The Comprehensive L

The Comprehensive L ^A TEX Symbol List

Scott Pakin <pakin@uiuc.edu>

29 September 2003

Abstract

This document lists 2826 symbols and the corresponding L^ATEX commands that produce them. Some of these symbols are guaranteed to be available in every L^ATEX 2εsystem; 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

1.1 Document Usage . . . 6

1.2 Frequently Requested Symbols . . . 6

2 Body-text symbols 7 Table 1: L^ATEX 2ε Escapable “Special” Characters . . . 7

Table 2: L^ATEX 2ε Commands Defined to Work in Both Math and Text Mode . . . 7

Table 3: Predefined L^ATEX 2ε Text-mode Commands . . . 7

Table 4: Non-ASCII Letters (Excluding Accented Letters) . . . 8

Table 5: Letters Used to Typeset African Languages . . . 8

Table 6: Punctuation Marks Not Found in OT1 . . . 8

Table 7: pifontDecorative Punctuation Marks . . . 8

Table 8: wasysymPhonetic Symbols . . . 8

Table 9: tipaPhonetic Symbols . . . 8

Table 10: wsuipaPhonetic Symbols . . . 10

Table 11: phoneticPhonetic Symbols . . . 10

Table 12: Text-mode Accents . . . 11

Table 13: tipaText-mode Accents . . . 11

Table 14: wsuipaText-mode Accents . . . 12

Table 15: phoneticText-mode Accents . . . 13

Table 16: wsuipaDiacritics . . . 13

Table 17: textcompDiacritics . . . 13

Table 18: textcompCurrency Symbols . . . 13

Table 19: marvosymCurrency Symbols . . . 14

Table 20: wasysymCurrency Symbols . . . 14

Table 21: eurosymEuro Signs . . . 14

Table 22: textcompLegal Symbols . . . 14

Table 23: textcompOld-style Numerals . . . 14

Table 24: MiscellaneoustextcompSymbols . . . 15

Table 25: MiscellaneouswasysymText-mode Symbols . . . 15

Table 26: AMSCommands Defined to Work in Both Math and Text Mode . . . 15

∗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 69 for more information about who did what.

3 Mathematical symbols 16

Table 27: Binary Operators . . . 16

Table 28: AMSBinary Operators . . . 16

Table 29: stmaryrdBinary Operators . . . 17

Table 30: wasysymBinary Operators . . . 17

Table 31: txfonts/pxfonts Binary Operators . . . 17

Table 32: mathabxBinary Operators . . . 18

Table 33: ulsyGeometric Binary Operators . . . 18

Table 34: mathabxGeometric Binary Operators . . . 18

Table 35: Variable-sized Math Operators . . . 18

Table 36: AMSVariable-sized Math Operators . . . 19

Table 37: stmaryrdVariable-sized Math Operators . . . 19

Table 38: wasysymVariable-sized Math Operators . . . 19

Table 39: mathabxVariable-sized Math Operators . . . 19

Table 40: txfonts/pxfonts Variable-sized Math Operators . . . 20

Table 41: esintVariable-sized Math Operators . . . 20

Table 42: Binary Relations . . . 21

Table 43: AMSBinary Relations . . . 21

Table 44: AMSNegated Binary Relations . . . 21

Table 45: stmaryrdBinary Relations . . . 21

Table 46: wasysymBinary Relations . . . 21

Table 47: txfonts/pxfontsBinary Relations . . . 22

Table 48: txfonts/pxfontsNegated Binary Relations . . . 22

Table 49: mathabxBinary Relations . . . 22

Table 50: mathabxNegated Binary Relations . . . 23

Table 51: trsymBinary Relations . . . 23

Table 52: trfsignsBinary Relations . . . 23

Table 53: Subset and Superset Relations . . . 23

Table 54: AMSSubset and Superset Relations . . . 23

Table 55: stmaryrdSubset and Superset Relations . . . 24

Table 56: wasysymSubset and Superset Relations . . . 24

Table 57: txfonts/pxfonts Subset and Superset Relations . . . 24

Table 58: mathabxSubset and Superset Relations . . . 24

Table 59: Inequalities . . . 24

Table 60: AMSInequalities . . . 24

Table 61: wasysymInequalities . . . 25

Table 62: txfonts/pxfonts Inequalities . . . 25

Table 63: mathabxInequalities . . . 25

Table 64: AMSTriangle Relations . . . 25

Table 65: stmaryrdTriangle Relations . . . 25

Table 66: mathabxTriangle Relations . . . 25

Table 67: Arrows . . . 26

Table 68: Harpoons . . . 26

Table 69: textcompText-mode Arrows . . . 26

Table 70: AMSArrows . . . 26

Table 71: AMSNegated Arrows . . . 26

Table 72: AMSHarpoons . . . 26

Table 73: stmaryrdArrows . . . 27

Table 74: txfonts/pxfontsArrows . . . 27

Table 75: mathabxArrows . . . 27

Table 76: mathabxNegated Arrows . . . 27

Table 77: mathabxHarpoons . . . 28

Table 78: chemarrowArrows . . . 28

Table 79: ulsyContradiction Symbols . . . 28

Table 80: Extension Characters . . . 28

Table 81: stmaryrdExtension Characters . . . 28

Table 82: txfonts/pxfontsExtension Characters . . . 28

Table 83: mathabxExtension Characters . . . 28

Table 84: Log-like Symbols . . . 29

Table 85: AMSLog-like Symbols . . . 29

Table 86: Greek Letters . . . 29

Table 87: AMSGreek Letters . . . 29

Table 88: txfonts/pxfonts Upright Greek Letters . . . 30

Table 89: upgreekUpright Greek Letters . . . 30

Table 90: txfonts/pxfonts Variant Latin Letters . . . 30

Table 91: AMSHebrew Letters . . . 30

Table 92: Letter-like Symbols . . . 30

Table 93: AMSLetter-like Symbols . . . 31

Table 94: txfonts/pxfonts Letter-like Symbols . . . 31

Table 95: mathabxLetter-like Symbols . . . 31

Table 96: trfsignsLetter-like Symbols . . . 31

Table 97: AMSDelimiters . . . 31

Table 98: stmaryrdDelimiters . . . 31

Table 99: mathabxDelimiters . . . 31

Table 100: nathDelimiters . . . 31

Table 101: Variable-sized Delimiters . . . 32

Table 102: Large, Variable-sized Delimiters . . . 32

Table 103: Variable-sizedstmaryrdDelimiters . . . 32

Table 104: mathabxVariable-sized Delimiters . . . 32

Table 105: nathVariable-sized Delimiters (Double) . . . 33

Table 106: nathVariable-sized Delimiters (Triple) . . . 33

Table 107: textcompText-mode Delimiters . . . 33

Table 108: Math-mode Accents . . . 34

Table 109: AMSMath-mode Accents . . . 34

Table 110: yhmathMath-mode Accents . . . 34

Table 111: trfsignsMath-mode Accents . . . 34

Table 112: Extensible Accents . . . 35

Table 113: overrightarrowExtensible Accents . . . 35

Table 114: yhmathExtensible Accents . . . 35

Table 115: AMSExtensible Accents . . . 35

Table 116: chemarrExtensible Accents . . . 36

Table 117: chemarrowExtensible Accents . . . 36

Table 118: mathabxExtensible Accents . . . 36

Table 119: esvectExtensible Accents . . . 37

Table 120: undertildeExtensible Accents . . . 37

Table 121: Dots . . . 37

Table 122: AMSDots . . . 37

Table 123: mathdotsDots . . . 38

Table 124: yhmathDots . . . 38

Table 125: Miscellaneous LATEX 2ε Symbols . . . 38

Table 126: MiscellaneousAMSSymbols . . . 38

Table 127: MiscellaneouswasysymSymbols . . . 38

Table 128: Miscellaneoustxfonts/pxfontsSymbols . . . 38

Table 129: Miscellaneousmathabx Symbols . . . 39

Table 130: MiscellaneoustextcompText-mode Math Symbols . . . 39

Table 131: mathcompMath Symbols . . . 39

Table 132: gensymbSymbols Defined to Work in Both Math and Text Mode . . . 39

Table 133: mathabxMayan Digits . . . 39

Table 134: marvosymMath Symbols . . . 39

Table 135: Math Alphabets . . . 40

4 Science and technology symbols 41

Table 136: wasysymElectrical and Physical Symbols . . . 41

Table 137: ifsymPulse Diagram Symbols . . . 41

Table 138: arAspect Ratio Symbol . . . 41

Table 139: textcompText-mode Science and Engineering Symbols . . . 41

Table 140: wasysymAstronomical Symbols . . . 41

Table 141: marvosymAstronomical Symbols . . . 42

Table 142: mathabxAstronomical Symbols . . . 42

Table 143: wasysymAstrological Symbols . . . 42

Table 144: marvosymAstrological Symbols . . . 42

Table 145: mathabxAstrological Symbols . . . 42

Table 146: wasysymAPL Symbols . . . 42

Table 147: wasysymAPL Modifiers . . . 42

Table 148: marvosymComputer Hardware Symbols . . . 43

Table 149: asciiControl Characters (IBM) . . . 43

Table 150: marvosymCommunication Symbols . . . 43

Table 151: marvosymEngineering Symbols . . . 43

Table 152: wasysymBiological Symbols . . . 43

Table 153: marvosymBiological Symbols . . . 43

Table 154: marvosymSafety-related Symbols . . . 44

5 Dingbats 45 Table 155: bbdingArrows . . . 45

Table 156: pifontArrows . . . 45

Table 157: marvosymScissors . . . 45

Table 158: bbdingScissors . . . 45

Table 159: pifontScissors . . . 45

Table 160: dingbatPencils . . . 45

Table 161: bbdingPencils and Nibs . . . 46

Table 162: pifontPencils and Nibs . . . 46

Table 163: dingbatHands . . . 46

Table 164: bbdingHands . . . 46

Table 165: pifontHands . . . 46

Table 166: bbdingCrosses and Plusses . . . 46

Table 167: pifontCrosses and Plusses . . . 46

Table 168: bbdingXs and Check Marks . . . 46

Table 169: pifontXs and Check Marks . . . 47

Table 170: wasysymXs and Check Marks . . . 47

Table 171: pifontCircled Numbers . . . 47

Table 172: wasysymStars . . . 47

Table 173: bbdingStars, Flowers, and Similar Shapes . . . 47

Table 174: pifontStars, Flowers, and Similar Shapes . . . 48

Table 175: wasysymGeometric Shapes . . . 48

Table 176: ifsymGeometric Shapes . . . 48

Table 177: bbdingGeometric Shapes . . . 49

Table 178: pifontGeometric Shapes . . . 49

Table 179: universaGeometric Shapes . . . 49

Table 180: manfntDangerous Bend Symbols . . . 49

Table 181: skullSymbols . . . 49

Table 182: Non-MathematicalmathabxSymbols . . . 49

Table 183: marvosymInformation Symbols . . . 49

Table 184: MiscellaneousdingbatDingbats . . . 50

Table 185: Miscellaneousbbding Dingbats . . . 50

Table 186: Miscellaneouspifont Dingbats . . . 50

6 Other symbols 51

Table 187: textcompGenealogical Symbols . . . 51

Table 188: wasysymGeneral Symbols . . . 51

Table 189: wasysymMusical Notes . . . 51

Table 190: wasysymCircles . . . 51

Table 191: Miscellaneousmanfnt Symbols . . . 51

Table 192: marvosymNavigation Symbols . . . 52

Table 193: marvosymLaundry Symbols . . . 52

Table 194: OthermarvosymSymbols . . . 52

Table 195: MiscellaneousuniversaSymbols . . . 52

Table 196: ifsymWeather Symbols . . . 53

Table 197: ifsymAlpine Symbols . . . 53

Table 198: ifsymClocks . . . 53

Table 199: OtherifsymSymbols . . . 53

Table 200: skakChess Informator Symbols . . . 54

7 Additional Information 55 7.1 Symbol Name Clashes . . . 55

7.2 Where can I find the symbol for. . . ? . . . 55

7.3 Math-mode spacing . . . 64

7.4 Bold mathematical symbols . . . 65

7.5 ASCII and Latin 1 quick reference . . . 66

7.6 About this document . . . 69

References 69

Index 71

1 Introduction

Welcome to the Comprehensive L^ATEX Symbol List! This document strives to be your primary source of L^ATEX symbol information: font samples, L^ATEX 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 L^ATEX 2ε 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 L^ATEX Symbol List contains samples of 2826 symbols—quite a large number. Some of these symbols are guaranteed to be available in every L^ATEX 2εsystem;

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 L^ATEX 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, “textcompOld-Style Numerals”, 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 L^ATEX) 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 encodingis, e.g., T1or 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 L^ATEX ASCII and Latin 1 tables, and provides some information about this document itself. The Comprehensive L^ATEX Symbol List ends with an index of all the 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 oncomp.text.tex. If you’re looking for such a symbol the following list will help you find it quickly.

, as in “Spaces are significant.” . . . 7

´ı, `ı, ¯ı, ˆı, etc. (versus ´i, `i, ¯i, and ˆi) . . . 11

¢ . . . 13

e . . . 14

©,®, and™ . . . 14

‰ . . . 15

. . . 20

∴ . . . 21

and . . . 22

and . . . 24

. .. . . . 38

°, as in “180°” or “15℃” . . . 39

L,F, etc. . . 40

N,Z,R, etc. . . 40

R− . . . 58

´¯ a, `ˆe, etc. (i.e., several accents per character) 60 <,>, and|(instead of ¡, ¿, and —) . . . 66

ˆ and ˜ (or∼) . . . 67

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.

Table1: L^ATEX 2ε Escapable “Special” Characters

$ \$ % \% \_^∗ } \} & \& # \# { \{

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

Table2: L^ATEX 2εCommands 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 LATEX 2ε provides by default, and the right one is the “true” symbol that textcompmakes available.

Table3: Predefined LATEX 2εText-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 LATEX 2ε provides by default, and the right one is the “true” symbol that textcompmakes available.

Table4: 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}

ž \B{d}  \m{D} „ \m{F}  \m{N} › \M{T}  \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} š \m{T} Å \T{O}

· \B{t} ¡ \m{d} À \m{I} Š \m{O} ® \m{u}^∗ å \T{o}

— \B{T} ‚ \m{E} à \m{i} ‘ \m{P} Ž \m{U}^∗   \m{b} ¢ \m{e} ‰ \m{J} ± \m{p}  \m{Y}

€ \m{B} ƒ \M{E} © \m{j} ¬ \m{s} ¯ \m{y}

 \m{C} £ \M{e} ˆ \m{K} Œ \m{S} ¶ \m{z}

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

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

Table6: Punctuation Marks Not Found in OT1

« \guillemotleft ‹ \guilsinglleft „ \quotedblbase " \textquotedbl

» \guillemotright › \guilsinglright ‚ \quotesinglbase

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

Table 7: pifontDecorative Punctuation Marks

❛ \ding{123} ❝ \ding{125} ❡ \ding{161} ❣ \ding{163}

❜ \ding{124} ❞ \ding{126} ❢ \ding{162}

Table8: wasysymPhonetic Symbols

D \DH \dh \openo

Þ \Thorn \inve þ \thorn

Table9: tipaPhonetic 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  \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

à \textdyoghlig 3 \textrevepsilon L \textturny dz \textdzlig Q \textrevglotstop U \textupsilon

E \textepsilon ¹ \textrevyogh • \textupstep

S \textesh Ç \textrhookrevepsilon ’ \textvertline R \textfishhookr Ä \textrhookschwa § \textvibyi

¥ \textg ~ \textrhoticity · \textvibyy

G \textgamma ¾ \textrptr ß \textwynn

— \textglobfall ã \textrtaild Z \textyogh

(continued on next page)

(continued from previous page)

– \textglobrise í \textrtaill

tipadefines 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.

Table10: wsuipaPhonetic 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

Table 11: phoneticPhonetic Symbols

j \barj f \flap i¯ \ibar A \rotvara i \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

Table12: Text-mode Accents

A¨¨a \"{A}\"{a} A``a \‘{A}\‘{a} A˝˝a \H{A}\H{a} A˘˘a \u{A}\u{a}

A´´a \’{A}\’{a} A

¯a

¯ \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˜˜a \~{A}\~{a}

A¯¯a \={A}\={a} A. a. \d{A}\d{a} Aa \t{A}\t{a}

Aˆˆa \^{A}\^{a} ŸAŸa \G{A}\G{a}^‡ ¼A¼a \U{A}\U{a}^‡

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

∗Requires thetextcomppackage.

†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 thefcpackage.

Also note the existence of \iand\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.)

Table13: tipaText-mode Accents Aa \textacutemacron{A}\textacutemacron{a}

Aa \textacutewedge{A}\textacutewedge{a}

Aa \textadvancing{A}\textadvancing{a}

A<<a \textbottomtiebar{A}\textbottomtiebar{a}

Aa \textbrevemacron{A}\textbrevemacron{a}

A››a \textcircumacute{A}\textcircumacute{a}

Aa \textcircumdot{A}\textcircumdot{a}

AŸŸa \textdotacute{A}\textdotacute{a}

Aa \textdotbreve{A}\textdotbreve{a}

Aa \textdotbreve{A}\textdotbreve{a}

Aa \textdoublegrave{A}\textdoublegrave{a}

Aa \textdoublevbaraccent{A}\textdoublevbaraccent{a}

Ašša \textgravecircum{A}\textgravecircum{a}

Ažža \textgravedot{A}\textgravedot{a}

Aa \textgravemacron{A}\textgravemacron{a}

A™™a \textgravemid{A}\textgravemid{a}

Aa \textinvsubbridge{A}\textinvsubbridge{a}

Aa \textlowering{A}\textlowering{a}

A˜˜a \textmidacute{A}\textmidacute{a}

Aa \textovercross{A}\textovercross{a}

(continued on next page)

(continued from previous page)

A

a \textoverw{A}\textoverw{a}

Aa \textpolhook{A}\textpolhook{a}

Aa \textraising{A}\textraising{a}

Aa \textretracting{A}\textretracting{a}

Aa \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}

Aa \textsublhalfring{A}\textsublhalfring{a}

Aa \textsubplus{A}\textsubplus{a}

Aa \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}

A"a

" \textsyllabic{A}\textsyllabic{a}

Aa \texttildedot{A}\texttildedot{a}

>A>a \texttoptiebar{A}\texttoptiebar{a}

Aœœa \textvbaraccent{A}\textvbaraccent{a}

tipadefines shortcut sequences for many of the above. See thetipadocumentation for more information.

Table 14: wsuipaText-mode Accents Agag \dental{A}\dental{a}

Aa \underarch{A}\underarch{a}

Table15: phoneticText-mode Accents A{a

{ \hill{A}\hill{a} Aa \rc{A}\rc{a} A

˜a

˜ \ut{A}\ut{a}

A˚a

˚ \od{A}\od{a} Aa \syl{A}\syl{a}

A{a{ \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}’’ → “p^h” with “p\textsuperscript{h}’’→“p^h”.

Table16: wsuipaDiacritics

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

Thewsuipapackage 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 “ra”. See thewsuipa doc- umentation for more information.

Table17: textcompDiacritics

˝ \textacutedbl ˇ \textasciicaron ¯ \textasciimacron

´ \textasciiacute ¨ \textasciidieresis ̏ \textgravedbl

˘ \textasciibreve ` \textasciigrave

Thetextcomppackage defines all of the above as ordinary characters, not as accents.

Table18: textcompCurrency Symbols

฿ \textbaht $ \textdollar \textguarani ₩ \textwon

¢ \textcent $ \textdollaroldstyle ₤ \textlira ¥ \textyen

¢ \textcentoldstyle ₫ \textdong ₦ \textnaira

₡ \textcolonmonetary € \texteuro \textpeso

¤ \textcurrency ƒ \textflorin £ \textsterling

Table19: marvosymCurrency 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 marvosymdigits listed in Table 134 (\EURdig).

Table 20: wasysymCurrency Symbols

¢ \cent ¤ \currency

Table21: eurosymEuro Signs

AC \geneuro BC \geneuronarrow CC \geneurowide e \officialeuro

\eurois 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.

Table22: textcompLegal Symbols

℗ \textcircledP ○ ©c \textcopyright ℠ \textservicemark \textcopyleft ○ ®r \textregistered ^TM ™ \texttrademark

Where two symbols are present, the left one is the “faked” symbol that L^ATEX 2ε provides by default, and the right one is the “true” symbol thattextcomp makes available.

Seehttp://www.tex.ac.uk/cgi-bin/texfaq2html?label=tradesymsfor solu- tions to common problems that occur when using these symbols (e.g., getting a “ r○” when you expected to get a “®”).

Table 23: textcompOld-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.

Table24: MiscellaneoustextcompSymbols

∗ \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 L^ATEX 2ε provides by default, and the right one is the “true” symbol that textcompmakes available.

Table 25: MiscellaneouswasysymText-mode Symbols \permil

Table26: AMSCommands Defined to Work in Both Math and Text Mode \checkmark \circledR \maltese

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 discussion invariably reveals innumerable ways to represent contradiction in a proof, including “ ” (\blitza),

“⇒⇐” (\Rightarrow\Leftarrow), “⊥” (\bot), “” (\nleftrightarrow), and “※” (\textreferencemark).

Because 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 61.

Table27: 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 L^ATEX 2ε. Use one of the packageslatexsym,amsfonts,amssymb, txfonts,pxfonts, or wasysym.

Table28: AMSBinary Operators

\barwedge \circledcirc \intercal \boxdot \circleddash \leftthreetimes

\boxminus \Cup \ltimes

\boxplus \curlyvee \rightthreetimes \boxtimes \curlywedge \rtimes

\Cap \divideontimes \smallsetminus

\centerdot \dotplus \veebar

\circledast \doublebarwedge

Table29: stmaryrdBinary 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

Table30: wasysymBinary Operators

\lhd \ocircle \RHD \unrhd

\LHD \rhd \unlhd

Table31: txfonts/pxfontsBinary Operators \circledbar \circledwedge \medcirc \circledbslash \invamp \sqcapplus \circledvee \medbullet \sqcupplus

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 pro- duces a large-operator version of the \Asteriskbinary operator, and\bigcoast produces a large-operator version of the\coAsterisk binary operator.

Table33: ulsyGeometric Binary Operators \odplus

Table34: mathabx Geometric Binary Operators

 \blacktriangledown i \boxright a \ominus

ž \blacktriangleleft m \boxslash ` \oplus

Ÿ \blacktriangleright b \boxtimes i \oright

œ \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 š \smalltriangleleft

d \boxdot g \ocoasterisk › \smalltriangleright

h \boxleft c \odiv ˜ \smalltriangleup

a \boxminus d \odot

` \boxplus h \oleft

Table35: Variable-sized Math Operators

T \ \bigcap N O

\bigotimes V ^

\bigwedge Q Y

\prod

S [ \bigcup F G

\bigsqcup ` a

\coprod P X

\sum

J K \bigodot U ]

\biguplus R Z

\int L M \bigoplus W _

\bigvee H I

\oint

Table 36: AMSVariable-sized Math Operators

\idotsint \iiint

\iiiint

\iint

Table37: stmaryrdVariable-sized Math Operators

3 4 \bigbox 5 6

\biginterleave \bigsqcap

7 8 \bigcurlyvee \bignplus 9 :

\bigtriangledown

; <

\bigcurlywedge = >

\bigparallel ? @

\bigtriangleup

Table38: wasysymVariable-sized Math Operators

\iiint \oiint

\varoint

\iint \varint

Table39: mathabxVariable-sized Math Operators

œ ¬ \bigcurlyvee Ý ý

\bigboxslash É é

\bigoright

– ¦ \bigsqcap Ò ò

\bigboxtimes Í í

\bigoslash

› « \bigcurlywedge Ú ú

\bigboxtop Ê ê

\bigotop Ö ö \bigboxasterisk ß ÿ

\bigboxtriangleup Ï ï

\bigotriangleup Þ þ \bigboxbackslash Ü ü

\bigboxvoid Ì ì

\bigovoid

Û û \bigboxbot ’ ¢

\bigcomplementop   

\bigplus

Õ õ \bigboxcirc Æ æ

\bigoasterisk ˜ ¨

\bigsquplus

× ÷ \bigboxcoasterisk Î î

\bigobackslash ‘ ¡

\bigtimes

Ó ó \bigboxdiv Ë ë

\bigobot µ ½

\iiint

Ô ô \bigboxdot Å å

\bigocirc ´ ¼

\iint

Ø ø \bigboxleft Ç ç

\bigocoasterisk ³ »

\int

Ñ ñ \bigboxminus à ã

\bigodiv · ¿

\oiint

Ð ð \bigboxplus È è

\bigoleft ¶ ¾

\oint

Ù ù \bigboxright Á á

\bigominus

Table40: txfonts/pxfontsVariable-sized Math Operators

\bigsqcapplus \ointclockwise

\bigsqcupplus \ointctrclockwise

\fint \sqiiint

\idotsint \sqiint

\iiiint \sqint

\iiint

\varoiiintclockwise

\iint ! "

\varoiiintctrclockwise

# $

\oiiintclockwise % &

\varoiintclockwise ' (

\oiiintctrclockwise ) *

\varoiintctrclockwise + ,

\oiiint - .

\varointclockwise / 0

\oiintclockwise 1 2

\varointctrclockwise 3 4

\oiintctrclockwise 5 6

\varprod

\oiint

Table 41: esintVariable-sized Math Operators

\dotsint

\ointclockwise

\fint

\ointctrclockwise

\iiiint \sqiint

\iiint

\sqint

\iint ! "

\varoiint

% &

\landdownint

\varointclockwise

# $

\landupint

\varointctrclockwise

\oiint

Table42: 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 L^ATEX 2ε. Use one of the packageslatexsym,amsfonts,amssymb, mathabx,txfonts,pxfonts, orwasysym.

Table43: AMSBinary 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

Table44: AMSNegated Binary Relations \ncong \nshortparallel \nVDash

\nmid \nsim \precnapprox

∦ \nparallel \nsucc \precnsim

⊀ \nprec \nsucceq \succnapprox

\npreceq \nvDash \succnsim

\nshortmid \nvdash

Table45: stmaryrdBinary Relations A \inplus B \niplus

Table46: wasysymBinary Relations \invneg \leadsto \wasypropto

\Join \logof

Table 47: txfonts/pxfontsBinary 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 0 \multimapdotbothBvert ∥ \varparallel 2 \eqcolon 3 \multimapdotbothvert 4 \varparallelinv 5 \eqqcolon 6 \multimapdotinv 7 \VvDash

8 \Eqqcolon 9 \multimapinv

\eqsim : \openJoin

Table48: txfonts/pxfontsNegated Binary Relations

; \napproxeq < \npreccurlyeq = \nthickapprox

> \nasymp ? \npreceqq @ \ntwoheadleftarrow A \nbacksim B \nprecsim C \ntwoheadrightarrow D \nbacksimeq E \nsimeq F \nvarparallel G \nbumpeq H \nsuccapprox I \nvarparallelinv J \nBumpeq K \nsucccurlyeq ! \nVdash

L \nequiv M \nsucceqq N \nprecapprox O \nsuccsim

Table49: 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

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 à \nsuccsim

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

Table51: trsymBinary Relations

\InversTransformHoriz \TransformHoriz \InversTransformVert \TransformVert

Table52: trfsignsBinary Relations c^..... \dfourier ^........... c \Dfourier c \fourier c \Fourier c s \laplace s c \Laplace c^..... s \ztransf s^........... c \Ztransf

Table53: Subset and Superset Relations 8 \sqsubset^∗ ) \sqsupseteq ⊃ \supset + \sqsubseteq ⊂ \subset ⊇ \supseteq 9 \sqsupset^∗ ⊆ \subseteq

∗Not predefined in L^ATEX 2ε. Use one of the packageslatexsym,amsfonts,amssymb, mathabx,txfonts,pxfonts, orwasysym.

Table 54: AMSSubset and Superset Relations

" \nsubseteq : \subseteqq # \supsetneqq

$ \nsupseteq % \subsetneq & \varsubsetneq ' \nsupseteqq ( \subsetneqq ) \varsubsetneqq 8 \sqsubset ; \Supset * \varsupsetneq 9 \sqsupset < \supseteqq + \varsupsetneqq

= \Subset , \supsetneq

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

Table56: wasysymSubset and Superset Relations 8 \sqsubset 9 \sqsupset

Table57: txfonts/pxfontsSubset and Superset Relations P \nsqsubset Q \nsqsupseteq R \nSupset S \nsqsubseteq T \nSubset

U \nsqsupset - \nsubseteqq

Table58: mathabxSubset and Superset Relations

‚ \nsqsubset ƒ \nsupset … \sqsupseteq … \supseteq

– \nsqSubset — \nSupset  \sqsupseteqq  \supseteqq

† \nsqsubseteq ‡ \nsupseteq ‰ \sqsupsetneq ‰ \supsetneq

Ž \nsqsubseteqq  \nsupseteqq ‘ \sqsupsetneqq ‘ \supsetneqq

ƒ \nsqsupset € \sqsubset € \subset Š \varsqsubsetneq

— \nsqSupset ” \sqSubset ” \Subset ’ \varsqsubsetneqq

‡ \nsqsupseteq „ \sqsubseteq „ \subseteq ‹ \varsqsupsetneq

 \nsqsupseteqq Œ \sqsubseteqq Œ \subseteqq “ \varsqsupsetneqq

‚ \nsubset ˆ \sqsubsetneq ˆ \subsetneq Š \varsubsetneq

– \nSubset  \sqsubsetneqq  \subsetneqq ’ \varsubsetneqq

† \nsubseteq • \sqSupset  \supset ‹ \varsupsetneq

Ž \nsubseteqq  \sqsupset • \Supset “ \varsupsetneqq

Table 59: Inequalities

≥ \geq 0 \gg ≤ \leq 2 \ll V \neq

Table 60: AMSInequalities

> \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

Table61: wasysymInequalities \apprge \apprle

Table62: txfonts/pxfontsInequalities

W \ngg X \ngtrsim Y \nlesssim

Z \ngtrapprox [ \nlessapprox \ \nll ] \ngtrless ^ \nlessgtr

Table63: mathabx Inequalities

· \eqslantgtr ½ \gtreqless À \lesssim £ \ngtr

¶ \eqslantless ¿ \gtreqqless ! \ll É \ngtrapprox

¥ \geq » \gtrless Î \lll à \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  \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

mathabxdefines\leqslantand\leas synonyms for\leq,\geqslantand\geas synonyms for \geq, \nleqslant as a synonym for \nleq, and \ngeqslant as a synonym for\ngeq.

Table64: AMSTriangle Relations

N \blacktriangleleft B \ntrianglelefteq \trianglelefteq \vartriangleleft O \blacktriangleright C \ntriangleright \triangleq \vartriangleright D \ntriangleleft E \ntrianglerighteq \trianglerighteq

Table 65: stmaryrdTriangle Relations

G \trianglelefteqslant H \trianglerighteqslant I \ntrianglelefteqslant J \ntrianglerighteqslant

Table66: mathabxTriangle Relations

š \ntriangleleft Ÿ \ntrianglerighteq ™ \triangleright ™ \vartriangleright

ž \ntrianglelefteq ˜ \triangleleft  \trianglerighteq

› \ntriangleright œ \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 L^ATEX 2ε. Use one of the packageslatexsym,amsfonts,amssymb, txfonts,pxfonts, or wasysym.

†See the note beneath Table 112 for information about how to put a diagonal arrow across a mathematical expression (as in “*⁰

∇ ·B ”) .

Table 68: Harpoons

\leftharpoondown \rightharpoondown \rightleftharpoons \leftharpoonup \rightharpoonup

Table 69: textcompText-mode Arrows

↓ \textdownarrow → \textrightarrow

← \textleftarrow ↑ \textuparrow

Table70: AMSArrows

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: AMSNegated Arrows

H \nLeftarrow I \nLeftrightarrow J \nRightarrow K \nleftarrow \nleftrightarrow L \nrightarrow

Table 72: AMSHarpoons

c \downharpoonleft d \leftrightharpoons e \upharpoonleft f \downharpoonright g \rightleftharpoons h \upharpoonright

Table73: stmaryrdArrows

K \leftarrowtriangle ⇐L \Mapsfrom M \shortleftarrow N \leftrightarroweq ←O \mapsfrom P \shortrightarrow Q \leftrightarrowtriangle a⇒ \Mapsto R \shortuparrow

S \lightning T \nnearrow U \ssearrow

⇐=L \Longmapsfrom V \nnwarrow W \sswarrow

←−O \longmapsfrom X \rightarrowtriangle

a

=⇒ \Longmapsto Y \shortdownarrow

Table74: txfonts/pxfontsArrows

b \boxdotLeft c \circleddotright d \Diamondleft e \boxdotleft f \circleleft g \Diamondright h \boxdotright i \circleright j \DiamondRight k \boxdotRight l \dashleftrightarrow m \leftsquigarrow

n \boxLeft o \DiamonddotLeft p \Nearrow

q \boxleft r \Diamonddotleft s \Nwarrow

t \boxright u \Diamonddotright i \Rrightarrow v \boxRight w \DiamonddotRight x \Searrow y \circleddotleft z \DiamondLeft { \Swarrow

Table75: 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

Table76: mathabxNegated Arrows

ö \nLeftarrow Ü \nleftrightarrow Û \nrightarrow Ú \nleftarrow ø \nLeftrightarrow ÷ \nRightarrow

Table77: 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

Table79: ulsy Contradiction Symbols

\blitza \blitzb \blitzc \blitzd \blitze

Table80: Extension Characters

− \relbar = \Relbar

Table81: stmaryrdExtension Characters Z \Arrownot L \Mapsfromchar a \Mapstochar [ \arrownot O \mapsfromchar

Table 82: txfonts/pxfontsExtension Characters

| \Mappedfromchar } \Mmappedfromchar ~ \Mmapstochar

 \mappedfromchar € \mmappedfromchar  \mmapstochar

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

Table84: 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 spac- ing. 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 L^ATEX [Dow00] for samples.

Table 85: AMSLog-like Symbols

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

Load theamsmathpackage to get these symbols. See Section 7.3 for some additional comments regarding log-like symbols. As\modand\podare arguably not symbols we refer the reader to the Short Math Guide for LATEX [Dow00] for samples.

Table86: 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.

Table87: AMSGreek Letters M \digamma κ \varkappa

1Michael J. Downes prefers the more general term, “atomic math objects”.

Table88: txfonts/pxfontsUpright 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

Table 89: upgreekUpright 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

upgreekutilizes 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).

Table90: txfonts/pxfontsVariant Latin Letters

\varg \varv \varw ! \vary

Pass thevargoption totxfonts/pxfontsto replaceg,v,w, andy with,, , and! in every mathematical expression in your document.

Table91: AMSHebrew Letters O \beth ג \gimel Q \daleth

\alephappears in Table 125 on page 38.

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

Table94: txfonts/pxfontsLetter-like Symbols

¢ \mathcent £ \mathsterling ‚ \notin ƒ \notni

Table95: 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

Table96: trfsignsLetter-like Symbols

e \e j \im

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

Table 98: stmaryrdDelimiters

„ \Lbag … \Rbag † \lbag ‡ \rbag

\ \llceil ] \rrceil ^ \llfloor _ \rrfloor

` \llparenthesis a \rrparenthesis

Table99: mathabxDelimiters v \lcorners w \rcorners x \ulcorner y \urcorner z \llcorner { \lrcorner

Table100: nathDelimiters

\niv \vin

Table101: Variable-sized Delimiters

↓ ??y \downarrow ⇓ ww \Downarrow [ h

[ ]

i ] D

\langle E

\rangle | |^∗ ' \|

I l

\lceil J m

\rceil ↑ x?? \uparrow ⇑ ~ww \Uparrow K j

\lfloor L k

\rfloor = x?y \updownarrow @ ~w \Updownarrow (

( )

) { n

\{ } o

\}

/ .

/ \ /

\backslash

When used with \left and \right, these symbols expand to the height of the enclosed 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\leftand\rightsymbols. A similar effect can be achieved in conventional L^ATEX using thebraket package.

Table102: Large, Variable-sized Delimiters 8;

8>

>>

>; \lmoustache 9:

9>

>>

>: \rmoustache 8:

8>

>>

>: \lgroup

9; 9>

>>

>; \rgroup

??

??

??

? \arrowvert ww ww ww

w \Arrowvert >>>>

>>

>>

>>

>>

>> \bracevert

These symbolsmust be used with\leftand\right. Themathabx package, how- ever, redefines\lgroupand\rgroupso that those symbols can work without\left and\right.

Table103: Variable-sizedstmaryrdDelimiters

ˆ 7

\llbracket ‰ 8

\rrbracket

Table104: mathabxVariable-sized Delimiters v 1

\lbbbrack w 9

\rbbbrack 7 77

77 \lfilet ? ??

?? \rfilet

~ \thickvert ~ \vvvert

Table105: nathVariable-sized Delimiters (Double) DD

\lAngle EE

\rAngle [[

hh

\lBrack ]]

ii

\rBrack II ll

\lCeil JJ mm

\rCeil KK jj

\lFloor LL kk

\rFloor

|| \lVert^∗ || \rVert^∗

∗nath redefines all of the above to include implicit \left and \right commands.

Hence, separate\lVertand\rVertcommands are needed to disambiguate whether

“|” is a left or right delimiter.

All of the symbols in Table 105 can also be expressed using the \doublemacro.

See thenathdocumentation for examples and additional information.

Table106: nathVariable-sized Delimiters (Triple) DDD

\triple< EEE

\triple>

[[[

hhh

\triple[ ]]]

iii

\triple]

||| \ltriple|^∗ ||| \rtriple|^∗

∗Similar to\lVertand\rVertin Table 105,\ltripleand\rtriplemust be used instead of \tripleto 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.

Table107: textcompText-mode Delimiters

〈 \textlangle 〉 \textrangle

〚 \textlbrackdbl 〛 \textrbrackdbl

⁅ \textlquill ⁆ \textrquill

Table 108: Math-mode Accents

´

a \acute{a} ˇa \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 38.) 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”.

Table109: AMSMath-mode Accents ...a \dddot{a} ....

a \ddddot{a}

These accents are also provided by themathabxpackage.

Table110: yhmathMath-mode Accents

˚a \ring{a}

This symbol is largely obsolete, as standard L^ATEX 2ε has supported \mathring since June, 1998 [L^AT98].

Table 111: trfsignsMath-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.

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 prob- lems [Gib97], an extensible long-division sign (“ )abc”) can be faked by putting a

“\big)” in atabularenvironment with an\hlineor\clinein the preceding row.

The article also presents a piece of code that automatically solves and typesets—by putting an\overlineatop “\big)” and the desired text—long-division problems.

See also thepolynompackage, which automatically solves and typesets polynomial- division problems in a similar manner.

∗Made more extensible by theyhmathpackage.

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

‡With an optional argument, \sqrt typesets nth roots. For example,

“\sqrt[3]{abc}” produces “√³

abc” and “\sqrt[n]{abc}” produces “√ⁿ abc”.

Table113: overrightarrowExtensible Accents

=⇒

abc \Overrightarrow{abc}

Table 114: yhmathExtensible Accents

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

ö˚

abc \widering{abc}

Table 115: AMSExtensible 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 L^ATEX [Dow00]

for further examples.

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

Table116: chemarrExtensible Accents

−−abc

−− \xrightleftharpoons{abc}

\xrightleftharpoonsis 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.

Table117: chemarrowExtensible Accents

D GGGGGGGabc def

\autoleftarrow{abc}{def}

GGGGGGGAabc def

\autorightarrow{abc}{def}

E GGGGGGGGGGGGGGCabc def

\autoleftrightharpoons{abc}{def}

GGGGGGGBabc F GGGGGGG

def

\autorightleftharpoons{abc}{def}

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

In addition to the symbols shown above, chemarrow also provides \larrowfill,

\rarrowfill, \leftrightharpoonsfill, and \rightleftharpoonsfillmacros.

Each of these takes a length argument and produces an arrow of the specified length.

Table118: mathabx Extensible Accents hkkikkj

abc \overbrace{abc} abc„ \widebar{abc}

hkkkkj

abc \overgroup{abc} abc| \widecheck{abc}

loomoonabc \underbrace{abc} abcΠ\wideparen{abc}

loooonabc \undergroup{abc} abcö˚ \widering{abc}

abcˆ \widearrow{abc}

The braces shown for\overbraceand\underbraceappear in their minimum size.

They can expand arbitrarily wide, however.

Table119: esvectExtensible Accents

# ”

abc \vv{abc}with package optiona

# „

abc \vv{abc}with package optionb

# «

abc \vv{abc}with package optionc

# »

abc \vv{abc}with package optiond

# –

abc \vv{abc}with package optione

# —

abc \vv{abc}with package optionf abc# \vv{abc}with package optiong

# ‰

abc \vv{abc}with package optionh

esvectalso defines a\vv* macro which is used to typeset arrows over vector vari- ables with subscripts. See the esvectdocumentation for more information.

Table120: undertildeExtensible Accents abcÝ \utilde{abc}

Because \utilde is based on\widetilde it is also made more extensible by the yhmathpackage.

Table121: Dots

· \cdotp : \colon^∗ . \ldotp ... \vdots^†

· · · \cdots . .. \ddots^† . . . \ldots

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

†Themathdots 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 L^ATEX 2ε’s

\ddotsand\vdotsmacros.

Table122: AMSDots

· · · \dotsb · · · \dotsi . . . \dotso

. . . \dotsc · · · \dotsm

TheAMS dot symbols are named according to their intended usage: \dotsb be- tween pairs of binary operators/relations,\dotscbetween pairs of commas,\dotsi between pairs of integrals,\dotsmbetween pairs of multiplication signs, and\dotso between other symbol pairs.