Appendix 1 MuPAD Libraries and Procedures In this appendix I have included all the libraries available in MuPAD, and almost all the procedures that are available in the most current version of MuPAD at the time of writing. I have tried to make this list as complete as it was possible. However, I could have missed a few things. There are many procedures that are either undocumented or considered to be internal. However, the border between internal procedures and those that are designated to be used by MuPAD users can be a bit dim. So, some of the procedures described here might also be internal and some other can become internal in the future. In fact, from the user's point of view there is little difference between internal and official procedures. You can use them, as long as you know their syntax and where to find them. For many procedures, I have provided a short syntax and description that may help the readers to identify the role of the procedure or find a procedure for a specific goal. You need to keep in mind that most of these procedures can be used in a wide variety of ways with a number of parameters. It is therefore not possible to describe in a small chapter all the forms of syntax and parameters that can be applied to them. My intention while developing this appendix was to provide you with the most basic information about what you can find in MuPAD's libraries and in the whole MuPAD system. There is huge number of procedures that I have grouped under the title "MuPAD Standard Collection". In fact, these procedures are not always included in any particular library; they are placed in various parts of the MuPAD system. However, you can access them directly without using the slot operator regardless of where they really are. Thus, if you can use a procedure like this, f1oat(1+exp(J)) but not like this, comb; nat: : bell (I5), then I will consider this procedure as a part of the so-called standard collection. Many of the procedures listed here were not even mentioned in my book. You can find information about them through MuPAD's help. My intention was to use this appendix instead of an index. Thus, 14 MuPAO Pro Computing Essentials MuPAD objects that I have described in this book shall have a page number attached, where you can find more information about them. The order of libraries and procedures is alphabetic. A 1.1 MuPAD Libraries (ver. 2.5, 18/01/2002) adt - basic collection ofabstract data types Ax - basic axiom call tmctors Cat - basic calegOlY constructors (:ombinat -func/iolls for combinatories detools - tools for differential equations Dom - domain call truc/ors fp - utilities forJunetional programming generate - utilities to generate foreign Jormats Jrom expressions groebner - calculatioll of Groebner-bases/or polYllomial ideals import - utilitiesfor reading data in different formats intlib - utilities for symbolic integration linalg - the linear algebra package linopt - package Jar linear optimizatioll listlib - utilitiesJor list operations matchlib -toolsJorpallem matching odule - IItilities Jar modllle management Network - package for handling directed graphs numeric -fllnctionsJorllumerical mathematics umlib - the package for elemen/my number theOlY orthpoly - tools for orthogonal polynomials output - utilities lor the output ofdata plot - graphical primitives andfimclion for two- and three-dimensional plot· polylib - utilities for polY/lomials prog - programming utilities property - properties ofidentifier. RGB - color definitions Series - tools and data structures for working with eries solvelib - methods for solving equations. :.)'stem a/equations and ineqllalities specfunc - element{//J' and special functions Appendix 1: MuPAD Libraries and Procedures 415 stats - stalisticalfimctions tringlib - utilities for workillg with strillgs tudent - the student package transform - librUlJI for illtegral transformatiollS A1.2 Operators Represented by Symbols : = -as ign a value to a variable (p. 26) +, -, /, *,11_ aritmetica{ operatioll (p. 9, 266) I -factorial operation (p. 9) , - derivative ofa filllction (p. 432) , <, <=, >=, > - equality and illequality relation (p. 266) -> - declaratioll ofa filllction (p. 28) ~> , <=> Booleall operators representillg implicatioll and equivalence (p. 31 J) . - dot operator to COllcatenate two fist or strillg (p. 96) .. - the range operator, 2.. 5 ... - range operator, Pl...5.1, returns afloatillg point interval illculdillg it · end', camp. {1II1f @ - composition offimclions @@ - iterate Clfunction givenllllfnber oftimes S - create a sequence (p. 93) ?word - display he{pfor the given word (p. 19, 110) :: - the 1010 erator, acces to object /ot A1.3 MuPAD Standard Collection This section lists only procedures that can be applied to objects different than numbers. All arithmetic functions are listed in section Al.32.1. implies - illtemal repre entation of implication alias{x=object) - deJines x CIS all alias ofthe givell object anames{All) - returns identifier that have values or properties ill currellt session of MuPAD (p. 28) and, or, not, xor - Booleall operators (p. 311) args x -fill/clion accessill rocedure arometer . 102) 416 MuPAD Pro Com uting Essentials array{kl .. nl. k2 .. n2, ... ) - creates an array assert{cond) - declares the condition to be true at the moment when statement is evaluated assign{List) - as igns values given in the form oflist ofequation(s) assignElements{L, i=v, .. ) - assigns values to entries ofa list. array assume{x. property) - assign a mathematical property to a MuPAD object (p.34) asymptlf, x) - computes asymptotic series expansion bool{expr) - produces Boolean vallie ofthe given e..rpression (p. 317) break - procedure terminating execution ofa loop or case structure (p. 57) byte!iO - returns the cun'ent memory use cardtpet) - produces cardinality ofa given set coeff(p) - returns sequence ofnon-zero coefficients ofa polynomial coerce{object, U) - tries to convert object into an object ofa domain U collect(p. x) - collects coefficients ofa given polynomial combfne{expr) - combines terms ofa given expression into a single power (p. 299) complexlnffnity - constant representing infinity in complex numbers conjugate{z) - produces conjugate ofa complex number (p. 273) contafns{A. object) - checks ifa given element A is contained inside ofa container object content(p) - computes the content ofthe polynomial. i.e. gcd ofits coefficients context{object) - evaluates object in the given context of the calling procedure contfrac{x) - produces continued fraction ofa given number copyClosure - copies the lexical closure ofa procedure O(/) - differential operator. equivalent to f' debugO, debug{statement) - starts MuPAD debugger for a given statement degree(p. x) - returns degree ofthe polynomial p with respect to x (p. 285) degreevec(p) - returns a list ofexponents ofthe leading term ofa polynomial delete{xi, x2... ) - deletes values ofthe given identifiers (p. 37) denom{expr) - produces denominator ofa given rational expression dffflf, x) - produces derivative ofafunction in respect to a given variable (p.432) dfscontlf, x) - produces all discontinuities ofafunctionj{x) dfv - produces results ofinteger division (p. 254) domtype{object) - returns domain type ofthe given object (p. 88) error{"message") - breaks nmningprocedure and produces error message ~ndfx 1: MuPAD libraries and Procedures 417 eval(object) • evaluates the given object evalassign(x, value, depth) . el'Oluates x with the given depths and assigns value to the result evalp{p, x=xO) • evaluates po(vnomial p for x=xO (p. 285) expand(erprenion) - erpands an arithmetical expression (p. 284) export(library, procedures) • erports procedures from a given library (p. l OS) expose (procedure) - displays the source code ofa given procedure or domain expr(object) • com"erts object into an element ofa basic domain expr2text(object) • converts object into a string ofc haracters extemal(, . ) -returns the function environment extnops(object) • returns the number ofoperands ofthe given object in intemal representation extop(object) • returns 0/1 operands ofa domain element extsubop(d, i=nC"K"e/) • produces a copy ofthe domo.in element with replaced j-th operand factor{p) -factors polynomial into i"educible polynomials (p. 254, 284) Factored(/) - domain ofobjects infactored form (po 354) fclose(n). closes thefile with descriptor n ffnput(filename) -reads MuPAD objects from the given binary or ASCII file fname(n) - returns the name ofthe file with specified descriptor fopen(fiJename) • opens the file with the gi\"en name fprlnt(filename, objects). writes MuPAD objects into aft/e fract(x) -fractional part ofth e number x frandom() -floating point number random function fread(tllename) - reads and erecutes the specified MuPAD file freeze(/) • creates an inactive copy ofth e functionf (p. 354) ftextlnput(filename, x) • procedure reads /ine from a extt file and assigns it to the identifier x funcenv(/). procl!dure crates afunction environment gcd{p,q, .. ) - produces the greatest common divisor ofpolynomiau (p. 285) gcdex(p, q, xl •th e erlended Eue/idean algorithm for polynomials genldent() - create a new identifier thaI was not wed be/ore in current session genpoty(n, b, x ) - creates apo/ynomial p with variable x such thotp(b) =- n ~etpldO - returns ID ofth e running MuPAD process In UNIX operating system getprop(~ r). returns mathe . I ro 01 /yerz,exprusfo 6 9 ~18 MuPAD Pro Com~uttnl Essential, ground(p) - returns the constanl coefficient ofp(O,O, .. O} haS(objectJ. objectl ) - procedure checks