >> ExpIntegralE[2.0, 2.0] z}] 0.0375343 FresnelS [z] ExpIntegralEi InverseErf ExpIntegralEi[z] InverseErf[z] returns the exponential integral function returns the inverse error function of z. $Ei(z)$.
>> InverseErf /@ {-1, 0, 1} >> ExpIntegralEi[2.0] {−∞, 0, ∞} 4.95423
>> Plot[InverseErf[x], {x, -1, 1}] ProductLog 1.0 0.5 ProductLog[z] returns the value of the Lambert W func- tion at z. −1.0 −0.5 0.5 1.0 −0.5 The defining equation: − 1.0 >> z == ProductLog[z] * E ^ ProductLog[z] True InverseErf[z] only returns numeric values for -1 <= z <= 1: Some special values: >> InverseErf /@ {0.9, 1.0, 1.1} >> ProductLog[0] {1.16309, ∞, InverseErf [1.1]} 0
>> ProductLog[E] InverseErfc 1 The graph of ProductLog: InverseErfc[ ] z >> Plot[ProductLog[x], {x, -1/E, E returns the inverse complementary error }] function of z. 1.0 >> InverseErfc /@ {0, 1, 2} 0.8 {∞, 0, − ∞} 0.6 0.4 Exponential Integral and 0.2 Special Functions 0.5 1.0 1.5 2.0 2.5 −0.2 Exponential Integral and Special Function
ExpIntegralE Gamma and Related Functions
ExpIntegralE[n, z] Gamma and Related Function returns the exponential integral function $E_n(z)$.
258 Gamma Pochhammer
In number theory the logarithm of the gamma The Pochhammer symbol or rising factorial of- function often appears. For positive real num- ten appears in series expansions for hypergeo- bers, this can be evaluated as Log[Gamma[z]]. metric functions. The Pochammer symbol has a definie value even when the gamma functions Gamma[z] which appear in its definition are infinite. is the gamma function on the complex number z. Pochhammer[a, n] Gamma[z, x] is the Pochhammer symbol (a)_n. is the upper incomplete gamma function. Gamma[z, x0, x1] >> Pochhammer[4, 8] is equivalent to Gamma[z, x0] - Gamma[ 6 652 800 z, x1].
Gamma[z] is equivalent to (z - 1)!: Orthogonal Polynomials >> Simplify[Gamma[z] - (z - 1)!] 0 Orthogonal Polynomial Exact arguments: >> Gamma[8] ChebyshevT 5 040 ChebyshevT[n, x] >> Gamma[1/2] √ returns the Chebyshev polynomial of the Pi first kind T_n(x).
>> Gamma[1, x] − >> ChebyshevT[8, x] E x 1 − 32x2 + 160x4 − 256x6 + 128x8 >> Gamma[0, x] ExpIntegralE [1, x] >> ChebyshevT[1 - I, 0.5] 0.800143 + 1.08198I Numeric arguments: >> Gamma[123.78] 4.21078 × 10204 ChebyshevU
>> Gamma[1. + I] ChebyshevU[n, x] 0.498016 − 0.15495I returns the Chebyshev polynomial of the Both Gamma and Factorial functions are contin- second kind U_n(x). uous: >> Plot[{Gamma[x], x!}, {x, 0, 4}] >> ChebyshevU[8, x] 12 1 − 40x2 + 240x4 − 448x6 + 256x8
10 >> ChebyshevU[1 - I, 0.5] 8 1.60029 + 0.721322I 6 4 GegenbauerC
1 2 3 4 GegenbauerC[n, m, x] returns the Gegenbauer polynomial ∧ C_n (m)(x).
259 >> GegenbauerC[6, 1, x] >> LaguerreL[3/2, 1.7] − −1 + 24x2 − 80x4 + 64x6 0.947134
>> GegenbauerC[4 - I, 1 + 2 I, 0.7] >> LaguerreL[5, 2, x] −3.2621 − 24.9739I 35x2 7x3 7x4 x5 21 − 35x + − + − 2 2 24 120 HermiteH LegendreP HermiteH[n, x] returns the Hermite polynomial H_n(x). LegendreP[n, x] returns the Legendre polynomial P_n(x). >> HermiteH[8, x] LegendreP[n, m, x] 2 returns the associated Legendre polyno- 1 680 − 13 440x + 13 ˜ ∧ mial P m_n(x). ˜440x4 − 3 584x6 + 256x8
>> HermiteH[3, 1 + I] >> LegendreP[4, x] − 28 + 4I 3 15x2 35x4 − + >> HermiteH[4.2, 2] 8 4 8
77.5291 >> LegendreP[5/2, 1.5] 4.17762
JacobiP >> LegendreP[1.75, 1.4, 0.53] −1.32619 JacobiP[n, a, b, x] >> LegendreP[1.6, 3.1, 1.5] returns the Jacobi polynomial ∧ P_n (a,b)(x). −0.303998 − 1.91937I LegendreP can be used to draw generalized Lis- >> JacobiP[1, a, b, z] ( ) sajous figures: a b a b >> ParametricPlot[ {LegendreP[7, x − + z 1 + + 2 2 2 2 ], LegendreP[5, x]}, {x, -1, 1}]
>> JacobiP[3.5 + I, 3, 2, 4 - I] 0.6 1 410.02 + 5 797.3I 0.4 0.2 LaguerreL −0.4 −0.2 0.2 0.4 −0.2 LaguerreL[n, x] −0.4 returns the Laguerre polynomial L_n(x). LaguerreL[n, a, x] −0.6 returns the generalised Laguerre polyno- ∧ mial L a_n(x).
>> LaguerreL[8, x] 28x3 35x4 1 − 8x + 14x2 − + 3 12 7x5 7x6 x7 x8 − + − + 15 180 630 40 320
260 LegendreQ Zeta
LegendreQ[n, x] Zeta[z] returns the Legendre function of the sec- returns the Riemann zeta function of z. ond kind Q_n(x). LegendreQ[n, m, x] >> Zeta[2] returns the associated Legendre function 2 ∧ Pi of the second Q m_n(x). 6
>> Zeta[-2.5 + I] >> LegendreQ[5/2, 1.5] 0.0235936 + 0.0014078I 0.036211 − 6.56219I
>> LegendreQ[1.75, 1.4, 0.53] 2.05499
>> LegendreQ[1.6, 3.1, 1.5] −1.71931 − 7.70273I
SphericalHarmonicY
SphericalHarmonicY[l, m, theta, phi] returns the spherical harmonic function ∧ Y_l m(theta, phi).
>> SphericalHarmonicY[3/4, 0.5, Pi /5, Pi/3] 0.254247 + 0.14679I
>> SphericalHarmonicY[3, 1, theta, phi] √ ( ) 21 1 − 5Cos [theta]2 EIphiSin [theta] √ 8 Pi
Exponential Integral and Special Functions
Exponential Integral and Special Function
LerchPhi
LerchPhi[z,s,a] gives the Lerch transcendent (z,s,a).
>> LerchPhi[2, 3, -1.5] 19.3893 − 2.1346I
>> LerchPhi[1, 2, 1/4] 17.1973
261 32. Strings and Characters
Contents
StringInsert .... 265 LetterCharacter .. 268 Characters in Strings . 262 StringJoin (<>) .. 265 StartOfLine .... 268 CharacterRange . 262 StringLength ... 265 StartOfString ... 268 Characters .... 262 StringPosition .. 265 StringCases .... 269 DigitQ ...... 262 StringReplace ... 266 StringExpression LetterQ ...... 263 StringReverse ... 266 (~~) .... 269 LowerCaseQ ... 263 StringRiffle .... 266 StringFreeQ .... 270 ToLowerCase ... 263 StringSplit .... 267 StringMatchQ .. 270 ToUpperCase ... 263 StringTake .... 267 WhitespaceChar- UpperCaseQ ... 263 acter .... 270 Character Codes 263 StringTrim .... 267 .... WordBoundary .. 270 FromCharacterCode 263 String Patterns ..... 267 WordCharacter .. 270 ToCharacterCode . 264 DigitCharacter .. 267 Regular Expressions .. 270 Operations on Strings . 264 EndOfLine .... 268 RegularExpression 270 StringDrop .... 264 EndOfString ... 268
Characters in Strings DigitQ
Characters in String DigitQ[string] yields True if all the characters in the string are digits, and yields False oth- CharacterRange erwise.
>> DigitQ["9"] CharacterRange["a‘‘,”b"] returns a list of the Unicode characters True from a to b inclusive. >> DigitQ["a"] False >> CharacterRange["a", "e"] {a, b, c, d, e} >> DigitQ ["01001101011000010111010001101000011010010110001101110011"] >> CharacterRange["b", "a"] {} True
>> DigitQ["-123456789"] Characters False
Characters["string"] LetterQ returns a list of the characters in string.
LetterQ[string] yields True if all the charac- >> Characters["abc"] ters in the string are letters, and yields False { } a, b, c otherwise.
262 >> LetterQ["m"] >> UpperCaseQ["ABC"] True True
>> LetterQ["9"] An empty string returns True. False >> UpperCaseQ[""] True >> LetterQ["Mathics"] True
>> LetterQ["Welcome to Mathics"] Character Codes False Character Code
LowerCaseQ FromCharacterCode
LowerCaseQ[s] FromCharacterCode[n] returns True if s consists wholly of lower returns the character corresponding to case characters. Unicode codepoint n. FromCharacterCode[{n1, n2, ...}] >> LowerCaseQ["abc"] returns a string with characters corre- True sponding to n_i. FromCharacterCode[{{n11, n12, ...}, { An empty string returns True. n21, n22, ...}, ...}] >> LowerCaseQ[""] returns a list of strings. True
>> FromCharacterCode[100] ToLowerCase d
>> FromCharacterCode[228, "ISO8859 ToLowerCase[s] -1"] returns s in all lower case. ä
>> FromCharacterCode[{100, 101, >> ToLowerCase["New York"] 102}] new york def
>> ToCharacterCode[%] ToUpperCase {100, 101, 102}
ToUpperCase[s] >> FromCharacterCode[{{97, 98, 99}, returns s in all upper case. {100, 101, 102}}] {abc, def} >> ToUpperCase["New York"] >> ToCharacterCode["abc 123"] // NEW YORK FromCharacterCode abc 123 UpperCaseQ
UpperCaseQ[s] returns True if s consists wholly of upper case characters.
263 ToCharacterCode StringDrop
ToCharacterCode["string"] StringDrop["string", n] converts the string to a list of character gives string with the first n characters codes (Unicode codepoints). dropped. ToCharacterCode[{"string1‘‘,”string2", StringDrop["string", -n] ...}] gives string with the last n characters converts a list of strings to character dropped. codes. StringDrop["string", {n}] gives string with the nth character >> ToCharacterCode["abc"] dropped. {97, 98, 99} StringDrop["string", {m, n}] gives string with the characters m through >> FromCharacterCode[%] n dropped. abc
>> StringDrop["abcde", 2] >> ToCharacterCode["\[Alpha]\[Beta ]\[Gamma]"] cde
{945, 946, 947} >> StringDrop["abcde", -2] abc >> ToCharacterCode["ä", "UTF8"] {195, 164} >> StringDrop["abcde", {2}] acde >> ToCharacterCode["ä", "ISO8859 -1"] >> StringDrop["abcde", {2,3}] {228} ade
>> StringDrop["abcd",{3,2}] >> ToCharacterCode[{"ab", "c"}] {{97, 98} , {99}} abcd
>> StringDrop["abcd",0] >> ToCharacterCode[{"ab", x}] abcd Stringorlistofstringsexpectedatposition1inToCharacterCode[{ab, x}]. [ ] ToCharacterCode {ab, x} StringInsert
>> ListPlot[ToCharacterCode["plot StringInsert["string‘‘,”snew", n] this string"], Filling -> Axis] yields a string with snew inserted starting 116 at position n in string. StringInsert[" ‘‘,” ", - ] 114 string snew n inserts a at position n from the end of 112 "string". 110 StringInsert["string‘‘,”snew", {n_1, 108 n_2, ...}] 106 inserts a copy of snew at each position n_i in string; the n_i are taken before any in- 5 10 15 sertion is done. StringInsert[{s_1, s_2, ...}, "snew", n] Operations on Strings gives the list of resutls for each of the s_i.
Operations on String >> StringInsert["noting", "h", 4] nothing
264 >> StringInsert["note", "d", -1] >> StringLength[x] noted Stringexpected.
>> StringInsert["here", "t", -5] StringLength [x] there
>> StringInsert["adac", "he", {1, StringPosition 5}] headache StringPosition["string", patt] gives a list of starting and ending posi- >> StringInsert[{"something", " sometimes"}, " ", 5] tions where patt matches "string". StringPosition["string", patt, n] {some thing, some times} returns the first n matches only. StringPosition["string", {patt1, patt2, >> StringInsert["1234567890123456", ...}, n] ".", Range[-16, -4, 3]] matches multiple patterns. 1.234.567.890.123.456 StringPosition[{s1, s2, ...}, patt] returns a list of matches for multiple strings. StringJoin (<>)
>> StringPosition["123 StringJoin["s1‘‘,”s2", ...] ABCxyABCzzzABCABC", "ABC"] returns the concatenation of the strings {{4, 6} , {9, 11} , {15, 17} , {18, 20}} s1, s2,. >> StringPosition["123
>> StringJoin["a", "b", "c"] ABCxyABCzzzABCABC", "ABC", 2] abc {{4, 6} , {9, 11}}
>> "a" <> "b" <> "c" // InputForm StringPosition can be useful for searching "abc" through text. >> data = Import["ExampleData/ StringJoin flattens lists out: EinsteinSzilLetter.txt"]; >> StringJoin[{"a", "b"}] //
InputForm >> StringPosition[data, "uranium"] "ab" {{299, 305} , {870, 876} , {1 538, 1 ˜ ˜544} , {1 671, 1 677} , {2 300, 2 306 >> Print[StringJoin[{"Hello", " ", {"world"}}, "!"]] } , {2 784, 2 790} , {3 093, 3 099}} Helloworld!
StringLength
StringLength["string"] gives the length of string.
>> StringLength["abc"] 3 StringLength is listable: >> StringLength[{"a", "bc"}] {1, 2}
265 StringReplace StringReverse
StringReplace["string‘‘,”a"->"b"] StringReverse["string"] replaces each occurrence of old with new reverses the order of the characters in in string. “string”. StringReplace["string", {"s1"->"sp1‘‘, ” "->" "}] s2 sp2 >> StringReverse["live"] performs multiple replacements of each si by the corresponding spi in string. evil StringReplace["string", srules, n] only performs the first n replacements. StringRiffle StringReplace[{"string1‘‘,”string2", ...}, srules] performs the replacements specified by StringRiffle[{s1, s2, s3, ...}] srules on a list of strings. returns a new string by concatenating all the si, with spaces inserted between StringReplace replaces all occurrences of one them. substring with another: StringRiffle[list, sep] inserts the separator sep between all ele- >> StringReplace["xyxyxyyyxxxyyxy", "xy" -> "A"] ments in list. StringRiffle[list, {‘‘left’, “sep”, AAAyyxxAyA “right”}]’ use left and right as delimiters after con- Multiple replacements can be supplied: catenation. >> StringReplace["xyzwxyzwxxyzxyzw ", {"xyz" -> "A", "w" -> "BCD"}] >> StringRiffle[{"a", "b", "c", "d ABCDABCDxAABCD ", "e"}] Only replace the first 2 occurences: a b c d e >> StringReplace["xyxyxyyyxxxyyxy", >> StringRiffle[{"a", "b", "c", "d "xy" -> "A", 2] ", "e"}, ", "] AAxyyyxxxyyxy a, b, c, d, e
Also works for multiple rules: >> StringRiffle[{"a", "b", "c", "d >> StringReplace["abba", {"a" -> "A ", "e"}, {"(", " ", ")"}] ", "b" -> "B"}, 2] (a b c d e) ABba StringReplace acts on lists of strings too: StringSplit >> StringReplace[{"xyxyxxy", " yxyxyxxxyyxy"}, "xy" -> "A"] StringSplit["s"] {AAxA, yAAxxAyA} splits the string s at whitespace, discard- StringReplace also can be used as an operator: ing the whitespace and returning a list of strings. >> StringReplace["y" -> "ies"][" city"] StringSplit["s‘‘,”d"] splits s at the delimiter d. cities StringSplit[s, {"d1‘‘,”d2", ...}] splits s using multiple delimiters. StringSplit[{s_1, $s_2, ...}, {"d1‘‘, ”d2", ...}] returns a list with the result of applying the function to each element.
266 >> StringSplit["abc,123", ","] >> StringTake[{"abcdef", "stuv", " {abc, 123} xyzw"}, -2] {ef, uv, zw} >> StringSplit["abc 123"] {abc, 123} StringTake also supports standard sequence specifications >> StringSplit["abc,123.456", {",", >> StringTake["abcdef", All] "."}] abcdef {abc, 123, 456}
>> StringSplit["a b c", StringTrim RegularExpression[" +"]] {a, b, c} StringTrim[s] returns a version of s with whitespace re- >> StringSplit[{"a b", "c d"}, moved from start and end. RegularExpression[" +"]]
{{a, b} , {c, d}} >> StringJoin["a", StringTrim[" \tb \n "], "c"] abc StringTake >> StringTrim["ababaxababyaabab", RegularExpression["(ab)+"]] StringTake["string", n] gives the first n characters in string. axababya StringTake["string", -n] gives the last n characters in string. StringTake["string", {n}] String Patterns gives the nth character in string. StringTake["string", {m, n}] String Pattern gives characters m through n in string. StringTake["string", {m, n, s}] gives characters m through n in steps of s. DigitCharacter StringTake[{s1, s2, ...} spec}] gives the list of results for each of the si. DigitCharacter represents the digits 0-9.
>> StringTake["abcde", 2] ab >> StringMatchQ["1", DigitCharacter ] >> StringTake["abcde", 0] True
>> StringTake["abcde", -2] >> StringMatchQ["a", DigitCharacter ] de False >> StringTake["abcde", {2}] >> StringMatchQ["12", b DigitCharacter] >> StringTake["abcd", {2,3}] False bc >> StringMatchQ["123245", >> StringTake["abcdefgh", {1, 5, DigitCharacter..] 2}] True ace Take the last 2 characters from several strings:
267 EndOfLine StartOfLine
EndOfString StartOfString represents the end of a line in a string. represents the start of a line in a string.
>> StringReplace["aba\nbba\na\nab", >> StringReplace["aba\nbba\na\nab", "a" ~~EndOfLine -> "c"] StartOfLine ~~"a" -> "c"] abc cba bbc bba c c ab cb
>> StringSplit["abc\ndef\nhij", >> StringSplit["abc\ndef\nhij", EndOfLine] StartOfLine] {abc, {abc def, , def hij} , hij}
EndOfString StartOfString
EndOfString StartOfString represents the end of a string. represents the start of a string.
Test whether strings end with “e”: Test whether strings start with “a”: >> StringMatchQ[#, __ ~~"e" ~~ >> StringMatchQ[#, StartOfString ~~ EndOfString] &/@ {"apple", " "a" ~~__] &/@ {"apple", "banana banana", "artichoke"} ", "artichoke"} {True, False, True} {True, False, True}
>> StringReplace["aab\nabb", "b" ~~ >> StringReplace["aba\nabb", EndOfString -> "c"] StartOfString ~~"a" -> "c"] aab cba abc abb
LetterCharacter
LetterCharacter represents letters.
>> StringMatchQ[#, LetterCharacter] & /@ {"a", "1", "A", " ", "."} {True, False, True, False, False}
LetterCharacter also matches unicode charac- ters. >> StringMatchQ["\[Lambda]", LetterCharacter] True
268 StringCases >> StringCases["a#ä_123", LetterCharacter] StringCases["string", pattern] {a, ä} gives all occurences of pattern in string. StringReplace["string", pattern -> form] gives all instances of form that stem from StringExpression (~~) occurences of pattern in string. StringCases["string", {pattern1, pattern2, ...}] StringExpression[s_1, s_2, ...] gives all occurences of pattern1, pattern2, represents a sequence of strings and sym- .... bolic string objects s_i. StringReplace["string", pattern, n] gives only the first n occurences. >> "a" ~~ "b" // FullForm StringReplace[{"string1‘‘,”string2", "ab" ...}, pattern] gives occurences in string1, string2, ... StringFreeQ
>> StringCases["axbaxxb", "a" ~~x_ ~~"b"] StringFreeQ["string", patt] {axb} returns True if no substring in string matches the string expression patt, and >> StringCases["axbaxxb", "a" ~~x__ returns False otherwise. ~~"b"] StringFreeQ[{‘‘s1’, “s2”, ...}, patt]’ returns the list of results for each element {axbaxxb} of string list.
>> StringCases["axbaxxb", Shortest StringFreeQ[‘‘string’, {p1, p2, ...}]’ ["a" ~~x__ ~~"b"]] returns True if no substring matches any of the pi. { } axb, axxb StringFreeQ[patt] represents an operator form of >> StringCases["-abc- def -uvw- xyz StringFreeQ that can be applied to ", Shortest["-" ~~x__ ~~"-"] -> an expression. x] {abc, uvw} >> StringFreeQ["mathics", "m" ~~__ ~~"s"] >> StringCases["-öhi- -abc- -.-", "-" ~~x : WordCharacter .. ~~"-" False -> x] >> StringFreeQ["mathics", "a" ~~__ {öhi, abc} ~~"m"]
>> StringCases["abc-abc xyz-uvw", True Shortest[x : WordCharacter .. ~~ >> StringFreeQ["Mathics", "MA" , "-" ~~x_] -> x] IgnoreCase -> True] { } abc False
>> StringCases["abba", {"a" -> 10, >> StringFreeQ[{"g", "a", "laxy", " "b" -> 20}, 2] universe", "sun"}, "u"] {10, 20} {True, True, True, False, False}
>> StringCases["a#ä_123", WordCharacter] {a, ä, 1, 2, 3}
269 >> StringFreeQ["e" ~~___ ~~"u"] /@ >> StringMatchQ[" \n", Whitespace] {"The Sun", "Mercury", "Venus", True "Earth", "Mars", "Jupiter", " Saturn", "Uranus", "Neptune"} {False, False, False, True, WordBoundary True, True, True, True, False} WordBoundary >> StringFreeQ[{"A", "Galaxy", "Far represents the boundary between words. ", "Far", "Away"}, {"F" ~~__ ~~" r", "aw" ~~___}, IgnoreCase -> >> StringReplace["apple banana True] orange artichoke", "e" ~~ {True, True, False, False, False} WordBoundary -> "E"] applE banana orangE artichokE StringMatchQ
>> StringMatchQ["abc", "abc"] WordCharacter True WordCharacter >> StringMatchQ["abc", "abd"] represents a single letter or digit charac- False ter.
>> StringMatchQ["15a94xcZ6", ( >> StringMatchQ[#, WordCharacter] DigitCharacter | LetterCharacter &/@ {"1", "a", "A", ",", " "} )..] {True, True, True, False, False} True Use StringMatchQ as an operator Test whether a string is alphanumeric: >> StringMatchQ["abc123DEF", >> StringMatchQ[LetterCharacter]["a "] WordCharacter..] True True
>> StringMatchQ["$b;123", WordCharacter..] WhitespaceCharacter False
WhitespaceCharacter represents a single whitespace character. Regular Expressions
>> StringMatchQ["\n", Regular Expression WhitespaceCharacter] True RegularExpression
>> StringSplit["a\nb\r\nc\rd", WhitespaceCharacter] RegularExpression[‘‘regex’]’ {a, b, c, d} represents the regex specified by the string $“regex”$. For sequences of whitespace characters use
Whitespace: >> StringSplit["1.23, 4.56 7.89", >> StringMatchQ[" \n", RegularExpression["(\\s|,)+"]] WhitespaceCharacter] {1.23, 4.56, 7.89} False
270 33. File Formats
Built-in Importers. Contents
PlaintextImport .. 271 TagsImport .... 272 HTML ...... 271 SourceImport ... 271 XMLGetString .. 272 DataImport .... 271 TitleImport .... 271 XMLObjectImport 272 HTMLGetString . 271 XMLObjectImport 271 HyperlinksImport 271 XML ...... 272 ImageLinksImport 271 PlaintextImport .. 272
HTML PlaintextImport
HTML >> DeleteDuplicates[StringCases[ Import["ExampleData/ Basic implementation for a HTML importer PrimeMeridian.html"], RegularExpression["Wiki[a-z DataImport ]+"]]]
>> Import["ExampleData/ PrimeMeridian.html", "Data"][[1, 1, 2, 3]] SourceImport
{Washington, D.C., 77ˇr0356.07W >> DeleteDuplicates[StringCases[ (1 897) or 77ˇr0402.24W (NAD 27) Import["ExampleData/ PrimeMeridian.html", "Source"], or 77ˇr0401.16W (NAD 83), New RegularExpression[""]]] Naval Observatory meridian} {, <tr>, <th>, <td>}</p><p>HTMLGetString TitleImport HyperlinksImport >> Import["ExampleData/ >> Import["ExampleData/ PrimeMeridian.html", "Title"] PrimeMeridian.html", "Hyperlinks Prime meridian - Wikipedia "][[1]] /wiki/Prime_meridian_(Greenwich) XMLObjectImport</p><p>ImageLinksImport >> Part[Import["ExampleData/ PrimeMeridian.html", "XMLObject >> Import["ExampleData/ "], 2, 3, 1, 3, 2] [ PrimeMeridian.html", "ImageLinks {} { "][[6]] XMLElement title, , ]Prime meridian - Wikipedia} //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Prime_meridian.jpg/180px-Prime_meridian.jpg</p><p>271 XML</p><p>XML</p><p>PlaintextImport</p><p>>> StringReplace[StringTake[Import ["ExampleData/InventionNo1.xml", "Plaintext"],31], FromCharacterCode[10]->"/"] MuseScore 1.2/2 012-09-12/5.7/40</p><p>TagsImport</p><p>>> Take[Import["ExampleData/ InventionNo1.xml", "Tags"], 10] {accidental, alter, arpeggiate, articulations, attributes, backup, bar-style, barline, beam, beat-type}</p><p>XMLGetString</p><p>>> Head[XML‘Parser‘XMLGetString["<a ></a>"]] XMLObject [Document]</p><p>XMLObjectImport</p><p>>> Part[Import["ExampleData/ InventionNo1.xml", "XMLObject"], 2, 3, 1] [ XMLElement{ identification[ , {} , {XMLElement [encoding, {} , XMLElement software] , {} { } , MuseScore[ 1.2 , XMLElement encoding-date]}]}] , {} , {2 012-09-12}</p><p>>> Part[Import["ExampleData/ Namespaces.xml"], 2] [ {} { XMLElement title, , ]Prime meridian - Wikipedia}</p><p>272 Part III.</p><p>License</p><p>273 A. GNU General Public License</p><p>Version 3, 29 June 2007 Copyright l’ 2007 <a href="/tags/Free_software/" rel="tag">Free Software</a> Foundation, Inc. http://fsf.org/ Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.</p><p>Preamble</p><p>The GNU General Public License is a free, copyleft license for software and other kinds of works. The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program—to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for them if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs, and that you know you can do these things. To protect your rights, we need to prevent others from denying you these rights or asking you to sur- render the rights. Therefore, you have certain responsibilities if you distribute copies of the software, or if you modify it: responsibilities to respect the freedom of others. For example, if you distribute copies of such a program, whether gratis or for a fee, you must pass on to the recipients the same freedoms that you received. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. Developers that use the GNU GPL protect your rights with two steps: (1) assert copyright on the soft- ware, and (2) offer you this License giving you legal permission to copy, distribute and/or modify it. For the developers and authors protection, the GPL clearly explains that there is no warranty for this free software. For both users and authors sake, the GPL requires that modified versions be marked as changed, so that their problems will not be attributed erroneously to authors of previous versions. Some devices are designed to deny users access to install or run modified versions of the software inside them, although the manufacturer can do so. This is fundamentally incompatible with the aim of protecting users’ freedom to change the software. The systematic pattern of such abuse occurs in the area of products for individuals to use, which is precisely where it is most unacceptable. Therefore, we have designed this version of the GPL to prohibit the practice for those products. If such problems arise substantially in other domains, we stand ready to extend this provision to those domains in future versions of the GPL, as needed to protect the freedom of users. Finally, every program is threatened constantly by software patents. States should not allow patents to restrict development and use of software on general-purpose computers, but in those that do, we wish to avoid the special danger that patents applied to a free program could make it effectively proprietary. To prevent this, the GPL assures that patents cannot be used to render the program non-free. The precise terms and conditions for copying, distribution and modification follow.</p><p>274 TERMS AND CONDITIONS</p><p>0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>275 2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so.</p><p>276 A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User</p><p>277 Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>278 8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License.</p><p>279 Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>280 14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>0. Definitions. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks.</p><p>281 The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as</p><p>282 your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>283 6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the</p><p>284 recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates</p><p>285 your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party.</p><p>286 If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published</p><p>287 by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>1. Source Code. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer</p><p>288 or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>289 3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange.</p><p>290 • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>291 7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per-</p><p>292 manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your</p><p>293 recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>294 15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>2. Basic Permissions. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this</p><p>295 criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the</p><p>296 work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and</p><p>297 only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re-</p><p>298 moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do</p><p>299 not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a</p><p>300 third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO</p><p>301 THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work.</p><p>302 A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice;</p><p>303 keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the</p><p>304 Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this</p><p>305 License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>306 10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent</p><p>307 license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>308 16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>4. Conveying Verbatim Copies. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major</p><p>309 Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>310 5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work.</p><p>311 A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or</p><p>312 service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts.</p><p>313 You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot</p><p>314 convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>315 17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>5. Conveying Modified Source Versions. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami-</p><p>316 cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices.</p><p>317 • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial</p><p>318 commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that</p><p>319 term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>320 11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>321 13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>322 6. Conveying Non-Source Forms. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>323 2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so.</p><p>324 A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User</p><p>325 Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>326 8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License.</p><p>327 Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>328 14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>7. Additional Terms. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks.</p><p>329 The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as</p><p>330 your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>331 6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the</p><p>332 recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates</p><p>333 your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party.</p><p>334 If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published</p><p>335 by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>8. Termination. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer</p><p>336 or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>337 3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange.</p><p>338 • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>339 7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per-</p><p>340 manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your</p><p>341 recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>342 15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>9. Acceptance Not Required for Having Copies. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this</p><p>343 criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the</p><p>344 work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and</p><p>345 only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re-</p><p>346 moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do</p><p>347 not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a</p><p>348 third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO</p><p>349 THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>10. Automatic Licensing of Downstream Recipients. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work.</p><p>350 A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice;</p><p>351 keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the</p><p>352 Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this</p><p>353 License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>354 10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent</p><p>355 license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>356 16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>11. Patents. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major</p><p>357 Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>358 5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work.</p><p>359 A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or</p><p>360 service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts.</p><p>361 You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot</p><p>362 convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>363 17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>12. No Surrender of Others’ Freedom. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami-</p><p>364 cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices.</p><p>365 • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial</p><p>366 commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that</p><p>367 term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>368 11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>369 13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>370 13. Use with the GNU Affero General Public License. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>371 2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so.</p><p>372 A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User</p><p>373 Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>374 8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License.</p><p>375 Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>376 14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>14. Revised Versions of this License. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks.</p><p>377 The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as</p><p>378 your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>379 6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the</p><p>380 recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates</p><p>381 your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party.</p><p>382 If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published</p><p>383 by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>15. Disclaimer of Warranty. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer</p><p>384 or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>385 3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange.</p><p>386 • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>387 7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per-</p><p>388 manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your</p><p>389 recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>390 15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>16. Limitation of Liability. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this</p><p>391 criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work. A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the</p><p>392 work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and</p><p>393 only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re-</p><p>394 moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do</p><p>395 not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a</p><p>396 third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO</p><p>397 THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>17. Interpretation of Sections 15 and 16. 0. Definitions.</p><p>This License refers to version 3 of the GNU General Public License. Copyright also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. The Program refers to any copyrightable work licensed under this License. Each licensee is addressed as you. Licensees and recipients may be individuals or organizations. To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a modified version of the earlier work or a work based on the earlier work. A covered work means either the unmodified Program or a work based on the Program. To propagate a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To convey a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con- venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the inter- face presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.</p><p>1. Source Code.</p><p>The source code for a work means the preferred form of the work for making modifications to it. Object code means any non-source form of a work.</p><p>398 A Standard Interface means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The System Libraries of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A Major Component, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The Corresponding Source for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work’s System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynami- cally linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work.</p><p>2. Basic Permissions.</p><p>All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited per- mission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sub- licensing is not allowed; section 10 makes it unnecessary.</p><p>3. Protecting Users’ Legal Rights From Anti-Circumvention Law.</p><p>No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technologi- cal measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the works users, your or third parties legal rights to forbid circumvention of technological measures.</p><p>4. Conveying Verbatim Copies.</p><p>You may convey verbatim copies of the Program’s source code as you receive it, in any medium, pro- vided that you conspicuously and appropriately publish on each copy an appropriate copyright notice;</p><p>399 keep intact all notices stating that this License and any non-permissive terms added in accord with sec- tion 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.</p><p>5. Conveying Modified Source Versions.</p><p>You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: • a) The work must carry prominent notices stating that you modified it, and giving a relevant date. • b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to keep intact all notices. • c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 addi- tional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. • d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; how- ever, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an aggregate if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation’s users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.</p><p>6. Conveying Non-Source Forms.</p><p>You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: • a) Convey the object code in, or embodied in, a physical product (including a physical distribu- tion medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. • b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. • c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. • d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the</p><p>400 Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. • e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A User Product is either (1) a consumer product, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, normally used refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. Installation Information for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.</p><p>7. Additional Terms.</p><p>Additional permissions are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own re- moval in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: • a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this</p><p>401 License; or • b) Requiring preservation of specified reasonable legal notices or author attributions in that ma- terial or in the Appropriate Legal Notices displayed by works containing it; or • c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or • d) Limiting the use for publicity purposes of names of licensors or authors of the material; or • e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or • f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered further restrictions within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.</p><p>8. Termination.</p><p>You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have re- ceived copies or rights from you under this License. If your rights have been terminated and not per- manently reinstated, you do not qualify to receive new licenses for the same material under section 10.</p><p>9. Acceptance Not Required for Having Copies.</p><p>You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.</p><p>402 10. Automatic Licensing of Downstream Recipients.</p><p>Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An entity transaction is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party’s predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.</p><p>11. Patents.</p><p>A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor’s contributor version. A contributor’s essential patent claims are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, control includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contrib- utor’s essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a patent license is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To grant such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. Knowingly relying means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient’s use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is discriminatory if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent</p><p>403 license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.</p><p>12. No Surrender of Others’ Freedom.</p><p>If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.</p><p>13. Use with the GNU Affero General Public License.</p><p>Notwithstanding any other provision of this License, you have permission to link or combine any cov- ered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.</p><p>14. Revised Versions of this License.</p><p>The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License or any later version applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obli- gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.</p><p>15. Disclaimer of Warranty.</p><p>THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM AS IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PRO- GRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.</p><p>404 16. Limitation of Liability.</p><p>IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GEN- ERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.</p><p>17. Interpretation of Sections 15 and 16.</p><p>If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS</p><p>How to Apply These Terms to Your New Programs</p><p>If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the copyright line and a pointer to where the full notice is found. <one line to give the program’s name and a brief idea of what it does.> Copyright (C) <year> <name of author></p><p>This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.</p><p>This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.</p><p>You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/ licenses/>. Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode: <program> Copyright (C) <year> <name of author> This program comes with ABSOLUTELY NO WARRANTY; for details type ‘ show w ’. This is free software, and you are welcome to redistribute it under certain conditions; type ‘show c’ for details.</p><p>405 The hypothetical commands ‘show w and ‘show c should show the appropriate parts of the General Public License. Of course, your program’s commands might be different; for a GUI interface, you would use an about box. You should also get your employer (if you work as a programmer) or school, if any, to sign a copyright disclaimer for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see http://www.gnu.org/licenses/. The GNU General Public License does not permit incorporating your program into proprietary pro- grams. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser Gen- eral Public License instead of this License. But first, please read http://www.gnu.org/philosophy/ why-not-lgpl.html.</p><p>406 B. Included software and data</p><p>Included data</p><p>Mathics includes data from Wikipedia that is published under the Creative Commons Attribution- Sharealike 3.0 Unported License and the GNU Free Documentation License contributed by the respec- tive authors that are listed on the websites specified in "data/elements.txt".</p><p>MathJax</p><p>Copyright l’ 2009-2010 Design Science, Inc. Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. mpmath</p><p>Copyright (c) 2005-2018 Fredrik Johansson and mpmath contributors All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted pro- vided that the following conditions are met: <ol> <li>Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. <li>Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. <li>Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. </ul> THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IM- PLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (IN- CLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</p><p>Prototype</p><p>Copyright l’ 2005-2010 Sam Stephenson</p><p>407 Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associ- ated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FIT- NESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AU- THORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABIL- ITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. pymimemagic</p><p>Copyright (c) 2009, Xiaohai Lu All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted pro- vided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. Neither the name of the <ORGANIZATION> nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IM- PLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAM- AGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SER- VICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</p><p>SciPy</p><p>Copyright l’ 2001, 2002 Enthought, Inc. All rights reserved. Copyright l’ 2003-2019 SciPy Developers. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. Neither the name of Enthought nor the names of the SciPy Developers may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DIS- CLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DI- RECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (IN-</p><p>408 CLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</p><p>Three.js</p><p>Copyright l’ 2010-2020 Three.js authors. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associ- ated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FIT- NESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AU- THORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABIL- ITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.</p><p>409 Index</p><p>$Aborted, 46 $UserBaseDirectory, 188 $Assumptions, 60 $UserName, 49 $BaseDirectory, 182 $Version, 49 $ByteOrdering, 46 $VersionNumber, 49 $CharacterEncoding, 102 $extensionMappings, 189 $CommandLine, 46 $formatMappings, 189 $DateStringFormat, 29 $ExportFormats, 189 Abort, 41 $Failed, 46 Abs, 59 $HistoryLength, 193 AbsoluteFileName, 182 $HomeDirectory, 186 AbsoluteThickness, 90 $ImportFormats, 190 AbsoluteTime, 27 $InitialDirectory, 186 AbsoluteTiming, 27 $Input, 177 Accumulate, 133 $InputFileName, 177 AiryAi, 252 $InstallationDirectory, 186 AiryAiPrime, 253 $Line, 194 AiryAiZero, 253 $Machine, 47 AiryBi, 253 $MachineEpsilon, 125 AiryBiPrime, 253 $MachineName, 47 AiryBiZero, 253 $MachinePrecision, 125 Algebraic Manipulation, 218 $MaxPrecision, 125 All, 114 $MinPrecision, 125 Alphabet, 102 $OperatingSystem, 187 Alternatives, 52 $Packages, 47 AngerJ, 254 $ParentProcessID, 48 AnglePath, 231 $Path, 187 AngleVector, 232 $PathnameSeparator, 187 Apart, 218 $Post, 193 Append, 205 $Pre, 193 AppendTo, 205 $PrePrint, 193 Apply, 83 $PreRead, 193 ApplyLevel, 83 $ProcessID, 48 ArcCos, 232 $ProcessorType, 48 ArcCosh, 232 $RandomState, 250 ArcCot, 232 $RootDirectory, 187 ArcCoth, 233 $ScriptCommandLine, 48 ArcCsc, 233 $SyntaxHandler, 193 ArcCsch, 233 $SystemCharacterEncoding, 104 ArcSec, 233 $SystemID, 48 ArcSech, 233 $SystemMemory, 48 ArcSin, 233 $SystemTimeZone, 30 ArcSinh, 233 $SystemWordLength, 48 ArcTan, 233 $TemporaryDirectory, 188 ArcTanh, 234 $TimeZone, 30 Arg, 59 Array, 202</p><p>410 ArrayDepth, 79 C, 231 ArrayQ, 79 Calculus, 226 Arrow, 90 CanberraDistance, 239 Arrowheads, 92 Cancel, 218 Association, 201 Cases, 205 AssociationQ, 202 Catalan, 224 Associations, 201 Catch, 41 Assuming, 60 Catenate, 211 AtomQ, 83 Ceiling, 237 Attributes, 74 Center, 33 Automatic, 107 CentralMoment, 114 Axes, 107 Character, 176 Axis, 107 Character Codes, 263 CharacterRange, 262 B64Decode, 188 Characters, 262 B64Encode, 189 Characters in Strings, 262 BarChart, 164 ChartLabels, 108 BaseForm, 32 ChartLegends, 108 Basic Arithmetic, 130 ChebyshevT, 259 Basic statistics, 215 ChebyshevU, 259 BernsteinBasis, 173 Check, 33 Bessel and Related Functions, 252 ChessboardDistance, 240 BesselI, 254 Chop, 124 BesselJ, 254 Circle, 92 BesselJZero, 254 ClearAttributes, 75 BesselK, 254 Close, 176 BesselY, 254 Closing, 154 BesselYZero, 255 ClusteringComponents, 115 BezierCurve, 173 CMYKColor, 134 BezierFunction, 173 Coefficient, 218 Binarize, 154 CoefficientArrays, 219 BinaryImageQ, 154 CoefficientList, 219 BinaryRead, 175 Collect, 220 BinarySearch, 84 Color Directives, 134 BinaryWrite, 175 Color Operations, 136 Binomial, 195 ColorCombine, 154 BitLength, 237 ColorConvert, 136 Black, 138 ColorData, 165 Blank, 52 ColorDistance, 134 BlankNullSequence, 53 Colorize, 155 BlankSequence, 53 ColorNegate, 137 Blend, 136 ColorQuantize, 155 Blue, 139 ColorSeparate, 155 Blur, 154 Combinatorial Functions, 195 Boole, 60 Compile, 69 Bottom, 108 CompiledFunction, 69 BoxData, 32 Complement, 211 BoxMatrix, 154 Complex, 60 BrayCurtisDistance, 239 Complexes, 226 Break, 41 ComplexInfinity, 224 Brown, 139 Composition, 67 Byte, 176 CompoundExpression, 42 ByteArray, 114 Condition, 53 ByteCount, 84 ConditionalExpression, 60 Conjugate, 61</p><p>411 Constant, 75 DigitCount, 237 ConstantArray, 203 DigitQ, 262 Constructing Lists, 202 Dilation, 155 ContainsOnly, 115 Dimensions, 80 Continue, 42 DirectedInfinity, 61 ContinuedFraction, 245 Directory, 183 CoprimeQ, 197 DirectoryName, 183 CopyDirectory, 182 DirectoryQ, 183 CopyFile, 182 DirectoryStack, 183 Correlation, 215 DiscreteLimit, 227 Cos, 234 DisjointQ, 116 Cosh, 234 Disk, 93 CosineDistance, 240 DiskMatrix, 155 Cot, 234 Dispatch, 53 Coth, 234 Divide, 130 Count, 206 Division-Related Functions, 197 Covariance, 215 Divisors, 246 CreateDirectory, 182 Do, 42 CreateFile, 182 DominantColors, 137 CreateTemporary, 182 Dot, 80 Cross, 240 Drop, 206 Csc, 234 DSolve, 231 Csch, 234 CubeRoot, 130 E, 224 Cuboid, 162 EasterSunday, 29 Cyan, 140 EdgeDetect, 155 Cylinder, 162 EdgeForm, 94 EditDistance, 151 D, 226 Eigensystem, 240 DamerauLevenshteinDistance, 151 Eigenvalues, 241 Darker, 137 Eigenvectors, 241 DataImport, 271 ElementData, 112 DateDifference, 28 Elements of Lists, 205 DateList, 28 EndOfFile, 176 DateObject, 28 EndOfLine, 268 DatePlus, 29 EndOfString, 268 DateString, 29 Environment, 46 Default, 71 Erf, 257 Degree, 224 Erfc, 257 Delete, 115 Erosion, 156 DeleteCases, 206 Error Function and Related Functions, 257 DeleteDirectory, 182 EuclideanDistance, 241 DeleteDuplicates, 211 EulerGamma, 224 DeleteFile, 182 EvenQ, 198 Denominator, 220 ExactNumberQ, 61 DensityPlot, 165 Except, 54 Depth, 84 Exp, 234 Derivative, 226 Expand, 220 DesignMatrix, 240 ExpandAll, 221 Det, 240 ExpandDenominator, 221 DiagonalMatrix, 79 ExpandFileName, 183 DiamondMatrix, 155 ExpIntegralE, 258 DiceDissimilarity, 195 ExpIntegralEi, 258 Differential Equations, 230 Exponent, 221 DigitCharacter, 267</p><p>412 Exponential Integral and Special Functions, 258, FreeQ, 85 261 FresnelC, 257 Exponential, Trigonometric and Hyperbolic Func- FresnelS, 257 tions, 231 FromCharacterCode, 263 Export, 189 FromContinuedFraction, 246 ExportString, 189 FromDigits, 238 Expression, 176 Full, 108 Extract, 206 FullForm, 33 FullSimplify, 222 Factor, 222 Function, 67 Factorial, 62 Factorial2, 62 Gamma, 259 FactorInteger, 246 Gamma and Related Functions, 258 FactorTermsList, 222 Gather, 211 Failure, 116 GatherBy, 212 Fibonacci, 199 GaussianFilter, 156 File and Stream Operations, 175 GCD, 198 FileBaseName, 183 GegenbauerC, 259 FileByteCount, 183 General, 33 FileDate, 183 Get, 177 FileExistsQ, 184 GetEnvironment, 46 FileExtension, 184 Glaisher, 225 FileFormat, 190 GoldenRatio, 225 FileHash, 184 Graphics, 95 FileInformation, 184 Graphics3D, 163 FileNameDepth, 185 Gray, 140 FileNameJoin, 185 GrayLevel, 135 FileNames, 185 Green, 141 FileNameSplit, 185 Grid, 33 FileNameTake, 185 FilePrint, 176 HammingDistance, 152 Filesystem Operations, 182 HankelH1, 255 FileType, 186 HankelH2, 255 FilledCurve, 94 HarmonicNumber, 199 Filling, 108 Hash, 124 FilterRules, 71 Haversine, 235 Find, 176 Head, 85 FindClusters, 116 HermiteH, 260 FindFile, 186 HexidecimalCharacter, 102 FindList, 186 Histogram, 166 FindRoot, 227 HoldAll, 75 First, 206 HoldAllComplete, 75 FirstCase, 207 HoldFirst, 75 FirstPosition, 207 HoldPattern, 54 FixedPoint, 42 HoldRest, 76 FixedPointList, 42 HTML, 271 Flat, 75 HTMLGetString, 271 Flatten, 84 Hue, 135 Floor, 237 HyperlinksImport, 271 Fold, 117 FoldList, 117 I, 62 FontColor, 95 Identity, 68 For, 43 IdentityMatrix, 80 Format, 33 If, 43 FractionalPart, 246 Im, 62</p><p>413 Image, 157 Joined, 109 Image[] and image related functions., 154 ImageAdd, 156 KelvinBei, 255 ImageAdjust, 156 KelvinBer, 255 ImageAspectRatio, 156 KelvinKei, 256 ImageChannels, 157 KelvinKer, 256 ImageColorSpace, 157 Key, 117 ImageConvolve, 157 Keys, 202 ImageData, 157 Khinchin, 225 ImageDimensions, 157 Kurtosis, 216 ImageImport, 157 ImageLinksImport, 271 LABColor, 135 ImageMultiply, 158 LaguerreL, 260 ImagePartition, 158 Large, 96 ImageQ, 158 Last, 207 ImageReflect, 158 LCHColor, 135 ImageResize, 159 LCM, 198 ImageRotate, 159 LeafCount, 118 ImageSize, 108 LeastSquares, 242 ImageSubtract, 159 Left, 34 ImageTake, 159 LegendreP, 260 ImageType, 159 LegendreQ, 261 Import, 190 Length, 207 Importing and Exporting, 188 LerchPhi, 261 ImportString, 191 LetterCharacter, 268 In, 193 LetterNumber, 102 Indeterminate, 225 LetterQ, 262 InexactNumberQ, 62 Level, 118 Infinity, 225 LevelQ, 118 Infix, 34 LightBlue, 141 Inner, 80 LightBrown, 142 InputForm, 34 LightCyan, 142 InputStream, 177 Lighter, 138 Insert, 117 LightGray, 143 Integer, 63 LightGreen, 143 Integer Functions, 236 LightMagenta, 144 IntegerDigits, 125, 238 LightOrange, 144 IntegerExponent, 246 LightPink, 145 IntegerLength, 238 LightPurple, 145 IntegerQ, 63 LightRed, 146 IntegerReverse, 239 LightYellow, 146 Integers, 228 Limit, 228 IntegerString, 239 Line, 96 Integrate, 228 Linear algebra, 239 Interrupt, 43 LinearModelFit, 242 IntersectingQ, 117 LinearSolve, 243 Intersection, 212 List, 119 Inverse, 242 Listable, 76 InverseErf, 258 ListLinePlot, 167 InverseErfc, 258 ListPlot, 167 InverseHaversine, 235 ListQ, 119 Locked, 76 JaccardDissimilarity, 196 Log, 235 JacobiP, 260 Log10, 235 Join, 117, 212 Log2, 235</p><p>414 LogisticSigmoid, 236 NextPrime, 247 Longest, 54 NHoldAll, 76 Lookup, 202 NHoldFirst, 76 LowerCaseQ, 263 NHoldRest, 76 LUVColor, 135 NIntegrate, 127 NonAssociative, 35 MachineNumberQ, 63 None, 119 MachinePrecision, 125 Norm, 243 Magenta, 147 Normal, 203 MakeBoxes, 34 Normalize, 244 ManhattanDistance, 243 NotListQ, 119 MantissaExponent, 246 NotOptionQ, 71 Map, 85 Now, 29 MapAt, 86 Null, 87 MapIndexed, 86 NullSpace, 244 MapThread, 87 Number, 177 MatchingDissimilarity, 196 Number theoretic functions, 245 MatchQ, 54 NumberForm, 35 Mathematical Constants, 224 NumberQ, 63 MathicsVersion, 47 NumberString, 103 MathMLForm, 34 Numerator, 223 MatrixExp, 243 NumericQ, 127 MatrixForm, 35 MatrixPower, 243 O, 229 MatrixQ, 81 OddQ, 198 MatrixRank, 243 Off, 35 MaxFilter, 160 On, 36 Maximize, 106 OneIdentity, 76 MaxRecursion, 109 OpenAppend, 177 Mean, 133 Opening, 160 Median, 215 OpenRead, 177 MedianFilter, 160 OpenWrite, 178 Medium, 96 Operate, 87 MemberQ, 207 Operations on Strings, 264 MemoryAvailable, 47 Optional, 54 MemoryInUse, 47 OptionQ, 72 Mesh, 109 Options, 72 Message, 35 OptionsPattern, 55 MessageName, 35 OptionValue, 72 MinFilter, 160 Orange, 147 MinimalPolynomial, 222 Order, 87 Minimize, 106 OrderedQ, 87 Minus, 130 Orderless, 77 Mod, 198 Orthogonal Polynomials, 259 Most, 208 Out, 194 Multinomial, 196 Outer, 81 OutputForm, 36 N, 126 OutputStream, 178 Named Colors, 138 Names, 47 PadLeft, 120 Nearest, 119 PadRight, 120 Needs, 187 ParametricPlot, 168 Nest, 43 ParentDirectory, 187 NestList, 44 Part, 208 NestWhile, 44 Partition, 212</p><p>415 PartitionsP, 247 Quiet, 37 Pattern, 55 Quotient, 199 PatternsOrderedQ, 87 QuotientRemainder, 199 PatternTest, 55 Pause, 30 Random, 248 Permutations, 203 Random number generation, 248 Pi, 225 RandomChoice, 248 Pick, 209 RandomComplex, 249 Piecewise, 63 RandomImage, 161 PieChart, 168 RandomInteger, 249 Pink, 148 RandomPrime, 248 PixelValue, 160 RandomReal, 249 PixelValuePositions, 160 RandomSample, 250 PlaintextImport, 271, 272 Range, 203 Plot, 170 RankedMax, 121 Plot3D, 171 RankedMin, 121 PlotPoints, 110 Rational, 64 PlotRange, 110 Rationalize, 128 Plotting Data, 164 Re, 65 Plus, 131 Read, 179 Pochhammer, 259 ReadList, 179 Point, 96 ReadProtected, 78 PointSize, 97 Real, 65 PolarPlot, 172 RealDigits, 128 Polygon, 97 RealNumberQ, 65 PolynomialQ, 223 Reals, 229 Position, 121 Reap, 203 PossibleZeroQ, 64 Rearranging and Restructuring Lists, 211 Postfix, 36 Record, 180 Power, 131 Rectangle, 98 PowerExpand, 223 Recurrence and Sum Functions, 199 PowerMod, 198 Red, 148 Precedence, 36 RegisterExport, 191 Precision, 127 RegisterImport, 191 Prefix, 37 Regular Expressions, 270 Prepend, 209 RegularExpression, 270 PrependTo, 209 RegularPolygon, 99 Prime, 247 RemoveDiacritics, 103 PrimePi, 247 RemoveLinearSyntax, 189 PrimePowerQ, 247 RenameDirectory, 187 PrimeQ, 199 RenameFile, 187 Print, 37 Repeated, 56 Product, 64 RepeatedNull, 56 ProductLog, 258 Replace, 56 Protect, 77 ReplaceAll, 57 Protected, 77 ReplaceList, 57 PseudoInverse, 244 ReplacePart, 210 Purple, 148 ReplaceRepeated, 57 Put, 178 ResetDirectory, 187 PutAppend, 178 Rest, 210 PythonForm, 37 Return, 44 Reverse, 213 QRDecomposition, 244 RGBColor, 135 Quantile, 215 Riffle, 213 Quartiles, 121 Right, 38</p><p>416 RogersTanimotoDissimilarity, 196 StandardDeviation, 216 Root, 229 StandardForm, 38 RotateLeft, 213 StartOfLine, 268 RotateRight, 213 StartOfString, 268 Round, 128 StirlingS1, 200 Row, 38 StirlingS2, 200 RowReduce, 244 StreamPosition, 180 RSolve, 51 Streams, 180 Rule, 58 String, 104 RuleDelayed, 58 String Distances and Similarity Measures, 151 Run, 48 String Patterns, 267 RussellRaoDissimilarity, 196 StringCases, 269 StringContainsQ, 103 Scan, 88 StringDrop, 264 Sec, 236 StringExpression, 269 Sech, 236 StringForm, 38 SeedRandom, 250 StringFreeQ, 269 Select, 210 StringInsert, 264 SequenceHold, 78 StringJoin, 265 Series, 229 StringLength, 265 SeriesData, 229 StringMatchQ, 270 SessionTime, 30 StringPosition, 265 SetAttributes, 78 StringQ, 103 SetDirectory, 188 StringRepeat, 104 SetFileDate, 188 StringReplace, 266 SetStreamPosition, 180 StringReverse, 266 Share, 48 StringRiffle, 266 Sharpen, 161 StringSplit, 266 Show, 99 StringTake, 267 Sign, 65 StringToStream, 181 Simplify, 223 StringTrim, 267 Sin, 236 StruveH, 256 SingularValueDecomposition, 245 StruveL, 256 Sinh, 236 Subscript, 38 Skewness, 216 SubsetQ, 122 Skip, 180 Subsets, 197 Slot, 68 Subsuperscript, 38 SlotSequence, 68 Subtract, 132 Small, 100 Sum, 65 SokalSneathDissimilarity, 196 Sums, Simple Statistics, 133 Solve, 229 Superscript, 38 Sort, 88 Switch, 44 SortBy, 88 Symbol, 89 SourceImport, 271 SymbolName, 88 Sow, 204 SymbolQ, 88 Span, 210 SympyForm, 39 SparseArray, 50 Syntax, 39 Special Moments, 215 Sphere, 164 Table, 204 SphericalHarmonicY, 261 TableForm, 39 Splines, 173 TagsImport, 272 Split, 121 Take, 211 SplitBy, 122 TakeLargest, 122 Sqrt, 132 TakeLargestBy, 122 SquaredEuclideanDistance, 245 TakeSmallest, 122</p><p>417 TakeSmallestBy, 123 Which, 45 Tally, 214 While, 45 Tan, 236 White, 149 Tanh, 236 Whitespace, 105 TeXForm, 39 WhitespaceCharacter, 270 Text, 100 Word, 181 TextData, 39 WordBoundary, 270 TextRecognize, 161 WordCharacter, 270 The Main Loop, 192 WordCloud, 161 Thick, 100 Write, 181 Thickness, 100 WriteString, 181 Thin, 101 Thread, 89 XML, 272 Three-Dimensional Graphics, 161 XMLGetString, 272 Threshold, 161 XMLObjectImport, 271, 272 Through, 89 XYZColor, 136 Throw, 45 TicksStyle, 110 Yellow, 149 TimeConstrained, 30 YuleDissimilarity, 197 TimeRemaining, 30 Zeta, 261 Times, 132 TimeUsed, 30 Timing, 31 Tiny, 101 TitleImport, 271 ToBoxes, 40 ToCharacterCode, 264 ToExpression, 104 ToFileName, 188 Together, 223 ToLowerCase, 263 Top, 111 ToString, 104 Total, 133 ToUpperCase, 263 Tr, 245 Transliterate, 105 Transpose, 81 Tuples, 204</p><p>Union, 214 UnitVector, 123 Unprotect, 78 UpperCaseQ, 263 URLFetch, 192 URLSave, 188</p><p>Values, 202 Variables, 224 Variance, 216 VectorAngle, 245 VectorQ, 82 Verbatim, 58</p><p>WeberE, 256</p><p>418</p>
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