The Comprehensive Latex Symbol List

The Comprehensive LATEXSymbolList

Scott Pakin ∗ 29 September 2003

Abstract

This document lists 2826 symbols and the corresponding LATEX commands that produce them. Some of these symbols are guaranteed to be available in every LATEX2ε system; others require fonts and packages that may not accompany a given distribution and that therefore need to be installed. All of the fonts and packages used to prepare this document—as well as this document itself—are freely available from the Comprehensive TEX Archive Network (http://www.ctan.org).

Contents

1 Introduction 6 1.1DocumentUsage...... 6 1.2FrequentlyRequestedSymbols...... 6

2 Body-text symbols 7 Table 1: LATEX2ε Escapable“Special”Characters...... 7 Table 2: LATEX2ε CommandsDefinedtoWorkinBothMathandTextMode...... 7 Table 3: Predefined LATEX2ε Text-modeCommands...... 7 Table4: Non-ASCIILetters(ExcludingAccentedLetters)...... 8 Table5: LettersUsedtoTypesetAfricanLanguages...... 8 Table6: PunctuationMarksNotFoundinOT1...... 8 Table 7: pifont DecorativePunctuationMarks...... 8 Table 8: wasysym PhoneticSymbols...... 8 Table 9: tipa PhoneticSymbols...... 9 Table 10: wsuipa PhoneticSymbols...... 10 Table 11: phonetic PhoneticSymbols...... 11 Table12:Text-modeAccents...... 11 Table 13: tipa Text-modeAccents...... 11 Table 14: wsuipa Text-modeAccents...... 13 Table 15: phonetic Text-modeAccents...... 13 Table 16: wsuipa Diacritics...... 13 Table 17: textcomp Diacritics...... 14 Table 18: textcomp CurrencySymbols...... 14 Table 19: marvosym CurrencySymbols...... 14 Table 20: wasysym CurrencySymbols...... 14 Table 21: eurosym EuroSigns...... 14 Table 22: textcomp LegalSymbols...... 15 Table 23: textcomp Old-styleNumerals...... 15 Table 24: Miscellaneous textcomp Symbols...... 15 Table 25: Miscellaneous wasysym Text-modeSymbols...... 15 Table 26: AMS CommandsDefinedtoWorkinBothMathandTextMode...... 16

∗The original version of this document was written by David Carlisle, with several additional tables provided by Alexander Holt. See Section 7.6 on page 73 for more information about who did what.

1 3 Mathematical symbols 17 Table 27: Binary Operators ...... 17 Table 28: AMS Binary Operators ...... 17 Table 29: stmaryrd BinaryOperators...... 18 Table 30: wasysym BinaryOperators...... 18 Table 31: txfonts/pxfonts BinaryOperators...... 18 Table 32: mathabx BinaryOperators...... 19 Table 33: ulsy Geometric Binary Operators ...... 19 Table 34: mathabx Geometric Binary Operators ...... 19 Table 35: Variable-sized Math Operators ...... 20 Table 36: AMS Variable-sized Math Operators ...... 20 Table 37: stmaryrd Variable-sizedMathOperators...... 20 Table 38: wasysym Variable-sizedMathOperators...... 20 Table 39: mathabx Variable-sizedMathOperators...... 21 Table 40: txfonts/pxfonts Variable-sizedMathOperators...... 22 Table 41: esint Variable-sized Math Operators ...... 22 Table42:BinaryRelations...... 23 Table 43: AMS BinaryRelations...... 23 Table 44: AMS Negated Binary Relations ...... 23 Table 45: stmaryrd BinaryRelations...... 23 Table 46: wasysym BinaryRelations...... 23 Table 47: txfonts/pxfonts BinaryRelations...... 24 Table 48: txfonts/pxfonts Negated Binary Relations ...... 24 Table 49: mathabx BinaryRelations...... 24 Table 50: mathabx Negated Binary Relations ...... 25 Table 51: trsym BinaryRelations...... 25 Table 52: trfsigns BinaryRelations...... 25 Table53:SubsetandSupersetRelations...... 25 Table 54: AMS SubsetandSupersetRelations...... 26 Table 55: stmaryrd SubsetandSupersetRelations...... 26 Table 56: wasysym SubsetandSupersetRelations...... 26 Table 57: txfonts/pxfonts SubsetandSupersetRelations...... 26 Table 58: mathabx SubsetandSupersetRelations...... 26 Table59:Inequalities...... 26 Table 60: AMS Inequalities...... 27 Table 61: wasysym Inequalities...... 27 Table 62: txfonts/pxfonts Inequalities...... 27 Table 63: mathabx Inequalities...... 27 Table 64: AMS TriangleRelations...... 28 Table 65: stmaryrd TriangleRelations...... 28 Table 66: mathabx TriangleRelations...... 28 Table67:Arrows...... 28 Table68:Harpoons...... 28 Table 69: textcomp Text-modeArrows...... 28 Table 70: AMS Arrows...... 29 Table 71: AMS Negated Arrows ...... 29 Table 72: AMS Harpoons...... 29 Table 73: stmaryrd Arrows...... 29 Table 74: txfonts/pxfonts Arrows...... 29 Table 75: mathabx Arrows...... 30 Table 76: mathabx Negated Arrows ...... 30 Table 77: mathabx Harpoons...... 30 Table 78: chemarrow Arrows...... 30 Table 79: ulsy ContradictionSymbols...... 30

2 Table80:ExtensionCharacters...... 30 Table 81: stmaryrd ExtensionCharacters...... 31 Table 82: txfonts/pxfonts ExtensionCharacters...... 31 Table 83: mathabx ExtensionCharacters...... 31 Table 84: Log-like Symbols ...... 31 Table 85: AMS Log-like Symbols ...... 31 Table86:GreekLetters...... 32 Table 87: AMS GreekLetters...... 32 Table 88: txfonts/pxfonts UprightGreekLetters...... 32 Table 89: upgreek UprightGreekLetters...... 33 Table 90: txfonts/pxfonts Variant Latin Letters ...... 33 Table 91: AMS HebrewLetters...... 33 Table92:Letter-likeSymbols...... 33 Table 93: AMS Letter-likeSymbols...... 33 Table 94: txfonts/pxfonts Letter-likeSymbols...... 34 Table 95: mathabx Letter-likeSymbols...... 34 Table 96: trfsigns Letter-likeSymbols...... 34 Table 97: AMS Delimiters...... 34 Table 98: stmaryrd Delimiters...... 34 Table 99: mathabx Delimiters...... 34 Table 100: nath Delimiters...... 34 Table 101: Variable-sized Delimiters ...... 35 Table 102: Large, Variable-sized Delimiters ...... 35 Table 103: Variable-sized stmaryrd Delimiters...... 35 Table 104: mathabx Variable-sizedDelimiters...... 35 Table 105: nath Variable-sizedDelimiters(Double)...... 36 Table 106: nath Variable-sizedDelimiters(Triple)...... 36 Table 107: textcomp Text-modeDelimiters...... 36 Table 108: Math-mode Accents ...... 37 Table 109: AMS Math-modeAccents...... 37 Table 110: yhmath Math-modeAccents...... 37 Table 111: trfsigns Math-modeAccents...... 37 Table 112: Extensible Accents ...... 38 Table 113: overrightarrow ExtensibleAccents...... 38 Table 114: yhmath ExtensibleAccents...... 38 Table 115: AMS ExtensibleAccents...... 39 Table 116: chemarr ExtensibleAccents...... 39 Table 117: chemarrow ExtensibleAccents...... 39 Table 118: mathabx ExtensibleAccents...... 40 Table 119: esvect ExtensibleAccents...... 40 Table 120: undertilde ExtensibleAccents...... 40 Table 121: Dots ...... 41 Table 122: AMS Dots ...... 41 Table 123: mathdots Dots ...... 41 Table 124: yhmath Dots ...... 41 Table 125: Miscellaneous LATEX2ε Symbols...... 42 Table 126: Miscellaneous AMS Symbols...... 42 Table 127: Miscellaneous wasysym Symbols...... 42 Table 128: Miscellaneous txfonts/pxfonts Symbols...... 42 Table 129: Miscellaneous mathabx Symbols...... 42 Table 130: Miscellaneous textcomp Text-modeMathSymbols...... 43 Table 131: mathcomp MathSymbols...... 43 Table 132: gensymb SymbolsDeﬁnedtoWorkinBothMathandTextMode...... 43 Table 133: mathabx MayanDigits...... 43

3 Table 134: marvosym MathSymbols...... 43 Table 135: Math Alphabets ...... 44

4 Science and technology symbols 45 Table 136: wasysym ElectricalandPhysicalSymbols...... 45 Table 137: ifsym PulseDiagramSymbols...... 45 Table 138: ar Aspect Ratio Symbol ...... 45 Table 139: textcomp Text-modeScienceandEngineeringSymbols...... 45 Table 140: wasysym AstronomicalSymbols...... 45 Table 141: marvosym AstronomicalSymbols...... 46 Table 142: mathabx AstronomicalSymbols...... 46 Table 143: wasysym AstrologicalSymbols...... 46 Table 144: marvosym AstrologicalSymbols...... 46 Table 145: mathabx AstrologicalSymbols...... 46 Table 146: wasysym APLSymbols...... 46 Table 147: wasysym APLModiﬁers...... 47 Table 148: marvosym ComputerHardwareSymbols...... 47 Table 149: ascii ControlCharacters(IBM)...... 47 Table 150: marvosym CommunicationSymbols...... 47 Table 151: marvosym EngineeringSymbols...... 47 Table 152: wasysym BiologicalSymbols...... 47 Table 153: marvosym BiologicalSymbols...... 48 Table 154: marvosym Safety-relatedSymbols...... 48

5 Dingbats 49 Table 155: bbding Arrows...... 49 Table 156: pifont Arrows...... 49 Table 157: marvosym Scissors...... 49 Table 158: bbding Scissors...... 49 Table 159: pifont Scissors...... 49 Table 160: dingbat Pencils...... 50 Table 161: bbding PencilsandNibs...... 50 Table 162: pifont PencilsandNibs...... 50 Table 163: dingbat Hands...... 50 Table 164: bbding Hands...... 50 Table 165: pifont Hands...... 50 Table 166: bbding CrossesandPlusses...... 50 Table 167: pifont CrossesandPlusses...... 51 Table 168: bbding XsandCheckMarks...... 51 Table 169: pifont XsandCheckMarks...... 51 Table 170: wasysym XsandCheckMarks...... 51 Table 171: pifont CircledNumbers...... 51 Table 172: wasysym Stars...... 51 Table 173: bbding Stars,Flowers,andSimilarShapes...... 52 Table 174: pifont Stars,Flowers,andSimilarShapes...... 52 Table 175: wasysym GeometricShapes...... 52 Table 176: ifsym GeometricShapes...... 53 Table 177: bbding GeometricShapes...... 53 Table 178: pifont GeometricShapes...... 54 Table 179: universa GeometricShapes...... 54 Table 180: manfnt DangerousBendSymbols...... 54 Table 181: skull Symbols...... 54 Table 182: Non-Mathematical mathabx Symbols...... 54 Table 183: marvosym InformationSymbols...... 54

4 Table 184: Miscellaneous dingbat Dingbats...... 54 Table 185: Miscellaneous bbding Dingbats...... 55 Table 186: Miscellaneous pifont Dingbats...... 55

6 Other symbols 56 Table 187: textcomp GenealogicalSymbols...... 56 Table 188: wasysym GeneralSymbols...... 56 Table 189: wasysym Musical Notes ...... 56 Table 190: wasysym Circles...... 56 Table 191: Miscellaneous manfnt Symbols...... 56 Table 192: marvosym Navigation Symbols ...... 57 Table 193: marvosym LaundrySymbols...... 57 Table 194: Other marvosym Symbols...... 57 Table 195: Miscellaneous universa Symbols...... 57 Table 196: ifsym WeatherSymbols...... 58 Table 197: ifsym AlpineSymbols...... 58 Table 198: ifsym Clocks...... 58 Table 199: Other ifsym Symbols...... 59 Table 200: skak Chess Informator Symbols ...... 59

7 Additional Information 60 7.1SymbolNameClashes...... 60 7.2 Where can I ﬁnd the symbol for ... ?...... 60 7.3Math-modespacing...... 70 7.4Boldmathematicalsymbols...... 71 7.5 ASCII and Latin 1 quick reference ...... 71 7.6Aboutthisdocument...... 73

References 75

Index 77

5 1 Introduction

Welcome to the Comprehensive LATEX Symbol List! This document strives to be your primary source of LATEX symbol information: font samples, LATEX commands, packages, usage details, caveats—everything needed to put thousands of diﬀerent symbols at your disposal. All of the fonts covered herein meet the following criteria:

1. They are freely available from the Comprehensive TEX Archive Network (http://www.ctan.org). 2. All of their symbols have LATEX2ε bindings. That is, a user should be able to access a symbol by name, not just by \charnumber.

These are not particularly limiting criteria; the Comprehensive LATEX Symbol List contains samples of 2826 symbols—quite a large number. Some of these symbols are guaranteed to be available in every LATEX2ε system; others require fonts and packages that may not accompany a given distribution and that therefore need to be installed. See http://www.tex.ac.uk/cgi-bin/texfaq2html?label=instpackages+wherefiles for help with installing new fonts and packages.

1.1 Document Usage Each section of this document contains a number of font tables. Each table shows a set of symbols, with the corresponding LATEX command to the right of each symbol. A table’s caption indicates what package needs to be loaded in order to access that table’s symbols. For example, the symbols in Table 23, “textcomp Old-Style Nu- merals”, are made available by putting “\usepackage{textcomp}” in your document’s preamble. “AMS”means to use the AMS packages, viz. amssymb and/or amsmath. Notes below a table provide additional information about some or all the symbols in that table. One note that appears a few times in this document, particularly in Section 2, indicates that certain symbols do not exist in the OT1 font encoding (Donald Knuth’s original, 7-bit font encoding, which is the default font encoding for LATEX) and that you should use fontenc to select a diﬀerent encoding, such as T1 (a common 8-bit font encoding). That means that you should put “\usepackage[encoding]{fontenc}” in your document’s preamble, where encoding is, e.g., T1 or LY1. To limit the change in font encoding to the current group, use “\fontencoding{encoding}\selectfont”. Section 7 contains some additional information about the symbols in this document. It shows which symbol names are not unique across packages, gives examples of how to create new symbols out of existing symbols, explains how symbols are spaced in math mode, presents a LATEX ASCII and Latin 1 tables, and provides some information about this document itself. The Comprehensive LATEXSymbolListendswithanindexofallthe symbols in the document and various additional useful terms.

1.2 Frequently Requested Symbols There are a number of symbols that are requested over and over again on comp.text.tex. If you’re looking for such a symbol the following list will help you ﬁnd it quickly.

,asin“Spacesare significant.” ...... 7 and ...... 27 ´ı, `ı, ¯ı, ˆı, etc. (versus í, ì, ¯i, and î) ...... 11 ...... 41 ¢ ...... 14 °, as in “180°” or “15℃” ...... 43 e ...... 14 L, F,etc...... 44 ©, ®,and™ ...... 15 N, Z, R,etc...... 44 ‰ ...... 15 R − ...... 63 ...... 22 ¯a,´ ˆè, etc. (i.e., several accents per character) 65 ∴ ...... 23 <, >,and| (insteadof¡,¿,and—) ...... 71 and ...... 24 ând˜(or∼) ...... 72

6 2 Body-text symbols

This section lists symbols that are intended for use in running text, such as punctuation marks, accents, ligatures, and currency symbols.

Table 1: LATEX2ε Escapable “Special” Characters $ \$ % \% \_ ∗ } \} & \& # \# { \{

∗ The underscore package redeﬁnes “_” to produce an underscore in text mode (i.e., it makes it unnecessary to escape the underscore character).

Table 2: LATEX2ε Commands Deﬁned to Work in Both Math and Text Mode $ \$ \_ ‡ \ddag { \{ ¶ \P ○©c \copyright ... \dots } \} § \S † \dag £ \pounds

Where two symbols are present, the left one is the “faked” symbol that LATEX2ε provides by default, and the right one is the “true” symbol that textcomp makes available.

Table 3: Predeﬁned LATEX2ε Text-mode Commands ˆ \textasciicircum < \textless ˜ \textasciitilde a ª \textordfeminine ∗ \textasteriskcentered o º \textordmasculine \ \textbackslash ¶ \textparagraph | \textbar · \textperiodcentered { \textbraceleft ¿ \textquestiondown } \textbraceright “ \textquotedblleft • \textbullet ” \textquotedblright ○©c \textcopyright ‘ \textquoteleft † \textdagger ’ \textquoteright ‡ \textdaggerdbl ○®r \textregistered $ \textdollar § \textsection ... \textellipsis £ \textsterling — \textemdash TM ™ \texttrademark – \textendash \textunderscore ¡ \textexclamdown \textvisiblespace > \textgreater

Where two symbols are present, the left one is the “faked” symbol that LATEX2ε provides by default, and the right one is the “true” symbol that textcomp makes available.

7 Table 4: Non-ASCII Letters (Excluding Accented Letters) ˚a \aa Ð \DH∗ L \L ø \o ß \ss A˚ \AA ð \dh∗ l \l Ø \O SS \SS Æ \AE Ð \DJ∗ Ŋ \NG∗ Œ \OE Þ \TH∗ æ \ae đ \dj∗ ŋ \ng∗ œ \oe þ \th∗

∗ Not available in the OT1 font encoding. Use the fontenc package to select an alternate font encoding, such as T1.

Table 5: Letters Used to Typeset African Languages Ð \B{D} ° \m{c} ¤ \m{f} ¨ \m{k} » \M{t} \m{Z} \B{d} \m{D} \m{F} \m{N} \M{T} Â \T{E} \B{H} ð \M{d} \m{G} \m{n} º \m{t} â \T{e} § \B{h} Ð \M{D} ¦ \m{g} ª \m{o} \m{T} Å \T{O} · \B{t} ¡ \m{d} À \m{I} \m{O} ® \m{u}∗ å \T{o} \B{T} \m{E} à \m{i} \m{P} \m{U}∗ \m{b} ¢ \m{e} \m{J} ± \m{p} \m{Y} \m{B} \M{E} © \m{j} ¬ \m{s} ¯ \m{y} \m{C} £ \M{e} \m{K} \m{S} ¶ \m{z}

These characters all need the T4 font encoding, which is provided by the fc package.

∗ \m{v} and \m{V} are synonyms for \m{u} and \m{U}.

Table 6: Punctuation Marks Not Found in OT1 « \guillemotleft ‹ \guilsinglleft „ \quotedblbase " \textquotedbl » \guillemotright › \guilsinglright ‚ \quotesinglbase

To get these symbols, use the fontenc package to select an alternate font encoding, such as T1.

Table 7: pifont Decorative Punctuation Marks ❛ \ding{123} ❝ \ding{125} ❡ \ding{161} ❣ \ding{163} ❜ \ding{124} ❞ \ding{126} ❢ \ding{162}

Table 8: wasysym Phonetic Symbols D \DH \dh \openo Þ \Thorn \inve þ \thorn

8 Table 9: tipa Phonetic Symbols

È \textbabygamma P \textglotstop ï \textrtailn b \textbarb ; \texthalflength ó \textrtailr c \textbarc » \texthardsign ù \textrtails d \textbard # \texthooktop ú \textrtailt é \textbardotlessj á \texthtb ü \textrtailz g \textbarg ê \texthtbardotlessj $ \textrthook Ü \textbarglotstop Á \texthtc À \textsca 1 \textbari â \texthtd à \textscb ª \textbarl ä \texthtg ¤ \textsce 8 \textbaro H \texthth å \textscg Ý \textbarrevglotstop Ê \texththeng Ë \textsch 0 \textbaru Î \texthtk @ \textschwa ì \textbeltl Ò \texthtp I \textsci B \textbeta Ó \texthtq ¨ \textscj ò \textbullseye £ \texthtrtaild Ï \textscl \textceltpal É \texthtscg ð \textscn X \textchi Ö \texthtt × \textscoelig Å \textcloseepsilon ÿ \texthvlig ± \textscomega Ñ \textcloseomega Û \textinvglotstop ö \textscr Æ \textcloserevepsilon K \textinvscr A \textscripta Þ \textcommatailz Ì \textiota g \textscriptg ^ \textcorner « \textlambda V \textscriptv \textcrb : \textlengthmark Ú \textscu ¡ \textcrd ³ \textlhookt Y \textscy g \textcrg ¦ \textlhtlongi \textsecstress è \textcrh ¶ \textlhtlongy º \textsoftsign Û \textcrinvglotstop Ô \textlonglegr Â \textstretchc ¬ \textcrlambda ½ \textlptr tC \texttctclig 2 \textcrtwo M \textltailm Ù \textteshlig C \textctc ñ \textltailn T \texttheta ¢ \textctd ë \textltilde þ \textthorn ¢ý \textctdctzlig Ð \textlyoghlig ¿ \texttoneletterstem ² \textctesh Í \textObardotlessj µ \texttslig J \textctj \textOlyoghlig 5 \textturna ® \textctn ° \textomega ¯ \textturncelig ´ \textctt _ \textopencorner 4 \textturnh ´C \textcttctclig O \textopeno © \textturnk ¸ \textctyogh % \textpalhook Õ \textturnlonglegr ý \textctz F \textphi W \textturnm dý \textdctzlig | \textpipe î \textturnmrleg S \textdoublebaresh " \textprimstress ô \textturnr } \textdoublebarpipe ¼ \textraiseglotstop õ \textturnrrtail =/ \textdoublebarslash § \textraisevibyi 6 \textturnscripta { \textdoublepipe 7 \textramshorns Ø \textturnt \textdoublevertline \ \textrevapostrophe 2 \textturnv \textdownstep 9 \textreve û \textturnw Ã \textdyoghlig 3 \textrevepsilon L \textturny dz \textdzlig Q \textrevglotstop U \textupsilon E \textepsilon ¹ \textrevyogh \textupstep

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S \textesh Ç \textrhookrevepsilon \textvertline R \textfishhookr Ä \textrhookschwa § \textvibyi ¥ \textg ~ \textrhoticity · \textvibyy G \textgamma ¾ \textrptr ß \textwynn \textglobfall ã \textrtaild Z \textyogh \textglobrise í \textrtaill

tipa deﬁnes shortcut characters for many of the above. It also deﬁnes a command \tone for denoting tone letters (pitches). See the tipa documentation for more information.

Table 10: wsuipa Phonetic Symbols

! \babygamma 8 \eng 4 \labdentalnas \schwa ¦ \barb \er / \latfric * \sci \bard M \esh 6 \legm : \scn ' \bari \eth E \legr J \scr . \barl D \flapr 1 \lz ¡ \scripta < \baro b \glotstop ¢ \nialpha \scriptg A \barp ¨ \hookb © \nibeta Y \scriptv + \barsci \hookd [ \nichi W \scu X \barscu \hookg \niepsilon ] \scy T \baru $ \hookh \nigamma § \slashb ; \clickb % \hookheng ) \niiota \slashc \clickc \hookrevepsilon 2 \nilambda \slashd R \clickt " \hv > \niomega U \slashu ? \closedniomega \inva C \niphi \taild \closedrevepsilon , \invf O \nisigma H \tailinvr ¥ \crossb d \invglotstop S \nitheta 0 \taill \crossd & \invh V \niupsilon 9 \tailn # \crossh I \invlegr 7 \nj F \tailr 3 \crossnilambda 5 \invm @ \oo L \tails \curlyc G \invr = \openo P \tailt N \curlyesh K \invscr \reve _ \tailz a \curlyyogh £ \invscripta f \reveject Q \tesh ^ \curlyz ¤ \invv \revepsilon B \thorn ( \dlbari Z \invw c \revglotstop - \tildel \dz \ \invy \scd ` \yogh e \ejective \ipagamma \scg

10 Table 11: phonetic Phonetic Symbols j f A i \barj \flap ¯i \ibar \rotvara \vari ¡ \barlambda ? \glottal c \openo w \rotw ¨ \varomega M \emgma B \hausaB ¯h \planck y \roty C \varopeno n \engma b \hausab U \pwedge e \schwa v \vod ˚ N \enya D \hausad ¢ \revD p \thorn h \voicedh " \epsi T \hausaD \riota u \ubar x \yogh s \esh k \hausak m \rotm u \udesc d \eth K \hausaK \rotOmega a \vara F \fj D \hookd r \rotr G \varg

Table 12: Text-mode Accents A¨ä \"{A}\"{a} A`à \‘{A}\‘{a} A˝˝a \H{A}\H{a} A˘˘a \u{A}\u{a} A´á \’{A}\’{a} Aa \b{A}\b{a} Ąą \k{A}\k{a}† Aˇˇa \v{A}\v{a} ¯¯ A˙˙ a \.{A}\.{a} A¸¸a \c{A}\c{a} A˚˚a \r{A}\r{a} A˜ã \~{A}\~{a}

A¯¯a \={A}\={a} A. a. \d{A}\d{a} Aa \t{A}\t{a} Aˆˆa \^{A}\^{a} Aa \G{A}\G{a}‡ A¼¼a \U{A}\U{a}‡

A a \newtie{A}\newtie{a}∗ ○A ○a \textcircled{A}\textcircled{a}

∗ Requires the textcomp package. † Not available in the OT1 font encoding. Use the fontenc package to select an alternate font encoding, such as T1. ‡ Requires the T4 font encoding, provided by the fc package.

Also note the existence of \i and \j, which produce dotless versions of “i” and “j” (viz., “ı” and “j”). These are useful when the accent is supposed to replace the dot. For example, “na\"{\i}ve” produces a correct “na¨ıve”, while “na\"{i}ve”would yield the rather odd-looking “na¨ive”. (“na\"{i}ve” does work in encodings other than OT1, however.)

Table 13: tipa Text-mode Accents ¡ A©a©¡ \textacutemacron{A}\textacutemacron{a} ¡ A§a§¡ \textacutewedge{A}\textacutewedge{a} A a \textadvancing{A}\textadvancing{a}

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¢ A a¢ \textcircumdot{A}\textcircumdot{a} Aa \textdotacute{A}\textdotacute{a}

A¨a¨ \textdotbreve{A}\textdotbreve{a}

A¨a¨ \textdotbreve{A}\textdotbreve{a} A a \textdoublegrave{A}\textdoublegrave{a} Aa \textdoublevbaraccent{A}\textdoublevbaraccent{a} Aa \textgravecircum{A}\textgravecircum{a} Aa \textgravedot{A}\textgravedot{a}

A©a© \textgravemacron{A}\textgravemacron{a} Aa \textgravemid{A}\textgravemid{a} Aa \textinvsubbridge{A}\textinvsubbridge{a} A a \textlowering{A}\textlowering{a} Aa \textmidacute{A}\textmidacute{a} Aa \textovercross{A}\textovercross{a} Aa \textoverw{A}\textoverw{a} A a \textpolhook{A}\textpolhook{a} A a \textraising{A}\textraising{a} A a \textretracting{A}\textretracting{a} ¦ A©¦a© \textringmacron{A}\textringmacron{a} Aa \textroundcap{A}\textroundcap{a} Aa \textseagull{A}\textseagull{a} Aa \textsubacute{A}\textsubacute{a} Aa \textsubarch{A}\textsubarch{a} Aa ©© \textsubbar{A}\textsubbar{a} Aa \textsubbridge{A}\textsubbridge{a} Aa \textsubcircum{A}\textsubcircum{a} ¢¢ Aa \textsubdot{A}\textsubdot{a}

Aa \textsubgrave{A}\textsubgrave{a} A a \textsublhalfring{A}\textsublhalfring{a} A a \textsubplus{A}\textsubplus{a} A a \textsubrhalfring{A}\textsubrhalfring{a} Aa \textsubring{A}\textsubring{a} ¦¦ Aa \textsubsquare{A}\textsubsquare{a} Aa \textsubtilde{A}\textsubtilde{a} ££ Aa \textsubumlaut{A}\textsubumlaut{a} ¤¤ Aa \textsubw{A}\textsubw{a} Aa \textsubwedge{A}\textsubwedge{a} §§ A&&a \textsuperimposetilde{A}\textsuperimposetilde{a} Aa \textsyllabic{A}\textsyllabic{a} " "

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£ A a£ \texttildedot{A}\texttildedot{a} >> Aa \texttoptiebar{A}\texttoptiebar{a} Aa \textvbaraccent{A}\textvbaraccent{a}

tipa deﬁnes shortcut sequences for many of the above. See the tipa documentation for more information.

Table 14: wsuipa Text-mode Accents

Ag ag \dental{A}\dental{a} Aa \underarch{A}\underarch{a}

Table 15: phonetic Text-mode Accents

Aa \hill{A}\hill{a} A© a© \rc{A}\rc{a} Aa \ut{A}\ut{a} { { ˜˜ Aa \od{A}\od{a} Aa \syl{A}\syl{a} ˚{˚{ Aa \ohill{A}\ohill{a} A....a \td{A}\td{a}

The phonetic package provides a few additional macros for linguistic accents. \acbar and \acarc compose characters with multiple accents; for example, \acbar{\’}{a} produces “a”¯´ and \acarc{\"}{e} produces “¯¨e”. \labvel joins two characters with an arc: \labvel{mn} → “mn”. \upbar is intended to go between characters as in “x\upbar{}y’’ → “x y”. Lastly, \uplett behaves like \textsuperscript but uses a smaller font. Contrast “p\uplett{h}’’ → “ph”with“p\textsuperscript{h}’’ → “ph”.

Table 16: wsuipa Diacritics s \ain v \leftp x \overring h \stress } \underwedge k \corner n \leftt ~ \polishhook j \syllabic t \upp u \downp q \length w \rightp r \underdots l \upt m \downt { \midtilde o \rightt y \underring p \halflength z \open i \secstress | \undertilde

The wsuipa package deﬁnes all of the above as ordinary characters, not as accents. However, it does provide \diatop and \diaunder commands, which are used to compose diacritics with other characters. For example, \diatop[\overring|a] produces “xa”, and \diaunder[\underdots|a] produces “a”.r See the wsuipa documentation for more information.

13 Table 17: textcomp Diacritics ˝ \textacutedbl ˇ \textasciicaron ¯ \textasciimacron ´ \textasciiacute ¨ \textasciidieresis ̏ \textgravedbl ˘ \textasciibreve ` \textasciigrave

The textcomp package deﬁnes all of the above as ordinary characters, not as accents.

Table 18: textcomp Currency Symbols ฿ \textbaht $ \textdollar \textguarani ₩ \textwon ¢ \textcent $ \textdollaroldstyle ₤ \textlira ¥ \textyen ¢ \textcentoldstyle ₫ \textdong ₦ \textnaira ₡ \textcolonmonetary € \texteuro \textpeso ¤ \textcurrency ƒ \textflorin £ \textsterling

Table 19: marvosym Currency Symbols ¢ \Denarius e \EUR D \EURdig e \EURtm £ \Pfund \Ecommerce d \EURcr c \EURhv ¦ \EyesDollar ¡ \Shilling

The diﬀerent euro signs are meant to be compatible with diﬀerent fonts—Courier (\EURcr), Helvetica (\EURhv), Times (\EURtm), and the marvosym digits listed in Table 134 (\EURdig).

Table 20: wasysym Currency Symbols ¢ \cent ¤ \currency

Table 21: eurosym Euro Signs AC \geneuro BC \geneuronarrow C \geneurowide e \officialeuro

\euro is automatically mapped to one of the above—by default, \officialeuro— based on a eurosym package option. See the eurosym documentation for more information. The \geneuro. . . characters are generated from the current body font’s “C” character and therefore may not appear exactly as shown.

14 Table 22: textcomp Legal Symbols ℗ \textcircledP ○©c \textcopyright ℠ \textservicemark \textcopyleft ○®r \textregistered TM ™ \texttrademark

Where two symbols are present, the left one is the “faked” symbol that LATEX2ε provides by default, and the right one is the “true” symbol that textcomp makes available. See http://www.tex.ac.uk/cgi-bin/texfaq2html?label=tradesyms for solu- tions to common problems that occur when using these symbols (e.g., getting a “○r ” whenyouexpectedtogeta“®”).

Table 23: textcomp Old-style Numerals 0 \textzerooldstyle 4 \textfouroldstyle 8 \texteightoldstyle 1 \textoneoldstyle 5 \textfiveoldstyle 9 \textnineoldstyle 2 \texttwooldstyle 6 \textsixoldstyle 3 \textthreeoldstyle 7 \textsevenoldstyle

Rather than use the bulky \textoneoldstyle, \texttwooldstyle, etc. commands shown above, consider using \oldstylenums{...} to typeset an old-style number.

Table 24: Miscellaneous textcomp Symbols ∗ \textasteriskcentered a ª \textordfeminine ‖ \textbardbl o º \textordmasculine ○ \textbigcircle ¶ \textparagraph ␢ \textblank · \textperiodcentered ¦ \textbrokenbar ‱ \textpertenthousand • \textbullet ‰ \textperthousand † \textdagger ¶ \textpilcrow ‡ \textdaggerdbl ' \textquotesingle 0 \textdblhyphen ‚ \textquotestraightbase 2 \textdblhyphenchar „ \textquotestraightdblbase 4 \textdiscount 5 \textrecipe ℮ \textestimated ※ \textreferencemark ‽ \textinterrobang § \textsection 9 \textinterrobangdown — \textthreequartersemdash ♪ \textmusicalnote < \texttildelow № \textnumero > \texttwelveudash ◦ \textopenbullet

Where two symbols are present, the left one is the “faked” symbol that LATEX2ε provides by default, and the right one is the “true” symbol that textcomp makes available.

Table 25: Miscellaneous wasysym Text-mode Symbols \permil

15 Table 26: AMS Commands Deﬁned to Work in Both Math and Text Mode \checkmark \circledR \maltese

16 3 Mathematical symbols

Most, but not all, of the symbols in this section are math-mode only. That is, they yield a “Missing $ inserted” error message if not used within $...$, \[...\], or another math-mode environment. Operators marked as “variable-sized” are taller in displayed formulas, shorter in in-text formulas, and possibly shorter still when used in various levels of superscripts or subscripts. Alphanumeric symbols (e.g., “L ”and“”) are usually produced using one of the math alphabets in Table 135 rather than with an explicit symbol command. Look there ﬁrst if you need a symbol for a transform, number set, or some other alphanumeric. Although there have been many requests on comp.text.tex for a contradiction symbol, the ensuing dis- cussion invariably reveals innumerable ways to represent contradiction in a proof, including “©”(\blitza), “⇒⇐”(\Rightarrow\Leftarrow), “⊥”(\bot), “”(\nleftrightarrow), and “※”(\textreferencemark). Be- cause of the lack of notational consensus, it is probably better to spell out “Contradiction!” than to use a symbol for this purpose. Similarly, discussions on comp.text.tex have revealed that there are a variety of ways to indicate the mathematical notion of “is deﬁned as”. Common candidates include “”(\triangleq), “≡”(\equiv), “”(\coloneqq), and “def=” (\stackrel{\text{\tiny def}}{=}). See also the example of \equalsfill on page 66.

Table 27: Binary Operators \amalg ∪ \cup ⊕ \oplus × \times ∗ \ast † \dagger \oslash \triangleleft \bigcirc ‡ \ddagger ⊗ \otimes \triangleright \bigtriangledown \diamond ± \pm \unlhd∗ \bigtriangleup ÷ \div \rhd∗ \unrhd∗ • \bullet \lhd∗ \ \setminus \uplus ∩ \cap ∓ \mp \sqcap ∨ \vee · \cdot \odot \sqcup ∧ \wedge ◦ \circ \ominus \star \wr

∗ Not predeﬁned in LATEX2ε. Use one of the packages latexsym, amsfonts, amssymb, txfonts, pxfonts,orwasysym.

Table 28: AMS Binary Operators \barwedge \circledcirc \intercal \boxdot \circleddash \leftthreetimes \boxminus \Cup \ltimes \boxplus \curlyvee \rightthreetimes \boxtimes \curlywedge \rtimes \Cap \divideontimes \smallsetminus \centerdot \dotplus \veebar \circledast \doublebarwedge

17 Table 29: stmaryrd Binary Operators \baro \interleave \varoast \bbslash \leftslice \varobar \binampersand \merge \varobslash \bindnasrepma \minuso \varocircle \boxast \moo \varodot \boxbar \nplus \varogreaterthan \boxbox \obar \varolessthan \boxbslash \oblong \varominus \boxcircle \obslash \varoplus \boxdot \ogreaterthan \varoslash \boxempty \olessthan \varotimes \boxslash \ovee \varovee \curlyveedownarrow \owedge ! \varowedge " \curlyveeuparrow # \rightslice $ \vartimes % \curlywedgedownarrow & \sslash ' \Ydown ( \curlywedgeuparrow ) \talloblong * \Yleft + \fatbslash , \varbigcirc - \Yright . \fatsemi / \varcurlyvee 0 \Yup 1 \fatslash 2 \varcurlywedge

Table 30: wasysym Binary Operators \lhd \ocircle \RHD \unrhd \LHD \rhd \unlhd

Table 31: txfonts/pxfonts Binary Operators \circledbar \circledwedge \medcirc \circledbslash \invamp \sqcapplus \circledvee \medbullet \sqcupplus

18 Table 32: mathabx Binary Operators ¦ \ast N \curlywedge [ \sqcap ¦ \Asterisk £ \divdot \ \sqcup X \barwedge \divideontimes ^ \sqdoublecap \bigstar ¡ \dotdiv _ \sqdoublecup \bigvarstar \dotplus ¥ \square \blackdiamond ¢ \dottimes ] \squplus X \cap Z \doublebarwedge ¤ \udot ¨ \circplus \ \doublecap Z \uplus § \coasterisk ] \doublecup \varstar § \coAsterisk \ltimes _ \vee \convolution © \pluscirc Y \veebar Y \cup \rtimes [ \veedoublebar O \curlyvee \sqbullet ^ \wedge

Many of the above glyphs go by multiple names. \centerdot is equivalent to \sqbullet,and\ast is equivalent to *. \asterisk produces the same glyph as \ast, but as an ordinary symbol, not a binary operator. Similarly, \bigast produces a large-operator version of the \Asterisk binary operator, and \bigcoast produces a large-operator version of the \coAsterisk binary operator.

Table 33: ulsy Geometric Binary Operators ¨ \odplus

Table 34: mathabx Geometric Binary Operators \blacktriangledown i \boxright a \ominus \blacktriangleleft m \boxslash ` \oplus \blacktriangleright b \boxtimes i \oright \blacktriangleup j \boxtop m \oslash f \boxasterisk o \boxtriangleup b \otimes n \boxbackslash l \boxvoid j \otop k \boxbot f \oasterisk o \otriangleup e \boxcirc n \obackslash l \ovoid g \boxcoasterisk k \obot \smalltriangledown c \boxdiv e \ocirc \smalltriangleleft d \boxdot g \ocoasterisk \smalltriangleright h \boxleft c \odiv \smalltriangleup a \boxminus d \odot ` \boxplus h \oleft

19 Table 35: Variable-sized Math Operators T \ N O V ^ Q Y \bigcap \bigotimes \bigwedge \prod S [ F G ` a P X \bigcup \bigsqcup \coprod \sum Z J K U ] R \bigodot \biguplus \int I L M W _ H \bigoplus \bigvee \oint

Table 36: AMS Variable-sized Math Operators \idotsint \iiint \iiiint \iint

Table 37: stmaryrd Variable-sized Math Operators 3 4 5 6 \bigbox \biginterleave \bigsqcap 7 8 9 : \bigcurlyvee \bignplus \bigtriangledown ; < = > ? @ \bigcurlywedge \bigparallel \bigtriangleup

Table 38: wasysym Variable-sized Math Operators \iiint \oiint \varoint

\iint \varint

20 Table 39: mathabx Variable-sized Math Operators ¬ Ý ý É é \bigcurlyvee \bigboxslash \bigoright ¦ Ò ò Í í \bigsqcap \bigboxtimes \bigoslash « Ú ú Ê ê \bigcurlywedge \bigboxtop \bigotop Ö ö ß ÿ Ï ï \bigboxasterisk \bigboxtriangleup \bigotriangleup Þ þ Ü ü Ì ì \bigboxbackslash \bigboxvoid \bigovoid Û û ¢ \bigboxbot \bigcomplementop \bigplus Õ õ Æ æ ¨ \bigboxcirc \bigoasterisk \bigsquplus × ÷ Î î ¡ \bigboxcoasterisk \bigobackslash ½ \bigtimes Ó ó Ë ë µ \bigboxdiv \bigobot \iiint ¼ Ô ô Å å ´ \bigboxdot \bigocirc \iint » Ø ø Ç ç ³ \bigboxleft \bigocoasterisk \int ¿ Ñ ñ Ã ã · \bigboxminus \bigodiv \oiint ¾ Ð ð È è ¶ \bigboxplus \bigoleft \oint Ù ù Á á \bigboxright \bigominus

21 Table 40: txfonts/pxfonts Variable-sized Math Operators \bigsqcapplus \ointclockwise \bigsqcupplus \ointctrclockwise \fint \sqiiint \idotsint \sqiint \iiiint \sqint \iiint \varoiiintclockwise ! " \iint \varoiiintctrclockwise # $ % & \oiiintclockwise \varoiintclockwise ' ( ) * \oiiintctrclockwise \varoiintctrclockwise + , - . \oiiint \varointclockwise / 0 1 2 \oiintclockwise \varointctrclockwise 4 3 5 6 \oiintctrclockwise \varprod \oiint

Table 41: esint Variable-sized Math Operators © \dotsint \ointclockwise \fint \ointctrclockwise ¨ § \iiiint \sqiint ¦ ¥ \iiint \sqint ¤ " £ ! \iint \varoiint & % \landdownint \varointclockwise $ # \landupint \varointctrclockwise

\oiint

22 Table 42: Binary Relations ≈ \approx ≡ \equiv ⊥ \perp \smile \asymp \frown ≺ \prec ! \succ \bowtie \Join∗ " \preceq # \succeq \cong | \mid ∝ \propto % \vdash & \dashv |= \models ∼ \sim \doteq ' \parallel ( \simeq

∗ Not predeﬁned in LATEX2ε. Use one of the packages latexsym, amsfonts, amssymb, mathabx, txfonts, pxfonts,orwasysym.

Table 43: AMS Binary Relations \approxeq \eqcirc \succapprox \backepsilon \fallingdotseq ! \succcurlyeq " \backsim # \multimap $ \succsim % \backsimeq & \pitchfork ∴ \therefore ∵ \because \precapprox ≈ \thickapprox ( \between ) \preccurlyeq ∼ \thicksim * \Bumpeq + \precsim ∝ \varpropto - \bumpeq . \risingdotseq / \Vdash 0 \circeq \shortmid 1 \vDash 2 \curlyeqprec \shortparallel 3 \Vvdash 4 \curlyeqsucc 5 \smallfrown 6 \doteqdot 7 \smallsmile

Table 44: AMS Negated Binary Relations \ncong \nshortparallel \nVDash \nmid \nsim \precnapprox ∦ \nparallel \nsucc \precnsim ⊀ \nprec \nsucceq \succnapprox \npreceq \nvDash \succnsim \nshortmid \nvdash

Table 45: stmaryrd Binary Relations A \inplus B \niplus

Table 46: wasysym Binary Relations \invneg \leadsto \wasypropto \Join \logof

23 Table 47: txfonts/pxfonts Binary Relations \circledgtr \lJoin \opentimes \circledless \lrtimes \Perp \colonapprox # \multimap \preceqq \Colonapprox \multimapboth \precneqq \coloneq \multimapbothvert \rJoin \Coloneq \multimapdot \strictfi \Coloneqq \multimapdotboth \strictif \coloneqq \multimapdotbothA \strictiff \Colonsim \multimapdotbothAvert \succeqq \colonsim \multimapdotbothB \succneqq \Eqcolon \multimapdotbothBvert ∥ \varparallel \eqcolon \multimapdotbothvert \varparallelinv \eqqcolon \multimapdotinv \VvDash \Eqqcolon \multimapinv \eqsim \openJoin

Table 48: txfonts/pxfonts Negated Binary Relations \napproxeq \npreccurlyeq \nthickapprox \nasymp \npreceqq \ntwoheadleftarrow \nbacksim \nprecsim \ntwoheadrightarrow \nbacksimeq \nsimeq \nvarparallel \nbumpeq \nsuccapprox \nvarparallelinv \nBumpeq \nsucccurlyeq ! \nVdash \nequiv \nsucceqq \nprecapprox \nsuccsim

Table 49: mathabx Binary Relations \between \divides \risingdotseq \botdoteq \dotseq Ç \succapprox \Bumpedeq \eqbumped ¥ \succcurlyeq \bumpedeq \eqcirc Í \succdot \circeq \eqcolon Á \succsim \coloneq \fallingdotseq 6 \therefore \corresponds Ï \ggcurly \topdoteq ¶ \curlyeqprec Î \llcurly ( \vDash · \curlyeqsucc Æ \precapprox , \Vdash ) \DashV ¤ \preccurlyeq ( \VDash ) \Dashv Ì \precdot , \Vvdash - \dashVv À \precsim

24 Table 50: mathabx Negated Binary Relations \napprox M \notperp * \nvDash \ncong ¢ \nprec * \nVDash ¸ \ncurlyeqprec È \nprecapprox . \nVdash ¹ \ncurlyeqsucc ¦ \npreccurlyeq & \nvdash + \nDashv ª \npreceq . \nVvash / \ndashV Â \nprecsim Ê \precnapprox ' \ndashv \nsim ¬ \precneq + \nDashV \nsimeq Ä \precnsim / \ndashVv £ \nsucc Ë \succnapprox \neq É \nsuccapprox \succneq \notasymp § \nsucccurlyeq Å \succnsim \notdivides « \nsucceq \notequiv Ã \nsuccsim

The \changenotsign command toggles the behavior of \not to produce either a vertical or a diagonal slash through a binary operator. Thus, “$a \not= b$”canbe made to produce either “a = b”or“a = b”.

Table 51: trsym Binary Relations ¡ \InversTransformHoriz \TransformHoriz £ \InversTransformVert ¢ \TransformVert

Table 52: trfsigns Binary Relations

c ...... c ... \dfourier ... \Dfourier c c \fourier \Fourier c s s c \laplace \Laplace c ... s s ... c ... \ztransf ... \Ztransf

Table 53: Subset and Superset Relations 8 \sqsubset∗ ) \sqsupseteq ⊃ \supset + \sqsubseteq ⊂ \subset ⊇ \supseteq 9 \sqsupset∗ ⊆ \subseteq

∗ Not predeﬁned in LATEX2ε. Use one of the packages latexsym, amsfonts, amssymb, mathabx, txfonts, pxfonts,orwasysym.

25 Table 54: AMS Subset and Superset Relations " \nsubseteq : \subseteqq # \supsetneqq $ \nsupseteq % \subsetneq & \varsubsetneq ' \nsupseteqq ( \subsetneqq ) \varsubsetneqq 8 \sqsubset ; \Supset * \varsupsetneq 9 \sqsupset < \supseteqq + \varsupsetneqq = \Subset , \supsetneq

Table 55: stmaryrd Subset and Superset Relations C \subsetplus D \supsetplus E \subsetpluseq F \supsetpluseq

Table 56: wasysym Subset and Superset Relations 8 \sqsubset 9 \sqsupset

Table 57: txfonts/pxfonts Subset and Superset Relations \nsqsubset \nsqsupseteq \nSupset \nsqsubseteq \nSubset \nsqsupset - \nsubseteqq

Table 58: mathabx Subset and Superset Relations \nsqsubset \nsupset \sqsupseteq \supseteq \nsqSubset \nSupset \sqsupseteqq \supseteqq \nsqsubseteq \nsupseteq \sqsupsetneq \supsetneq \nsqsubseteqq \nsupseteqq \sqsupsetneqq \supsetneqq \nsqsupset \sqsubset \subset \varsqsubsetneq \nsqSupset \sqSubset \Subset \varsqsubsetneqq \nsqsupseteq \sqsubseteq \subseteq \varsqsupsetneq \nsqsupseteqq \sqsubseteqq \subseteqq \varsqsupsetneqq \nsubset \sqsubsetneq \subsetneq \varsubsetneq \nSubset \sqsubsetneqq \subsetneqq \varsubsetneqq \nsubseteq \sqSupset \supset \varsupsetneq \nsubseteqq \sqsupset \Supset \varsupsetneqq

Table 59: Inequalities ≥ \geq 0 \gg ≤ \leq 2 \ll \neq

26 Table 60: AMS Inequalities > \eqslantgtr ≷ \gtrless . \lneq @ \eqslantless \gtrsim / \lneqq A \geqq 0 \gvertneqq 1 \lnsim B \geqslant C \leqq 2 \lvertneqq ≫ \ggg E \leqslant 3 \ngeq 4 \gnapprox F \lessapprox 5 \ngeqq 6 \gneq 7 \lessdot 8 \ngeqslant 9 \gneqq G \lesseqgtr ≯ \ngtr ; \gnsim H \lesseqqgtr < \nleq I \gtrapprox ≶ \lessgtr = \nleqq > \gtrdot \lesssim ? \nleqslant K \gtreqless ≪ \lll ≮ \nless M \gtreqqless A \lnapprox

Table 61: wasysym Inequalities \apprge \apprle

Table 62: txfonts/pxfonts Inequalities \ngg \ngtrsim \nlesssim \ngtrapprox \nlessapprox \nll \ngtrless \nlessgtr

Table 63: mathabx Inequalities · \eqslantgtr ½ \gtreqless À \lesssim £ \ngtr ¶ \eqslantless ¿ \gtreqqless ! \ll É \ngtrapprox ¥ \geq » \gtrless Î \lll Ã \ngtrsim ¯ \geqq Á \gtrsim Ê \lnapprox ¦ \nleq " \gg µ \gvertneqq ¬ \lneq ° \nleqq Ï \ggg ¤ \leq ² \lneqq ¢ \nless Ë \gnapprox ® \leqq Ä \lnsim È \nlessapprox \gneq Æ \lessapprox ´ \lvertneqq Â \nlesssim ³ \gneqq Ì \lessdot ¹ \neqslantgtr « \nvargeq Å \gnsim ¼ \lesseqgtr ¸ \neqslantless ª \nvarleq Ç \gtrapprox ¾ \lesseqqgtr § \ngeq © \vargeq Í \gtrdot º \lessgtr ± \ngeqq ¨ \varleq

mathabx deﬁnes \leqslant and \le as synonyms for \leq, \geqslant and \ge as synonyms for \geq, \nleqslant as a synonym for \nleq,and\ngeqslant as a synonym for \ngeq.

27 Table 64: AMS Triangle Relations N \blacktriangleleft B \ntrianglelefteq \trianglelefteq \vartriangleleft O \blacktriangleright C \ntriangleright \triangleq \vartriangleright D \ntriangleleft E \ntrianglerighteq \trianglerighteq

Table 65: stmaryrd Triangle Relations G \trianglelefteqslant H \trianglerighteqslant I \ntrianglelefteqslant J \ntrianglerighteqslant

Table 66: mathabx Triangle Relations \ntriangleleft \ntrianglerighteq \triangleright \vartriangleright \ntrianglelefteq \triangleleft \trianglerighteq \ntriangleright \trianglelefteq \vartriangleleft

Table 67: Arrows ⇓ \Downarrow ←− \longleftarrow 5 \nwarrow ↓ \downarrow ⇐= \Longleftarrow ⇒ \Rightarrow ← \hookleftarrow ←→ \longleftrightarrow → \rightarrow → \hookrightarrow ⇐⇒ \Longleftrightarrow 7 \searrow \leadsto∗ 8−→ \longmapsto 9 \swarrow ← \leftarrow =⇒ \Longrightarrow ↑ \uparrow ⇐ \Leftarrow −→ \longrightarrow ⇑ \Uparrow ⇔ \Leftrightarrow 8→ \mapsto = \updownarrow ↔ \leftrightarrow ? \nearrow† @ \Updownarrow

∗ Not predeﬁned in LATEX2ε. Use one of the packages latexsym, amsfonts, amssymb, txfonts, pxfonts,orwasysym.

† See the note beneath Table 112 for information about how to put a diagonal arrow 0 ¨¨* across a mathematical expression (as in “¨∇·B ”) .

Table 68: Harpoons \leftharpoondown \rightharpoondown \rightleftharpoons \leftharpoonup \rightharpoonup

Table 69: textcomp Text-mode Arrows ↓ \textdownarrow → \textrightarrow ← \textleftarrow ↑ \textuparrow

28 Table 70: AMS Arrows P \circlearrowleft ⇔ \leftleftarrows R \rightleftarrows S \circlearrowright T \leftrightarrows ⇒ \rightrightarrows F \curvearrowleft V \leftrightsquigarrow W \rightsquigarrow G \curvearrowright X \Lleftarrow Y \Rsh \dashleftarrow Z \looparrowleft [ \twoheadleftarrow \dashrightarrow \ \looparrowright ] \twoheadrightarrow ^ \downdownarrows _ \Lsh ` \upuparrows a \leftarrowtail b \rightarrowtail

Table 71: AMS Negated Arrows H \nLeftarrow I \nLeftrightarrow J \nRightarrow K \nleftarrow \nleftrightarrow L \nrightarrow

Table 72: AMS Harpoons c \downharpoonleft d \leftrightharpoons e \upharpoonleft f \downharpoonright g \rightleftharpoons h \upharpoonright

Table 73: stmaryrd Arrows K \leftarrowtriangle ⇐L \Mapsfrom M \shortleftarrow N \leftrightarroweq ←O \mapsfrom P \shortrightarrow Q \leftrightarrowtriangle ⇒ \Mapsto R \shortuparrow S \lightning T \nnearrow U \ssearrow ⇐=L \Longmapsfrom V \nnwarrow W \sswarrow ←− O \longmapsfrom X \rightarrowtriangle = ⇒ \Longmapsto Y \shortdownarrow

Table 74: txfonts/pxfonts Arrows \boxdotLeft \circleddotright \Diamondleft \boxdotleft \circleleft \Diamondright \boxdotright \circleright \DiamondRight \boxdotRight \dashleftrightarrow \leftsquigarrow \boxLeft \DiamonddotLeft \Nearrow \boxleft \Diamonddotleft \Nwarrow \boxright \Diamonddotright i \Rrightarrow \boxRight \DiamonddotRight \Searrow \circleddotleft \DiamondLeft \Swarrow

29 Table 75: mathabx Arrows ö \circlearrowleft Ð \leftarrow Ô \nwarrow ÷ \circlearrowright Ð \leftleftarrows æ \restriction ó \curvearrowbotleft Ø \leftrightarrow Ñ \rightarrow õ \curvearrowbotleftright Ô \leftrightarrows Õ \rightleftarrows ô \curvearrowbotright ú \leftrightsquigarrow Ñ \rightrightarrows ð \curvearrowleft ø \leftsquigarrow ù \rightsquigarrow ò \curvearrowleftright ü \lefttorightarrow ý \righttoleftarrow ñ \curvearrowright î \looparrowdownleft é \Rsh ê \dlsh ï \looparrowdownright × \searrow Ó \downdownarrows ì \looparrowleft Ö \swarrow ÿ \downtouparrow í \looparrowright Ö \updownarrows × \downuparrows è \Lsh þ \uptodownarrow ë \drsh Õ \nearrow Ò \upuparrows

Table 76: mathabx Negated Arrows ö \nLeftarrow Ü \nleftrightarrow Û \nrightarrow Ú \nleftarrow ø \nLeftrightarrow ÷ \nRightarrow

Table 77: mathabx Harpoons Þ \barleftharpoon à \leftharpoonup é \rightleftharpoons ß \barrightharpoon Ø \leftleftharpoons Ù \rightrightharpoons Û \downdownharpoons à \leftrightharpoon ê \updownharpoons å \downharpoonleft è \leftrightharpoons ä \upharpoonleft ç \downharpoonright Ý \rightbarharpoon æ \upharpoonright ë \downupharpoons ã \rightharpoondown Ú \upupharpoons Ü \leftbarharpoon á \rightharpoonup â \leftharpoondown á \rightleftharpoon

Table 78: chemarrow Arrows A \chemarrow

Table 79: ulsy Contradiction Symbols © \blitza \blitzb \blitzc \blitzd \blitze

Table 80: Extension Characters − \relbar = \Relbar

30 Table 81: stmaryrd Extension Characters Z \Arrownot L \Mapsfromchar \Mapstochar [ \arrownot O \mapsfromchar

Table 82: txfonts/pxfonts Extension Characters \Mappedfromchar \Mmappedfromchar \Mmapstochar \mappedfromchar \mmappedfromchar \mmapstochar

Table 83: mathabx Extension Characters ß \mapsfromchar Þ \mapstochar û \Mapsfromchar ú \Mapstochar

Table 84: Log-like Symbols \arccos \cos \csc \exp \ker \limsup \min \sinh \arcsin \cosh \deg \gcd \lg \ln \Pr \sup \arctan \cot \det \hom \lim \log \sec \tan \arg \coth \dim \inf \liminf \max \sin \tanh

Calling the above “symbols” may be a bit misleading.1 Each log-like symbol merely produces the eponymous textual equivalent, but with proper surrounding spacing. See Section 7.3 for more information about log-like symbols. As \bmod and \pmod are arguably not symbols we refer the reader to the Short Math Guide for LATEX [Dow00] for samples.

Table 85: AMS Log-like Symbols

inj lim \injlim −lim→ \varinjlim lim \varlimsup proj lim \projlim lim \varliminf ←lim− \varprojlim

Load the amsmath package to get these symbols. See Section 7.3 for some additional comments regarding log-like symbols. As \mod and \pod are arguably not symbols we refer the reader to the Short Math Guide for LATEX [Dow00] for samples. 1Michael J. Downes prefers the more general term, “atomic math objects”.

31 Table 86: Greek Letters α \alpha θ \theta o o τ \tau β \beta ϑ \vartheta π \pi υ \upsilon γ \gamma ι \iota \varpi φ \phi δ \delta κ \kappa ρ \rho ϕ \varphi \epsilon λ \lambda \varrho χ \chi ε \varepsilon µ \mu σ \sigma ψ \psi ζ \zeta ν \nu ς \varsigma ω \omega η \eta ξ \xi

Γ \Gamma Λ \Lambda Σ \Sigma Ψ \Psi ∆ \Delta Ξ \Xi Υ \Upsilon Ω \Omega Θ \Theta Π \Pi Φ \Phi

The remaining Greek majuscules can be produced with ordinary Latin letters. The symbol “M”, for instance, is used for both an uppercase “m” and an uppercase “µ”. See Section 7.4 for examples of how to produce bold Greek letters.

Table 87: AMS Greek Letters M \digamma κ \varkappa

Table 88: txfonts/pxfonts Upright Greek Letters α \alphaup θ \thetaup π \piup φ \phiup β \betaup ϑ \varthetaup \varpiup ϕ \varphiup γ \gammaup ι \iotaup ρ \rhoup χ \chiup δ \deltaup κ \kappaup \varrhoup ψ \psiup \epsilonup λ \lambdaup σ \sigmaup ω \omegaup ε \varepsilonup µ \muup ς \varsigmaup ζ \zetaup ν \nuup τ \tauup η \etaup ξ \xiup υ \upsilonup

32 Table 89: upgreek Upright Greek Letters α \upalpha θ \uptheta π \uppi φ \upphi β \upbeta ϑ \upvartheta ϖ \upvarpi ϕ \upvarphi γ \upgamma ι \upiota ρ \uprho χ \upchi δ \updelta κ \upkappa ρ \upvarrho ψ \uppsi ε \upepsilon λ \uplambda σ \upsigma ω \upomega ε \upvarepsilon µ \upmu σ \upvarsigma ζ \upzeta ν \upnu τ \uptau η \upeta ξ \upxi υ \upupsilon

Γ \Upgamma Λ \Uplambda Σ \Upsigma Ψ \Uppsi ∆ \Updelta Ξ \Upxi Υ \Upupsilon Ω \Upomega Θ \Uptheta Π \Uppi Φ \Upphi upgreek utilizes upright Greek characters from either the PostScript Symbol font (depicted above) or Euler Roman. As a result, the glyphs may appear slightly diﬀerent from the above. Contrast, for example, “Γ∆Θαβγ”(Symbol)with“Γ∆Θαβγ”(Euler).

Table 90: txfonts/pxfonts Variant Latin Letters \varg \varv \varw ! \vary

Pass the varg option to txfonts/pxfonts to replace g, v, w,andy with , , ,and! in every mathematical expression in your document.

Table 91: AMS Hebrew Letters gimel Q \daleth\ ג O \beth

\aleph appears in Table 125 on page 42.

Table 92: Letter-like Symbols ⊥ \bot ∀ \forall ı \imath C \ni D \top ) \ell R \hbar ∈ \in ∂ \partial ℘ \wp ∃ \exists G \Im j \jmath H \Re

Table 93: AMS Letter-like Symbols k \Bbbk j \complement R \hbar \circledR S \Finv T \hslash k \circledS U \Game V \nexists

33 Table 94: txfonts/pxfonts Letter-like Symbols ¢ \mathcent £ \mathsterling \notin \notni

Table 95: mathabx Letter-like Symbols V \barin P \in L \nottop T \varnotin A \complement E \nexists Q \owns U \varnotowner D \exists M \notbot W \ownsbar F \Finv R \notin B \partial G \Game S \notowner C \partialslash

Table 96: trfsigns Letter-like Symbols e \e j \im

Table 97: AMS Delimiters l \ulcorner m \urcorner n \llcorner o \lrcorner

Table 98: stmaryrd Delimiters \Lbag \Rbag \lbag \rbag \ \llceil ] \rrceil ^ \llfloor _ \rrfloor ` \llparenthesis a \rrparenthesis

Table 99: mathabx Delimiters v \lcorners w \rcorners

x \ulcorner y \urcorner z \llcorner { \lrcorner

Table 100: nath Delimiters \niv \vin

34 Table 101: Variable-sized Delimiters ? w h i ? w ↓ y \downarrow ⇓ \Downarrow [ [ ] ] D E

\langle \rangle | |∗ ' \| l m x ~ ? w I \lceil J \rceil ↑ ? \uparrow ⇑ w \Uparrow j k x ~ ? w K \lfloor L \rfloor = y \updownarrow @ \Updownarrow n o ( ( ) ) { \{ } \} . / / / \ \backslash

When used with \left and \right, these symbols expand to the height of the en- closed math expression. Note that \vert is a synonym for |,and\Vert is a synonym for \|.

∗ ε-TEX provides a \middle analogue to \left and \right that can be used to make an internal “|” (often used to indicate “evaluated at”) expand to the height of the surrounding \left and \right symbols. A similar eﬀect can be achieved in conventional LATEX using the braket package.

Table 102: Large, Variable-sized Delimiters 8 9 8 9 8 > 9 > 8 > 9 > ; > : > : > ; > ;> \lmoustache :> \rmoustache :> \lgroup ;> \rgroup ? w > ? ? w w > > ? ? w w > > ? \arrowvert w \Arrowvert > > \bracevert ? w >

These symbols must be used with \left and \right.Themathabx package, however, redeﬁnes \lgroup and \rgroup so that those symbols can work without \left and \right.

Table 103: Variable-sized stmaryrd Delimiters 7 8 \llbracket \rrbracket

Table 104: mathabx Variable-sized Delimiters 1 9 v \lbbbrack w \rbbbrack 7 ? 7 ? 7 ? 7 7 \lfilet ? ? \rfilet ~ \thickvert ~ \vvvert

35 Table 105: nath Variable-sized Delimiters (Double) DD EE \lAngle \rAngle hh ii [[ \lBrack ]] \rBrack ll mm II \lCeil JJ \rCeil jj kk KK \lFloor LL \rFloor

|| \lVert∗ || \rVert∗

∗ nath redeﬁnes all of the above to include implicit \left and \right commands. Hence, separate \lVert and \rVert commands are needed to disambiguate whether “|” is a left or right delimiter.

All of the symbols in Table 105 can also be expressed using the \double macro. See the nath documentation for examples and additional information.

Table 106: nath Variable-sized Delimiters (Triple) DDD EEE \triple< \triple> hhh iii [[[ \triple[ ]]] \triple]

||| \ltriple|∗ ||| \rtriple|∗

∗ Similar to \lVert and \rVert in Table 105, \ltriple and \rtriple must be used instead of \triple to disambiguate whether “|” is a left or right delimiter.

Note that \triple—and the corresponding \double—is actually a macro that takes a delimiter as an argument.

Table 107: textcomp Text-mode Delimiters 〈 \textlangle 〉 \textrangle 〚 \textlbrackdbl 〛 \textrbrackdbl ⁅ \textlquill ⁆ \textrquill

36 Table 108: Math-mode Accents a´ \acute{a} aˇ \check{a} a` \grave{a} a˜ \tilde{a} a¯ \bar{a} a¨ \ddot{a} aˆ \hat{a} a \vec{a} a˘ \breve{a} a˙ \dot{a} ˚a \mathring{a}

Also note the existence of \imath and \jmath, which produce dotless versions of “i” and “j ”. (See Table 125 on page 42.) These are useful when the accent is supposed to replace the dot. For example, “\hat{\imath}” produces a correct “ˆı ”, while “\hat{i}” would yield the rather odd-looking “ˆi ”.

Table 109: AMS Math-mode Accents ...... a \dddot{a} a \ddddot{a}

These accents are also provided by the mathabx package.

Table 110: yhmath Math-mode Accents ˚a \ring{a}

This symbol is largely obsolete, as standard LATEX2ε has supported \mathring since June, 1998 [LAT98].

Table 111: trfsigns Math-mode Accents

a \dft{a} a \DFT{a}

The above are a sort of “reverse accent” in that the argument text serves as a subscript to the transform line.

37 Table 112: Extensible Accents

abcÝ \widetilde{abc}∗ abcÓ \widehat{abc}∗ ←− −→ abc \overleftarrow{abc}† abc \overrightarrow{abc}† abc \overline{abc} abc \underline{abc} z}|{ abc \overbrace{abc} |{z}abc \underbrace{abc} √ abc \sqrt{abc}‡

As demonstrated in a 1997 TUGboat article about typesetting long-division problems [Gib97], an extensible long-division sign (“ )abc ”) can be faked by putting a “\big)”inatabular environment with an \hline or \cline in the preceding row. The article also presents a piece of code that automatically solves and typesets—by putting an \overline atop “\big)” and the desired text—long-division problems. See also the polynom package, which automatically solves and typesets polynomialdivision problems in a similar manner.

∗ Made more extensible by the yhmath package.

† If you’re looking for an extensible diagonal line or arrow to be used for canceling or : 5 reducing mathematical subexpressions (e.g., “x +−x”or“3 + 2 ”) then consider using the cancel package.

‡ With an optional argument,√ \sqrt typesets nth roots. For√ example, n “\sqrt[3]{abc}”produces“3 abc ”and“\sqrt[n]{abc}”produces“ abc ”.

Table 113: overrightarrow Extensible Accents =⇒ abc \Overrightarrow{abc}

Table 114: yhmath Extensible Accents

abcö \wideparen{abc} abcé \widetriangle{abc} ˚ abcö \widering{abc}

38 Table 115: AMS Extensible Accents ←→ abc \overleftrightarrow{abc} ←abc→ \underleftrightarrow{abc} ←abc− \underleftarrow{abc} −abc→ \underrightarrow{abc}

The following are a sort of “reverse accent” in that the argument text serves as a superscript to the arrow. In addition, the optional ﬁrst argument (not shown) serves as a subscript to the arrow. See the Short Math Guide for LATEX [Dow00] for further examples.

abc abc ←−− \xleftarrow{abc} −−→ \xrightarrow{abc}

Table 116: chemarr Extensible Accents abc −−− − \xrightleftharpoons{abc}

\xrightleftharpoons is a sort of “reverse accent” in that the argument text serves as a superscript to the arrows. In addition, the optional ﬁrst argument (not shown) serves as a subscript to the arrows.

Table 117: chemarrow Extensible Accents

abc abc D GGGGGGG \autoleftarrow{abc}{def} GGGGGGGA \autorightarrow{abc}{def} def def

abc abc EGGGGGGGC GGGGGGG \autoleftrightharpoons{abc}{def} FGGGGGGGB GGGGGGG \autorightleftharpoons{abc}{def} def def

These symbols are all “reverse accents” in that the two arguments serve, respectively, as a superscript and a subscript to the arrows.

In addition to the symbols shown above, chemarrow also provides \larrowfill, \rarrowfill, \leftrightharpoonsfill,and\rightleftharpoonsfill macros. Each of these takes a length argument and produces an arrow of the speciﬁed length.

39 Table 118: mathabx Extensible Accents hkkikkj abc \overbrace{abc} abc \widebar{abc} hkkkkj abc \overgroup{abc} abc| \widecheck{abc}

loomoonabc \underbrace{abc} abc \wideparen{abc} ˚ loooonabc \undergroup{abc} abcö \widering{abc}

abc \widearrow{abc}

The braces shown for \overbrace and \underbrace appear in their minimum size. They can expand arbitrarily wide, however.

Table 119: esvect Extensible Accents # ” abc \vv{abc} with package option a # „ abc \vv{abc} with package option b # « abc \vv{abc} with package option c # » abc \vv{abc} with package option d # – abc \vv{abc} with package option e # — abc \vv{abc} with package option f # abc \vv{abc} with package option g # ‰ abc \vv{abc} with package option h esvect also deﬁnes a \vv* macro which is used to typeset arrows over vector variables with subscripts. See the esvect documentation for more information.

Table 120: undertilde Extensible Accents abc \utilde{abc} Ý Because \utilde is based on \widetilde it is also made more extensible by the yhmath package.

40 Table 121: Dots . · \cdotp : \colon∗ . \ldotp . \vdots† . ··· \cdots .. \ddots† ... \ldots

∗ While “:” is valid in math mode, \colon uses diﬀerent surrounding spacing. See Section 7.3 and the Short Math Guide for LATEX [Dow00] for more information on math-mode spacing.

† The mathdots package redeﬁnes \ddots and \vdots to make them scale properly with font size. (They normally scale horizontally but not vertically.) \fixedddots and \fixedvdots provide the original, ﬁxed-height functionality of LATEX2ε’s \ddots and \vdots macros.

Table 122: AMS Dots ··· \dotsb ··· \dotsi ... \dotso ... \dotsc ··· \dotsm

The AMS dot symbols are named according to their intended usage: \dotsb between pairs of binary operators/relations, \dotsc between pairs of commas, \dotsi between pairs of integrals, \dotsm between pairs of multiplication signs, and \dotso between other symbol pairs.

Table 123: mathdots Dots . .. \iddots

Table 124: yhmath Dots . .. \adots

41 Table 125: Miscellaneous LATEX2ε Symbols ℵ \aleph \Diamond∗ ∞ \infty P \prime \angle ♦ \diamondsuit W \mho∗ - \sharp ‡ \ \backslash ∅ \emptyset ∇ \nabla √♠ \spadesuit p \Box∗,† 0 \flat 1 \natural \surd ♣ \clubsuit ♥ \heartsuit ¬ \neg \triangle

∗ Not predeﬁned in LATEX2ε. Use one of the packages latexsym, amsfonts, amssymb, txfonts, pxfonts,orwasysym.

† To use \Box—or any other symbol—as an end-of-proof (Q.E.D.) marker, consider using the ntheorem package, which properly juxtaposes a symbol with the end of the proof text.

‡ Many people prefer the look of AMS’s \varnothing (Table 126) to that of LATEX’s \emptyset.

Table 126: Miscellaneous AMS Symbols ∠ \angle r \blacktriangledown W \mho s \backprime X \diagdown t \sphericalangle u \bigstar Y \diagup p \square v \blacklozenge ð \eth w \triangledown x \blacksquare ♦ \lozenge ∅ \varnothing \blacktriangle \measuredangle \vartriangle

Table 127: Miscellaneous wasysym Symbols \Box W \mho∗ ∴ \wasytherefore \Diamond \varangle

∗ wasysym also deﬁnes an \agemO symbol, which is the same glyph as \mho but is intended for use in text mode.

Table 128: Miscellaneous txfonts/pxfonts Symbols \Diamondblack \lambdaslash \varheartsuit \Diamonddot \varclubsuit \varspadesuit \lambdabar \vardiamondsuit

Table 129: Miscellaneous mathabx Symbols 0 \degree 4 \fourth > \measuredangle 2 \second å \diagdown # \hash & \pitchfork ? \sphericalangle ä \diagup 8 \infty 9 \propto 3 \third I \diameter $ \leftthreetimes % \rightthreetimes # \varhash

42 Table 130: Miscellaneous textcomp Text-mode Math Symbols ° \textdegree∗ ½ \textonehalf† ¾ \textthreequarters† ÷ \textdiv ¼ \textonequarter† ³ \textthreesuperior ⁄ \textfractionsolidus ¹ \textonesuperior × \texttimes ¬ \textlnot ± \textpm ² \texttwosuperior − \textminus √ \textsurd

∗ If you prefer a larger degree symbol you might consider deﬁning one as “\ensuremath{^\circ}”(“◦”).

† nicefrac (part of the units package) can be used to construct vulgar fractions like “1/2”, “1/4”, “3/4”, and even “c/o”.

Table 131: mathcomp Math Symbols ℃ \tccentigrade Ω \tcohm ‰ \tcperthousand µ \tcmu ‱ \tcpertenthousand

Table 132: gensymb Symbols Deﬁned to Work in Both Math and Text Mode ℃ \celsius µ \micro ‰ \perthousand ° \degree Ω \ohm

Table 133: mathabx Mayan Digits 0 \maya{0} 2 \maya{2} 4 \maya{4} 1 \maya{1} 3 \maya{3} 5 \maya{5}

Table 134: marvosym Math Symbols 0 \MVZero 2 \MVTwo 4 \MVFour 6 \MVSix 8 \MVEight 1 \MVOne 3 \MVThree 5 \MVFive 7 \MVSeven 9 \MVNine

W \Anglesign ÷ \Squaredot P \Vectorarrowhigh = \Corresponds p \Vectorarrow

43 Table 135: Math Alphabets Required package ABCdef123 \mathrm{ABCdef123} none ABCdef123 \mathit{ABCdef123} none ABCdef123 \mathnormal{ABCdef123} none ABC \mathcal{ABC} none ABC \mathscr{ABC} mathrsfs or \mathcal{ABC} calrsfs ABC \mathcal{ABC} euscript with the mathcal option or \mathscr{ABC} euscript with the mathscr option ABCdef123 \mathpzc{ABCdef123} none;manuallydeﬁned∗ ABC \mathbb{ABC} amsfonts,§ amssymb, txfonts,orpxfonts º»¼ \varmathbb{ABC} txfonts or pxfonts ABCdef123 \mathbb{ABCdef123} bbold or mathbbol† ABCdef123 \mathbb{ABCdef123} mbboard† ABCdef12 \mathbbm{ABCdef12} bbm ABCdef12 \mathbbmss{ABCdef12} bbm ABCdef12 \mathbbmtt{ABCdef12} bbm ABC1 \mathds{ABC1} dsfont ABC1 \mathds{ABC1} dsfont with the sans option ABCdef123 \mathfrak{ABCdef123} eufrak ABCdef123 \textfrak{ABCdef123} yfonts‡ ABCdef123 \textswab{ABCdef123} yfonts‡ ABCˇf123 \textgoth{ABCdef123} yfonts‡

∗ Put “\DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it}” in your document’s preamble to make \mathpzc typeset its argument in Zapf Chancery.

† The mathbbol package deﬁnes some additional blackboard bold characters: parenthe- ses, square brackets, angle brackets, and—if the bbgreekl option is passed to matbbol—Greek letters. For instance, “<[( )]>”isproducedby“\mathbb{\Langle \Lbrack\Lparen\bbalpha\bbbeta\bbgamma\Rparen\Rbrack\Rangle}”.

mbboard extends the blackboard bold symbol set signiﬁcantly further. It supports not only the Greek alphabet—including “Greek-like” symbols such as \bbnabla (“”)— but also all punctuation marks, various currency symbols such as \bbdollar (“$”) and \bbeuro (“û”), and the Hebrew alphabet (e.g., “\bbfinalnun\bbyod\bbqof \bbpe” → “ÏÉ×Ô”).

‡ As their \text. . . names imply, the fonts provided by the yfonts package are actually text fonts. They are included in Table 135 because they are frequently used in a mathematical context.

§ An older (i.e., prior to 1991) version of the AMS’s fonts rendered C, N, R, S,andZ as C, N, R, S,andZ. As some people prefer the older glyphs—much to the AMS’s surprise—and because those glyphs fail to build under modern versions of META- FONT, Berthold Horn uploaded PostScript fonts for the older blackboard-bold glyphs to CTAN, to the fonts/msym10 directory. As of this writing, however, there are no LATEX2ε packages for utilizing the now-obsolete glyphs.

44 4 Science and technology symbols

This section lists symbols that are employed in various branches of science and engineering (and, because we were extremely liberal in our classiﬁcation, astrology, too).

Table 136: wasysym Electrical and Physical Symbols ¬ \AC \VHF ¬¬¬¬ \photon ¬ \HF \gluon

Table 137: ifsym Pulse Diagram Symbols ! \FallingEdge ' \LongPulseLow % \PulseLow " \ShortPulseHigh & \LongPulseHigh $ \PulseHigh \RaisingEdge # \ShortPulseLow

In addition, within \textifsym{...}, the following codes are valid:

l l m m h h d d < < > > L L M M H H D D = << ? >>

This enables one to write “\textifsym{mmmm}”toget“mmmm”or “\textifsym{L|H|L|H|L}”toget“L|H|L|H|L”. See also the timing package, which provides a wide variety of pulse-diagram symbols within an environment designed speciﬁcally for typesetting pulse diagrams.

Finally, \textifsym supports the display of segmented digits, as would appear on an LCD: “\textifsym{-123.456}”produces“-123.456”. “\textifsym{b}”outputs a blank with the same width as an “8”.

Table 138: ar Aspect Ratio Symbol A \AR

Table 139: textcomp Text-mode Science and Engineering Symbols ℃ \textcelsius ℧ \textmho µ \textmu Ω \textohm

Table 140: wasysym Astronomical Symbols \ascnode \jupiter \newmoon ♀ \venus \astrosun \leftmoon \pluto \vernal ! \descnode ♂ \mars # \rightmoon ♁ \earth % \mercury & \saturn \fullmoon ' \neptune ( \uranus

45 Table 141: marvosym Astronomical Symbols Â \Mercury Ä \Mars Ç \Uranus À \Sun Ã \Venus Å \Jupiter È \Neptune Á \Moon Ê \Earth Æ \Saturn É \Pluto

Table 142: mathabx Astronomical Symbols A \Mercury C \Earth E \Jupiter G \Uranus I \Pluto B \Venus D \Mars F \Saturn H \Neptune

M \fullmoon K \leftmoon N \newmoon L \rightmoon @ \Sun J \varEarth

mathabx also deﬁnes \girl as an alias for \Venus, \boy as an alias for \Mars,and \Moon as an alias for \leftmoon.

Table 143: wasysym Astrological Symbols \aries ) \cancer * \libra + \capricornus , \taurus \leo - \scorpio . \aquarius / \gemini 0 \virgo 1 \sagittarius 2 \pisces

3 \conjunction 4 \opposition

Table 144: marvosym Astrological Symbols à \Aries ã \Cancer æ \Libra é \Capricorn á \Taurus ä \Leo ç \Scorpio ê \Aquarius â \Gemini å \Virgo è \Sagittarius ë \Pisces

Note that \Aries ...\Pisces can also be speciﬁed with \Zodiac{1} ...\Zodiac{12}.

Table 145: mathabx Astrological Symbols P \Aries Q \Taurus R \Gemini

Table 146: wasysym APL Symbols 5 \APLbox ÷5 \APLinv 6 \APLstar 7 \APLcomment 8 \APLleftarrowbox 9 \APLup : \APLdown \APLlog ; \APLuparrowbox − < \APLdownarrowbox \APLminus −\ \notbackslash = \APLinput > \APLrightarrowbox −/ \notslash

46 Table 147: wasysym APL Modiﬁers ◦ \APLcirc{} ∼ \APLnot{} | \APLvert{}

Table 148: marvosym Computer Hardware Symbols Í \ComputerMouse Ñ \ParallelPort Î \SerialInterface Ï \Keyboard Ò \Printer Ð \SerialPort

Table 149: ascii Control Characters (IBM) \SOH • \BEL ♪ \CR ‼ \DCc ↓ \EM \US \STX \BS ♫ \SO ¶ \DCd → \SUB ¦ \splitvert ♥ \ETX \HT \SI § \NAK ← \ESC \DEL ♦ \EOT \LF \DLE \SYN └ \FS ♣ \ENQ ♂ \VT \DCa \ETB ↔ \GS ♠ \ACK ♀ \FF \DCb ↑ \CAN \RS

SOH, STX, ETX, ..., US are the names of ASCII characters 1–31. DEL is the name of ASCII character 127. \splitvert doesn’t correspond to a control character but is merely the “|” character shown IBM style.

These characters must be entered with the ascii font in eﬀect, for example, “{\ascii\STX}”. See the ascii package documentation for more information.

Table 150: marvosym Communication Symbols k \Email t \fax v \Faxmachine E \Lightning A \Pickup z \Emailct u \FAX B \Letter H \Mobilefone T \Telefon

Table 151: marvosym Engineering Symbols " \Beam l \Force ‘ \Octosteel \RoundedTTsteel # \Bearing ’ \Hexasteel ˜ \Rectpipe — \Squarepipe › \Circpipe & \Lefttorque ” \Rectsteel “ \Squaresteel • \Circsteel L \Lineload ' \Righttorque œ \Tsteel % \Fixedbearing $ \Loosebearing Ÿ \RoundedLsteel∗ š \TTsteel – \Flatsteel ™ \Lsteel \RoundedTsteel∗

∗ \RoundedLsteel and \RoundedTsteel seem to be swapped, at least in the 2000/05/01 version of marvosym.

Table 152: wasysym Biological Symbols ♀ \female ♂ \male

47 Table 153: marvosym Biological Symbols ~ \Female … \FemaleMale ‚ \MALE { \Neutral \FEMALE } \Hermaphrodite | \Male „ \FemaleFemale \HERMAPHRODITE ƒ \MaleMale

Table 154: marvosym Safety-related Symbols h \Biohazard C \CEsign ` \Explosionsafe j \Radioactivity n \BSEfree J \Estatically a \Laserbeam ! \Stopsign

48 5 Dingbats

Dingbats are symbols such as stars, arrows, and geometric shapes. They are commonly used as bullets in itemized lists or, more generally, as a means to draw attention to the text that follows. The pifont dingbat package warrants special mention. Among other capabilities, pifont provides a LATEX interface to the Zapf Dingbats font (one of the standard 35 PostScript fonts). However, rather than name each of the dingbats individually, pifont merely provides a single \ding command, which outputs the character that lies at a given position in the font. The consequence is that the pifont symbols can’t be listed by name in this document’s index, so be mindful of that fact when searching for a particular symbol.

Table 155: bbding Arrows y \ArrowBoldDownRight z \ArrowBoldRightShort x \ArrowBoldUpRight { \ArrowBoldRightCircled w \ArrowBoldRightStrobe

Table 156: pifont Arrows ➔ \ding{212} ➝ \ding{221} ➦ \ding{230} ➯ \ding{239} ➹ \ding{249} → \ding{213} ➞ \ding{222} ➧ \ding{231} ➱ \ding{241} ➺ \ding{250} ↔ \ding{214} ➟ \ding{223} ➨ \ding{232} ➲ \ding{242} ➻ \ding{251} ↕ \ding{215} ➠ \ding{224} ➩ \ding{233} ➳ \ding{243} ➼ \ding{252} ➘ \ding{216} ➡ \ding{225} ➪ \ding{234} ➴ \ding{244} ➽ \ding{253} ➙ \ding{217} ➢ \ding{226} ➫ \ding{235} ➵ \ding{245} ➾ \ding{254} ➚ \ding{218} ➣ \ding{227} ➬ \ding{236} ➶ \ding{246} ➛ \ding{219} ➤ \ding{228} ➭ \ding{237} ➷ \ding{247} ➜ \ding{220} ➥ \ding{229} ➮ \ding{238} ➸ \ding{248}

Table 157: marvosym Scissors s \Cutleft q \Cutright S \Leftscissors r \Cutline R \Kutline Q \Rightscissors

Table 158: bbding Scissors § \ScissorHollowLeft ¥ \ScissorLeftBrokenTop ¦ \ScissorHollowRight ¡ \ScissorRight ¤ \ScissorLeft \ScissorRightBrokenBottom £ \ScissorLeftBrokenBottom ¢ \ScissorRightBrokenTop

Table 159: pifont Scissors ✁ \ding{33} ✂ \ding{34} ✃ \ding{35} ✄ \ding{36}

49 Table 160: dingbat Pencils

W \largepencil P \smallpencil

Table 161: bbding Pencils and Nibs \NibLeft \PencilLeft \PencilRightDown \NibRight \PencilLeftDown \PencilRightUp \NibSolidLeft \PencilLeftUp \NibSolidRight \PencilRight

Table 162: pifont Pencils and Nibs ✎ \ding{46} ✏ \ding{47} ✐ \ding{48} ✑ \ding{49} ✒ \ding{50}

Table 163: dingbat Hands

R \leftpointright L \rightpointleft N \rightpointright D \leftthumbsdown d \rightthumbsdown U \leftthumbsup u \rightthumbsup

Table 164: bbding Hands \HandCuffLeft \HandCuffRightUp \HandPencilLeft \HandCuffLeftUp \HandLeft \HandRight \HandCuffRight \HandLeftUp \HandRightUp

Table 165: pifont Hands ☛ \ding{42} ☞ \ding{43} ✌ \ding{44} ✍ \ding{45}

Table 166: bbding Crosses and Plusses * \Cross + \CrossOpenShadow & \PlusOutline - \CrossBoldOutline , \CrossOutline ) \PlusThinCenterOpen 4 \CrossClowerTips ' \Plus . \CrossMaltese ( \PlusCenterOpen

50 Table 167: pifont Crosses and Plusses ✙ \ding{57} ✛ \ding{59} ✝ \ding{61} ✟ \ding{63} ✚ \ding{58} ✜ \ding{60} ✞ \ding{62} ✠ \ding{64}

Table 168: bbding Xs and Check Marks ! \Checkmark # \XSolid % \XSolidBrush " \CheckmarkBold $ \XSolidBold

Table 169: pifont Xs and Check Marks ✓ \ding{51} ✕ \ding{53} ✗ \ding{55} ✔ \ding{52} ✖ \ding{54} ✘ \ding{56}

Table 170: wasysym Xs and Check Marks ? \CheckedBox p \Square @ \XBox

Table 171: pifont Circled Numbers ① \ding{172} ❶ \ding{182} ➀ \ding{192} ➊ \ding{202} ② \ding{173} ❷ \ding{183} ➁ \ding{193} ➋ \ding{203} ③ \ding{174} ❸ \ding{184} ➂ \ding{194} ➌ \ding{204} ④ \ding{175} ❹ \ding{185} ➃ \ding{195} ➍ \ding{205} ⑤ \ding{176} ❺ \ding{186} ➄ \ding{196} ➎ \ding{206} ⑥ \ding{177} ❻ \ding{187} ➅ \ding{197} ➏ \ding{207} ⑦ \ding{178} ❼ \ding{188} ➆ \ding{198} ➐ \ding{208} ⑧ \ding{179} ❽ \ding{189} ➇ \ding{199} ➑ \ding{209} ⑨ \ding{180} ❾ \ding{190} ➈ \ding{200} ➒ \ding{210} ⑩ \ding{181} ❿ \ding{191} ➉ \ding{201} ➓ \ding{211}

pifont (part of the psnfss package) provides a dingautolist environment which resembles enumerate but uses circled numbers as bullets.2 See the psnfss documentation for more information.

Table 172: wasysym Stars A \davidsstar B \hexstar C \varhexstar

2In fact, dingautolist can use any set of consecutive Zapf Dingbats symbols.

51 Table 173: bbding Stars, Flowers, and Similar Shapes N \Asterisk P \FiveFlowerPetal 2 \JackStar A \AsteriskBold 8 \FiveStar 3 \JackStarBold B \AsteriskCenterOpen ; \FiveStarCenterOpen O \SixFlowerAlternate X \AsteriskRoundedEnds ? \FiveStarConvex U \SixFlowerAltPetal C \AsteriskThin 7 \FiveStarLines M \SixFlowerOpenCenter D \AsteriskThinCenterOpen 9 \FiveStarOpen Q \SixFlowerPetalDotted 0 \DavidStar : \FiveStarOpenCircled L \SixFlowerPetalRemoved / \DavidStarSolid < \FiveStarOpenDotted [ \SixFlowerRemovedOpenPetal Z \EightAsterisk = \FiveStarOutline G \SixStar S \EightFlowerPetal > \FiveStarOutlineHeavy K \SixteenStarLight Y \EightFlowerPetalRemoved @ \FiveStarShadow ` \Snowflake H \EightStar 1 \FourAsterisk ^ \SnowflakeChevron I \EightStarBold V \FourClowerOpen _ \SnowflakeChevronBold F \EightStarConvex W \FourClowerSolid ] \Sparkle E \EightStarTaper 5 \FourStar \ \SparkleBold R \FiveFlowerOpen 6 \FourStarOpen J \TwelweStar

Table 174: pifont Stars, Flowers, and Similar Shapes ✡ \ding{65} ✪ \ding{74} ✳ \ding{83} ✼ \ding{92} ❅ \ding{101} ✢ \ding{66} ✫ \ding{75} ✴ \ding{84} ✽ \ding{93} ❆ \ding{102} ✣ \ding{67} ✬ \ding{76} ✵ \ding{85} ✾ \ding{94} ❇ \ding{103} ✤ \ding{68} ✭ \ding{77} ✶ \ding{86} ✿ \ding{95} ❈ \ding{104} ✥ \ding{69} ✮ \ding{78} ✷ \ding{87} ❀ \ding{96} ❉ \ding{105} ✦ \ding{70} ✯ \ding{79} ✸ \ding{88} ❁ \ding{97} ❊ \ding{106} ✧ \ding{71} ✰ \ding{80} ✹ \ding{89} ❂ \ding{98} ❋ \ding{107} ★ \ding{72} ✱ \ding{81} ✺ \ding{90} ❃ \ding{99} ✩ \ding{73} ✲ \ding{82} ✻ \ding{91} ❄ \ding{100}

Table 175: wasysym Geometric Shapes D \hexagon E \octagon F \pentagon G \varhexagon

52 Table 176: ifsym Geometric Shapes % \BigCircle T \FilledBigTriangleRight E \SmallCircle \BigCross Q \FilledBigTriangleUp \SmallCross & \BigDiamondshape e \FilledCircle F \SmallDiamondshape \BigHBar ¨ \FilledDiamondShadowA \SmallHBar _ \BigLowerDiamond © \FilledDiamondShadowC \SmallLowerDiamond / \BigRightDiamond f \FilledDiamondshape O \SmallRightDiamond \BigSquare u \FilledSmallCircle @ \SmallSquare # \BigTriangleDown v \FilledSmallDiamondshape C \SmallTriangleDown " \BigTriangleLeft p \FilledSmallSquare B \SmallTriangleLeft $ \BigTriangleRight s \FilledSmallTriangleDown D \SmallTriangleRight ! \BigTriangleUp r \FilledSmallTriangleLeft A \SmallTriangleUp \BigVBar t \FilledSmallTriangleRight \SmallVBar 5 \Circle q \FilledSmallTriangleUp * \SpinDown \Cross ` \FilledSquare ) \SpinUp ¥ \DiamondShadowA £ \FilledSquareShadowA 0 \Square ¦ \DiamondShadowB ¤ \FilledSquareShadowC \SquareShadowA § \DiamondShadowC c \FilledTriangleDown ¡ \SquareShadowB 6 \Diamondshape b \FilledTriangleLeft ¢ \SquareShadowC U \FilledBigCircle d \FilledTriangleRight 3 \TriangleDown V \FilledBigDiamondshape a \FilledTriangleUp 2 \TriangleLeft P \FilledBigSquare \HBar 4 \TriangleRight S \FilledBigTriangleDown o \LowerDiamond 1 \TriangleUp R \FilledBigTriangleLeft ? \RightDiamond \VBar

The ifsym documentation points out that one can use \rlap to combine some of the above into useful, new symbols. For example, \BigCircle and \FilledSmallCircle combine to give “ %u ”. Likewise, \Square and \Cross combine to give “0”. See Section 7.2 for more information about constructing new symbols out of existing symbols.

Table 177: bbding Geometric Shapes d \CircleShadow u \Rectangle j \SquareShadowTopLeft a \CircleSolid v \RectangleBold i \SquareShadowTopRight p \DiamondSolid t \RectangleThin g \SquareSolid b \Ellipse f \Square o \TriangleDown e \EllipseShadow k \SquareCastShadowBottomRight n \TriangleUp c \EllipseSolid m \SquareCastShadowTopLeft s \HalfCircleLeft l \SquareCastShadowTopRight r \HalfCircleRight h \SquareShadowBottomRight

53 Table 178: pifont Geometric Shapes ● \ding{108} ❏ \ding{111} ❒ \ding{114} ◆ \ding{117} ❙ \ding{121} ❍ \ding{109} ❐ \ding{112} ▲ \ding{115} ◗ \ding{119} ❚ \ding{122} ■ \ding{110} ❑ \ding{113} ▼ \ding{116} ❘ \ding{120}

Table 179: universa Geometric Shapes ¡ \baucircle \bausquare ¢ \bautriangle

Table 180: manfnt Dangerous Bend Symbols \dbend \lhdbend \reversedvideodbend

Note that these symbols descend far beneath the baseline. manfnt also deﬁnes non- descending versions, which it calls, correspondingly, \textdbend, \textlhdbend,and \textreversedvideodbend.

Table 181: skull Symbols A \skull

Table 182: Non-Mathematical mathabx Symbols O \rip

Table 183: marvosym Information Symbols ® \Bicycle o \Football Z \Pointinghand V \Checkedbox x \Gentsroom w \Wheelchair U \Clocklogo I \Industry b \Writinghand K \Coffeecup i \Info X \Crossedbox y \Ladiesroom

Table 184: Miscellaneous dingbat Dingbats

O \anchor E \eye S \Sborder C \carriagereturn C \filledsquarewithdots B \squarewithdots D \checkmark I \satellitedish Z \Zborder

54 Table 185: Miscellaneous bbding Dingbats \Envelope \Peace © \PhoneHandset T \SunshineOpenCircled q \OrnamentDiamondSolid ¨ \Phone \Plane \Tape

Table 186: Miscellaneous pifont Dingbats ☎ \ding{37} ✈ \ding{40} ❤ \ding{164} ❧ \ding{167} ♠ \ding{171} ✆ \ding{38} ✉ \ding{41} ❥ \ding{165} ♣ \ding{168} ♦ \ding{169} ✇ \ding{39} ❖ \ding{118} ❦ \ding{166} ♥ \ding{170}

55 6Othersymbols

The following are all the symbols that didn’t ﬁt neatly or unambiguously into any of the previous sections. (Do weather symbols belong under “Science and technology”? Should dice be considered “mathematics”?) While some of the tables contain clearly related groups of symbols (e.g., musical notes), others represent motley assortments of whatever the font designer felt like drawing.

Table 187: textcomp Genealogical Symbols M \textborn N \textdivorced O \textmarried P \textdied Q \textleaf

Table 188: wasysym General Symbols H \ataribox I \clock \LEFTarrow J \smiley K \bell L \diameter M \lightning ☼ \sun O \blacksmiley P \DOWNarrow Q \phone R \UParrow S \Bowtie T \frownie U \pointer ◊ \wasylozenge W \brokenvert X \invdiameter Y \recorder ? \checked Z \kreuz \RIGHTarrow

Table 189: wasysym Musical Notes [ \eighthnote \ \halfnote ] \twonotes ^ \fullnote ♩ \quarternote

See also \flat, \sharp,and\natural (Table 125 on page 42).

Table 190: wasysym Circles \CIRCLE ` \LEFTcircle a \RIGHTcircle b \rightturn \Circle c \Leftcircle d \Rightcircle ` \LEFTCIRCLE a \RIGHTCIRCLE e \leftturn

Table 191: Miscellaneous manfnt Symbols \manboldkidney \manpenkidney \manconcentriccircles \manquadrifolium \manconcentricdiamond \manquartercircle \mancone \manrotatedquadrifolium \mancube \manrotatedquartercircle \manerrarrow \manstar \manfilledquartercircle \mantiltpennib \manhpennib \mantriangledown \manimpossiblecube \mantriangleright \mankidney \mantriangleup \manlhpenkidney \manvpennib

56 Table 192: marvosym Navigation Symbols · \Forward » \MoveDown ´ \RewindToIndex ¼ \ToTop ¸ \ForwardToEnd º \MoveUp µ \RewindToStart ¹ \ForwardToIndex ¶ \Rewind ½ \ToBottom

Table 193: marvosym Laundry Symbols Ø \AtForty Ü \Handwash Ô \ShortNinetyFive Ó \AtNinetyFive ¯ \IroningI Ö \ShortSixty Õ \AtSixty ° \IroningII Û \ShortThirty Ë \Bleech ± \IroningIII Ú \SpecialForty « \CleaningA Ì \NoBleech \Tumbler ¾ \CleaningF ¨ \NoChemicalCleaning ‰ \WashCotton ¿ \CleaningFF ² \NoIroning Š \WashSynthetics ¬ \CleaningP \NoTumbler ‹ \WashWool \CleaningPP × \ShortFifty Ý \Dontwash Ù \ShortForty

Table 194: Other marvosym Symbols ˆ \Ankh † \Cross Œ \Heart © \Smiley ý \Bat F \FHBOlogo ÿ \MartinVogel þ \Womanface ¥ \Bouquet f \FHBOLOGO m \Mundus Y \Yinyang ‡ \Celtcross § \Frowny @ \MVAt ª \CircledA \FullFHBO : \Rightarrow∗

∗ Standard LATEX2ε defines \Rightarrow to display “⇒”, while marvosym redefines it to display “:” (or “:” in math mode). This conflict can be problematic for math symbols defined in terms of \Rightarrow,suchas\Longleftrightarrow,whichends up looking like “⇐ :”.

Table 195: Miscellaneous universa Symbols

¤ \bauforms £ \bauhead

57 Table 196: ifsym Weather Symbols \Cloud \Hail \Sleet \WeakRain \FilledCloud \HalfSun \Snow \WeakRainCloud ! \FilledRainCloud \Lightning \SnowCloud $ \FilledSnowCloud # \FilledSunCloud \NoSun \Sun " \FilledWeakRainCloud \Rain \SunCloud \Fog \RainCloud \ThinFog

In addition, \Thermo{0}...\Thermo{6} produce thermometers that are between 0/6 and 6/6 full of mercury: ¥¦§¨©

Similarly, \wind{sun}{angle}{strength} will draw wind symbols with a given amount of sun (0–4), a given angle (in degrees), and a given strength in km/h (0– 100). For example, \wind{0}{0}{0} produces “ 0 ”, \wind{2}{0}{0} produces “¢ 0 ”, and \wind{4}{0}{100} produces “¤ : ”.

Table 197: ifsym Alpine Symbols \SummitSign \Summit \SurveySign \HalfFilledHut \StoneMan \Mountain \Joch \VarSummit \Hut \IceMountain \Flag \FilledHut \VarMountain \VarFlag \Village \VarIceMountain \Tent

Table 198: ifsym Clocks

\Interval \StopWatchStart \VarClock \Wecker \StopWatchEnd \Taschenuhr \VarTaschenuhr

ifsym also exports a \showclock macro. \showclock{hours}{minutes} outputs a clock displaying the corresponding time. For instance, “\showclock{5}{40}”produces “D”. hours must be an integer from 0 to 11, and minutes must be an integer multiple of 5 from 0 to 55.

58 Table 199: Other ifsym Symbols ¢ \FilledSectioningDiamond \Letter \Radiation \Fire ¤ \PaperLandscape ¡ \SectioningDiamond \Irritant £ \PaperPortrait @ \Telephone

X \StrokeOne XXX \StrokeThree Y \StrokeFive XX \StrokeTwo XXXX \StrokeFour

In addition, \Cube{1}...\Cube{6} produce dice with the corresponding number of spots: ¥¦§¨©

Table 200: skak Chess Informator Symbols g \bbetter d \doublepawns N \novelty R \various i \bdecisive L \ending F \onlymove f \wbetter b \betteris j \equal o \opposbishops h \wdecisive a \bishoppair P \etc r \passedpawn J \weakpt e \bupperhand H \file M \qside w \with I \centre O \kside s \samebishops A \withattack RR \comment x \markera l \see E \withidea n \compensation y \markerb q \seppawns C \withinit V \counterplay m \mate T \timelimit v \without t \devadvantage S \morepawns k \unclear c \wupperhand G \diagonal U \moreroom u \unitedpawns D \zugzwang

The above symbols are merely the named informator symbol. skak can typeset many more chess-related symbols, including those for all of the pieces (KQRBNP/ kqrbnp), but only in the context of moves and boards, not as individual, named LATEXsymbols.

59 7 Additional Information

Unlike the previous sections of this document, Section 7 does not contain new symbol tables. Rather, it provides additional help in using the Comprehensive LATEX Symbol List. First, it draws attention to symbol names used by multiple packages. Next, it provides some guidelines for ﬁnding symbols and gives some examples regarding how to construct missing symbols out of existing ones. Then, it comments on the spacing surrounding symbols in math mode. After that, it presents an ASCII and Latin 1 quick-reference guide, showing how to enter all of the standard ASCII/Latin 1 symbols in LATEX. And ﬁnally, it lists some statistics about this document itself.

7.1 Symbol Name Clashes Unfortunately, a number of symbol names are not unique; they appear in more than one package. Depending on how the symbols are defined in each package, LATEX will either output an error message or replace an earlier- defined symbol with a later-defined symbol. Table 201 presents a selection of name clashes that appear in this document. Using multiple symbols with the same name in the same document—or even merely loading conflicting symbol packages—can be tricky, but, as evidenced by the existence of Table 201, not impossible. The general procedure is to load the first package, rename the conflicting symbols, and then load the second package. Examine the LATEX source for this document (symbols.tex)—especially the \savesymbol and \restoresymbol macros and their subsequent usage—to see one possible way to handle symbol conflicts. txfonts and pxfonts redefine a huge number of symbols—essentially, all of the symbols defined by latexsym, textcomp,thevariousAMS symbol sets, and LATEX2ε itself. Similarly, mathabx redefines a vast number of math symbols in an attempt to improve their look. The txfonts, pxfonts,andmathabx conflicts are not listed in Table 201 because they are designed to be compatible with the symbols they replace. Table 202 on page 62 illustrates what “compatible” means in this context. To use the new txfonts/pxfonts symbols without altering the document’s main font, merely reset the default font families back to their original values after loading one of those packages:

\renewcommand\rmdefault{cmr} \renewcommand\sfdefault{cmss} \renewcommand\ttdefault{cmtt}

7.2 Where can I ﬁnd the symbol for ... ? If you can’t ﬁnd some symbol you’re looking for in this document, there are a few possible explanations:

• The symbol isn’t intuitively named. As a few examples, the command to draw dice is “\Cube”; a plus sign with a circle around it (“exclusive or” to computer engineers) is “\oplus”; and lightning bolts in fonts designed by German speakers may have “blitz” in their names. The moral of the story is to be creative with synonyms when searching the index. • The symbol is deﬁned by some package that I overlooked (or deemed unimportant). If there’s some symbol package that you think should be included in the Comprehensive LATEX Symbol List, please send me e-mail at the address listed on the title page. • The symbol isn’t deﬁned in any package whatsoever.

Even in the last case, all is not lost. Sometimes, a symbol exists in a font, but there is no LATEX binding for it. For example, the PostScript Symbol font contains a “↵” symbol, which may be useful for representing a carriage return, but there is no package for accessing that symbol (as far as I know). To produce an unnamed symbol, you need to switch to the font explicitly with LATEX2ε’s low-level font commands [LAT00] and use TEX’s primitive \char command [Knu86a] to request a speciﬁc character number in the font.3 In fact, \char is not strictly necesssary; the character can often be entered symbolically. For example, the symbol for a Tate-Shafarevich group (“X”)

3pifont deﬁnes a convenient \Pisymbol command for accessing symbols in PostScript fonts by number. For example, “\Pisymbol{psy}{191}” produces “↵”.

60 Table 201: Symbol Name Clashes

Symbol LATEX2ε AMS stmaryrd wasysym mathabx marvosym bbding ifsym dingbat wsuipa \baro 9 < \bigtriangledown ? \bigtriangleup \checkmark D \Circle 5 \Cross † * 61 \ggg ≫ Ï \Letter B \lightning S M \Lightning E \lll ≪ Î \Rightarrow ⇒ ñ : \Square p f 0 \Sun @ À \TriangleDown o 3 \TriangleUp n 1 Table 202: Example of a Benign Name Clash

Default txfonts Symbol (Computer Modern) (Times Roman)

R R R \textrecipe is actually an uppercase sha in the Cyrillic alphabet. (Cyrillic is supported by the OT2 font encoding, for instance). While a sha can be deﬁned numerically as “{\fontencoding{OT2}\selectfont\char88}”itmaybe more intuitive to use the OT2 font encoding’s “SH” ligature: “{\fontencoding{OT2}\selectfont SH}”.

Reﬂecting and rotating existing symbols A common request on comp.text.tex is for a reversed or rotated version of an existing symbol. As a last re-

sort, these effects can be achieved with the graphicx (or graphics) package’s \reflectbox and \rotatebox macros. For example, \rotatebox[origin=c]{180}{$\iota$} produces the definite-description operator (“ ”).ι The dis- 4 advantage of the graphicx/graphics approach is that not every TEX backend handles graphical transformations. Far better is to find a suitable font that contains the desired symbol in the correct orientation. For instance, if the phonetic package is available, then \textit{\riota} will yield a backend-independent “ ”. Similarly, tipa’s \textrevepsilon (“3”) or wsuipa’s \revepsilon (“”) may be used to express the mathematical notion of “such that” in a cleaner manner than with \reflectbox or \rotatebox.

Joining and overlapping existing symbols

Symbols that do not exist in any font can sometimes be fabricated out of existing symbols. The LATEX2ε source file fontdef.dtx contains a number of such definitions. For example, \models (see Table 42 on page 23) is defined in that file with:

\def\models{\mathrel|\joinrel=} where \mathrel and \joinrel are used to control the horizontal spacing. \def is the TEX primitive upon which LATEX’s \newcommand is based. See The TEXbook [Knu86a] for more information on all three of those commands. With some simple pattern-matching, one can easily deﬁne a backward \models sign (“=|”):

\def\ismodeledby{=\joinrel\mathrel|}

In general, arrows/harpoons, horizontal lines (“=”, “-”, “\relbar”, and “\Relbar”), and the various math- extension characters can be combined creatively with miscellaneous other characters to produce a variety of new symbols. Of course, new symbols can be composed from any set of existing characters. For instance, LATEX deﬁnes \hbar (“R”) as a “¯” character (\mathchar’26) followed by a backspace of 9 math units (\mkern-9mu), followed by the letter “h”:

\def\hbar{{\mathchar’26\mkern-9muh}}

We can just as easily deﬁne other barred letters:

\def\bbar{{\mathchar’26\mkern-9mu b}} \def\dbar{{\mathchar’26\mkern-12mu d}}

4As an example, Xdvi ignores both \reflectbox and \rotatebox.

62 (The space after the “mu” is optional but is added for clarity.) \bbar and \dbar deﬁne “¯b”and“¯d”, respectively. Note that \dbar requires a greater backward math kern than \bbar;a−9mukernwouldhaveproducedthe less-attractive “¯d” glyph.

ThereisaTEX primitive called \mathaccent which centers one mathematical symbol atop another. For example, one can define \dotcup (“∪· ”)—the composition of a \cup and a \cdot—as follows: \newcommand{\dotcup}{\ensuremath{\mathaccent\cdot\cup}} The catch is that \mathaccent requires the accent to be a “math character”. That is, it must be a character in a math font as opposed to a symbol defined in terms of other symbols. See The TEXbook [Knu86a] for more information. The slashed package, although originally designed for producing Feynman slashed-character notation, in fact facilitates the production of arbitrary overlapped symbols. The default behavior is to overwrite a given character with “/”. For example, \slashed{D} produces “D/”. However, the \declareslashed command provides the flexibility to specify the mathematical context of the composite character (operator, relation, punctuation, etc., as will be discussed in Section 7.3), the overlapping symbol, horizontal and vertical adjustments in symbol- relative units, and the character to be overlapped. Consider, for example, the symbol for reduced quadrupole moment (“I-”). This can be declared as follows:

\newcommand{\rqm}{{% \declareslashed{}{\text{-}}{0.04}{0}{I}\slashed{I}}} \declareslashed{·}{·}{·}{·}{I} aﬀects the meaning of all subsequent \slashed{I} commands in the same scope. The preceding deﬁnition of \rqm therefore uses an extra set of curly braces to limit that scope to a single \slashed{I}. In addition, \rqm uses amstext’s \text macro (described on the next page) to make \declareslashed use a text-mode hyphen (“-”) instead of a math-mode minus sign (“−”) and to ensure that the hyphen scales properly in size in subscripts and superscripts. See slashed’s documentation (located in slashed.sty itself) for a detailed usage description of the \slashed and \declareslashed commands.

Making new symbols work in superscripts and subscripts

To make composite symbols work properly within subscripts and superscripts, you may need to use TEX’s \mathchoice primitive. \mathchoice evaluates one of four expressions, based on whether the current math style is display, text, script, or scriptscript. (See The TEXbook [Knu86a] for a more complete description.) For example, the following LATEX code—posted to comp.text.tex by Torsten Bronger—composes a sub/superscriptable “⊥D”symboloutof\top and \bot (“D”and“⊥”): \def\topbotatom#1{\hbox{\hbox to 0pt{$#1\bot$\hss}$#1\top$}} \newcommand*{\topbot}{\mathrel{\mathchoice{\topbotatom\displaystyle} {\topbotatom\textstyle} {\topbotatom\scriptstyle} {\topbotatom\scriptscriptstyle}}} The following is another example that uses \mathchoice to construct symbols in diﬀerent math modes. The code deﬁnes a principal value integral symbol, which is an integral sign with a line through it.

\def\Xint#1{\mathchoice {\XXint\displaystyle\textstyle{#1}}% {\XXint\textstyle\scriptstyle{#1}}% {\XXint\scriptstyle\scriptscriptstyle{#1}}% {\XXint\scriptscriptstyle\scriptscriptstyle{#1}}% \!\int} \def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$} \vcenter{\hbox{$#2#3$}}\kern-.5\wd0}} \def\ddashint{\Xint=} \def\dashint{\Xint-}

63 (The preceding code was taken verbatim from the UK TERXUsers’GroupFAQathttp://www.tex.ac.uk/ faq.) R\dashint produces a single-dashed integral sign (“−”), while \ddashint produces a double-dashedR one (“=”). The \Xint macroR defined above can also be usedR to generate a wealthR of new integrals: “” (\Xint\circlearrowright), “”(\Xint\circlearrowleft), “⊂”(\Xint\subset), “∞”(\Xint\infty), and so forth. LATEX2ε provides a simple wrapper for \mathchoice that sometimes helps produce terser symbol definitions. The macro is called \mathpalette and it takes two arguments. \mathpalette invokes the first argument, passing it one of “\displaystyle”, “\textstyle”, “\scriptstyle”, or “\scriptscriptstyle”, followed by the second argument. \mathpalette is useful when a symbol macro must know which math style is currently in use (e.g., to set it explicitly within an \mbox). Donald Arseneau posted the following \mathpalette-based definition of a probabilistic-independence symbol (“⊥⊥”) to comp.text.tex:

\newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}} \def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}}

The \independent macro uses \mathpalette to pass the \independenT helper macro both the current math style and the \perp symbol. \independenT typesets \perp in the current math style, moves two math units to the right, and ﬁnally typesets a second—overlapping—copy of \perp, again in the current math style. \rlap, which enables text overlap, is described later on this page. √ Some people like√ their square-root signs√ with a trailing “hook” (i.e., “ ”) as this helps visually distinguish expressions like “ 3x ”fromthoselike“ 3x”. Dan Luecking posted a \mathpalette-based deﬁnition of a hooked square-root symbol to comp.text.tex:

\def\hksqrt{\mathpalette\DHLhksqrt} \def\DHLhksqrt#1#2{\setbox0=\hbox{$#1\sqrt{#2\,}$}\dimen0=\ht0 \advance\dimen0-0.2\ht0 \setbox2=\hbox{\vrule height\ht0 depth -\dimen0}% {\box0\lower0.4pt\box2}}

Notice how \DHLhksqrt uses \mathpalette to recover the outer math style (argument #1)fromwithinan\hbox. The rest of the code is simply using TEX primitives to position a hook of height 0.2 times the \sqrt height at the right of the \sqrt.SeeTheTEXbook [Knu86a] for more understanding of TEX “boxes” and “dimens”. Sometimes, however, amstext’s \text macro is all that is necessary to make composite symbols appear correctly in subscripts and superscripts, as in the following deﬁnitions of \neswarrow (“?9”) and \nwsearrow (“57”):5

\newcommand{\neswarrow}{\mathrel{\text{$\nearrow$\llap{$\swarrow$}}}} \newcommand{\nwsearrow}{\mathrel{\text{$\nwarrow$\llap{$\searrow$}}}}

\text resembles LATEX’s \mbox command but shrinks its argument appropriately when used within a subscript or superscript. \llap (“left overlap”) and its counterpart, \rlap (“right overlap”), appear frequently when creating composite characters. \llap outputs its argument to the left of the current position, overlapping whatever text is already there. Similarly, \rlap overlaps whatever text would normally appear to the right of its argument. For example, “A\llap{B}”and“\rlap{A}B” each produce “AB”. However, the result of the former is the width of “A”, and the result of the latter is the width of “B”—\llap{...} and \rlap{...} take up zero space. In a June 2002 post to comp.text.tex, Donald Arseneau presented a general macro for aligning an arbitrary number of symbols on their horizontal centers and vertical baselines:

\makeatletter \def\moverlay{\mathpalette\mov@rlay} \def\mov@rlay#1#2{\leavevmode\vtop{% \baselineskip\z@skip \lineskiplimit-\maxdimen \ialign{\hfil$#1##$\hfil\cr#2\crcr}}} \makeatother 5 Note that if your goal is to typeset commutative diagrams, then you should probably be using XY-pic.

64 \moverlay takes a list of symbols separated by \cr (TEX’s equivalent of LATEX’s \\). For example, the \topbot command deﬁned on page 63 could have been expressed as “\moverlay{\top\cr\bot}” and the \neswarrow command deﬁned on the previous page could have been expressed as “\moverlay{\nearrow\cr\swarrow}”. The basic concept behind \moverlay’s implementation is that \moverlay typesets the given symbols in a table that utilizes a zero \baselineskip. This causes every row to be typeset at the same vertical position. See The TEXbook [Knu86a] for explanations of the TEX primitives used by \moverlay.

Modifying LATEX-generated symbols Oftentimes, symbols composed in the LATEX2ε source code can be modiﬁed with minimal eﬀort to produce useful variations. For example, fontdef.dtx composes the \ddots symbol (see Table 121 on page 41) out of three periods, raised 7 pt., 4 pt., and 1 pt., respectively:

\def\ddots{\mathinner{\mkern1mu\raise7\p@ \vbox{\kern7\p@\hbox{.}}\mkern2mu \raise4\p@\hbox{.}\mkern2mu\raise\p@\hbox{.}\mkern1mu}}

\p@ is a LATEX2ε shortcut for “pt”or“1.0pt”. The remaining commands are deﬁned in The TEXbook [Knu86a]. To draw a version of \ddots with the dots going along the opposite diagonal, we merely have to reorder the \raise7\p@, \raise4\p@,and\raise\p@:

\makeatletter \def\revddots{\mathinner{\mkern1mu\raise\p@ \vbox{\kern7\p@\hbox{.}}\mkern2mu \raise4\p@\hbox{.}\mkern2mu\raise7\p@\hbox{.}\mkern1mu}} \makeatother

The \makeatletter and \makeatother commands are needed to coerce LATEX into accepting “@” as part of a macro name. \revddots is essentially identical to the mathdots package’s \iddots command or the yhmath package’s \adots command.

Producing complex accents Accents are a special case of combining existing symbols to make new symbols. While various tables in this document show how to add an accent to an existing symbol, some applications, such as transliterations from non- Latin alphabets, require multiple accents per character. For instance, the creator of pdfTEX writes his name as “Hàn ThˆéThành”. The wsuipa package defines \diatop and \diaunder macros for putting one or more diacritics or accents above or below a given character. For example, \diaunder[{\diatop[\’|\=]}|\textsubdot{r}] produces “¯´r”. See the wsuipa documentation for more information.

The accents package facilitates the fabrication of accents in math mode. Its \accentset command enables any character to be used as an accent. For instance, \accentset{\star}{f} produces “f ”and\accentset{e}{X} e produces “X”. \underaccent does the same thing, but places the accent beneath the character. This enables constructs like \underaccent{\tilde}{V}, which produces “V ”. accents provides other accent-related features as well; see the documentation for more information. ˜

A more complex example of composing accents is the following deﬁnition of extensible \overbracket, \underbracket, \overparenthesis,and\underparenthesis symbols, taken from a comp.text.tex post by Donald Arseneau:

\makeatletter \def\overbracket#1{\mathop{\vbox{\ialign{##\crcr\noalign{\kern3\p@} \downbracketfill\crcr\noalign{\kern3\p@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}}\limits} \def\underbracket#1{\mathop{\vtop{\ialign{##\crcr $\hfil\displaystyle{#1}\hfil$\crcr\noalign{\kern3\p@\nointerlineskip}

65 \upbracketfill\crcr\noalign{\kern3\p@}}}}\limits} \def\overparenthesis#1{\mathop{\vbox{\ialign{##\crcr\noalign{\kern3\p@} \downparenthfill\crcr\noalign{\kern3\p@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}}\limits} \def\underparenthesis#1{\mathop{\vtop{\ialign{##\crcr $\hfil\displaystyle{#1}\hfil$\crcr\noalign{\kern3\p@\nointerlineskip} \upparenthfill\crcr\noalign{\kern3\p@}}}}\limits} \def\downparenthfill{$\m@th\braceld\leaders\vrule\hfill\bracerd$} \def\upparenthfill{$\m@th\bracelu\leaders\vrule\hfill\braceru$} \def\upbracketfill{$\m@th\makesm@sh{\llap{\vrule\@height3\p@\@width.7\p@}}% \leaders\vrule\@height.7\p@\hfill \makesm@sh{\rlap{\vrule\@height3\p@\@width.7\p@}}$} \def\downbracketfill{$\m@th \makesm@sh{\llap{\vrule\@height.7\p@\@depth2.3\p@\@width.7\p@}}% \leaders\vrule\@height.7\p@\hfill \makesm@sh{\rlap{\vrule\@height.7\p@\@depth2.3\p@\@width.7\p@}}$} \makeatother

Table 203 showcases these accents. The TEXbook [Knu86a] or another book on TEXprimitivesisindispensible for understanding how the preceding code works. The basic idea is that \downparenthfill, \upparenthfill, \downbracketfill,and\upbracketfill do all of the work; they output a left symbol (e.g., \braceld [“z”] for \downparenthfill), a horizontal rule that stretches as wide as possible, and a right symbol (e.g., \bracerd [“{”] for \downparenthfill). \overbracket, \underbracket, \overparenthesis,and\underparenthesis merely create a table whose width is determined by the given text, thereby constraining the width of the horizontal rules.

Table 203: Manually Composed Extensible Accents z { abc \overbracket{abc} abc \overparenthesis{abc}

abc \underbracket{abc} |abc} \underparenthesis{abc}

A similar, but simpler example, stems from another comp.text.tex post by Donald Arseneau. The following code deﬁnes an equals sign that extends as far to the right as possible (just like LATEX’s \hrulefill command):

\makeatletter \def\equalsfill{$\m@th\mathord=\mkern-7mu \cleaders\hbox{$\!\mathord=\!$}\hfill \mkern-7mu\mathord=$} \makeatother

TEX’s \cleaders and \hfill primitives are the key to understanding \equalsfill’s extensibility. Essentially, \equalsfill repeats a box containing “=” plus some negative space until it fills the maximum available horizontal space. \equalsfill is intended to be used with LAT X’s \stackrel command, which stacks one mathematical E a expression (slightly reduced in size) atop another. Hence, “\stackrel{a}{\rightarrow}” produces “→”and“X definition \stackrel{\text{definition}}{\hbox{\equalsfill}} Y” produces “X ======Y ”. If all that needs to extend are horizontal and vertical lines—as opposed to repeated symbols such as the “=” in the previous example—LATEX’s array or tabular environments may suffice. Consider the following code (also presented in a comp.text.tex post by Donald Arseneau) for typesetting annuities:

\DeclareRobustCommand{\annu}[1]{_{% \def\arraystretch{0}% \setlength\arraycolsep{1pt}% adjust these \setlength\arrayrulewidth{.2pt}% two settings

66 \begin{array}[b]{@{}c|}\hline \\[\arraycolsep]% \scriptstyle #1% \end{array}% }}

One can then use, e.g., “$A\annu{x:n}$”toproduce“Ax:n ”.

Creating new symbols from scratch Sometimes is it simply not possible to define a new symbol in terms of existing symbols. Fortunately, most, if not all, TEX distributions are shipped with a tool called METAFONT which is designed specifically for creating fonts to be used with TEX. The METAFONTbook [Knu86b] is the authoritative text on METAFONT. If you plan to design your own symbols with METAFONT,TheMETAFONTbook is essential reading. Nevertheless, the following is an extremely brief tutorial on how to create a new LATEXsymbolusingMETAFONT. Its primary purpose is to cover the LATEX-specific operations not mentioned in The METAFONTbook and to demonstrate that symbol-font creation is not necessarily a difficult task. Suppose we need a symbol to represent a light bulb (“A”).6 The first step is to draw this in METAFONT. It is common to separate the font into two files: a size-dependent file, which specifies the design size and various font-specific parameters that are a function of the design size; and a size-independent file, which draws characters in the given size. Figure 1 shows the METAFONT code for lightbulb10.mf. lightbulb10.mf specifies various parameters that produce a 10 pt. light bulb then loads lightbulb.mf. Ideally, one should produce lightbulbsize.mf files for a variety of sizes. This is called “optical scaling”. It enables, for example, the lines that make up the light bulb to retain the same thickness at different font sizes, which looks much nicer than the alternative—and default—“mechanical scaling”. When a lightbulbsize.mf file does not exist for a given size size, the computer mechanically produces a wider, taller, thicker symbol:

A A A A A vs. A vs. A vs. vs. vs. vs. 10 pt. 20 pt. 30 pt. 40 pt. 50 pt. 60 pt. 70 pt.

font identiﬁer := "LightBulb10"; % Name the font. font size 10pt#; % Specify the design size. em# := 10pt#; % “M” width is 10 points. cap# := 7pt#; % Capital letter height is 7 points above the baseline. # # sb := 1/4pt ; % Leave this much space on the side of each character. # # o := 1/16pt ; % Amount that curves overshoot borders. input lightbulb % Load the ﬁle that draws the actual glyph.

Figure 1: Sample METAFONT size-speciﬁc ﬁle (lightbulb10.mf)

lightbulb.mf, shown in Figure 2, draws a light bulb using the parameters defined in lightbulb10.mf. Note that the the filenames “lightbulb10.mf”and“lightbulb.mf” do not follow the Berry font-naming scheme [Ber01]; the Berry font-naming scheme is largely irrelevant for symbol fonts, which generally lack bold, italic, small-caps, slanted, and other such variants. The code in Figures 1 and 2 is heavily commented and should demonstrate some of the basic concepts behind METAFONT usage: declaring variables, defining points, drawing lines and curves, and preparing to debug or fine- tune the output. Again, The METAFONTbook [Knu86b] is the definitive reference on METAFONT programming.

6I’m not a very good artist; you’ll have to pretend that “A” looks like a light bulb.

67 mode setup; % Target a given printer. define pixels(em, cap, sb); % Convert to device-specific units. define corrected pixels(o); % Same, but add a device-specific fudge factor. %% Define a light bulb at the character position for “A” # # # %% with width 1/2em , height cap , and depth 1pt . # # # beginchar("A", 1/2em , cap , 1pt ); "A light bulb"; pickup pencircle scaled 1/2pt; % Use a pen with a small, circular tip. %% Define the points we need. top z1 =(w/2,h+ o); % z1 is at the top of a circle. rt z2 =(w + sb + o − x4,y4); % z2 is at the same height as z4 but the opposite side. bot z3 =(z1 − (0,w− sb − o)); % z3 is at the bottom of the circle. 1 lft z4 =(sb − o, /2[y1,y3]); % z4 is on the left of the circle. path bulb; % Define a path for the bulb itself. bulb = z1 ..z2 ..z3 ..z4 . . cycle; % The bulb is a closed path.

1 z5 = point 2 − /3 of bulb;%z5 lies on the bulb, a little to the right of z3. z6 =(x5, 0); % z6 is at the bottom, directly under z5. z7 =(x8, 0); % z7 is at the bottom, directly under z8. 1 z8 = point 2+ /3 of bulb;%z8 lies on the bulb, a little to the left of z3. 1 1 bot z67 =(/2[x6,x7], pen bot − o − /8pt); % z67 lies halfway between z6 and z7 butajotlower. %% Draw the bulb and the base. draw bulb; % Draw the bulb proper. draw z5 --z6 ..z67 ..z7 --z8; % Draw the base of the bulb. %% Display key positions and points to help us debug. makegrid(0, sb,w/2,w− sb)(0, −1pt,y2,h); % Label “interesting” x and y coordinates. penlabels(1, 2, 3, 4, 5, 6, 67, 7, 8); % Label control points for debugging. endchar; end

Figure 2: Sample METAFONT size-independent ﬁle (lightbulb.mf)

METAFONT can produce “proofs” of fonts—large, labeled versions that showcase the logical structure of each character. In fact, proof mode is METAFONT’s default mode. To produce a proof of lightbulb10.mf, issue the following commands at the operating-system prompt:

prompt> mf lightbulb10.mf ⇐ Produces lightbulb10.2602gf prompt> gftodvi lightbulb10.2602gf ⇐ Produces lightbulb10.dvi

You can then view lightbulb10.dvi with any DVI viewer. The result is shown in Figure 3. Observe how the grid defined with makegrid at the bottom of Figure 2 draws vertical lines at positions 0, sb, w/2, and w − sb and horizontal lines at positions 0, −1pt, y2,andh. Similarly, observe how the penlabels command labels all of the important coordinates: z1,z2,...,z8 and z67,whichlightbulb.mf defines to lie between z6 and z7. Most, if not all, TEX distributions include a Plain TEX file called testfont.tex which is useful for testing new fonts in a variety of ways. One useful routine produces a table of all of the characters in the font:

prompt> tex testfont This is TeX, Version 3.14159 (Web2C 7.3.1) (/usr/share/texmf/tex/plain/base/testfont.tex Name of the font to test = lightbulb10 Now type a test command (\help for help):) *\table

68 1

4 2

8 5 3

7 67 6

Figure 3: Proof diagram of lightbulb10.mf

*\bye [1] Output written on testfont.dvi (1 page, 1516 bytes). Transcript written on testfont.log.

The resulting table, stored in testfont.dvi and illustrated in Figure 4, shows every character in the font. To understand how to read the table, note that the character code for “A”—the only character deﬁned by lightbulb10.mf—is 41 in hexadecimal (base 16) and 101 in octal (base 8).

Test of lightbulb10 on March 11, 2003 at 1127

´0 ´1 ´2 ´3 ´4 ´5 ´6 ´7 ´10x A ˝4x ´11x ˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F

Figure 4: Font table produced by testfont.tex

The LightBulb10 font is now usable by TEX. LATEX2ε, however, needs more information before documents can use the font. First, we create a font-description file that tells LATEX2ε how to map fonts in a given font family and encoding to a particular font in a particular font size. For symbol fonts, this mapping is fairly simple. Symbol fonts almost always use the “U” (“Unknown”) font encoding and frequently occur in only one variant: normal weight and non-italicized. The filename for a font-description file important; it must be of the form “encodingfamily.fd”, where encoding is the lowercase version of the encoding name (typically “u” for symbol fonts) and family is the name of the font family. For LightBulb10, let’s call this “bulb”. Figure 5 lists the contents of ubulb.fd.Thedocument“LATEX2ε Font Selection” [LAT00] describes \DeclareFontFamily and \DeclareFontShape in detail, but the gist of ubulb.fd is first to declare a U-encoded version of the bulb font family and then to specify that a LATEX2ε request for a U-encoded version of bulb with a (m)edium font series (as opposed to, e.g., bold) and a (n)ormal font shape (as opposed to, e.g., italic) should translate into a TEXrequest for lightbulb10.tfm mechanically scaled to the current font size. The final step is to write a LATEX2ε style file that defines a name for each symbol in the font. Because we have only one symbol our style file, lightbulb.sty (Figure 6), is rather trivial. Note that instead of typesetting “A”we could have had \lightbulb typeset “\char65”, “\char"41”, or “\char’101” (respectively, decimal, hexadecimal,

69 \DeclareFontFamily{U}{bulb}{} \DeclareFontShape{U}{bulb}{m}{n}{<-> lightbulb10}{}

Figure 5: LATEX2ε font-description file (ubulb.fd) and octal character offsets into the font). For a simple, one-character symbol font such as LightBulb10 it would be reasonable to merge ubulb.fd into lightbulb.sty instead of maintaining two separate files. In either case, a document need only include “\usepackage{lightbulb}”tomakethe\lightbulb symbol available.

\newcommand{\lightbulb}{{\usefont{U}{bulb}{m}{n}A}}

Figure 6: LATEX2ε style ﬁle (lightbulb.sty)

METAFONT normally produces bitmapped fonts. However, it is also possible, with the help of some external tools, to produce PostScript Type 1 fonts. These have the advantages of rendering better in Adobe® Acrobat® (at least in versions prior to 6.0) and of being more memory-eﬃcient when handled by a PostScript interpreter. See http://www.tex.ac.uk/cgi-bin/texfaq2html?label=textrace for pointers to tools that can produce Type 1 fonts from METAFONT.

7.3 Math-mode spacing Terms such as “binary operators”, “relations”, and “punctuation” in Section 3 primarily regard the surrounding spacing. (See the Short Math Guide for LATEX [Dow00] for a nice exposition on the subject.) To use a symbol for a different purpose, you can use the TEX commands \mathord, \mathop, \mathbin, \mathrel, \mathopen, \mathclose,and\mathpunct. For example, if you want to use \downarrow as a variable (an “ordinary” symbol) instead of a delimiter, you can write “$3 x + \mathord{\downarrow}$” to get the properly spaced “3x+↓” rather than the awkward-looking “3x+ ↓”. Similarly, to create a dotted-union symbol (“∪˙ ”) that spaces like the ordinary set-union symbol (\cup)itmustbedefinedwith\mathbin,justas\cup is. Contrast “$A \dot{\cup} B$” (“A∪˙ B”) with “$A \mathbin{\dot{\cup}} B$”(“A ∪˙ B”). See The TEXbook [Knu86a] for the definitive description of math-mode spacing. The purpose of the “log-like symbols” in Tables 84 and 85 is to provide the correct amount of spacing around and within multiletter function names. Table 204 contrasts the output of the log-like symbols with various, na¨ıve alternatives. In addition to spacing, the log-like symbols also handle subscripts properly. For example, “\max_{p \in P}”produces“maxp∈P ” in text, but “max” as part of a displayed formula. p∈P

Table 204: Spacing Around/Within Log-like Symbols

LATEX expression Output $r \sin \theta$ r sin θ (best) $r sin \theta$ rsinθ $r \mbox{sin} \theta$ rsinθ

The amsmath package makes it straightforward to deﬁne new log-like symbols:

\DeclareMathOperator{\atan}{atan} \DeclareMathOperator*{\lcm}{lcm}

The diﬀerence between \DeclareMathOperator and \DeclareMathOperator* involves the handling of subscripts. With \DeclareMathOperator*, subscripts are written beneath log-like symbols in display style and to the right in text style. This is useful for limit operators (e.g., \lim) and functions that tend to map over a set (e.g., \min). In contrast, \DeclareMathOperator tells TEX that subscripts should always be displayed to the right of the operator, as is common for functions that take a single parameter (e.g., \log and \cos). Table 205 contrasts

70 symbols declared with \DeclareMathOperator and \DeclareMathOperator* in both text style ($...$) and display style (\[...\]).7

Table 205: Deﬁning new log-like symbols

Declaration function $\newlogsym {p \in P}$ \[ \newlogsym {p \in P} \]

\DeclareMathOperator newlogsymp∈P newlogsymp∈P

\DeclareMathOperator* newlogsymp∈P newlogsym p∈P

It is common to use a thin space (\,) between the words of a multiword operators, as in “\DeclareMathOperator*{\argmax}{arg\,max}”. \liminf, \limsup, and all of the log-like symbols shown in Table 85 utilize this spacing convention.

7.4 Bold mathematical symbols

LATEX does not normally use bold symbols when typeseting mathematics. However, bold symbols are occasionally needed, for example when naming vectors. Any of the approaches described at http://www.tex.ac.uk/cgi-bin/ texfaq2html?label=boldgreek can be used to produce bold mathematical symbols. Table 206 contrasts the output produced by these various techniques. As the table illustrates, these techniques exhibit variation in their formatting of Latin letters (upright vs. italic), formatting of Greek letters (bold vs. normal), formatting of operators and relations (bold vs. normal), and spacing.

Table 206: Producing bold mathematical symbols

Package Code Output none $\alpha+b=\Gamma \div D$ α + b =Γ÷ D (no bold) none $\mathbf{\alpha+b=\Gamma \div D}$ α + b = Γ ÷ D none \boldmath$\alpha+b=\Gamma \div D$ α + b =Γ÷ D amsbsy $\pmb{\alpha+b=\Gamma \div D}$ α + b =Γ÷ D (faked bold) amsbsy $\boldsymbol{\alpha + b = \Gamma \div D}$ α + b =Γ÷ D bm $\bm{\alpha+b=\Gamma \div D}$ α + b =Γ÷ D ﬁxmath $\mathbold{\alpha+b=\Gamma \div D}$ α + b = Γ ÷ D

7.5 ASCII and Latin 1 quick reference Table 207 on the next page amalgamates data from various other tables in this document into a convenient reference for LATEX2ε typesetting of ASCII characters, i.e., the characters available on a typical U.S. computer keyboard. The ﬁrst two columns list the character’s ASCII code in decimal and hexadecimal. The third column shows what the character looks like. The fourth column lists the LATEX2ε command to typeset the character as a text character. And the fourth column lists the LATEX2ε command to typeset the character within a \texttt{...} command (or, more generally, when \ttfamily is in eﬀect). The following are some additional notes about the contents of Table 207: • “"” is not available in the OT1 font encoding. • Thecharacters“<”, “>”, and “|” do work as expected in math mode, although they produce, respectively, “¡”, “¿”, and “—” in text mode.8 Hence, $<$, $>$,and$|$ serve as a terser alternative to \textless,

7Note that \displaystyle can be used to force display style within $...$ and \textstyle can be used to force text style within \[...\]. 8Donald Knuth didn’t think such symbols were important outside of mathematics, so he omitted them from the OT1 font encoding.

71 Table 207: LATEX2ε ASCII Table

Dec Hex Char Body text \texttt Dec Hex Char Body text \texttt 33 21 ! !!62 3E > \textgreater > 34 22 " \textquotedbl " 63 3F ? ?? 35 23 # \# \# 64 40 @ @@ 36 24 $ \$ \$ 65 41 A AA 37 25 % \% \% 66 42 B BB & C 38 26 \& \& 67. 43. . .CC. 39 27 ’ ’’. . . . . 40 28 ( ((90 5A Z ZZ 41 29 ) ))91 5B [ [[ 42 2A * **92 5C \ \textbackslash \char‘\\ 43 2B + ++93 5D ] ]] 44 2C , ,,94 5E ˆ \^{} \^{} 45 2D - --95 5F \_ \char‘\_ 46 2E . ..96 60 ‘ ‘‘ 47 2F / //97 61 a aa 48 30 0 0098 62 b bb 1 c 49 31 1199. 63. . .cc. 2 . . . . . 50. 32. . .22...... 122 7A z zz 57 39 9 99123 7B { \{ \char‘\{ 58 3A : ::124 7C | \textbar | 59 3B ; ;;125 7D } \} \char‘\} 60 3C < \textless < 126 7E ˜ \~{} \~{} 61 3D = ==

\textgreater,and\textbar. Note that for typesetting metavariables many people prefer \textlangle and \textrangle to \textless and \textgreater, i.e., “ﬁlename” instead of “<ﬁlename>”.

• Although “/” does not require any special treatment, LATEX additionally deﬁnes a \slash command which outputs the same glyph but permits a line break afterwards. That is, “increase/decrease”isalways typeset as a single entity while “increase\slash{}decrease” may be typeset with “increase/” on one line and “decrease” on the next.

• The various \char commands within \texttt are necessary only in the OT1 font encoding. In other encodings (e.g., T1), commands such as \{, \}, \_,and\textbackslash all work properly. • \textasciicircum can be used instead of \^{},and\textasciitilde can be used instead of \~{}. Note that \textasciitilde and \~{} produce raised, diacritic tildes. “Text” (i.e., vertically centered) tildes can be generated with either the math-mode \sim command (shown in Table 42 on page 23), which produces asomewhatwide“∼”, or the textcomp package’s \texttildelow (shown in Table 24 on page 15), which produces a vertically centered “~” in most fonts but a baseline-oriented “<”inComputerModern,txfonts, pxfonts, and various other fonts originating from the TEX world. If your goal is to typeset tildes in URLs or Unix ﬁlenames, your best bet is to use the url package, which has a number of nice features such as proper line-breaking of such names. • The IBM version of ASCII characters 1 to 31 can be typeset using the ascii package. See Table 149 on page 47.

• To replace “‘”and“’” with the more computer-like (and more visibly distinct) “`”and“'”withina verbatim environment, use the upquote package. Outside of verbatim, you can use \char18 and \char13

72 to get the modiﬁed quote characters. (The former is actually a grave accent.)

Similar to Table 207, Table 208 on the next page is an amalgamation of data from other tables in this document. While Table 207 shows how to typeset the 7-bit ASCII character set, Table 208 shows the Latin 1 (Western European) character set, also known as ISO-8859-1. The following are some additional notes about the contents of Table 208:

• A“(tc)” after a symbol name means that the textcomp package must be loaded to access that symbol. A “(T1)” means that the symbol requires the T1 font encoding. The fontenc package can change the font encoding document-wide.

• Many of the \text. . . accents can also be produced using the accent commands shown in Table 12 on page 11 plus an empty argument. For instance, \={} is essentially the same as \textasciimacron.

• The commands in the “LATEX2ε” columns work both in body text and within a \texttt{...} command (or, more generally, when \ttfamily is in eﬀect). • Microsoft® Windows® normally uses a superset of Latin 1 called “CP1252” (Code Page 1252). CP1252 adds codes in the range 128–159 (hexadecimal 80–9F), including characters such as dashes, daggers, and quotation marks. If there’s suﬃcient interest, a future version of the Comprehensive LATEX Symbol List may include a CP1252 table.

While too large to incorporate into this document, a listing of ISO 8879:1986 SGML/XML character entities and their LATEX equivalents is available from http://www.bitjungle.com/~isoent/. Some of the characters presented there make use of isoent,aLATEX2ε package (available from the same URL) that fakes some of the 9 missing ISO glyphs using the LATEX picture environment.

7.6 About this document History David Carlisle wrote the ﬁrst version of this document in October, 1994. It originally contained all of the native LATEX symbols (Tables 27, 35, 42, 67, 84, 86, 101, 102, 108, 112, 125, and a few tables that have since been reorganized) and was designed to be nearly identical to the tables in Chapter 3 of Leslie Lamport’s book [Lam86]. Even the table captions and the order of the symbols within each table matched! The AMS symbols (Tables 28, 43, 44, 70, 71, 87, 91, 97, and 126) and an initial Math Alphabets table (Table 135) were added thereafter. Later, Alexander Holt provided the stmaryrd tables (Tables 29, 37, 45, 73, 81, and 98). In January, 2001, Scott Pakin took responsibility for maintaining the symbol list and has since implemented a complete overhaul of the document. The result, now called, “The Comprehensive LATEX Symbol List”, includes the following new features:

• the addition of a handful of new math alphabets, dozens of new font tables, and thousands of new symbols • the categorization of the symbol tables into body-text symbols, mathematical symbols, science and technology symbols, dingbats, and other symbols, to provide a more user-friendly document structure • an index, table of contents, and a frequently-requested symbol list, to help users quickly locate symbols • symbol tables rewritten to list the symbols in alphabetical order

• appendices to provide additional information relevant to using symbols in LATEX • tables showing how to typeset all of the characters in the ASCII and Latin 1 font encodings

Furthermore, the internal structure of the document has been completely altered from David’s original version. Most of the changes are geared towards making the document easier to extend, modify, and reformat.

9isoent is not featured in this document, because it is not available from CTAN and because the faked symbols are not “true” characters; they exist in only one size, regardless of the body text’s font size.

73 Table 208: LATEX2ε Latin 1 Table

Dec Hex Char LATEX2ε Dec Hex Char LATEX2ε 161 A1 ¡ !‘ 209 D1 N˜ \~{N} 162 A2 ¢ \textcent (tc) 210 D2 O` \‘{O} £ 163 A3 \pounds 211 D3 O´ \’{O} ¤ 164 A4 \textcurrency (tc) 212 D4 Oˆ \^{O} ¥ (tc) 165 A5 \textyen 213 D5 O˜ \~{O} 166 A6 ¦ \textbrokenbar (tc) 214 D6 O¨ \"{O} 167 A7 § \S 215 D7 × \texttimes (tc) 168 A8 ¨ \textasciidieresis (tc) © 216 D8 Ø \O 169 A9 \textcopyright ` ª 217 D9 U \‘{U} 170 AA \textordfeminine ´ 171 AB « \guillemotleft (T1) 218 DA U \’{U} ˆ 172 AC ¬ \textlnot (tc) 219 DB U \^{U} ¨ 174 AE ® \textregistered 220 DC U \"{U} 175 AF ¯ \textasciimacron (tc) 221 DD Y´ \’{Y} 176 B0 ° \textdegree (tc) 222 DE Þ \TH (T1) 177 B1 ± \textpm (tc) 223 DF ß \ss 178 B2 ² \texttwosuperior (tc) 224 E0 à \‘{a} 179 B3 ³ \textthreesuperior (tc) 225 E1 á \’{a} 180 B4 ´ \textasciiacute (tc) 226 E2 â \^{a} 181 B5 µ \textmu (tc) 227 E3 ã \~{a} 182 B6 ¶ \P 228 E4 ä \"{a} 183 B7 · \textperiodcentered 229 E5 ˚a \aa 184 B8 ¸ \c{} 230 E6 æ \ae 185 B9 ¹ \textonesuperior (tc) 231 E7 ¸c \c{c} 186 BA º \textordmasculine 232 E8 è \‘{e} 187 BB » \guillemotright 233 E9 é \’{e} 188 BC ¼ \textonequarter (tc) 234 EA ê \^{e} 189 BD ½ \textonehalf (tc) 235 EB ë \"{e} 190 BE ¾ \textthreequarters (tc) 236 EC `ı \‘{ı} 191 BF ¿ ?‘ 237 ED ´ı \’{ı} 192 C0 A` \‘{A} 238 EE ˆı \^{ı} 193 C1 A´ \’{A} 239 EF ¨ı \"{ı} ð (T1) 194 C2 Aˆ \^{A} 240 F0 \dh 241 F1 n˜ \~{n} 195 C3 A˜ \~{A} 242 F2 ò \‘{o} 196 C4 A¨ \"{A} 243 F3 ó \’{o} A˚ 197 C5 \AA 244 F4 ô \^{o} Æ 198 C6 \AE 245 F5 õ \~{o} Ç 199 C7 \c{C} 246 F6 ö \"{o} ` 200 C8 E \‘{E} 247 F7 ÷ \textdiv (tc) ´ 201 C9 E \’{E} 248 F8 ø \o 202 CA Eˆ \^{E} 249 F9 u` \‘{u} 203 CB E¨ \"{E} 250 FA u´ \’{u} 204 CC Ì \‘{I} 251 FB uˆ \^{u} 205 CD Í \’{I} 252 FC u¨ \"{u} 206 CE Î \^{I} 253 FD y´ \’{y} þ 207 CF Ï \"{I} 254 FE \th (T1) 208 D0 Ð \DH (T1) 255 FF y¨ \"{y}

74 Build characteristics Table 209 lists some of this document’s build characteristics. Most important is the list of packages that LATEX couldn’t find, but that symbols.tex otherwise would have been able to take advantage of. Complete, prebuilt versions of this document are available from CTAN (http://www.ctan.org/ or one of its many mirror sites) in the directory tex-archive/info/symbols/comprehensive. Table 210 shows the package date (specified in the .sty file with \ProvidesPackage) for each package that was used to build this document and that specifies a package date. Packages are not listed in any particular order in either Table 209 or 210.

Table 209: Document Characteristics Characteristic Value Source ﬁle: symbols.tex Build date: September 29, 2003 Symbols documented: 2826 Packages included: textcomp latexsym amssymb stmaryrd euscript wasysym pifont manfnt bbding undertilde ifsym tipa wsuipa phonetic ulsy ar txfonts mathabx fclfont skak ascii dingbat skull eurosym esvect yfonts yhmath esint mathdots trsym universa upgreek overrightarrow chemarr chemarrow nath trfsigns accents nicefrac bm mathrsfs zapfchan bbold mbboard dsfont bbm Packages omitted: none

References

[Ber01] Karl Berry. Fontname: Filenames for TEX fonts, June 2001. Available from http://www.ctan.org/ tex-archive/info/fontname.

[Dow00] Michael Downes. Short math guide for LATEX, July 19, 2000. Version 1.07. Available from http:// www.ams.org/tex/short-math-guide.html. [Gib97] Jeremy Gibbons. Hey—it works! TUGboat, 18(2):75–78, June 1997. Available from http:// www.tug.org/TUGboat/Articles/tb18-2/tb55works.pdf.

[Knu86a] Donald E. Knuth. The TEXbook, volume A of Computers and Typesetting. Addison-Wesley, Reading, MA, USA, 1986. [Knu86b] Donald E. Knuth. The METAFONTbook, volume C of Computers and Typesetting. Addison-Wesley, Reading, MA, USA, 1986.

[Lam86] Leslie Lamport. LATEX: A document preparation system. Addison-Wesley, Reading, MA, USA, 1986. [LAT98] LATEX3 Project Team. A new math accent. LATEX News. Issue 9, June 1998. Available from http:// www.ctan.org/tex-archive/macros/latex/doc/ltnews09.pdf (also included in many TEXdistribu- tions).

[LAT00] LATEX3 Project Team. LATEX2ε font selection, January 30, 2000. Available from http://www.ctan.org/ tex-archive/macros/latex/doc/fntguide.ps (also included in many TEX distributions).

75 Table 210: Package versions used in the preparation of this document

Name Date textcomp 2000/08/30 latexsym 1998/08/17 amssymb 1996/11/03 stmaryrd 1994/03/03 euscript 1995/01/06 wasysym 1999/05/13 pifont 2000/01/12 manfnt 1999/07/01 bbding 1999/04/15 undertilde 2000/08/08 ifsym 2000/04/18 tipa 2001/12/31 wsuipa 1994/07/16 txfonts 2000/12/15 skak 2003/01/25 dingbat 2001/04/27 skull 2002/01/23 eurosym 1998/08/06 yfonts 2003/01/08 mathdots 2001/02/28 trsym 2000/06/25 universa 98/08/01 upgreek 2003/02/12 chemarr 2001/06/22 accents 2000/08/06 nicefrac 1998/08/04 bm 1999/07/05

76 Index

If you’re having trouble locating a symbol, try looking under “T” for “\text...”. Many text-mode commands begin with that prefix. Also, accents are shown over/under a black box, e.g., “ á ”for“\’”. Some symbol entries appear to be listed repeatedly. This happens when multiple packages define identical (or nearly identical) glyphs with the same symbol name.10

Symbols \ae (æ)...... 8 \APLinv (÷) ...... 46 \" (ä) ...... 11 \agemO () ...... 42 \APLleftarrowbox () ..... 46 \# (#) ...... 7,72 \ain (s) ...... 13 \APLlog () ...... 46 − \$ ($)...... 7,72 \aleph (ℵ) ...... 33,42 \APLminus ( ) ...... 46 \% (%) ...... 7,72 \alpha (α) ...... 32 \APLnot (∼) ...... 47 \& (&) ...... 7,72 alphabets \APLrightarrowbox () ..... 46 \’ (á) ...... 11 African ...... 8 \APLstar () ...... 46 ( (() ...... 35 Cyrillic ...... 62 \APLup () ...... 46 ) ()) ...... 35 Greek ...... 32, 33, 44 \APLuparrowbox () ...... 46 * (*)...... 19 Hebrew ...... 33, 44 \APLvert ( | ) ...... 47 \, ...... 71 math...... 44 \apprge () ...... 27 \. (˙a) ...... 11 phonetic ...... 8–11 \apprle () ...... 27 / (/) ...... 35 \alphaup (α) ...... 32 \approx (≈) ...... 23 [ ([) ...... 35 alpinesymbols...... 58 \approxeq () ...... 23 ] (]) ...... 35 \amalg () ...... 17 \Aquarius (ê) ...... 46 \^ (â) ...... 11 ampersand ...... see \& \aquarius () ...... 46 \^{} (ˆ) ...... 72 AMS . . 6, 16, 17, 20, 23, 26–29, \AR (A) ...... 45 \| () ...... 35 31–34, 37, 39, 41, 42, 44, 60, ar (package) ...... 45,75 \= (¯a) ...... 11 73 \arccos (arccos) ...... 31 \={} (¯) ...... 73 amsbsy (package) ...... 71 arcminutes ...... see \prime | | ( ) ...... 35 amsfonts (package) 17, 23, 25, 28, arcseconds ...... see \second \_ ( ) ...... 7,72 42, 44 \arcsin (arcsin) ...... 31 { \{ ( ) ...... 7,35,72 amsmath (package) . . . 6, 31, 70 \arctan (arctan)...... 31 } \} ( ) ...... 7,35,72 amssymb (package) 6, 17, 23, 25, \arg (arg)...... 31 \‘ (à) ...... 11 28, 42, 44, 75–77 \Aries (P) ...... 46 \~ (ã) ...... 11 amstext (package) ...... 63, 64 \Aries (à) ...... 46 \~{} (˜) ...... 72 \anchor (O) ...... 54 \aries ( ) ...... 46 y A and...... see \wedge \ArrowBoldDownRight ( )..49 ∠ { a (esvect package option) . . . . 40 \angle ( ) ...... 42 \ArrowBoldRightCircled ( )49 \angle ( ) ...... 42 z \AA (A)...... ˚ 8 \ArrowBoldRightShort ( ) ... 49 angles ...... 42,43 \aa (˚a) ...... 8 \ArrowBoldRightStrobe (w).49 \Anglesign (W) ...... 43 abzüglich . . see \textdiscount \ArrowBoldUpRight (x) .... 49 Angstr¨˚ om unit \AC () ...... 45 \Arrownot () ...... 31 math mode . see \mathring \acarc ...... 13 \arrownot () ...... 31 textmode ...... see \AA \acbar ...... 13 arrows ...... 28–30, 49, 60 angular minutes . . . . see \prime accents . . . 11–14, 37, 38, 40, 47, diagonal, for reducing subex- angular seconds . . . . see \second 65–66 pressions ...... 38 \Ankh (ˆ) ...... 57 any character as ...... 65 double-headed, diagonal . 64 \annu ( ) ...... 67 extensible . . . 38–40, 65–66 extensible ...... 38–40 multiple per character . . 65 annuities...... 66 negatedw ...... 29, 30 accents (package) . . . . 65, 75, 76 APL \Arrowvert (w) ...... 35 \accentset ...... 65 modifiers ...... 47 ? \arrowvert (?) ...... 35 \ACK (♠) ...... 47 symbols...... 46 \acute (´) ...... 37 \APLbox ( ) ...... 46 Arseneau, Donald ...... 64–66 ◦ AdobeAcrobat ...... 70 \APLcirc ( ) ...... 47 ASCII...... 6,8,47,71–73 \APLcomment () ...... 46 table ...... 72 .. \adots (. ) ...... 41,65 \APLdown () ...... 46 ascii (package) ...... 47, 72, 75 advancing . . see \textadvancing \APLdownarrowbox () ..... 46 \ascnode () ...... 45 \AE (Æ) ...... 8 \APLinput () ...... 46 aspectratio...... 45

10This occurs frequently between amssymb and mathabx, for example.

77 Ø \ast (¦) ...... 19 \barp (A) ...... 10 \bigboxleft ( Ñ) ...... 21 \ast (∗) ...... 17 barred letters ...... 62 \bigboxminus Ð( ) ...... 21 \Asterisk (¦) ...... 19 \barrightharpoon (ß) ..... 30 \bigboxplus ( Ù) ...... 21 \Asterisk (N) ...... 52 \barsci (+) ...... 10 \bigboxright (Ý) ...... 21 \asterisk (¦) ...... 19 \barscu (X) ...... 10 \bigboxslash (Ò) ...... 21 \baru (T) ...... 10 \bigboxtimes ( ) ...... 21 \AsteriskBold (A) ...... 52 Ú \barwedge (X) ...... 19 \bigboxtop ( ) ...... ß 21 \AsteriskCenterOpen (B) ... 52 \barwedge ( ) ...... 17 \bigboxtriangleupÜ ( ) .... 21 X \AsteriskRoundedEnds ( )..52 \Bat (ý) ...... 57 \bigboxvoidT ( ) ...... 21 asterisks ...... 19,52 \baucircle (¡) ...... 54 \bigcap ( ) ...... 20 \AsteriskThin (C) ...... 52 \bigcirc ( ) ...... 17 \bauforms (¤) ...... 57 \AsteriskThinCenterOpen (D)52 \BigCircle (%) ...... 53 £ astrologicalsymbols...... 46 \bauhead ( ) ...... 57 \bigcoast (§) ...... 19 astronomical symbols . . . . 45, 46 \bausquare ( ) ...... 54 \bigcomplementop ( ) ...... 21 (¢) ...... 54 \astrosun ( ) ...... 45 \bautriangle \BigCrossS( ) ...... 53 ( ) ...... 23 \bbalpha ( ) ...... 44 \asymp \bigcup ( ) ...... 20 (atan) ...... 70 \bbar (¯b) ...... 63 \atan \bigcurlyvee ( ) ...... 21 () ...... 56 \bbbeta ( ) ...... 44 \ataribox \bigcurlyvee ( ) ...... 20 (Ø) ...... 57 \Bbbk (k) ...... 33 \AtForty \bigcurlywedge ( ) ...... 21 \AtNinetyFive (Ó) ...... 57 bbding (package) . 49–53, 55, 61, \bigcurlywedge ( ) ...... 20 atomic math objects . . . . 31, 71 75, 76 \BigDiamondshape (&) ..... 53 \AtSixty (Õ) ...... 57 \bbdollar ($) ...... 44 \BigHBar () ...... 53 \bbetter (g) ...... 59 \autoleftarrow (D GGGGG ) .... 39 \biginterleave ( ) ...... 20 \bbeuro (û) ...... 44 _ \bbfinalnun (Ï) ...... 44 \BigLowerDiamond ( ) ..... 53 EGGGGGGG G G GC \autoleftrightharpoons ( ) \bbgamma ( ) ...... 44 \bignplus ( )Æ ...... 20 \bigoasterisk ( ) ...... 21 ...... 39 bbgreekl (mathbbol package option) Î ...... 44 \bigobackslashË ( ) ...... 21 \autorightarrow (GG G G GA )...39 bbm (package) ...... 44,75 \bigobot ( Å) ...... 21 \bbnabla () ...... 44 \bigocirc ( ) ...... Ç 21 \autorightleftharpoons (FGGGGGGG G G GB ) bbold (package) ...... 44, 75 \bigocoasteriskÃ ( ) ...... 21 \bbpe (Ô) ...... 44 \bigodiv (J) ...... 21 ...... 39 \bbqof (×) ...... 44 \bigodot ( È) ...... 20 \bigoleft ( ) ...... 21 B \bbslash ( ) ...... 18 Á \bbyod (É) ...... 44 \bigominus L( ) ...... 21 \B ...... 8 \bigoplus ( ) ...... 20 \bdecisive (i) ...... 59 É b (esvect package option) . . . . 40 \bigoright ( ) ...... 21 \Beam (") ...... 47 Í \b (a) ...... 11 \bigoslash ( ) ...... 21 ¯ ! \Bearing (#) ...... 47 N \babygamma ( ) ...... 10 \bigotimes ( ) ...... 20 \because (∵) ...... 23 Ê \backepsilon ( ) ...... 23 \bigotop ( ) ...... 21 s \BEL (•) ...... 47 Ï \backprime ( ) ...... 42 \bigotriangleup ( ) ...... 21 " \bell () ...... 56 Ì \backsim ( ) ...... 23 \bigovoid ( ) ...... 21 % Berry, Karl ...... 75 \backsimeq ( ) ...... 23 \bigparallel ( ) ...... 20 \ \beta (β) ...... 32 \backslash ( ) ...... 35,42 \bigplus ( ) ...... 21 banana brackets ...... \betaup (β) ...... 32 \BigRightDiamond (/) ..... 53 .. see \llparenthesis and \beth (O) ...... 33 \bigsqcap ( ) ...... 21 \rrparenthesis \betteris (b) ...... 59 \bigsqcap ( ) ...... 20 \bar (¯) ...... 37 \between ( ) ...... 24 \bigsqcapplus ( ) ...... 22 \barb (¦) ...... 10 \between (() ...... 23 F \bigsqcup ( ) ...... 20 \bard () ...... 10 \Bicycle (®) ...... 54 \bigsqcupplus ( ) ...... 22 \bari (') ...... 10 \bigast (¦) ...... 19 \BigSquare ( ) ...... 53 \barin (V) ...... 34 \bigbox ( ) ...... Ö 20 \bigsquplus ( ) ...... 21 \barj (j) ...... 11 \bigboxasterisk ( Þ) ...... 21 \bigstar () ...... 19 \barl (.) ...... 10 \bigboxbackslashÛ ( ) ..... 21 \bigstar (u) ...... 42 \barlambda (¡) ...... 11 \bigboxbot ( Õ) ...... 21 \bigtimes ( ) ...... 21 \barleftharpoon (Þ) ...... 30 \bigboxcirc ( ) ...... × 21 \baro ( vs. <) ...... 61 \bigboxcoasteriskÓ ( ) .... 21 \BigTriangleDown ( #) ..... 53 \baro () ...... 18 \bigboxdiv (Ô) ...... 21 \bigtriangledown ( ) ..... 20 \baro (<) ...... 10 \bigboxdot ( ) ...... 21 \bigtriangledown ( vs. ).61

78 \bigtriangledown ( ) ..... 17 \boxast () ...... 18 \CAN (↑) ...... 47 f \BigTriangleLeft (") ..... 53 \boxasterisk ( ) ...... 19 cancel (package) ...... 38 \boxbackslash (n) ...... 19 \Cancer (ã) ...... 46 \BigTriangleRight ($) .... 53 \boxbar () ...... 18 \cancer () ...... 46 (!) ...... 53 \BigTriangleUp \boxbot (k) ...... 19 \Cap () ...... 17 ( ) ...... 20 \bigtriangleup \boxbox () ...... 18 \cap (X) ...... 19 ( vs. )..61 \bigtriangleup \boxbslash () ...... 18 \cap (∩) ...... 17 ( ) ...... 17 \bigtriangleupU \boxcirc (e) ...... 19 \Capricorn (é) ...... 46 ( ) ...... 20 \biguplus \boxcircle () ...... 18 \capricornus () ...... 46 \bigvarstar ( ) ...... 19 \boxcoasterisk (g) ...... 19 cardsuits ...... 42,55 \BigVBar W() ...... 53 \boxdiv (c) ...... 19 cardinality ...... see \aleph \bigvee ( )V ...... 20 \boxdot (d) ...... 19 care of (c/o) ...... 43 \bigwedge ( ) ...... 20 \boxdot () ...... 17,18 caret ...... see \^ \binampersand ( ) ...... 18 \boxdotLeft () ...... 29 Carlisle,David ...... 1,73 binary operators ...... 17–19 \boxdotleft () ...... 29 carriage return 47, 54, 60, see also binary relations ...... 23–27 \boxdotRight () ...... 29 \hookleftarrow negated ...... 23–25 \boxdotright () ...... 29 \carriagereturn (C) ...... 54 \bindnasrepma ( ) ...... 18 \boxempty () ...... 18 castle ...... see chess symbols \Biohazard (h) ...... 48 \boxLeft () ...... 29 catamorphism see \llparenthesis biologicalsymbols ...... 48 \boxleft (h) ...... 19 and \rrparenthesis bishop...... see chess symbols \boxleft () ...... 29 \cdot (·) ...... 17,63 \bishoppair (a) ...... 59 \boxminus (a) ...... 19 \cdotp (·) ...... 41 blackboard bold . see alphabets, \boxminus () ...... 17 \cdots (···) ...... 41 math \boxplus (`) ...... 19 Cedi . . see \textcolonmonetary \blackdiamond ( ) ...... 19 \boxplus () ...... 17 cedilla...... see accents \blacklozenge (v) ...... 42 \boxRight () ...... 29 \celsius (℃) ...... 43 \blacksmiley () ...... 56 \boxright (i) ...... 19 \Celtcross (‡) ...... 57 \blacksquare (x) ...... 42 \boxright () ...... 29 \cent (¢) ...... 14 m \blacktriangle () ...... 42 \boxslash ( ) ...... 19 \centerdot ( ) ...... 19 \blacktriangledown ()....19 \boxslash ( ) ...... 18 \centerdot () ...... 17 b \blacktriangledown (r) .... 42 \boxtimes ( ) ...... 19 \centre (I) ...... 59 \blacktriangleleft ()....19 \boxtimes ( ) ...... 17 cents...... see \textcent j \blacktriangleleft (N) .... 28 \boxtop ( ) ...... 19 \CEsign (C) ...... 48 o \blacktriangleright () ... 19 \boxtriangleup ( ) ...... 19 \changenotsign ...... 25 l \blacktriangleright (O)...28 \boxvoid ( ) ...... 19 \char ...... 6,60 D \blacktriangleup () ...... 19 \boy ( ) ...... 46 \check (ˇ) ...... 37 z blank ...... see \textblank \braceld ( ) ...... 66 check marks ...... 51, 54 { (Ë) ...... 57 \bracerd ( )> ...... 66 \Bleech > \checked ( ) ...... 56 \blitza (©) ...... 17,30 \bracevert (>) ...... 35 \CheckedBox () ...... 51 \blitzb ( ) ...... 30 brackets ...... see delimiters \Checkedbox (V) ...... 54

\blitzc ( ) ...... 30 braket (package) ...... 35 \Checkmark (!) ...... 51

\blitzd ( ) ...... 30 \breve (˘) ...... 37 \checkmark () ...... 16 \blitze ( ) ...... 30 \brokenvert () ...... 56 \checkmark (D) ...... 54 bm (package) ...... 71,75,76 Bronger, Torsten ...... 63 (") ...... 51 \bm ...... 71 \BS () ...... 47 \CheckmarkBold chemarr (package) . . . 39, 75, 76 \bmod ...... 31 \BSEfree (n) ...... 48 body-text symbols ...... 7–16 \bullet (•) ...... 17 chemarrow (package) . 30, 39, 75 A boldsymbols...... 71 bullseye . . . see \textbullseye \chemarrow ( ) ...... 30 chesssymbols ...... 59 \boldmath ...... 71 \Bumpedeq () ...... 24 (χ) ...... 32 \boldsymbol ...... 71 \bumpedeq () ...... 24 \chi (χ) ...... 32 born ...... see \textborn \Bumpeq (*) ...... 23 \chiup (◦) ...... 17,43 \bot (⊥) ...... 17,33,63 \bumpeq (-) ...... 23 \circ \circeq () ...... 24 \botdoteq () ...... 24 \bupperhand (e) ...... 59 (0) ...... 23 \Bouquet (¥) ...... 57 \circeq () ...... 56 \Bowtie () ...... 56 C \CIRCLE \bowtie ( ) ...... 23 c (esvect package option) . . . . 40 \Circle (5) ...... 53 \Box (p) ...... 42 \c (¸a) ...... 11,74 \Circle ( vs. 5) ...... 61 \Box () ...... 42 calrsfs (package) ...... 44 \Circle () ...... 56

79 \circlearrowleft (ö) ..... 30 \colon (:) ...... 41 cruciﬁxes...... 50,51,57 \circlearrowleft (P) ..... 29 \Colonapprox () ...... 24 \csc (csc)...... 31 \circlearrowright (÷) ..... 30 \colonapprox () ...... 24 CTAN . see Comprehensive TEX \circlearrowright (S) ..... 29 \Coloneq () ...... 24 Archive Network circlednumbers...... 51 \coloneq () ...... 24 \Cube ...... 59,60 \CircledA (ª) ...... 57 \coloneq () ...... 24 cuberoot ...... see \sqrt \circledast () ...... 17 \Coloneqq () ...... 24 \Cup () ...... 17 \circledbar () ...... 18 \coloneqq () ...... 17,24 \cup (Y) ...... 19 \circledbslash () ...... 18 \Colonsim () ...... 24 \cup (∪) ...... 17,63,70 \circledcirc ( ) ...... 17 \colonsim () ...... 24 \curlyc ( ) ...... 10 \circleddash () ...... 17 \comment (RR) ...... 59 \curlyeqprec (¶) ...... 24 \circleddot ...... see \odot communicationsymbols..... 47 \curlyeqprec (2) ...... 23 \circleddotleft () ..... 29 comp.text.tex (newsgroup) 6, 17, \curlyeqsucc (·) ...... 24 \circleddotright () ..... 29 62–66 \curlyeqsucc (4) ...... 23 \circledgtr () ...... 24 \compensation (n) ...... 59 \curlyesh (N) ...... 10 \circledless () ...... 24 \complement (A) ...... 34 \curlyvee (O) ...... 19 \circledminus .... see \ominus \complement (j) ...... 33 \curlyvee () ...... 17 \circledotleft ...... see complex numbers (C) ..... see \curlyveedownarrow () .... 18 \circleddotleft alphabets, math \curlyveeuparrow () ...... 18 \circledotright ...... see Comprehensive TEX Archive Net- \curlywedge (N) ...... 19 \circleddotright work ...... 1,6,44,73, \curlywedge () ...... 17 \circledplus ..... see \oplus 75 \curlywedgedownarrow ()..18 \circledR () ...... 16,33 computer hardware symbols . . 47 \curlywedgeuparrow () .... 18 \circledS (k) ...... 33 \ComputerMouse (Í) ...... 47 \curlyyogh (a) ...... 10 \circledslash .... see \oslash \cong ( ) ...... 23 \curlyz (^) ...... 10 \circledtimes .... see \otimes \conjunction ( ) ...... 46 \currency (¤) ...... 14 \circledvee () ...... 18 contradiction symbols . . . 17, 30 currency symbols ...... 14, 44 \circledwedge () ...... 18 control characters ...... 47 \curvearrowbotleft (ó)...30

\circleleft () ...... 29 \convolution` ( ) ...... 19 \curvearrowbotleftright (õ)30 \circleright () ...... 29 \coprod ( ) ...... 20 \curvearrowbotright (ô)...30 © circles...... 53,54,56 \copyright ( ) ...... 7 \curvearrowleft (ð) ...... 30 k d \corner ( ) ...... 13 \curvearrowleft (F) ...... 29 \CircleShadow ( ) ...... 53 = \Corresponds ( ) ...... 43 \curvearrowleftright (ò)..30 \CircleSolid (a) ...... 53 \corresponds ( ) ...... 24 (ñ) ..... 30 \Circpipe (›) ...... 47 \curvearrowright \cos (cos)...... 31,70 (G) ..... 29 \circplus (¨) ...... 19 \curvearrowright \cosh (cosh) ...... 31 (s) ...... 49 \Circsteel (•) ...... 47 \Cutleft \cot (cot)...... 31 r circumﬂex...... see accents \Cutline ( ) ...... 49 \coth (coth) ...... 31 cutoﬀ subtraction . . see \CleaningA («) ...... 57 \dotdiv \counterplay (V) ...... 59 (q) ...... 49 \CleaningF (¾) ...... 57 \Cutright Courier (PostScript font) . . . . 14 \CleaningFF (¿) ...... 57 CP1252...... 73 D \CleaningP (¬) ...... 57 \CR (♪) ...... 47 d (esvect package option) . . . . 40 \CleaningPP () ...... 57 \d (a) ...... 11 \clickb (;) ...... 10 \Cross ( ) ...... 53 . \dag (†) ...... 7 \clickc ( ) ...... 10 \Cross († vs. * vs. ) ...... 61 \dagger (†) ...... 17 \clickt (R) ...... 10 \Cross (†) ...... 57 \daleth (Q) ...... 33 \clock () ...... 56 \Cross (*) ...... 50 dangerous bend symbols . . . . 54 clocksymbols ...... 58 \crossb (¥) ...... 10 \dasharrow see \dashrightarrow \Clocklogo (U) ...... 54 - R \CrossBoldOutline ( ) ..... 50 − \closedniomega (?) ...... 10 \dashint ( ) ...... 64 \CrossClowerTips (4) ..... 50 \closedrevepsilon () ..... 10 \dashleftarrow () ...... 29 \crossd ( ) ...... 10 \Cloud () ...... 58 \dashleftrightarrow () ... 29 \Crossedbox (X) ...... 54 clovers ...... 52 \dashrightarrow () ...... 29 crosses ...... 50,51,57 clubs(suit) ...... 42,55 \DashV ()) ...... 24 \crossh (#) ...... 10 \clubsuit (♣) ...... 42 \Dashv ()) ...... 24 (.) ...... 50 \coAsterisk (§) ...... 19 \CrossMaltese \dashv () ...... 23 (3) ...... 10 \coasterisk (§) ...... 19 \crossnilambda \dashVv (-) ...... 24 \Coffeecup (K) ...... 54 \CrossOpenShadow (+) ...... 50 \davidsstar () ...... 51 \colon ...... 41 \CrossOutline (,) ...... 50 \DavidStar (0) ...... 52

80 \DavidStarSolid (/) ...... 52 \Diamond () ...... 42 does not divide . . . . . see \nmid \dbar (¯d) ...... 63 \Diamond () ...... 42 does not exist . . . . see \nexists \dbend () ...... 54 \diamond () ...... 17 dollar ...... see \textdollar \DCa () ...... 47 \Diamondblack () ...... 42 dollarsign...... see \$ \DCb () ...... 47 \Diamonddot () ...... 42 \Dontwash (Ý) ...... 57 \DCc (‼) ...... 47 \DiamonddotLeft () ..... 29 \dot ( ˙ ) ...... 37 \DCd (¶) ...... 47 \Diamonddotleft () ..... 29 dotsymbols ...... 41 \ddag (‡) ...... 7 \DiamonddotRight () ..... 29 \dotcup (∪· ) ...... 63 \ddagger (‡)R ...... 17 \Diamonddotright () ..... 29 \dotdiv (¡) ...... 19 \ddashint (=) ...... 64 \DiamondLeft () ...... 29 \Doteq ...... see \doteqdot .... \Diamondleft () ...... 29 \doteq () ...... 23 \ddddot ...( ) ...... 37 \dddot ( ) ...... 37 \DiamondRight () ...... 29 \doteqdot (6) ...... 23 \ddot (¨) ...... 37 \Diamondright () ...... 29 dotless i (ı) . diamonds ...... 53, 54 math mode ...... 37, 42 .. \ddots ( ) ...... 41,65 diamonds (suit) ...... 42, 55 textmode ...... 11 \DeclareFontFamily ...... 69 j j \DiamondShadowA (¥) ...... 53 dotless ( ) \DeclareFontShape ...... 69 math mode ...... 37, 42 \DiamondShadowB (¦) ...... 53 \DeclareMathOperator . . 70, 71 textmode ...... 11 § \DeclareMathOperator* . 70, 71 \DiamondShadowC ( ) ...... 53 \dotplus ( ) ...... 19

\declareslashed ...... 63 \Diamondshape (6) ...... 53 \dotplus () ...... 17 definite-description operator ( )62ι \DiamondSolid (p) ...... 53 \dots (...) ...... 7 definition symbols ...... 17, 66 \diamondsuit (♦) ...... 42 dots (ellipses) . . . . 7, 41, 42, 65 \deg (deg) ...... 31 \diatop ...... 13,65 \dotsb (···) ...... 41 0 \degree ( ) ...... 42 \diaunder ...... 13,65 \dotsc (...) ...... 41 ° \degree ( ) ...... 43 dice ...... 59,60 \dotseq () ...... 24 degrees ...... see \textdegree dictionary symbols . see phonetic \dotsi (···©) ...... 41 \DEL () ...... 47 symbols \dotsint ( ) ...... 22 \Deleatur ...... see \Denarius died ...... see \textdied \dotsm (···) ...... 41 delimiters ...... 34–36 differential, inexact . . see \dbar \dotso (...) ...... 41 text-mode ...... 36 \digamma (M) ...... 32 dotted union (∪˙ ) ...... 70 variable-sized ...... 35, 36 digits ...... 43 \dottimes (¢) ...... 19 \Delta (∆) ...... 32 circled ...... 51 \double ...... 36 δ \delta ( ) ...... 32 LCD ...... 45 \doublebarwedge (Z) ...... 19 δ \deltaup ( ) ...... 32 Mayan...... 43 \doublebarwedge () ...... 17 ¢ \Denarius ( ) ...... 14 old-style...... 15 \doublecap ...... see \Cap g \dental (a) ...... 13 segmented ...... 45 \doublecap (\) ...... 19 derivitive, partial . . see \partial \dim (dim) ...... 31 \doublecup ...... see \Cup \descnode ( ) ...... 45 \ding ...... 8,49–52, 54, 55 \doublecup (]) ...... 19 \det (det)...... 31 dingautolist ...... 51 \doublepawns (d) ...... 59 \devadvantage (t) ...... 59 dingbat (package) . 50, 54, 61, 75, \DOWNarrow () ...... 56 ... c \Dfourier ( ... ) ...... 25 76 \Downarrow (⇓) ...... 28,35 c ... dingbat symbols ...... 49–55 \dfourier ( ... ) ...... 25 \downarrow ...... 70 discount . . . see \textdiscount \downarrow (↓) ...... 28,35 \DFT ( ) ...... 37 \displaystyle . . . . . 63–65, 71 \downbracketfill ...... 66 \dft ( ) ...... 37 ditto marks . see \textquotedbl \downdownarrows (Ó) ...... 30 Ð \DH ( ) ...... 8 \div (÷) ...... 17 \downdownarrows (^) ...... 29 \DH (D)...... 8 \divdot (£) ...... 19 \downdownharpoons (Û) ..... 30 \dh (ð) ...... 8 \divideontimes ( ) ...... 19 Downes, Michael J...... 31, 75 \dh ( ) ...... 8 \divideontimes () ...... 17 \downharpoonleft (å) ...... 30 diacritics...... see accents \divides () ...... 24 \downharpoonleft (c) ...... 29 diæresis ...... see accents division...... 17,38 \downharpoonright (ç) ..... 30 \diagdown (å) ...... 42 division times see \divideontimes \downharpoonright (f) ..... 29 \diagdown (X) ...... 42 divorced . . . see \textdivorced \downp (u) ...... 13 \diagonal (G) ...... 59 \DJ (Ð) ...... 8 \downparenthfill ...... 66 \diagup (ä) ...... 42 \dj (đ) ...... 8 \downt (m) ...... 13 \diagup (Y) ...... 42 \dlbari (() ...... 10 \downtouparrow (ÿ) ...... 30 \diameter (I) ...... 42 \DLE () ...... 47 \downuparrows (×) ...... 30 \diameter () ...... 56 \dlsh (ê) ...... 30 \downupharpoons (ë) ...... 30

81 \drsh (ë) ...... 30 \Eqqcolon () ...... 24 \FallingEdge (!) ...... 45 dsfont (package) ...... 44, 75 \eqqcolon () ...... 24 \fatbslash () ...... 18 \dz () ...... 10 \eqsim ( ) ...... 24 \fatsemi () ...... 18 \eqslantgtr (·) ...... 27 \fatslash () ...... 18 E \eqslantgtr (>) ...... 27 \FAX (u) ...... 47 e (esvect package option) . . . . 40 \eqslantless (¶) ...... 27 \fax (t) ...... 47 \e (e) ...... 34 \eqslantless (@) ...... 27 \Faxmachine (v) ...... 47 ε -TEX ...... 35 \equal (j) ...... 59 fc (package) ...... 8,11 C \Earth ( ) ...... 46 \equalsfill ...... 17,66 fclfont (package) ...... 75 \Earth (Ê) ...... 46 equilibrium ...... see feet ...... see \prime and \earth (♁) ...... 45 \rightleftharpoons \textquotesingle \Ecommerce ( ) ...... 14 \equiv (≡) ...... 17,23 \FEMALE () ...... 48 \EightAsterisk (Z) ...... 52 \er () ...... 10 \Female (~) ...... 48 ♀ \EightFlowerPetal (S) .... 52 \ESC (←) ...... 47 \female ( ) ...... 47 escapable characters ...... 7 \FemaleFemale („) ...... 48 \EightFlowerPetalRemoved (Y) M \FemaleMale (…) ...... 48 ...... 52 \esh ( ) ...... 10 s Feynman slashed character nota- \eighthnote (') ...... 56 \esh ( ) ...... 11 esint (package) ...... 22,75 tion ...... 63 \EightStar (H) ...... 52 \Estatically (J) ...... 48 \FF (♀) ...... 47 I \EightStarBold ( ) ...... 52 estimated . . see \textestimated \FHBOLOGO (f) ...... 57 \EightStarConvex (F) ..... 52 esvect (package) ...... 40, 75 \FHBOlogo (F) ...... 57 \EightStarTaper (E) ...... 52 \eta (η) ...... 32 \file (H) ...... 59 η \ejective (e) ...... 10 \etaup ( ) ...... 32 \FilledBigCircle (U) ..... 53 \ETB () ...... 47 electricalsymbols ...... 45 \FilledBigDiamondshape (V)53 electromotive force (E) ..... see \etc (P) ...... 59 \FilledBigSquare (P) ..... 53 alphabets, math \eth (ð) ...... 42 S \ell ( ) ...... 33 \eth () ...... 10 \FilledBigTriangleDown ( )53 R \Ellipse (b) ...... 53 \eth (d) ...... 11 \FilledBigTriangleLeft ( )53 ellipses (dots) . . . . 7, 41, 42, 65 \ETX (♥) ...... 47 \FilledBigTriangleRight (T)53 ellipses(ovals)...... 53 eufrak (package) ...... 44 \FilledBigTriangleUp (Q)..53 EulerRoman...... 33 \EllipseShadow (e) ...... 53 \FilledCircle (e) ...... 53 \EUR (e ) ...... 14 \EllipseSolid (c) ...... 53 \FilledCloud ( ) ...... 58 \EURcr (d) ...... 14 \EM (↓) ...... 47 ¨ \EURdig (D) ...... 14 \FilledDiamondShadowA ( ).53 \Email (k) ...... 47 \EURhv (c) ...... 14 \FilledDiamondShadowC (©).53 \Emailct (z) ...... 47 \euro ...... 14 \FilledDiamondshape (f) ... 53 \emgma (M) ...... 11 euro signs ...... 14 (∅) ...... 42 \FilledHut ( ) ...... 58 \emptyset blackboard bold ...... 44 endofproof ...... 42 \FilledRainCloud (!) ..... 58 eurosym (package) . . . 14, 75, 76 L ¢ \ending ( ) ...... 59 \EURtm (e) ...... 14 \FilledSectioningDiamond ( ) \eng (8) ...... 10 euscript (package) . . . 44, 75, 76 ...... 59 engineering symbols . . . . . 45, 47 evaluated at (|) ...... 35 \FilledSmallCircle (u) ... 53 n \engma ( ) ...... 11 exclusiveor...... 60 (v) ♣ \FilledSmallDiamondshape \ENQ ( ) ...... 47 \exists (D) ...... 34 ...... 53 entails...... see \models ∃ \exists ( ) ...... 33 \FilledSmallSquare (p) ... 53 enter...... see carriage return \exp (exp) ...... 31 \FilledSmallTriangleDown (s) \Envelope ( ) ...... 55 \Explosionsafe (`) ...... 48 ...... 53 \enya (N) ...... 11 extensible accents . 38–40, 65–66 r \EOT (♦) ...... 47 extensible arrows ...... 38–40 \FilledSmallTriangleLeft ( ) \epsi (") ...... 11 extensibletildes...... 38,40 ...... 53 \epsilon ( ) ...... 32 extension characters . . . . 30, 31 \FilledSmallTriangleRight (t) \epsilonup () ...... 32 \eye (E) ...... 54 ...... 53 \eqbumped () ...... 24 \EyesDollar (¦) ...... 14 \FilledSmallTriangleUp (q)53 () ...... 24 \eqcirc \FilledSnowCloud ($) ..... 58 \eqcirc ( ) ...... 23 F \FilledSquare (`) ...... 53 \Eqcolon () ...... 24 f (esvect package option) . . . . 40 \eqcolon () ...... 24 \fallingdotseq () ...... 24 \FilledSquareShadowA (£)..53 \eqcolon () ...... 24 \fallingdotseq ( ) ...... 23 \FilledSquareShadowC (¤)..53

82 \filledsquarewithdots (C).54 fonts, PostScript \geqq (¯) ...... 27 A \FilledSunCloud (#) ...... 58 Courier ...... 14 \geqq ( ) ...... 27 Helvetica ...... 14 \geqslant (B) ...... 27 \FilledTriangleDown (c) ... 53 Symbol ...... 33,60 \gets ...... see \leftarrow b \FilledTriangleLeft ( ) ... 53 Times ...... 14 \gg (") ...... 27 \FilledTriangleRight (d)..53 Type1 ...... 70 \gg () ...... 26 \FilledTriangleUp (a) .... 53 Zapf Chancery ...... 44 \ggcurly (Ï) ...... 24 Ï \FilledWeakRainCloud (")..58 Zapf Dingbats . . . . . 49, 51 \ggg ( ) ...... 27 (o) ...... 54 \ggg (≫ vs. Ï) ...... 61 \fint ( ) ...... 22 \Football ∀ ≫ \fint ( ) ...... 22 \forall ( ) ...... 33 \ggg ( ) ...... 27 l \Finv (F) ...... 34 \Force ( ) ...... 47 \gggtr ...... see \ggg \Finv (S) ...... 33 \Forward (·) ...... 57 Gibbons, Jeremy ...... 75 33 ...... (ג) gimel\ 57 ...... (¸) \Fire ( ) ...... 59 \ForwardToEnd (¹) ..... 57 \girl (B ) ...... 46 fishhook...... see \strictif \ForwardToIndex \glotstop (b) ...... 10 R \FourAsterisk (1) ...... 52 \FiveFlowerOpen ( ) ...... 52 \glottal (?) ...... 11 \FourClowerOpen (V) ...... 52 \FiveFlowerPetal (P) ..... 52 \gluon (,------.) ...... 45 (W) ..... 52 \FiveStar (8) ...... 52 \FourClowerSolid \gnapprox (Ë) ...... 27 c (4) ...... 27 \FiveStarCenterOpen (;) ... 52 \Fourier ( ) ...... 25 \gnapprox c () ...... 27 ? \fourier ( ) ...... 25 \gneq \FiveStarConvex ( ) ...... 52 6 Fourier transform (F) ..... see \gneq ( ) ...... 27 \FiveStarLines (7) ...... 52 ³ alphabets, math \gneqq ( ) ...... 27 9 9 \FiveStarOpen ( ) ...... 52 \FourStar (5) ...... 52 \gneqq ( ) ...... 27 : \gnsim (Å) ...... 27 \FiveStarOpenCircled ( )..52 \FourStarOpen (6) ...... 52 \gnsim (;) ...... 27 \FiveStarOpenDotted (<) ... 52 \fourth (4) ...... 42 graphics (package) ...... 62 = fractions ...... 43 \FiveStarOutline ( ) ..... 52 graphicx (package) ...... 62 fraktur . . . . see alphabets, math \FiveStarOutlineHeavy (>).52 \grave (`) ...... 37 \frown () ...... 23 \FiveStarShadow (@) ...... 52 greater-than signs see inequalities \frownie ()) ...... 56 \Fixedbearing (%) ...... 47 Greek ...... 32,33 (§) ...... 57 \Frowny blackboard bold ...... 44 .. └ \fixedddots ( .) ...... 41 \FS ( ) ...... 47 bold ...... 32,71 \FullFHBO () ...... 57 . upright ...... 32, 33 \fixedvdots (.)...... 41 M \fullmoon ( ) ...... 46 \GS (↔) ...... 47 fixmath (package) ...... 71 \fullmoon ( ) ...... 45 \gtrapprox (Ç) ...... 27 \fj (F) ...... 11 * \fullnote ( ) ...... 56 \gtrapprox (I) ...... 27 \Flag ( ) ...... 58 \gtrdot (Í) ...... 27 f G \flap ( ) ...... 11 \gtrdot (>) ...... 27 D a \flapr ( ) ...... 10 \G ( ) ...... 11 \gtreqless (½) ...... 27 \flat ( ) ...... 42,56 g (esvect package option) . . . . 40 \gtreqless (K) ...... 27 \Flatsteel (–) ...... 47 \Game (G) ...... 34 \gtreqqless (¿) ...... 27 florin ...... see \textflorin \Game (U) ...... 33 flowers ...... 52 \Gamma (Γ) ...... 32 \gtreqqless (M) ...... 27 \Fog () ...... 58 \gamma (γ) ...... 32 \gtrless (») ...... 27 fontencodings...... 6 \gammaup (γ) ...... 32 \gtrless (≷) ...... 27 7-bit ...... 6 \gcd (gcd) ...... 31 \gtrsim (Á) ...... 27 8-bit ...... 6 \ge ...... see \geq \gtrsim () ...... 27 ASCII ...... 73 \Gemini (R ) ...... 46 \guillemotleft («) ...... 8,74 document...... 73 \Gemini (â) ...... 46 \guillemotright (») ..... 8,74 Latin1 ...... 73 \gemini (+) ...... 46 \guilsinglleft (‹) ...... 8 limitingscopeof...... 6 genealogical symbols ...... 56 \guilsinglright (›) ...... 8 LY1...... 6 \geneuro (AC) ...... 14 \gvertneqq (µ) ...... 27 OT1 ...... 6, 8, 11, 71, 72 \geneuronarrow (BC) ...... 14 \gvertneqq (0) ...... 27 OT2 ...... 62 \geneurowide (CC) ...... 14 T1 ...... 6, 8, 11, 72, 73 gensymb (package) ...... 43 H T4...... 8,11 \Gentsroom (x) ...... 54 \H (˝a) ...... 11 fontdef.dtx (file) ...... 62, 65 geometric shapes ...... 52–54 h (esvect package option) . . . . 40 fontenc (package) . . . 6, 8, 11, 73 \geq (¥) ...... 27 háˇcek ...... see accents \fontencoding ...... 6 \geq (≥) ...... 26,27 \Hail () ...... 58

83 \HalfCircleLeft (s) ...... 53 \hookrightarrow (→) ...... 28 \interleave () ...... 18 \HalfCircleRight (r) ...... 53 Horn, Berthold ...... 44 intersection...... see \cap T ( ) ...... 58 \hslash ( ) ...... 33 \Interval () ...... 58 \HalfFilledHut \halflength (p) ...... 13 \HT ( ) ...... 47 \inva ( ) ...... 10 \halfnote (/) ...... 56 Hungarian umlaut . . see accents \invamp () ...... 18 \Hut () ...... 58 (2) ...... 56 \HalfSun () ...... 58 \invdiameter (") ...... 10 3 Hamiltonian (H). see alphabets, \hv \inve ( ) ...... 8 \InversTransformHoriz (¡)25 math I \HandCuffLeft () ...... 50 \InversTransformVert (£)..25 \i (ı) ...... 11 \invf (,) ...... 10 \HandCuffLeftUp ( ) ...... 50 (i) ...... 11 \ibar ¯ \invglotstop (d) ...... 10 \HandCuffRight ( ) ...... 50 IBM ...... 47,72 \invh (&) ...... 10 () ...... 58 \HandCuffRightUp ( ) ..... 50 \IceMountain \invlegr (I) ...... 10 . \HandLeft () ...... 50 .. \invm (5) ...... 10 \iddots ( ) ...... 41,65 (4) ...... 23 \HandLeftUp ( ) ...... 50 \idotsint ( ) ...... 20,22 \invneg \invr (G) ...... 10 \HandPencilLeft () ...... 50 \iff . see \Longleftrightarrow \invscr (K) ...... 10 \HandRight () ...... 50 ifsym (package) 45, 53, 58, 59, 61, \invscripta (£) ...... 10 75, 76 \HandRightUp ( ) ...... 50 \invv (¤) ...... 10 \iiiint ( ) ...... 20,22 hands ...... 50 § \invw (Z) ...... 10 Ü ( ) ...... 22 \Handwash ( ) ...... 57 \iiiint µ \invy (\) ...... 10 ( ) ...... 21 harpoons ...... 28–30 \iiint \iota (ι) ...... 32 # \hash ( ) ...... 42 \iiint (¥ ) ...... 20,22 \iotaup (ι) ...... 32 hashmark...... see \# \iiint ´( ) ...... 22 \ipagamma ( ) ...... 10 \hat (ˆ) ...... 37 \iint () ...... 21 \IroningI (¯) ...... 57 \hausaB (B) ...... 11 \iint ( ) ...... 20,22 \IroningII (°) ...... 57 b £ \hausab ( ) ...... 11 \iint ( ) ...... 22 \IroningIII (±) ...... 57 T \hausaD ( ) ...... 11 \Im ( ) ...... 33 D \Irritant ( ) ...... 59 \hausad ( ) ...... 11 \im (j) ...... 34 | K \ismodeledby (= ) ...... 62 \hausaK ( ) ...... 11 \imath (ı) ...... 33,37 k ISO character entities ...... 73 \hausak ( ) ...... 11 \impliedby . see \Longleftarrow isoent (package) ...... 73 \HBar () ...... 53 \implies . see \Longrightarrow \hbar (R) ...... 33,62 and \vdash J \Heart (Œ) ...... 57 \in (P) ...... 34 \j (j) ...... 11 hearts (suit) ...... 42, 55 \in (∈) ...... 33 \JackStar (2) ...... 52 (♥) ...... 42 \heartsuit inches...... see \second and \JackStarBold (3) ...... 52 Hebrew ...... 33,44 \textquotedbl Jewishstar ...... 51,52 Helvetica (PostScript font) . . . 14 independence \jmath (j) ...... 33,37 () ...... 48 \HERMAPHRODITE probabilistic ...... 64 \Joch () ...... 58 (}) ...... 48 \Hermaphrodite statistical...... 64 \Join () ...... 23 0 \hexagon ( ) ...... 52 stochastic ...... see \bot \joinrel ...... 62 ’ ⊥⊥ \Hexasteel ( ) ...... 47 \independent ( ) ...... 64 \Jupiter (E ) ...... 46 1 I \hexstar ( ) ...... 51 \Industry ( ) ...... 54 \Jupiter (Å) ...... 46 \HF ( ) ...... 45 inequalities ...... 7,26,27 \jupiter (5) ...... 45 Hilbert space (H) see alphabets, inexact diﬀerential . . . see \dbar math \inf (inf) ...... 31 K \hill (a) ...... 13 \Info (i) ...... 54 ˛ { √ \k ( ) ...... 11 \hksqrt ( ) ...... 64 information symbols ...... 54 \kappa (κ) ...... 32 Holt, Alexander ...... 1, 73 informator symbols ...... 59 \kappaup (κ) ...... 32 \hom (hom)...... 31 \infty (8) ...... 42 \ker (ker)...... 31 \hookb (¨) ...... 10 \infty (∞) ...... 42 \Keyboard (Ï) ...... 47 \hookd () ...... 10 \injlim (injlim) ...... 31 king ...... see chess symbols \hookd (D) ...... 11 \inplus³ () ...... 23 knight...... see chess symbols \hookg () ...... 10 \int (R) ...... 21 Knuth, Donald E. . . . . 6, 71, 75 \hookh ($) ...... 10 \int ( ) ...... 20 symbols by ...... 54, 56 \hookheng (%) ...... 10 integers (Z).see alphabets, math \kreuz (6) ...... 56 \hookleftarrow (←) ...... 28 integrals ...... 20–22, 63–64 \kside (O) ...... 59 \hookrevepsilon () ...... 10 \intercal () ...... 17 \Kutline (R) ...... 49

84 L \leftarrow (←) ...... 28 \lesseqgtr (G) ...... 27 \L (L)...... 8 \leftarrowtail (a) ...... 29 \lesseqqgtr (¾) ...... 27 \l (l) ...... 8 \leftarrowtriangle () ... 29 \lesseqqgtr (H) ...... 27 \labdentalnas (4) ...... 10 \leftbarharpoon (Ü) ...... 30 º \labvel ...... 13 \LEFTCIRCLE (8) ...... 56 \lessgtr ( ) ...... 27 ≶ \Ladiesroom (y) ...... 54 \LEFTcircle (8) ...... 56 \lessgtr ( ) ...... 27 À Lagrangian (L).. see alphabets, \Leftcircle (9) ...... 56 \lesssim ( ) ...... 27 math \leftharpoondown (â) ..... 30 \lesssim ( ) ...... 27

\Lambda (Λ) ...... 32 \leftharpoondown () ..... 28 \Letter ( ) ...... 59 B \lambda (λ) ...... 32 \leftharpoonup (à) ...... 30 \Letter ( vs. ) ...... 61 B \lambdabar () ...... 42 \leftharpoonup () ...... 28 \Letter ( ) ...... 47 \lambdaslash () ...... 42 \leftleftarrows (Ð) ...... 30 letter-like symbols ...... 33, 34 \lambdaup (λ) ...... 32 \leftleftarrows (⇔) ...... 29 letters...... see alphabets Lamport,Leslie...... 73,75 \leftleftharpoons (Ø)....30 barred ...... 62 \land ...... % see \wedge \leftmoon (K ) ...... 46 non-ASCII ...... 8 \landdownint# ( ) ...... 22 \leftmoon (:) ...... 45 slashed ...... 63 \landupint ( ) ...... 22 \leftp (v) ...... 13 variantLatin ...... 33 \Langle (<) ...... 44 \leftpointright (R) ..... 50 \LF () ...... 47 \lAngle (##) ...... 36 \Leftrightarrow (⇔) ...... 28 \lfilet (7) ...... 35 \langle (#) ...... 35 \leftrightarrow (Ø) ...... 30 \lFloor ())) ...... 36 s c ↔ \Laplace ( ) ...... 25 \leftrightarrow ( ) ...... 28 \lfloor ()) ...... 35 c s \leftrightarroweq () ..... 29 \laplace ( ) ...... 25 \lg (lg)...... 8 31 \leftrightarrows (Ô) ..... 30 Laplace transform (L) ..... see : \leftrightarrows (T) ..... 29 \lgroup ( ) ...... 35 alphabets, math \leftrightarrowtriangle ()29 \LHD (7) ...... 18 \leftrightharpoon (à)....30 \lhd ( ) ...... 17,18 \largepencil (W) ...... 50 \leftrightharpoons (è)...30 \lhdbend () ...... 54 \larrowfill ...... 39 \leftrightharpoons (d) ... 29 \Libra (æ) ...... 46 a \Laserbeam ( ) ...... 48 \leftrightharpoonsfill .... 39 \libra (<) ...... 46 A LTEX 1, 6, 31, 35, 39, 41, 42, 49, \leftrightsquigarrow (ú)30 \lightbulb (A) ...... 69 59, 60, 62–67, 70–73, 75 \leftrightsquigarrow (V).29 lightbulb.mf (file) . . . . . 67, 68 A LTEX2ε ...... 1, 6, 7, 15, 17, \Leftscissors (S) ...... 49 lightbulb.sty (file) . . . . 69, 70 23, 25, 28, 37, 41, 42, 44, 57, \leftslice () ...... 18 lightbulb10.2602gf (file) . . . 68 ø 60–62, 64, 65, 69–75 \leftsquigarrow ( ) ..... 30 lightbulb10.dvi (file) ..... 68 latexsym (package) 17, 23, 25, 28, \leftsquigarrow ( ) ...... 29 lightbulb10.mf (file) . . . 67–69 n 42, 60, 75, 76 \leftt ( ) ...... 13 lightbulb10.tfm (file) ..... 69 \latfric (/) ...... 10 \leftthreetimes ($) ...... 42 \Lightning (E vs. ) ...... 61 Latin1 ...... 6,73 \leftthreetimes () ...... 17 \Lightning (E) ...... 47 table ...... 74 \leftthumbsdown (D) ..... 50 laundry symbols ...... 57 \leftthumbsup (U) ...... 50 \Lightning ( ) ...... 58 = \Lbag () ...... 34 \lefttorightarrow (ü)....30 \lightning ( vs. ) ...... 61 \lbag () ...... 34 \Lefttorque (&) ...... 47 \lightning ( ) ...... 29 = \lbbbrack (v) ...... 35 \leftturn (;) ...... 56 \lightning ( ) ...... 56 \Lbrack ([) ...... 44 \legm (6) ...... 10 \lim (lim)...... 31,70 \lBrack ([[)...... 36 \legr (E) ...... 10 \liminf (liminf) ...... 31,71 LCDdigits ...... 45 \length (q) ...... 13 limits ...... 31 \lCeil ($$) ...... 36 \Leo (ä) ...... 46 \limsup (lim sup) ...... 31, 71 \lceil ($) ...... 35 \leo () ...... 46 linear implication see \multimap \lcm (lcm) ...... 70 \leq (¤) ...... 27 \Lineload (L) ...... 47 \lcorners (v) ...... 34 \leq (≤) ...... 26,27 linguistic symbols ...... 8–11 \ldotp (.) ...... 41 \leqq (®) ...... 27 \lJoin () ...... 24 \ldots (...) ...... 41 \leqq (C) ...... 27 \ll (!) ...... 27 \le ...... see \leq \leqslant (E) ...... 27 \ll (*) ...... 26 \leadsto () ...... 23,28 less-than signs . . see inequalities \llap ...... 64 leaf...... see \textleaf \lessapprox (Æ) ...... 27 \llbracket () ...... 35 \left ...... 35,36 \lessapprox (F) ...... 27 \llceil ( ) ...... 34 \LEFTarrow (7) ...... 56 \lessdot (Ì) ...... 27 \llcorner (z) ...... 34 \Leftarrow (⇐) ...... 17,28 \lessdot (7) ...... 27 \llcorner (n) ...... 34 \leftarrow (Ð) ...... 30 \lesseqgtr (¼) ...... 27 \llcurly (Î) ...... 24

85 \Lleftarrow (X) ...... 29 \Lsh (_) ...... 29 \mapstochar ()Þ ...... 31 \llfloor ( ) ...... 34 \Lsteel (™) ...... 47 \markera (x) ...... 59 \lll (Î) ...... 27 \ltimes ( ) ...... 19 \markerb (y) ...... 59 \lll (≪ vs. Î) ...... 61 \ltimes () ...... 17 married..... see \textmarried \lll (≪) ...... 27 \ltriple ...... 36 \Mars (D ) ...... 46 \llless ...... see \lll Luecking,Dan...... 64 \Mars (Ä) ...... 46 \llparenthesis8 (!) ...... 34 \lVert (||) ...... 36 \mars (♂) ...... 45 ´ ÿ \lmoustache (;) ...... 35 \lvertneqq ( ) ...... 27 \MartinVogel ( ) ...... 57 \lvertneqq (2) ...... 27 marvosym (package) 14, 43, 46–49, \ln (ln) ...... 31 \lz (1) ...... 10 54, 57, 61 Ê \lnapprox ( ) ...... 27 matbbol (package) ...... 44 \lnapprox (A) ...... 27 M \mate (m) ...... 59 \lneq (¬) ...... 27 \M ...... 8 math alphabets ...... 44 \lneq (.) ...... 27 \m ...... 8 mathabx (package) 19, 21, 23–28, \lneqq (²) ...... 27 macron ...... see accents 30, 31, 34, 35, 37, 40, 42, 43, \lneqq (/) ...... 27 majuscules ...... 32 46, 54, 60, 61, 75, 77 \lnot ...... see \neg \makeatletter ...... 65 ...... 63 \lnsim (Ä) ...... 27 \mathaccent \makeatother ...... 65 \mathbb ...... 44 \lnsim (1) ...... 27 ‚ \MALE ( ) ...... 48 \mathbbm ...... 44 local ring (O) see alphabets, math | \Male ( ) ...... 48 \mathbbmss ...... 44 \log (log) ...... 31,70 ♂ \male ( ) ...... 47 \mathbbmtt ...... 44 log-like symbols ...... 31, 71 ƒ \MaleMale ( ) ...... 48 mathbbol (package) ...... 44 logical operators () ...... 16 \maltese \mathbf ...... 71 and ...... see \wedge () ...... 56 \manboldkidney \mathbin ...... 70 not . . . . see \neg and \sim ().56 \manconcentriccircles \mathbold ...... 71 or ...... see \vee \manconcentricdiamond ().56 mathcal (euscript package option) \logof ( ) ...... 23 \mancone ( ) ...... 56 lollipop...... see ...... 44 \multimap \mancube ( ) ...... 56 longdivision ...... 38 \mathcal ...... 44 \manerrarrow () ...... 56 (⇐=)...... 28 \mathcent (¢) ...... 34 \Longleftarrow \manfilledquartercircle ()56 ←− \mathchoice ...... 63,64 \longleftarrow ( ) ...... 28 manfnt (package) . . 54, 56, 75, 76 ...... 57 \mathclose ...... 70 \Longleftrightarrow \manhpennib () ...... 56 (⇐⇒ ).28 mathcomp (package) ...... 43 \Longleftrightarrow \manimpossiblecube () .... 56 \longleftrightarrow (←→ ).28 mathdots (package) 41, 65, 75, 76 \mankidney () ...... 56 \Longmapsfrom (⇐=)" ...... 29 \mathds ...... 44 \manlhpenkidney () ...... 56 \longmapsfrom (←− )# ...... 29 mathematical symbols . . . 17–44 \manpenkidney () ...... 56 \Longmapsto (= ⇒) ...... 29 \mathfrak ...... 44 \longmapsto (,−→ ) ...... 28 \manquadrifolium ( ) ..... 56 \mathit ...... 44

\LongPulseHigh (&) ...... 45 \manquartercircle ( ) ..... 56 \mathnormal ...... 44 \LongPulseLow (') ...... 45 \manrotatedquadrifolium ( )56 \mathop ...... 70 \Longrightarrow (=⇒) ..... 28 \manrotatedquartercircle ( )56 \mathopen ...... 70 \longrightarrow (−→ ) ..... 28 \manstar () ...... 56 \mathord ...... 70 \looparrowdownleft (î)...30 \mantiltpennib () ...... 56 \mathpalette ...... 64 \looparrowdownright (ï)...30 \mantriangledown () ...... 56 \mathpunct ...... 70 \looparrowleft (ì) ...... 30 \mantriangleright () ..... 56 \mathpzc ...... 44 \looparrowleft (Z) ...... 29 \mantriangleup () ...... 56 \mathrel ...... 62,70 \looparrowright (í) ...... 30 \manvpennib () ...... 56 \mathring (˚) ...... 37 \looparrowright (\) ...... 29 \Mappedfromchar () ...... 31 \mathrm ...... 44 \Loosebearing ($) ...... 47 \mappedfromchar () ...... 31 mathrsfs (package) ...... 44, 75 \lor ...... see \vee \Mapsfrom (⇐)" ...... 29 mathscr (euscript package option) \LowerDiamond (o) ...... 53 \mapsfrom (←)# ...... 29 ...... 44 lowering . . . see \textlowering \Mapsfromchar ()û ...... 31 \mathscr ...... 44 \lozenge (♦) ...... 42 \Mapsfromchar ()" ...... 31 \mathsterling (£) ...... 34 \Lparen (() ...... 44 \mapsfromchar ()ß ...... 31 \max (max) ...... 31 \lrcorner ({) ...... 34 \mapsfromchar ()# ...... 31 \maya ...... 43 \lrcorner (o) ...... 34 \Mapsto (⇒) ...... 29 mbboard (package) ...... 44, 75 \lrJoin ...... see \Join \mapsto (,→) ...... 28 \mbox ...... 64 \lrtimes () ...... 24 \Mapstochar ()ú ...... 31 \measuredangle (>) ...... 42 \Lsh (è) ...... 30 \Mapstochar () ...... 31 \measuredangle () ...... 42

86 mechanical scaling ...... 67, 69 \muup (µ) ...... 32 \ng (ŋ) ...... 8 \medbullet () ...... 18 \MVAt (@) ...... 57 \ngeq (§) ...... 27 \medcirc () ...... 18 \MVEight (8) ...... 43 \ngeq (3) ...... 27 \Mercury (A ) ...... 46 \MVFive (5) ...... 43 \ngeqq (±) ...... 27 \Mercury (Â) ...... 46 \MVFour (4) ...... 43 \ngeqq (5) ...... 27 ? 9 \mercury ( ) ...... 45 \MVNine ( ) ...... 43 \ngeqslant (8) ...... 27 $ (1) ...... 43 \merge ( ) ...... 18 \MVOne \ngg () ...... 27 METAFONT (7) ...... 43 ...... 44, 67, 68, 70 \MVSeven \ngtr (£) ...... 27 METAFONT (6) ...... 43 book symbols . . . . 56 \MVSix \ngtr (≯) ...... 27 W (3) ...... 43 \mho ( ) ...... 42 \MVThree \ngtrapprox (É) ...... 27 (2) ...... 43 micro ...... see \textmu \MVTwo \ngtrapprox () ...... 27 µ (0) ...... 43 \micro ( ) ...... 43 \MVZero \ngtrless () ...... 27 MicrosoftWindows ...... 73 \ngtrsim (Ã) ...... 27 | N \mid ( ) ...... 23 \ngtrsim () ...... 27 ...... 35 \nabla (∇) ...... 42 \middle \ni (1) ...... 33 ({) ...... 13 \NAK (§) ...... 47 \midtilde \nialpha (¢) ...... 10 (min) ...... 31,70 \napprox () ...... 25 \min \nibar ...... see \ownsbar minus ...... see \napproxeq () ...... 24 \textminus \nibeta (©) ...... 10 \minuso (%) ...... 18 \nasymp () ...... 24 \NibLeft () ...... 50 minutes, angular . . . see \prime nath (package) ...... 34, 36, 75 miscellaneous symbols 42, 54–59 \natural () ...... 42,56 \NibRight () ...... 50 “Missing $ inserted” ..... 17 natural numbers (N) ...... see nibs ...... 50 \Mmappedfromchar () ...... 31 alphabets, math \NibSolidLeft ( ) ...... 50 navigationsymbols ...... 57 \mmappedfromchar () ...... 31 \NibSolidRight ( ) ...... 50 () ...... 24 \Mmapstochar () ...... 31 \nbacksim nicefrac (package) . . . 43, 75, 76 \nbacksimeq () ...... 24 \mmapstochar () ...... 31 \nichi ([) ...... 10 \nBumpeq () ...... 24 \Mobilefone (H) ...... 47 \niepsilon () ...... 10 \nbumpeq () ...... 24 \mod ...... 31 \nigamma ( ) ...... 10 \ncong () ...... 25 \models (|=) ...... 23,62 \niiota ()) ...... 10 \ncong () ...... 23 moduli space see alphabets, math \nilambda (2) ...... 10 \ncurlyeqprec (¸) ...... 25 monetary symbols ...... 14, 44 \niomega (>) ...... 10 \ncurlyeqsucc (¹) ...... 25 \moo (&) ...... 18 \niphi (C) ...... 10 \nDashV (+) ...... 25 \Moon (K ) ...... 46 \niplus (') ...... 23 \nDashv (+) ...... 25 \Moon (Á) ...... 46 \nisigma (O) ...... 10 \ndashV (/) ...... 25 S \nitheta (S) ...... 10 \morepawns ( ) ...... 59 \ndashv (') ...... 25 \niupsilon (V) ...... 10 \moreroom (U) ...... 59 \ndashVv (/) ...... 25 \niv ( ) ...... 34 \Mountain () ...... 58 \ne ...... see \neq \nj (7) ...... 10 mouse..... see \ComputerMouse \Nearrow () ...... 29 \nLeftarrow (ö) ...... 30 \MoveDown (») ...... 57 \nearrow (Õ) ...... 30 \nLeftarrow (H) ...... 29 \moverlay ...... 65 \nearrow (/) ...... 28, 64, 65 \nleftarrow (Ú) ...... 30 \MoveUp (º) ...... 57 \neg (¬) ...... 42 \nleftarrow (K) ...... 29 \mp (∓) ...... 17 negation . . . . see \neg and \sim \nLeftrightarrow (ø) ..... 30 \mu (µ) ...... 32 \Neptune (H ) ...... 46 \nLeftrightarrow (I) ..... 29 \multimap (#) ...... 23,24 \Neptune (È) ...... 46 \nleftrightarrow (Ü) ..... 30 \multimapboth () ...... 24 \neptune (@) ...... 45 \nleftrightarrow () . . 17, 29 \multimapbothvert () ..... 24 \neq () ...... 25 (¦) ...... 27 \multimapdot () ...... 24 \neq () ...... 26 \nleq (<) ...... 27 \multimapdotboth () ..... 24 \neqslantgtr (¹) ...... 27 \nleq (°) ...... 27 \multimapdotbothA () .... 24 \neqslantless (¸) ...... 27 \nleqq = \multimapdotbothAvert ()..24 \nequiv () ...... 24 \nleqq ( ) ...... 27 \multimapdotbothB () .... 24 \neswarrow (/0) ...... 64,65 \nleqslant (?) ...... 27 \multimapdotbothBvert ()..24 \Neutral ({) ...... 48 \nless (¢) ...... 27 \multimapdotbothvert () ... 24 \newmoon (N ) ...... 46 \nless (≮) ...... 27 \multimapdotinv () ...... 24 \newmoon () ...... 45 \nlessapprox (È) ...... 27 \multimapinv () ...... 24 \newtie (a) ...... 11 \nlessapprox () ...... 27 multiple accents per character 65 \nexists (E) ...... 34 \nlessgtr () ...... 27 \Mundus (m) ...... 57 \nexists (V) ...... 33 \nlesssim (Â) ...... 27 musical notes ...... 15, 42, 56 \NG (Ŋ) ...... 8 \nlesssim () ...... 27

87 \nll () ...... 27 \nsqsupset () ...... 26 \nvdash (&) ...... 25 \nmid () ...... 23 \nsqsupseteq () ...... 26 \nvdash () ...... 23 \nnearrow (() ...... 29 \nsqsupseteq () ...... 26 \nVvash (.) ...... 25 \nnwarrow ()) ...... 29 \nsqsupseteqq () ...... 26 \Nwarrow () ...... 29 \NoBleech (Ì) ...... 57 \nSubset () ...... 26 \nwarrow (Ô) ...... 30 \NoChemicalCleaning (¨) ... 57 \nSubset () ...... 26 \nwarrow (2) ...... 28,64 \NoIroning (²) ...... 57 \nsubset () ...... 26 \nwsearrow (23) ...... 64 \NoSun () ...... 58 \nsubseteq ( ) ...... 26 " O not...... see \neg \nsubseteq ( ) ...... 26 \not ...... 25 \nsubseteqq ( ) ...... 26 \O (Ø) ...... 8 - not equal (=vs. =) ...... 25 \nsubseteqq ( ) ...... 26 \o (ø)...... 8 (£) ...... 25 o \notasymp () ...... 25 \nsucc o ( ) ...... 32 () ...... 23 f \notbackslash (−\ ) ...... 46 \nsucc \oasterisk ( ) ...... 19 (É) ...... 25 n \notbot (M) ...... 34 \nsuccapprox \obackslash ( ) ...... 19 () ...... 24 , \notdivides ( ) ...... 25 \nsuccapprox \obar ( ) ...... 18 \nsucccurlyeq (§) ...... 25 - \notequiv () ...... 25 \oblong ( ) ...... 18 \nsucccurlyeq () ...... 24 k \notin (R) ...... 34 \obot ( ) ...... 19 \nsucceq («) ...... 25 . \notin () ...... 34 \obslash ( ) ...... 18 \nsucceq () ...... 23 e \notni () ...... 34 \ocirc ( ) ...... 19 \nsucceqq () ...... 24 \notowner (S) ...... 34 \ocircle ( ) ...... 18 \nsuccsim (Ã) ...... 25 g \notowns ... see \notowner and \ocoasterisk ( ) ...... 19 \nsuccsim () ...... 24 A \notni \octagon ( ) ...... 52 \nSupset () ...... 26 ‘ \notperp (M) ...... 25 \Octosteel ( ) ...... 47 \nSupset () ...... 26 \notslash (−/ ) ...... 46 \od (a) ...... 13 \nsupset () ...... 26 ˚(c) ...... 19 \nottop (L) ...... 34 \odiv \nsupseteq () ...... 26 (d) ...... 19 \NoTumbler () ...... 57 \odot \nsupseteq ($) ...... 26 () ...... 17 \novelty (N) ...... 59 \odot \nsupseteqq () ...... 26 (¨) ...... 19 \nparallel (∦) ...... 23 \odplus \nsupseteqq (') ...... 26 (Œ) ...... 8 \nplus () ...... 18 \OE ntheorem (package) ...... 42 (œ)...... 8 \nprec (¢) ...... 25 \oe \nthickapprox () ...... 24 (e) ...... 14 \nprec (⊀) ...... 23 \officialeuro \ntriangleleft () ...... 28 ogonek ...... see accents \nprecapprox (È) ...... 25 \ntriangleleft (D) ...... 28 (/) ...... 18 \nprecapprox () ...... 24 \ogreaterthan \ntrianglelefteq () ..... 28 (a{) ...... 13 \npreccurlyeq (¦) ...... 25 \ohill \ntrianglelefteq (B) ..... 28 ohm ...... see () ...... 24 \textohm \npreccurlyeq \ntrianglelefteqslant (*).28 Ω ª \ohm ( )+ ...... 43 \npreceq ( ) ...... 25 \ntriangleright () ...... 28 \oiiint ( ) ...... 22 \npreceq ( ) ...... 23 \ntriangleright (C) ...... 28 # \oiiintclockwise ( ) ..... 22 \npreceqq ( ) ...... 24 \ntrianglerighteq () ..... 28 ' Â \nprecsim ( ) ...... 25 \ntrianglerighteq (E) ..... 28 \oiiintctrclockwise· ( )..22 \nprecsim ( ) ...... 24 \ntrianglerighteqslant (+)28 \oiint () ...... 21 (÷) ...... 30 \nRightarrow \ntwoheadleftarrow () .... 24 \oiint ( ) ...... 20,22 \nRightarrow (J) ...... 29 \ntwoheadrightarrow () ... 24 \oiint ( ) ...... / 22 \nrightarrow (Û) ...... 30 ν \nu ( ) ...... 32 \oiintclockwise ( )3 ...... 22 \nrightarrow (L) ...... 29 nullset ...... 42 \oiintctrclockwise¶ ( ) ... 22 \nshortmid () ...... 23 number...... see \textnumero \oint ( ) ...... 21 \nshortparallel () ...... 23 number sets see alphabets, math H \oint ( ) ...... 20 \nsim () ...... 25 numbers ...... see digits ( ) ...... 22 \nsim () ...... 23 \nuup (ν) ...... 32 \ointclockwise \nsimeq () ...... 25 \nvargeq («) ...... 27 \ointclockwise ( ) ...... 22 \nsimeq () ...... 24 \nvarleq (ª) ...... 27 \ointctrclockwise ( ) ..... 22 \nsqSubset () ...... 26 \nvarparallel () ...... 24 \ointctrclockwise ( ) ..... 22 \nsqsubset () ...... 26 \nvarparallelinv () ...... 24 old-styledigits...... 15 \nsqsubset () ...... 26 \nVDash (*) ...... 25 \oldstylenums ...... 15 \nsqsubseteq () ...... 26 \nVDash () ...... 23 \oleft (h) ...... 19 \nsqsubseteq () ...... 26 \nVdash (.) ...... 25 \olessthan (0) ...... 18 \nsqsubseteqq () ...... 26 \nVdash (!) ...... 24 \Omega (Ω) ...... 32 \nsqSupset () ...... 26 \nvDash (*) ...... 25 \omega (ω) ...... 32 \nsqsupset () ...... 26 \nvDash () ...... 23 \omegaup (ω) ...... 32

88 \ominus (a) ...... 19 package options mathcomp ...... 43 \ominus (4) ...... 17 a (esvect) ...... 40 mathdots . . . . 41, 65, 75, 76 \onlymove (F) ...... 59 bbgreekl (mathbbol) .... 44 mathrsfs ...... 44,75 \oo (@) ...... 10 b (esvect) ...... 40 mbboard ...... 44,75 \open (z) ...... 13 c (esvect) ...... 40 nath ...... 34,36,75 \openJoin () ...... 24 d (esvect) ...... 40 nicefrac ...... 43,75,76 \openo (=) ...... 10 e (esvect) ...... 40 ntheorem ...... 42 \openo (c) ...... 11 f (esvect) ...... 40 overrightarrow ...... 38,75 \openo (B) ...... 8 g (esvect) ...... 40 phonetic . . . . . 11, 13, 62, 75 \opentimes () ...... 24 h (esvect) ...... 40 pifont . . 8, 49–52, 54, 55, 60, operators mathcal (euscript) ...... 44 75, 76 binary ...... 17–19 mathscr (euscript) ...... 44 polynom ...... 38 logical . see logical operators sans (dsfont) ...... 44 psnfss ...... 51 set...... see set operators varg (txfonts/pxfonts)...33 pxfonts 17, 18, 22–29, 31–34, \oplus (`) ...... 19 packages 42, 44, 60, 72 \oplus (⊕) ...... 17,60 accents ...... 65,75,76 skak ...... 59,75,76 amsbsy ...... 71 (o) ...... 59 skull ...... 54,75,76 \opposbishops amsfonts 17, 23, 25, 28, 42, 44 (C) ...... 46 slashed ...... 63 \opposition amsmath ...... 6,31,70 opticalscaling ...... 67 stmaryrd . 18, 20, 23, 26, 28, amssymb 6, 17, 23, 25, 28, 42, options . . . . see package options 29, 31, 34, 35, 61, 73, 75, 76 44, 75–77 or...... see textcomp 6, 7, 11, 14, 15, 28, \vee amstext ...... 63,64 \oright (i) ...... 19 36, 43, 45, 56, 60, 72, 73, 75, ar ...... 45,75 76 \OrnamentDiamondSolid (q).55 ascii ...... 47,72,75 timing ...... 45 orthogonal to ...... see \bot bbding 49–53, 55, 61, 75, 76 tipa . . . 9–11, 13, 62, 75, 76 \oslash (m) ...... 19 bbm ...... 44,75 trfsigns ...... 25, 34, 37, 75 \oslash (6) ...... 17 bbold ...... 44,75 trsym ...... 25,75,76 \otimes (b) ...... 19 bm ...... 71,75,76 txfonts 17, 18, 22–29, 31–34, \otimes (⊗) ...... 17 braket ...... 35 42, 44, 60, 62, 72, 75, 76 \otop (j) ...... 19 calrsfs ...... 44 ulsy ...... 19,30,75 \otriangleup (o) ...... 19 cancel ...... 38 underscore ...... 7 ovals...... 53 chemarrow . . . . . 30, 39, 75 undertilde ...... 40, 75, 76 \ovee (1) ...... 18 chemarr ...... 39,75,76 hkkikkj units ...... 43 dingbat . . 50, 54, 61, 75, 76 \overbrace ( ) ...... 40 universa . . . . . 54, 57, 75, 76 z}|{ dsfont ...... 44,75 upgreek ...... 33,75,76 \overbrace ( ) ...... 38 esint ...... 22,75 upquote ...... 72 \overbracket ...... 65,66 esvect ...... 40,75 url ...... 72 ( ) ...... 66 eufrak ...... 44 \overbrackethkkkkj wasysym ...... 8,14, eurosym ...... 14,75,76 \overgroup ( ) ...... 40 15, 17, 18, 20, 23, 25–28, 42, ←− euscript ...... 44,75,76 \overleftarrow ( ) ...... 38 45–47, 51, 52, 56, 61, 75, 76 ←→ fclfont ...... 75 \overleftrightarrow ( )..39 wsuipa 10, 13, 61, 62, 65, 75, fc ...... 8,11 \overline ...... 38 76 ﬁxmath ...... 71 \overline ( ) ...... 38 yfonts ...... 44,75,76 fontenc ...... 6,8,11,73 \overparenthesis ...... 65,66 yhmath 37, 38, 40, 41, 65, 75 z{ gensymb ...... 43 zapfchan ...... 75 \overparenthesis ( ) ..... 66 graphics ...... 62 =⇒ \Overrightarrow ( ) ...... 38 graphicx ...... 62 Pakin, Scott ...... 1, 73 ¤ overrightarrow (package) . . 38, 75 ifsym 45, 53, 58, 59, 61, 75, 76 \PaperLandscape ( ) ...... 59 −→ \overrightarrow ( ) ...... 38 isoent ...... 73 \PaperPortrait (£) ...... 59 \overring (x) ...... 13 latexsym . 17, 23, 25, 28, 42, par...... see \invamp \ovoid (l) ...... 19 60, 75, 76 paragraph mark ...... see \P \owedge (2) ...... 18 manfnt ...... 54, 56, 75, 76 parallel . . see also \varparallel \owns ...... see \ni marvosym . 14, 43, 46–49, 54, \parallel () ...... 23 \owns (Q) ...... 34 57, 61 \ParallelPort (Ñ) ...... 47 \ownsbar (W) ...... 34 matbbol ...... 44 \partial (B) ...... 34 mathabx . . 19, 21, 23–28, 30, \partial (∂) ...... 33 P 31, 34, 35, 37, 40, 42, 43, 46, \partialslash (C) ...... 34 \P (¶) ...... 7,74 54, 60, 61, 75, 77 parts per thousand ...... see \p@ ...... 65 mathbbol ...... 44 \textperthousand

89 \passedpawn (r) ...... 59 \pm (±) ...... 17 \qside (M) ...... 59 pawn ...... see chess symbols \pmb ...... 71 \quarternote (♩) ...... 56 \Peace () ...... 55 \pmod ...... 31 quaternions (H).see alphabets, \PencilLeft () ...... 50 \pod ...... 31 math (I) ...... 56 queen ...... see chess symbols \PencilLeftDown () ...... 50 \pointer \Pointinghand (Z) ...... 54 \quotedblbase („) ...... 8 \PencilLeftUp () ...... 50 \polishhook (~) ...... 13 \quotesinglbase (‚) ...... 8 \PencilRight ( ) ...... 50 polygons ...... 52 \PencilRightDown () ..... 50 polynom (package) ...... 38 R \PencilRightUp () ...... 50 polynomialdivision ...... 38 \r (˚a) ...... 11 pencils ...... 50 PostScript fonts 14, 33, 44, 49, 51, \Radiation () ...... 59 \pentagon (D) ...... 52 60, 70 radicals . . . see \sqrt and \surd percentsign ...... see \% \pounds (£) ...... 7,74 \Radioactivity (j) ...... 48 E P \permil ( ) ...... 15 power set ( )... see alphabets, \Rain () ...... 58 \Perp () ...... 24 math \RainCloud () ...... 58 \perp (⊥) ...... 23,64 \Pr (Pr) ...... 31 raising . . . . . see \textraising \perthousand (‰) ...... 43 \prec (≺) ...... 23 \RaisingEdge ( ) ...... 45 \Pfund (£) ...... 14 \precapprox (Æ) ...... 24 \Rangle (>) ...... 44 pharmaceutical prescription . see \precapprox () ...... 23 \rAngle (<<) ...... 36 \textrecipe \preccurlyeq (¤) ...... 24 \rangle (<) ...... 35 \Phi (Φ)...... 32 \preccurlyeq ()) ...... 23 \rarrowfill ...... 39 \phi (φ) ...... 32 \precdot (Ì) ...... 24 rational numbers (Q) ...... see \phiup (φ) ...... 32 \preceq (9) ...... 23 alphabets, math ¨ \preceqq () ...... 24 \Phone ( ) ...... 55 rationalized Planck constant . see F \precnapprox (Ê) ...... 25 \phone ( ) ...... 56 \hbar \precnapprox () ...... 23 \PhoneHandset (©) ...... 55 \Rbag () ...... 34 \precneq (¬) ...... 25 phonetic (package) . 11, 13, 62, 75 \rbag () ...... 34 \precneqq () ...... 24 phonetic symbols ...... 8–11 \rbbbrack (w) ...... 35 \precnsim (Ä) ...... 25 \photon () ...... 45 \Rbrack (]) ...... 44 \precnsim () ...... 23 physicalsymbols ...... 45 \rBrack (]])...... 36 \precsim (À) ...... 24 \Pi (Π)...... 32 \rc (a©) ...... 13 \precsim (+) ...... 23 \pi (π) ...... 32 \rCeil (==) ...... 36 A prescription . . . see \textrecipe \Pickup ( ) ...... 47 \rceil (=) ...... 35 \prime (:) ...... 42 pifont (package) 8, 49–52, 54, 55, \rcorners (w) ...... 34 \Printer (Ò) ...... 47 60, 75, 76 \Re (>) ...... 33 probabilistic independence . . . 64 pilcrow ...... see \P Q real numbers (R). see alphabets, ( ) ...... 20 pipe ...... see \textpipe \prod math ë \projlim (projlim) ...... 31 \Pisces ( ) ...... 46 recipe ...... see \textrecipe G pronunciation symbols . .... see \pisces ( ) ...... 46 \recorder (K) ...... 56 \Pisymbol ...... 60 phonetic symbols \Rectangle (u) ...... 53 \pitchfork (&) ...... 42 proof,endof ...... 42 v \pitchfork (&) ...... 23 \propto (9) ...... 42 \RectangleBold ( ) ...... 53 \piup (π) ...... 32 \propto (∝) ...... 23 rectangles ...... 53,54 \planck (¯h) ...... 11 \ProvidesPackage ...... 75 \RectangleThin (t) ...... 53 ˜ \Plane ( ) ...... 55 \Psi (Ψ)...... 32 \Rectpipe ( ) ...... 47 ψ planets ...... 45,46 \psi ( ) ...... 32 \Rectsteel (”) ...... 47 ψ playing cards . . . . see card suits \psiup ( ) ...... 32 reduced quadrupole moment see psnfss (package) ...... 51 \rqm \Plus (') ...... 50 pulse diagram symbols ...... 45 \reflectbox ...... 62 plus-or-minus sign . . . . . see \pm \PulseHigh ($) ...... 45 registered trademark ...... see ( \PlusCenterOpen ( ) ...... 50 \PulseLow (%) ...... 45 \textregistered © \pluscirc ( ) ...... 19 punctuation ...... 8 relational symbols ...... 23 \PlusOutline (&) ...... 50 \pwedge (U) ...... 11 binary ...... 23–27 plusses ...... 50,51 pxfonts (package) . 17, 18, 22–29, negated binary . . . . . 23–25 \PlusThinCenterOpen ()) ... 50 31–34, 42, 44, 60, 72 triangle ...... 28 \Pluto (I) ...... 46 \Relbar (=) ...... 30,62 \Pluto (É) ...... 46 Q \relbar (−) ...... 30,62 \pluto (H) ...... 45 Q.E.D...... 42 \restoresymbol ...... 60

90 \restriction ...... see \rightrightarrows (Ñ)....30 \samebishops (s) ...... 59 \upharpoonright \rightrightarrows (⇒) .... 29 sans (dsfont package option) . . 44 (æ) ...... 30 (Ù)...30 \restriction \rightrightharpoons \satellitedish (I) ...... 54 retracting . see (Q) ...... 49 \textretracting \Rightscissors \Saturn (F ) ...... 46 return ...... see carriage return (4) ...... 18 \rightslice \Saturn (Æ) ...... 46 \revD (¢) ...... 11 \rightsquigarrow (ù) .... 30 . \saturn (R) ...... 45 . \rightsquigarrow (W) ..... 29 \revddots (. ) ...... 65 \savesymbol ...... 60 \rightt (o) ...... 13 \reve ( ) ...... 10 \Sborder (S) ...... 54 (%) ..... 42 \reveject (f) ...... 10 \rightthreetimes scaling () ..... 17 \revepsilon () ...... 10,62 \rightthreetimes mechanical ...... 67, 69 (d) .... 50 reversesolidus...... see \rightthumbsdown optical...... 67 \rightthumbsup (u) ...... 50 \textbackslash \scd () ...... 10 \righttoleftarrow (ý)....30 reversedsymbols ...... 62 \scg () ...... 10 \Righttorque (') ...... 47 \reversedvideodbend ( )..54 \schwa () ...... 10 c \rightturn (P) ...... 56 \revglotstop ( ) ...... 10 \schwa (e) ...... 11 ¶ \ring (˚) ...... 37 \Rewind ( ) ...... 57 \sci (*) ...... 10 ´ ring equal to ...... see \circeq \RewindToIndex ( ) ...... 57 scientiﬁcsymbols...... 45–48 \RewindToStart (µ) ...... 57 ring in equal to . . . . see \eqcirc \ScissorHollowLeft (§) ... 49 \rfilet (?) ...... 35 \riota ( ) ...... 11 (O) ...... 54 \ScissorHollowRight (¦)..49 \rFloor (??) ...... 36 \rip () ...... 24 ¤ \rfloor (?) ...... 35 \risingdotseq \ScissorLeft ( ) ...... 49 9 . \risingdotseq ( ) ...... 23 \ScissorLeftBrokenBottom (£) \rgroup (;) ...... 35 \rJoin ( ) ...... 24 ...... 49 L \rlap ...... 53,64 \RHD ( ) ...... 18 9 \ScissorLeftBrokenTop (¥).49 \rhd ( ) ...... 17,18 : \rmoustache ( ) ...... 35 \ScissorRight (¡) ...... 49 \rho (ρ) ...... 32 rook ...... see chess symbols \rhoup (ρ) ...... 32 \ScissorRightBrokenBottom ( ) roots...... see \right ...... 35,36 \sqrt ...... 49 ...... 62 \RIGHTarrow (L) ...... 56 \rotatebox \ScissorRightBrokenTop (¢)49 rotatedsymbols...... 62 \Rightarrow ...... 57 m scissors ...... 49 (⇒ vs. : vs. ñ)61 \rotm ( ) ...... 11 : \Rightarrow \scn ( ) ...... 10 (⇒) ...... 17,28 \rotOmega ( ) ...... 11 ç \Rightarrow r \Scorpio ( ) ...... 46 (:) ...... 57 \rotr ( ) ...... 11 S \Rightarrow A \scorpio ( ) ...... 46 (Ñ) ...... 30 \rotvara ( ) ...... 11 J \rightarrow w \scr ( ) ...... 10 \rightarrow (→) ...... 28 \rotw ( ) ...... 11 script letters see alphabets, math (y) ...... 11 \rightarrowtail (b) ...... 29 \roty \scripta (¡) ...... 10 \RoundedLsteel (Ÿ) ...... 47 \rightarrowtriangle (3) ... 29 \scriptg () ...... 10 \RoundedTsteel () ...... 47 \rightbarharpoon (Ý) ..... 30 \scriptscriptstyle . . . . 63, 64 \RoundedTTsteel () ...... 47 \RIGHTCIRCLE (M) ...... 56 \scriptstyle ...... 63,64 \Rparen ()) ...... 44 \RIGHTcircle (M) ...... 56 \scriptv (Y) ...... 10 \rqm (I-) ...... 63 \Rightcircle (N) ...... 56 \scu (W) ...... 10 \rrbracket () ...... 35 \RightDiamond (?) ...... 53 \scy (]) ...... 10 \rrceil (5) ...... 34 \rightharpoondown (ã)....30 seagull . . . . . see \textseagull \rrfloor (6) ...... 34 \rightharpoondown () .... 28 \Searrow () ...... 29 \Rrightarrow (i) ...... 29 \rightharpoonup (á) ...... 30 \searrow (×) ...... 30 \rrparenthesis (7) ...... 34 \rightharpoonup ( ) ...... 28 \searrow (3) ...... 28,64 \RS () ...... 47 \rightleftarrows (Õ) ..... 30 \sec (sec)...... 31 \Rsh (é) ...... 30 \rightleftarrows (R) ..... 29 \second (2) ...... 42 \Rsh (Y) ...... 29 \rightleftharpoon (á)....30 seconds, angular . . . see \second \rtimes ( ) ...... 19 \rightleftharpoons (é)...30 \secstress (i) ...... 13 \rtimes () ...... 17 \rightleftharpoons (g) ... 29 sectionmark ...... see \S \rtriple ...... 36 \rightleftharpoons ( ) ... 28 ¡ \rVert (||) ...... 36 \SectioningDiamond ( ) ... 59 \rightleftharpoonsfill .... 39 \see (l) ...... 59 \rightmoon (L ) ...... 46 S segmenteddigits ...... 45 \rightmoon (O) ...... 45 \S (§) ...... 7,74 \selectfont ...... 6 \rightp (w) ...... 13 safety-relatedsymbols ...... 48 semanticvaluation...... see \rightpointleft (L) ..... 50 \Sagittarius (è) ...... 46 \llbracket/\rrbracket and \rightpointright (N) .... 50 \sagittarius (Q) ...... 46 \lbbbrack/\rbbbrack

91 semidirect products . . 17, 19, 42 \SmallCircle (E) ...... 53 \sqcupplus () ...... 18 \seppawns (q) ...... 59 \SmallCross () ...... 53 \sqdoublecap (^) ...... 19 \sqdoublecup (_) ...... 19 \SerialInterface (Î) ..... 47 \SmallDiamondshape (F) ... 53 \SerialPort (Ð) ...... 47 \smallfrown (5) ...... 23 \sqiiint ( ) ...... 22 set operators \sqiint ( ) ...... 22 \SmallHBar () ...... 53 intersection . . . . . see \cap \sqiint ( ) ...... 22 \SmallLowerDiamond () ... 53 union...... see \cup \sqint ( ) ...... 22 \ \smallpencil (P) ...... 50 \setminus ( ) ...... 17 \sqint ( ) ...... 22 \SmallRightDiamond (O) ... 53 √ SGML ...... 73 \sqrt ( ) ...... 38,64 \smallsetminus () ...... 17 sha . . see Tate-Shafarevich group \sqSubset () ...... 26 \smallsmile (7) ...... 23 \sharp ( ) ...... 42,56 \sqsubset () ...... 26 ¡ @ \Shilling ( ) ...... 14 \SmallSquare ( ) ...... 53 \sqsubset (8) ...... 25,26 8 \shortdownarrow ( ) ...... 29 \SmallTriangleDown (C) ... 53 \sqsubseteq () ...... 26 × \ShortFifty ( ) ...... 57 \smalltriangledown () .... 19 \sqsubseteq (D) ...... 25 \ShortForty (Ù) ...... 57 \SmallTriangleLeft (B) ... 53 \sqsubseteqq () ...... 26 (9) ...... 29 \shortleftarrow () .... 19 \sqsubsetneq () ...... 26 \smalltriangleleft \shortmid ( ) ...... 23 \sqsubsetneqq () ...... 26 Ô \SmallTriangleRight (D) ... 53 \ShortNinetyFive ( ) ..... 57 \sqSupset () ...... 26 \smalltriangleright () ... 19 \shortparallel ( ) ...... 23 \sqsupset () ...... 26 " (A) ..... 53 \ShortPulseHigh ( ) ...... 45 \SmallTriangleUp \sqsupset (9) ...... 25,26 () ...... 19 \ShortPulseLow (#) ...... 45 \smalltriangleup \sqsupseteq ( ) ...... 26 \shortrightarrow (:) ..... 29 \SmallVBar ( ) ...... 53 \sqsupseteq (E) ...... 25 \ShortSixty (Ö) ...... 57 \smile (") ...... 23 \sqsupseteqq () ...... 26 \ShortThirty (Û) ...... 57 \Smiley (©) ...... 57 \sqsupsetneq () ...... 26 \shortuparrow (;) ...... 29 \smiley (T) ...... 56 \sqsupsetneqq () ...... 26 ...... 58 \showclock smiley faces ...... 47, 56, 57 \Square (0) ...... 53 \SI ( ) ...... 47 \Snow ( ) ...... 58 \Square (p vs. f vs. 0)....61 \Sigma (Σ) ...... 32 \SnowCloud ( ) ...... 58 \Square (p) ...... 51 \sigma (σ) ...... 32 ` f \sigmaup (σ) ...... 32 \Snowflake ( ) ...... 52 \Square ( ) ...... 53 ¥ \sim (∼) ...... 23,72 \SnowflakeChevron (^) .... 52 \square ( ) ...... 19 p \simeq (@) ...... 23 \SnowflakeChevronBold (_).52 \square ( ) ...... 42 \sin (sin) ...... 31 snowﬂakes...... 52 square root ...... see \sqrt \sinh (sinh) ...... 31 \SO (♫) ...... 47 hooked ...... see \hksqrt \SquareCastShadowBottomRight \SixFlowerAlternate (O) ... 52 \SOH () ...... 47 (k) ...... 53 \SixFlowerAltPetal (U)...52 space thin...... 71 \SquareCastShadowTopLeft (m) (M)..52 \SixFlowerOpenCenter space,visible...... 7 ...... 53 (Q).52 \SixFlowerPetalDotted spades (suit) ...... 42, 55 \SquareCastShadowTopRight (l) \SixFlowerPetalRemoved (L)52 \spadesuit (♠) ...... 42 ...... 53 \SixFlowerRemovedOpenPetal \Sparkle (]) ...... 52 \Squaredot (÷) ...... 43 ([) ...... 52 — \SparkleBold (\) ...... 52 \Squarepipe ( ) ...... 47 \SixStar (G) ...... 52 sparkles ...... 52 squares ...... 53,54 \SixteenStarLight (K) .... 52 “special”characters...... 7 \SquareShadowA ( ) ...... 53 skak (package) ...... 59, 75, 76 \SpecialForty (Ú) ...... 57 \SquareShadowB (¡) ...... 53 ? skull (package) ...... 54,75,76 \sphericalangle ( ) ...... 42 \SquareShadowBottomRight (h) t \skull (A) ...... 54 \sphericalangle ( ) ...... 42 ...... 53 * \slash (/) ...... 72 \SpinDown () ...... 53 \SquareShadowC (¢) ...... 53 \slashb (§) ...... 10 ) \SpinUp () ...... 53 \SquareShadowTopLeft (j)..53 \slashc ( ) ...... 10 \splitvert ...... 47 \SquareShadowTopRight (i).53 \slashd () ...... 10 \splitvert (¦) ...... 47 g slashed (package) ...... 63 \sqbullet ( ) ...... 19 \SquareSolid ( ) ...... 53 “ \slashed ...... 63 \sqcap ([) ...... 19 \Squaresteel ( ) ...... 47 slashedletters ...... 63 \sqcap (B) ...... 17 \squarewithdots (B) ...... 54 slashed.sty (ﬁle) ...... 63 \sqcapplus () ...... 18 \squplus (]) ...... 19 \slashu (U) ...... 10 \sqcup (\) ...... 19 \SS (SS) ...... 8 \Sleet () ...... 58 \sqcup (C) ...... 17 \ss (ß) ...... 8

92 \ssearrow (<) ...... 29 \succnsim (Å) ...... 25 definition ...... 17, 66 \sslash (=) ...... 18 \succnsim () ...... 23 dictionary . . . see symbols, \sswarrow (>) ...... 29 \succsim (Á) ...... 24 phonetic \stackrel ...... 17,66 \succsim ($) ...... 23 dingbat ...... 49–55 \star (#) ...... 17,65 such thatP (3) ...... 62 dot ...... 41 Star of David ...... 51, 52 \sum ( ) ...... 20 electrical ...... 45 stars...... 42,51,52 \Summit () ...... 58 engineering ...... 45, 47 statistical independence ..... 64 genealogical ...... 56 \SummitSign () ...... 58 sterling ...... see \pounds general ...... 56 \Sun (@) ...... 46 stmaryrd (package) 18, 20, 23, 26, information ...... 54 À @ 28, 29, 31, 34, 35, 61, 73, 75, \Sun ( vs. vs. ) ...... 61 informator ...... 59 À 76 \Sun ( ) ...... 46 Knuth’s...... 54,56 stochastic independence see \bot \Sun () ...... 58 laundry ...... 57 \StoneMan () ...... 58 \sun (☼) ...... 56 letter-like...... 33,34 \Stopsign (!) ...... 48 \SunCloud () ...... 58 linguistic ...... 8–11 \StopWatchEnd () ...... 58 \SunshineOpenCircled (T)..55 log-like ...... 31,71 \sup (sup) ...... 31 mathematical ...... 17–44 \StopWatchStart () ...... 58 METAFONT superscripts book ...... 56 \stress (h) ...... 13 new symbols used in . . . . 63 miscellaneous . . . 42, 54–59 \strictfi () ...... 24 supersets...... 25,26 monetary ...... 14, 44 \strictif () ...... 24 () ...... 26 navigation ...... 57 \strictiff () ...... 24 \Supset \Supset (;) ...... 26 phonetic ...... 8–11 \StrokeFive (;) ...... 59 physical...... 45 \supset () ...... 26 :::: pulse diagram ...... 45 \StrokeFour ( ) ...... 59 \supset (⊃) ...... 25 relational ...... 23 \StrokeOne (:) ...... 59 \supseteq ( ) ...... 26 reversed...... 62 \StrokeThree (:::) ...... 59 \supseteq (⊇) ...... 25 rotated ...... 62 :: \supseteqq () ...... 26 \StrokeTwo ( ) ...... 59 safety-related...... 48 \supseteqq (<) ...... 26 \STX ( ) ...... 47 scientific ...... 45–48 → \supsetneq () ...... 26 \SUB ( ) ...... 47 subset and superset . 25, 26 \supsetneq (,) ...... 26 subscripts technological ...... 45–48 \supsetneqq () ...... 26 new symbols used in . . . . 63 T Xbook ...... 54,56 \supsetneqq (#) ...... 26 E \Subset ( ) ...... 26 upside-down...... 62 = \supsetplus (A) ...... 26 \Subset ( ) ...... 26 variable-sized ...... 20–22 \supsetpluseq (B) ...... 26 \subset ( ) ...... 26 √ weather ...... 58 \subset (⊂) ...... 25 \surd ( ) ...... 42 zodiacal...... 46 \subseteq () ...... 26 \SurveySign ( ) ...... 58 symbols.tex (file) ...... 60, 75 \subseteq (⊆) ...... 25 \Swarrow ( ) ...... 29 Ö \SYN ( ) ...... 47 \subseteqq () ...... 26 \swarrow ( ) ...... 30 0 \subseteqq (:) ...... 26 \swarrow ( ) ...... 28, 64, 65 T swungdash...... see \sim \subsetneq ( ) ...... 26 \T ...... 8 (a) ...... 13 \subsetneq (%) ...... 26 \syl (a) ...... 11 j \t \subsetneqq () ...... 26 \syllabic ( ) ...... 13 tacks...... 23,33 ( Symbol (PostScript font) . 33, 60 \subsetneqq ( ) ...... 26 \taild () ...... 10 ? symbols \subsetplus ( ) ...... 26 \tailinvr (H) ...... 10 @ alpine ...... 58 \subsetpluseq ( ) ...... 26 \taill (0) ...... 10 APL ...... 46 subsets ...... 25,26 \tailn (9) ...... 10 H astrological ...... 46 \succ ( ) ...... 23 \tailr (F) ...... 10 Ç \succapprox ( ) ...... 24 astronomical ...... 45, 46 \tails (L) ...... 10 \succapprox ( ) ...... 23 biological...... 48 \tailt (P) ...... 10 ¥ \succcurlyeq ( ) ...... 24 body-text ...... 7–16 \tailz (_) ...... 10 ! \succcurlyeq ( ) ...... 23 bold ...... 71 \talloblong (C) ...... 18 \succdot (Í) ...... 24 chess ...... 59 tallymarkers...... 59 I \succeq ( ) ...... 23 clock ...... 58 \tan (tan)...... 31 \succeqq ( ) ...... 24 communication...... 47 \tanh (tanh) ...... 31 \succnapprox (Ë) ...... 25 computer hardware . . . . . 47 \Tape ( ) ...... 55 \succnapprox () ...... 23 contradiction ...... 17, 30 \succneq () ...... 25 currency ...... 14, 44 \Taschenuhr () ...... 58 \succneqq ( ) ...... 24 dangerous bend ...... 54 Tate-Shafarevich group (X)..60

93 \tau (τ) ...... 32 \textbraceleft ({) ...... 7 \textdotacute (a) ...... 12 \Taurus (Q) ...... 46 \textbraceright (}) ...... 7 \textdotbreve (a¨ ) ...... 12 \Taurus (á) ...... 46 \textbrevemacron (a©¨) ...... 11 \textdoublebaresh (S) ...... 9 \taurus (V) ...... 46 \textbrokenbar (¦) . . . . . 15, 74 \textdoublebarpipe (}) ..... 9 \tauup (τ) ...... 32 \textbullet (•) ...... 7,15 \textdoublebarslash (=/ ) .... 9 \tccentigrade (℃) ...... 43 \textbullseye (ò) ...... 9 \textdoublegrave (a ) ...... 12 \tcmu (µ) ...... 43 \textcelsius (℃) ...... 45 \textdoublepipe ({) ...... 9 \tcohm (Ω) ...... 43 \textceltpal ( ) ...... 9 \textdoublevbaraccent (a)..12 \tcpertenthousand (‱) ... 43 \textcent (¢) ...... 14,74 \textdoublevertline () .... 9 \tcperthousand (‰) ...... 43 \textcentoldstyle (¢) ..... 14 \textdownarrow (↓) ...... 28 \td (a..) ...... 13 \textchi (X) ...... 9 \textdownstep ( ) ...... 9 technological symbols . . . 45–48 \textcircled (○) ...... 11 \textdyoghlig (Ã) ...... 9 \Telefon (T) ...... 47 \textcircledP (℗) ...... 15 \textdzlig (dz ) ...... 9 8 \Telephone (() ...... 59 \textcircumacute (a) ...... 11 \texteightoldstyle ( ) .... 15 \textcircumdot (a¢ ) ...... 12 \textellipsis (...) ...... 7 \Tent () ...... 58 \textcloseepsilon (Å) ...... 9 \textemdash (—) ...... 7 \tesh (Q) ...... 10 \textcloseomega (Ñ) ...... 9 \textendash (–) ...... 7 testfont.dvi (file) ...... 69 \textcloserevepsilon (Æ) .... 9 \textepsilon (E) ...... 9 testfont.tex (file) . . . . . 68, 69 \textcolonmonetary (₡) .... 14 \textesh (S) ...... 10 T X ...... 60, 62–70, 72, 75 E \textcommatailz (Þ) ...... 9 \textestimated (℮) ...... 15 T Xbook, The ...... 62–66, 70 E textcomp (package) . 6, 7, 11, 14, \texteuro (€) ...... 14 symbols from ...... 54, 56 15, 28, 36, 43, 45, 56, 60, 72, \textexclamdown (¡) ...... 7 ...... 17,63,64 \text 73, 75, 76 \textfishhookr (R) ...... 10 (˝) ...... 14 \textacutedbl \textcopyleft () ...... 15 \textfiveoldstyle (5) ..... 15 (a©¡) ...... 11 \textacutemacron \textcopyright (©) . . 7, 15, 74 \textflorin (ƒ) ...... 14 (a§¡) ...... 11 \textacutewedge \textcorner (^) ...... 9 \textfouroldstyle (4) ..... 15 (a) ...... 11 \textadvancing \textcrb ( ) ...... 9 \textfractionsolidus (⁄) ... 43 ´ \textasciiacute ( ) . . . . 14, 74 \textcrd (¡) ...... 9 \textfrak ...... 44 ˘ \textasciibreve ( ) ...... 14 \textcrg (g) ...... 9 \textg (¥) ...... 10 ˇ \textasciicaron ( ) ...... 14 \textcrh (è) ...... 9 \textgamma (G) ...... 10 \textasciicircum (ˆ) . . . . 7, 72 \textcrinvglotstop (Û) ..... 9 \textglobfall () ...... 10 ¨ \textasciidieresis ( ) . 14, 74 \textcrlambda (¬) ...... 9 \textglobrise () ...... 10 ` \textasciigrave ( ) ...... 14 \textcrtwo (2) ...... 9 \textglotstop (P) ...... 9 \textasciimacron ...... 73 \textctc (C) ...... 9 \textgoth ...... 44 ¯ \textasciimacron ( ) . . 14, 74 \textctd (¢) ...... 9 \textgravecircum (a) ...... 12 \textasciitilde (˜)..... 7,72 \textctdctzlig (¢ý ) ...... 9 \textgravedbl ( )̏ ...... 14 ∗ \textasteriskcentered ( )7,15 \textctesh (²) ...... 9 \textgravedot (a) ...... 12 È \textbabygamma ( ) ...... 9 \textctj (J) ...... 9 \textgravemacron (a© ) ...... 12 \ \textbackslash ( ) ...... 7,72 \textctn (®) ...... 9 \textgravemid (a) ...... 12 ฿ \textbaht ( ) ...... 14 \textctt (´) ...... 9 \textgreater (>) ...... 7,72 | \textbar ( ) ...... 7,72 \textcttctclig (Ć ) ...... 9 \textguarani (() ...... 14 b \textbarb ( ) ...... 9 \textctyogh (¸) ...... 9 \texthalflength (;) ...... 9 c \textbarc ( ) ...... 9 \textctz (ý) ...... 9 \texthardsign (») ...... 9 d \textbard ( ) ...... 9 \textcurrency (¤) ..... 14,74 \texthooktop (#) ...... 9 ‖ \textbardbl ( ) ...... 15 \textdagger (†) ...... 7,15 \texthtb (á) ...... 9 \textbardotlessj (é) ...... 9 \textdaggerdbl (‡) ...... 7,15 \texthtbardotlessj (ê) ...... 9 \textbarg (g) ...... 9 \texthtc (Á) ...... 9 \textbarglotstop (Ü) ...... 9 \textdbend ( ) ...... 54 \texthtd (â) ...... 9 \textbari (1) ...... 9 \textdblhyphen () ...... 15 \texthtg (ä) ...... 9 \textbarl (ª) ...... 9 \textdblhyphenchar () ..... 15 \texthth (H) ...... 9 \textbaro (8) ...... 9 \textdctzlig (dý ) ...... 9 \texththeng (Ê) ...... 9 \textbarrevglotstop (Ý) .... 9 \textdegree (°) ...... 43,74 \texthtk (Î) ...... 9 \textbaru (0) ...... 9 \textdied () ...... 56 \texthtp (Ò) ...... 9 \textbeltl (ì) ...... 9 \textdiscount () ...... 15 \texthtq (Ó) ...... 9 \textbeta (B) ...... 9 \textdiv (÷) ...... 43 \texthtrtaild (£) ...... 9 \textbigcircle (○) ...... 15 \textdivorced ( ) ...... 56 \texthtscg (É) ...... 9 \textblank (␢) ...... 15 \textdollar ($) ...... 7,14 \texthtt (Ö) ...... 9 \textborn () ...... 56 \textdollaroldstyle ($) ... 14 \texthvlig (ÿ) ...... 9 \textbottomtiebar (a<) ..... 11 \textdong (₫) ...... 14 \textifsym ...... 45

94 \textinterrobang (‽) ...... 15 \textphi (F) ...... 9 \textscn (ð) ...... 9 \textinterrobangdown (*)...15 \textpilcrow (¶) ...... 15 \textscoelig (×) ...... 9 \textinvglotstop (Û) ...... 9 \textpipe (|) ...... 9 \textscomega (±) ...... 9 \textinvscr (K) ...... 9 \textpm (±) ...... 43,74 \textscr (ö) ...... 9 \textinvsubbridge (a) ..... 12 \textpolhook (a ) ...... 12 \textscripta (A) ...... 9 \textiota (Ì) ...... 9 \textprimstress (") ...... 9 \textscriptg (g) ...... 9 \textlambda («) ...... 9 \textquestiondown (¿) ...... 7 \textscriptv (V) ...... 9 \textlangle (〈) ...... 36,72 \textquotedbl (") ...... 8,71 \textscu (Ú) ...... 9 \textlbrackdbl (〚) ...... 36 \textquotedblleft (“) ...... 7 \textscy (Y) ...... 9 \textleaf (-) ...... 56 \textquotedblright (”) ..... 7 \textseagull (a) ...... 12 \textleftarrow (←) ...... 28 \textquoteleft (‘) ...... 7 \textsecstress () ...... 9 \textlengthmark (:) ...... 9 \textquoteright (’) ...... 7 \textsection (§) ...... 7,15 \textless (<) ...... 7,71,72 \textquotesingle (') ...... 15 \textservicemark (℠) ...... 15 \textquotestraightbase (‚).15 \textsevenoldstyle (7) .... 15 \textlhdbend ( ) ...... 54 \textquotestraightdblbase („) \textsixoldstyle (6) ...... 15 ³ \textlhookt ( ) ...... 9 ...... 15 \textsoftsign (º) ...... 9 ¦ ¼ \textlhtlongi ( ) ...... 9 \textraiseglotstop ( ) ..... 9 \textsterling (£) ...... 7,14 ¶ § \textlhtlongy ( ) ...... 9 \textraisevibyi ( ) ...... 9 \textstretchc (Â) ...... 9 ₤ \textlira ( ) ...... 14 \textraising (a) ...... 12 \textstyle ...... 63,64,71 ¬ 7 \textlnot ( ) ...... 43,74 \textramshorns ( ) ...... 9 \textsubacute (a) ...... 12 (Ô) ...... 9 〉 \textlonglegr \textrangle ( ) ...... 36,72 \textsubarch (a) ...... 12 (a) ...... 12 〛 \textlowering \textrbrackdbl ( ) ...... 36 \textsubbar (a) ...... 12 (½) ...... 9 A © \textlptr \textrecipe ( ) ...... 15,62 \textsubbridge (a) ...... 12 \textlquill (⁅) ...... 36 ※ \textreferencemark ( ) . 15, 17 \textsubcircum (a) ...... 12 \textltailm (M) ...... 9 ® ¢ \textregistered ( ) . 7, 15, 74 \textsubdot (a) ...... 12 \textltailn (ñ) ...... 9 \textretracting (a ) ...... 12 \textsubgrave (a) ...... 12 \textltilde (ë) ...... 9 \textrevapostrophe (\) ...... 9 \textsublhalfring (a) ..... 12 \textlyoghlig (Ð) ...... 9 \textreve (9) ...... 9 \textsubplus (a) ...... 12 \textmarried (1) ...... 56 \textrevepsilon (3) ..... 9,62 \textsubrhalfring (a) ..... 12 \textmho (℧) ...... 45 \textsubring (a) ...... 12 \textmidacute (a) ...... 12 \textreversedvideodbend ( ). ¦ \textsubsquare (a) ...... 12 \textminus (−) ...... 43 ...... 54 \textsubtilde (a) ...... 12 \textmu (µ) ...... 45,74 \textrevglotstop (Q) ...... 9 £ \textsubumlaut (a) ...... 12 \textmusicalnote (♪) ...... 15 \textrevyogh (¹) ...... 9 ¤ \textsubw (a) ...... 12 \textnaira (₦) ...... 14 \textrhookrevepsilon (Ç)..10 \textsubwedge (a) ...... 12 \textnineoldstyle (9) ..... 15 \textrhookschwa (Ä) ...... 10 § \textsuperimposetilde (a)..12 \textnumero (№) ...... 15 \textrhoticity (~) ...... 10 & \textObardotlessj (Í) ...... 9 \textrightarrow (→) ...... 28 \textsuperscript ...... 13 √ \textohm (Ω) ...... 45 \textringmacron (¦a©) ...... 12 \textsurd ( ) ...... 43 \textOlyoghlig () ...... 9 \textroundcap (a) ...... 12 \textswab ...... 44 \textsyllabic (a) ...... 12 \textomega (°) ...... 9 \textrptr (¾) ...... 10 " \textonehalf (½) ...... 43,74 \textrquill (⁆) ...... 36 \texttctclig (tC ) ...... 9 \textoneoldstyle ...... 15 \textrtaild (ã) ...... 10 \textteshlig (Ù) ...... 9 \textoneoldstyle (1) ...... 15 \textrtaill (í) ...... 10 \texttheta (T) ...... 9 \textonequarter (¼) . . . . 43, 74 \textrtailn (ï) ...... 9 \textthorn (þ) ...... 9 \textonesuperior (¹) . . . 43, 74 \textrtailr (ó) ...... 9 \textthreeoldstyle (3) .... 15 \textopenbullet (◦) ...... 15 \textrtails (ù) ...... 9 \textthreequarters (¾) . 43, 74 \textopencorner (_) ...... 9 \textrtailt (ú) ...... 9 \textthreequartersemdash (—). \textopeno (O) ...... 9 \textrtailz (ü) ...... 9 ...... 15 \textordfeminine (ª) . 7, 15, 74 \textrthook ($) ...... 9 \textthreesuperior (³) . 43, 74 £ \textordmasculine (º) 7, 15, 74 \textsca (À) ...... 9 \texttildedot (a ) ...... 13 K \textovercross (a) ...... 12 \textscb (à) ...... 9 \texttildelow ( ) . . . . . 15, 72 \textoverw (a) ...... 12 \textsce (¤) ...... 9 \texttimes (×) ...... 43 \textpalhook (%) ...... 9 \textscg (å) ...... 9 \texttoneletterstem (¿) ..... 9 > \textparagraph (¶) ..... 7,15 \textsch (Ë) ...... 9 \texttoptiebar (a) ...... 13 \textperiodcentered (·) 7, 15, 74 \textschwa (@) ...... 9 \texttrademark (™) ..... 7,15 \textpertenthousand (‱)..15 \textsci (I) ...... 9 \texttslig (µ) ...... 9 \textperthousand (‰) ..... 15 \textscj (¨) ...... 9 \textturna (5) ...... 9 \textpeso (9) ...... 14 \textscl (Ï) ...... 9 \textturncelig (¯) ...... 9

95 \textturnh (4) ...... 9 Times(PostScriptfont) ..... 14 \u (˘a) ...... 11 \textturnk (©) ...... 9 timing (package) ...... 45 \ubar (u) ...... 11 \textturnlonglegr (Õ) ...... 9 tipa (package) 9–11, 13, 62, 75, 76 ubulb.fd (file) ...... 69,70 \textturnm (W) ...... 9 \to ...... see \rightarrow \udesc (u) ...... 11 \textturnmrleg (î) ...... 9 \ToBottom (½) ...... 57 \udot (¤) ...... 19 \textturnr (ô) ...... 9 \tone ...... 10 \ulcorner (x) ...... 34 \textturnrrtail (õ) ...... 9 \top (L) ...... 33,63 \ulcorner (l) ...... 34 \textturnscripta (6) ...... 9 \topbot (⊥L) ...... 63,65 ulsy (package) ...... 19, 30, 75 \textturnt (Ø) ...... 9 \topdoteq () ...... 24 umlaut ...... see accents \textturnv (2) ...... 9 \ToTop (¼) ...... 57 \unclear (k) ...... 59 \textturnw (û) ...... 9 trademark . . see \texttrademark \underaccent ...... 65 \textturny (L) ...... 9 \TransformHoriz ( ) ..... 25 \underarch (a) ...... 13 \texttwelveudash (L) ...... 15 transforms . . . . 25, 37, see also \underbrace (loomoon) ...... 40 \texttwooldstyle ...... 15 alphabets, math \underbrace (|{z}) ...... 38 \texttwooldstyle (2) ...... 15 \TransformVert (¢) ...... 25 \texttwosuperior (²) . . . 43, 74 transversality . . see \pitchfork \underbracket ...... 65,66 \textunderscore ( ) ...... 7 trfsigns (package) . . 25, 34, 37, 75 \underbracket ( ) ...... 66 ↑ \textuparrow ( ) ...... 28 \triangle ( ) ...... 42 \underdots (r) ...... 13 U \textupsilon ( ) ...... 9 triangle relations ...... 28 \undergroup (loooon) ...... 40 \textupstep () ...... 9 3 \TriangleDown ( ) ...... 53 ( ) ...... 39 \textvbaraccent (a) ...... 13 \underleftarrow ←− \TriangleDown (o vs. 3)...61 \textvertline () ...... 10 \underleftrightarrow (←→).39 (o) ...... 53 \textvibyi (§) ...... 10 \TriangleDown \underline ( ) ...... 38 (w) ...... 42 \textvibyy (·) ...... 10 \triangledown \underparenthesis ..... 65,66 2 \textvisiblespace ( ) ...... 7 \TriangleLeft ( ) ...... 53 \underparenthesis (|}) .... 66 \textwon (₩) ...... 14 \triangleleft () ...... 28 \underrightarrow ( ) ..... 39 \textwynn (ß) ...... 10 \triangleleft () ...... 17 −→ (y) ...... 13 \textyen (¥) ...... 14,74 \trianglelefteq () ...... 28 \underring underscore ...... see \textyogh (Z) ...... 10 \trianglelefteq () ...... 28 \_ underscore (package) ...... 7 \textzerooldstyle (0) ..... 15 \trianglelefteqslant (D)..28 undertilde (package) . . 40, 75, 76 \TH (Þ) ...... 8 \triangleq () ...... 17,28 \undertilde (|) ...... 13 \th (þ) ...... 8 \TriangleRight (4) ...... 53 \underwedge (}) ...... 13 Thành, Hàn Thˆé ...... 65 \triangleright () ...... 28 union ...... see \cup \therefore (6) ...... 24 \triangleright () ...... 17 (u) ...... 59 \therefore (∴) ...... 23 \trianglerighteq () ..... 28 \unitedpawns units (package) ...... 43 \Thermo ...... 58 \trianglerighteq ( ) ..... 28 unity (1)...see alphabets, math \Theta (Θ) ...... 32 \trianglerighteqslant (E).28 universa (package) . 54, 57, 75, 76 \theta (θ) ...... 32 triangles ...... 42, 53, 54 \unlhd () ...... 17,18 \thetaup (θ) ...... 32 \TriangleUp (1) ...... 53 \unrhd ( ) ...... 17,18 \thickapprox (≈) ...... 23 n 1 \TriangleUp ( vs. ) ..... 61 \upalpha (α) ...... 33 \thicksim (∼) ...... 23 \TriangleUp (n) ...... 53 \UParrow (X) ...... 56 \thickvert (~) ...... 35 \triple ...... 36 \Uparrow (⇑) ...... 28,35 thinspace...... 71 trsym (package) . . . . . 25, 75, 76 \uparrow (↑) ...... 28,35 \ThinFog ( ) ...... 58 \Tsteel (œ) ...... 47 \upbar ...... 13 3 \third ( ) ...... 42 \TTsteel (š) ...... 47 \upbeta (β) ...... 33 Þ \Thorn ( ) ...... 8 TUGboat ...... 38 \upbracketfill ...... 66 B \thorn ( ) ...... 10 \Tumbler () ...... 57 \upchi (χ) ...... 33 \thorn (p) ...... 11 \TwelweStar (J) ...... 52 \Updelta (∆) ...... 33 \thorn (þ) ...... 8 \twoheadleftarrow ([) .... 29 \updelta (δ) ...... 33 tilde . 7, 9–11, 13, 15, 37, 38, 40, \twoheadrightarrow (]) ... 29 \Updownarrow (O) ...... 28, 35 65, 72 \twonotes (W) ...... 56 \updownarrow (P) ...... 28,35 extensible ...... 38, 40 txfonts (package) . 17, 18, 22–29, \updownarrows (Ö) ...... 30 vertically centered . . . . . 72 31–34, 42, 44, 60, 62, 72, 75, \updownharpoons (ê) ...... 30 (˜) ...... 37,65 \tilde 76 \upepsilon (ε) ...... 33 (-) ...... 10 \tildel Type 1 (PostScript font) . . . . 70 \upeta (η) ...... 33 timeofday ...... 58 \Upgamma (Γ) ...... 33 \timelimit (T) ...... 59 U \upgamma (γ) ...... 33 \times (×) ...... 17 \U (¼a) ...... 11 upgreek (package) . . . 33, 75, 76

96 \upharpoonleft (ä) ...... 30 \ut (a) ...... 13 \varolessthan (O) ...... 18 ˜ \upharpoonleft (e) ...... 29 \utilde ( ) ...... 40 \varomega (¨) ...... 11 e \upharpoonright (æ) ...... 30 \varominus (P) ...... 18 \upharpoonright (h) ...... 29 V \varopeno (C) ...... 11 \upiota (ι) ...... 33 \v (ˇa) ...... 11 \varoplus (Q) ...... 18 \upkappa (κ) ...... 33 \vara (a) ...... 11 \varoslash (R) ...... 18 \Uplambda (Λ) ...... 33 \varangle (Z) ...... 42 \varotimes (S) ...... 18 \uplambda (λ) ...... 33 \varbigcirc (F) ...... 18 \varovee (T) ...... 18 \uplett ...... 13 \VarClock () ...... 58 \varowedge (U) ...... 18 \uplus (Z) ...... 19 \varclubsuit () ...... 42 \varparallel (∥) ...... 24 \uplus (Q) ...... 17 \varcurlyvee (G) ...... 18 \varparallelinv () ...... 24 \upmu (µ) ...... 33 \varcurlywedge (H) ...... 18 \varphi (ϕ) ...... 32 \upnu (ν) ...... 33 \vardiamondsuit () ...... 42 \varphiup (ϕ) ...... 32 \Upomega (Ω) ...... 33 \varEarth (J) ...... 46 \varpi (() ...... 32 ω \upomega ( ) ...... 33 \varepsilon (ε) ...... 32 \varpiup (5) ...... 32 \upp (t) ...... 13 \varepsilonup (ε) ...... 32 \varprod ( ) ...... 22 \upparenthfill ...... 66 (lim) ...... 31 \VarFlag () ...... 58 \varprojlim ←− (Φ) ...... 33 ∝ \Upphi varg (txfonts/pxfonts package op- \varpropto ( ) ...... 23 (φ) ...... 33 ) \upphi tion) ...... 33 \varrho ( ) ...... 32 \Uppi (Π) ...... 33 \varg () ...... 33 \varrhoup ( ) ...... 32 \uppi (π) ...... 33 ς \varg (G) ...... 11 \varsigma ( ) ...... 32 \Uppsi (Ψ) ...... 33 ς \vargeq (©) ...... 27 \varsigmaup ( ) ...... 32 \uppsi (ψ) ...... 33 \varhash (#) ...... 42 \varspadesuit ( ) ...... 42 upquote (package) ...... 72 \varheartsuit () ...... 42 \varsqsubsetneq ( ) ...... 26 \uprho (ρ) ...... 33 \varhexagon ([) ...... 52 \varsqsubsetneqq ( ) ..... 26 upright Greek letters . . . . 32, 33 \varhexstar (\) ...... 51 \varsqsupsetneq ( ) ...... 26 upside-downsymbols...... 62 \vari (i) ...... 11 \varsqsupsetneqq ( ) ..... 26 \Upsigma (Σ) ...... 33 variable-sized symbols . . . 20–22 \varstar ( ) ...... 19 \upsigma (σ) ...... 33 \VarIceMountain () ...... 58 \varsubsetneq ( ) ...... 26 \Upsilon (Υ) ...... 32 \varsubsetneq (&) ...... 26 \varinjlim (lim−→) ...... 31 \upsilon (υ) ...... 32 ] \varsubsetneqq () ...... 26 \varint ( ) ...... 20 \upsilonup (υ) ...... 32 ()) ...... 26 (R) ...... 59 \varsubsetneqq \upt (l) ...... 13 \various κ \VarSummit () ...... 58 \uptau (τ) ...... 33 \varkappa ( ) ...... 32 ¨ \varsupsetneq () ...... 26 (Θ) ...... 33 \varleq ( ) ...... 27 \Uptheta \varsupsetneq (*) ...... 26 (θ) ...... 33 \varliminf (lim) ...... 31 \uptheta \varsupsetneqq () ...... 26 (þ) ...... 30 \varlimsup (lim)...... 31 \uptodownarrow \varsupsetneqq (+) ...... 26 \upuparrows (Ò) ...... 30 \varmathbb ...... 44 \upuparrows (`) ...... 29 \VarMountain ( ) ...... 58 \VarTaschenuhr () ...... 58 ∅ \upupharpoons (Ú) ...... 30 \varnothing ( ) ...... 42 \vartheta (ϑ) ...... 32 T \Upupsilon (Υ) ...... 33 \varnotin ( ) ...... 34 \varthetaup (ϑ) ...... 32 U \upupsilon (υ) ...... 33 \varnotowner ( ) ...... 34 \vartimes (V) ...... 18 I \upvarepsilon (ε) ...... 33 \varoast ( ) ...... 18 \vartriangle () ...... 42 J \upvarphi (ϕ) ...... 33 \varobar ( ) ...... 18 \vartriangleleft () ..... 28 K \upvarpi (ϖ) ...... 33 \varobslash ( ) ...... 18 \vartriangleleft ( ) ..... 28 L \upvarrho (ρ) ...... 33 \varocircle ( ) ...... 18 \vartriangleright () ..... 28 M \upvarsigma (σ) ...... 33 \varodot ( ) ...... 18 \vartriangleright ( ) ..... 28 N \upvartheta (ϑ) ...... 33 \varogreaterthan ( ) ..... 18 \varv ( ) ...... 33 \Upxi (Ξ) ...... 33 \varoiiintclockwise ( )..22! \varw ( ) ...... 33 ξ ! \upxi ( ) ...... 33 \varoiiintctrclockwise! ( )22 \vary ( ) ...... 33 (ζ) ...... 33 \upzeta \varoiint ( ) ...... % 22 \VBar () ...... 53 \Uranus (G ) ...... 46 \varoiintclockwise ( )) ... 22 \VDash (() ...... 24 (Ç) ...... 46 \Uranus ( ).22 \Vdash (,) ...... 24 Y \varoiintctrclockwise^ \uranus ( ) ...... 45 \Vdash (/) ...... 23 y \varoint ( ) ...... - 20 \urcorner ( ) ...... 34 \vDash (() ...... 24 m \varointclockwise ( ) ..... 22 \urcorner ( ) ...... 34 \vDash (1) ...... 23 \varointclockwise ( ) ..... 22 url (package) ...... 72 1 \vdash (R) ...... 23 \US () ...... 47 \varointctrclockwise ( )..22 . \usepackage ...... 6 \varointctrclockwise ( )...22 \vdots (.) ...... 41

97 \vec (,) ...... 37 \weakpt (J) ...... 59 \Xi (Ξ)...... 32 \Vectorarrow ()p ...... 43 \WeakRain () ...... 58 \xi (ξ) ...... 32 \Vectorarrowhigh ()P ...... 43 \WeakRainCloud () ...... 58 \xiup (ξ) ...... 32 \vee (_) ...... 19 weathersymbols ...... 58 \xleftarrow (←−) ...... 39 (∨) ...... 17 \vee \Wecker () ...... 58 XML ...... 73 Y \veebar ( ) ...... 19 \wedge (^) ...... 19 −→ \xrightarrow ( ) ...... 39 \veebar ( ) ...... 17 \wedge (∧) ...... 17 [ − − \veedoublebar ( ) ...... 19 Weierstrass ℘ function . . see \wp \xrightleftharpoons ( )..39 B \Venus ( ) ...... 46 \Wheelchair (w) ...... 54 Xs ...... 51,54 Ã \Venus ( ) ...... 46 \widearrow (t) ...... 40 # ♀ \XSolid ( ) ...... 51 \venus ( ) ...... 45 \widebar (s) ...... 40 \XSolidBold ($) ...... 51 \vernal ( ) ...... 45 \widecheck (q) ...... 40 \XSolidBrush (%) ...... 51 \Vert ( ) ...... 35 \widehat (b) ...... 38 X -pic ...... 64 \vert (|) ...... 35 \wideparen (u) ...... 40 Y \VHF (_) ...... 45 ó \wideparen ( ) ...... 38 Y ˚ \Village ( ) ...... 58 \widering (ó) ...... 40 \Ydown (W) ...... 18 \vin ( ) ...... 34 ˚ yen...... see ó \textyen \Virgo (å) ...... 46 \widering ( ) ...... 38 yfonts (package) . . . . . 44, 75, 76 e \virgo (`) ...... 46 \widetilde ( ) ...... 38,40 yhmath (package) . 37, 38, 40, 41, æ \vod (v) ...... 11 \widetriangle ( ) ...... 38 ˚ 65, 75 \voicedh (h) ...... 11 \wind ...... 58 \Yinyang (Y) ...... 57 \VT (♂) ...... 47 Windows...... 73 (X) ...... 18 #» \Yleft \vv ( ) ...... 40 \with (w) ...... 59 \yogh (`) ...... 10 \VvDash () ...... 24 \withattack (A) ...... 59 \yogh (x) ...... 11 , Y \Vvdash ( ) ...... 24 \withidea (E) ...... 59 \Yright ( ) ...... 18 \Vvdash (3) ...... 23 \Yup (Z) ...... 18 \withinit (C) ...... 59 \vvvert (~) ...... 35 \without (v) ...... 59 Z W \Womanface (þ) ...... 57 Zapf Chancery (PostScript font) 44 \WashCotton (‰) ...... 57 won ...... see \textwon Zapf Dingbats (PostScript font) 49, ℘ \WashSynthetics (Š) ..... 57 \wp ( ) ...... 33 51 (U) ...... 17 \WashWool (‹) ...... 57 \wr zapfchan (package) ...... 75 wreath product ...... see \wasylozenge (◊) ...... 56 \wr \Zborder (Z) ...... 54 (b) ...... 54 \wasypropto (b) ...... 23 \Writinghand \zeta (ζ) ...... 32 wsuipa (package) . 10, 13, 61, 62, wasysym (package) ...... 8, 14, \zetaup (ζ) ...... 32 65, 75, 76 15, 17, 18, 20, 23, 25–28, 42, \Zodiac ...... 46 (c) ...... 59 45–47, 51, 52, 56, 61, 75, 76 \wupperhand zodiacalsymbols ...... 46 ∴ s ...... c \wasytherefore ( ) ...... 42 X \Ztransf ( ) ...... 25 f c ...... s \wbetter ( ) ...... 59 \XBox (d) ...... 51 \ztransf ( ) ...... 25 \wdecisive (h) ...... 59 Xdvi...... 62 \zugzwang (D) ...... 59