the comprehensive latex symbol list - uspthe comprehensive latex symbol list - usp ... atex 7

The Comprehensive LATEX Symbol List

Scott Pakin ltscott+clslpakinorggtlowast

3 January 2008

Abstract

This document lists 4947 symbols and the corresponding LATEX commands that produce them Someof these symbols are guaranteed to be available in every LATEX 2ε system others require fonts and packagesthat may not accompany a given distribution and that therefore need to be installed All of the fontsand packages used to prepare this documentmdashas well as this document itselfmdashare freely available from theComprehensive TEX Archive Network (httpwwwctanorg)

Contents

1 Introduction 711 Document Usage 712 Frequently Requested Symbols 7

2 Body-text symbols 8Table 1 LATEX 2ε Escapable ldquoSpecialrdquo Characters 8Table 2 Predefined LATEX 2ε Text-mode Commands 8Table 3 LATEX 2ε Commands Defined to Work in Both Math and Text Mode 8Table 4 AMS Commands Defined to Work in Both Math and Text Mode 8Table 5 Non-ASCII Letters (Excluding Accented Letters) 9Table 6 Letters Used to Typeset African Languages 9Table 7 Letters Used to Typeset Vietnamese 9Table 8 Punctuation Marks Not Found in OT1 9Table 9 pifont Decorative Punctuation Marks 9Table 10 tipa Phonetic Symbols 10Table 11 tipx Phonetic Symbols 11Table 13 wsuipa Phonetic Symbols 11Table 14 wasysym Phonetic Symbols 12Table 15 phonetic Phonetic Symbols 12Table 16 t4phonet Phonetic Symbols 13Table 17 semtrans Transliteration Symbols 13Table 18 Text-mode Accents 13Table 19 tipa Text-mode Accents 13Table 20 extraipa Text-mode Accents 15Table 21 wsuipa Text-mode Accents 15Table 22 phonetic Text-mode Accents 15Table 23 metre Text-mode Accents 16Table 24 t4phonet Text-mode Accents 16Table 25 arcs Text-mode Accents 16Table 26 semtrans Accents 16Table 27 wsuipa Diacritics 16Table 28 textcomp Diacritics 17Table 29 textcomp Currency Symbols 17Table 30 marvosym Currency Symbols 17lowastThe original version of this document was written by David Carlisle with several additional tables provided by Alexander

Holt See Section 77 on page 104 for more information about who did what

1

Table 31 wasysym Currency Symbols 17Table 32 eurosym Euro Signs 17Table 33 textcomp Legal Symbols 18Table 34 cclicenses Creative Commons License Icons 18Table 35 textcomp Old-style Numerals 18Table 36 Miscellaneous textcomp Symbols 19Table 37 Miscellaneous wasysym Text-mode Symbols 19

3 Mathematical symbols 20Table 38 Math-Mode Versions of Text Symbols 20Table 39 cmll Unary Operators 20Table 40 Binary Operators 20Table 41 AMS Binary Operators 21Table 42 stmaryrd Binary Operators 21Table 43 wasysym Binary Operators 21Table 44 txfontspxfonts Binary Operators 21Table 45 mathabx Binary Operators 22Table 46 MnSymbol Binary Operators 23Table 47 mathdesign Binary Operators 23Table 48 cmll Binary Operators 23Table 49 ulsy Geometric Binary Operators 24Table 50 mathabx Geometric Binary Operators 24Table 51 MnSymbol Geometric Binary Operators 24Table 52 Variable-sized Math Operators 25Table 53 AMS Variable-sized Math Operators 25Table 54 stmaryrd Variable-sized Math Operators 25Table 55 wasysym Variable-sized Math Operators 25Table 56 mathabx Variable-sized Math Operators 26Table 57 txfontspxfonts Variable-sized Math Operators 27Table 58 esint Variable-sized Math Operators 28Table 59 MnSymbol Variable-sized Math Operators 29Table 60 mathdesign Variable-sized Math Operators 29Table 61 cmll Large Math Operators 30Table 62 Binary Relations 30Table 63 AMS Binary Relations 30Table 64 AMS Negated Binary Relations 30Table 65 stmaryrd Binary Relations 30Table 66 wasysym Binary Relations 30Table 67 txfontspxfonts Binary Relations 31Table 68 txfontspxfonts Negated Binary Relations 31Table 69 mathabx Binary Relations 31Table 70 mathabx Negated Binary Relations 32Table 71 MnSymbol Binary Relations 32Table 72 MnSymbol Negated Binary Relations 33Table 73 mathtools Binary Relations 34Table 74 turnstile Binary Relations 34Table 75 trsym Binary Relations 35Table 76 trfsigns Binary Relations 35Table 77 cmll Binary Relations 36Table 78 Subset and Superset Relations 36Table 79 AMS Subset and Superset Relations 36Table 80 stmaryrd Subset and Superset Relations 36Table 81 wasysym Subset and Superset Relations 36Table 82 txfontspxfonts Subset and Superset Relations 36Table 83 mathabx Subset and Superset Relations 37Table 84 MnSymbol Subset and Superset Relations 37Table 85 Inequalities 37Table 86 AMS Inequalities 37

2

Table 87 wasysym Inequalities 38Table 88 txfontspxfonts Inequalities 38Table 89 mathabx Inequalities 38Table 90 MnSymbol Inequalities 39Table 91 AMS Triangle Relations 39Table 92 stmaryrd Triangle Relations 40Table 93 mathabx Triangle Relations 40Table 94 MnSymbol Triangle Relations 40Table 95 Arrows 41Table 96 Harpoons 41Table 97 textcomp Text-mode Arrows 41Table 98 AMS Arrows 41Table 99 AMS Negated Arrows 41Table 100 AMS Harpoons 41Table 101 stmaryrd Arrows 42Table 102 txfontspxfonts Arrows 42Table 103 mathabx Arrows 42Table 104 mathabx Negated Arrows 42Table 105 mathabx Harpoons 43Table 106 MnSymbol Arrows 43Table 107 MnSymbol Negated Arrows 44Table 108 MnSymbol Harpoons 46Table 109 MnSymbol Negated Harpoons 46Table 110 chemarrow Arrows 47Table 111 fge Arrows 47Table 112 MnSymbol Spoons 47Table 113 MnSymbol Pitchforks 47Table 114 MnSymbol Smiles and Frowns 48Table 115 ulsy Contradiction Symbols 48Table 116 Extension Characters 48Table 117 stmaryrd Extension Characters 48Table 118 txfontspxfonts Extension Characters 48Table 119 mathabx Extension Characters 49Table 120 Log-like Symbols 49Table 121 AMS Log-like Symbols 49Table 122 Greek Letters 49Table 123 AMS Greek Letters 49Table 124 txfontspxfonts Upright Greek Letters 50Table 125 upgreek Upright Greek Letters 50Table 126 txfontspxfonts Variant Latin Letters 50Table 127 AMS Hebrew Letters 50Table 128 MnSymbol Hebrew Letters 50Table 129 Letter-like Symbols 51Table 130 AMS Letter-like Symbols 51Table 131 txfontspxfonts Letter-like Symbols 51Table 132 mathabx Letter-like Symbols 51Table 133 MnSymbol Letter-like Symbols 51Table 134 trfsigns Letter-like Symbols 51Table 135 mathdesign Letter-like Symbols 51Table 136 fge Letter-like Symbols 52Table 137 AMS Delimiters 52Table 138 stmaryrd Delimiters 52Table 139 mathabx Delimiters 52Table 140 nath Delimiters 52Table 141 Variable-sized Delimiters 53Table 142 Large Variable-sized Delimiters 53Table 143 AMS Variable-sized Delimiters 53

3

Table 144 stmaryrd Variable-sized Delimiters 53Table 145 mathabx Variable-sized Delimiters 54Table 146 MnSymbol Variable-sized Delimiters 54Table 147 mathdesign Variable-sized Delimiters 55Table 148 nath Variable-sized Delimiters (Double) 55Table 149 nath Variable-sized Delimiters (Triple) 55Table 150 textcomp Text-mode Delimiters 56Table 151 metre Text-mode Delimiters 56Table 152 Math-mode Accents 56Table 153 AMS Math-mode Accents 56Table 154 MnSymbol Math-mode Accents 56Table 155 fge Math-mode Accents 56Table 156 yhmath Math-mode Accents 57Table 157 Extensible Accents 57Table 158 overrightarrow Extensible Accents 57Table 159 yhmath Extensible Accents 57Table 160 AMS Extensible Accents 58Table 161 MnSymbol Extensible Accents 58Table 162 mathtools Extensible Accents 58Table 163 mathabx Extensible Accents 58Table 164 esvect Extensible Accents 59Table 165 undertilde Extensible Accents 59Table 166 AMS Extensible Arrows 59Table 167 mathtools Extensible Arrows 59Table 168 chemarr Extensible Arrows 59Table 169 chemarrow Extensible Arrows 60Table 170 trfsigns Extensible Arrows 60Table 171 extarrows Extensible Arrows 60Table 172 extpfeil Extensible Arrows 60Table 173 holtpolt Non-commutative Division Symbols 60Table 174 Dots 61Table 175 AMS Dots 61Table 176 wasysym Dots 61Table 177 MnSymbol Dots 61Table 178 mathdots Dots 62Table 179 yhmath Dots 62Table 180 mathcomp Math Symbols 62Table 181 mathabx Mayan Digits 62Table 182 marvosym Digits 62Table 183 fge Digits 62Table 184 Miscellaneous LATEX 2ε Math Symbols 62Table 185 Miscellaneous AMS Math Symbols 63Table 186 Miscellaneous wasysym Math Symbols 63Table 187 Miscellaneous txfontspxfonts Math Symbols 63Table 188 Miscellaneous mathabx Math Symbols 63Table 189 Miscellaneous MnSymbol Math Symbols 63Table 190 Miscellaneous Internal MnSymbol Math Symbols 64Table 191 Miscellaneous textcomp Text-mode Math Symbols 64Table 192 Miscellaneous marvosym Math Symbols 64Table 193 Miscellaneous fge Math Symbols 64Table 194 Miscellaneous mathdesign Math Symbols 64Table 195 Miscellaneous arev Math Symbols 64Table 196 Math Alphabets 65

4

4 Science and technology symbols 67Table 197 gensymb Symbols Defined to Work in Both Math and Text Mode 67Table 198 wasysym Electrical and Physical Symbols 67Table 199 ifsym Pulse Diagram Symbols 67Table 200 ar Aspect Ratio Symbol 67Table 201 textcomp Text-mode Science and Engineering Symbols 67Table 202 wasysym Astronomical Symbols 68Table 203 marvosym Astronomical Symbols 68Table 204 mathabx Astronomical Symbols 68Table 205 wasysym APL Symbols 68Table 206 wasysym APL Modifiers 68Table 207 marvosym Computer Hardware Symbols 69Table 208 keystroke Computer Keys 69Table 209 ascii Control Characters (CP437) 69Table 210 marvosym Communication Symbols 69Table 211 marvosym Engineering Symbols 70Table 212 wasysym Biological Symbols 70Table 213 marvosym Biological Symbols 70Table 214 marvosym Safety-related Symbols 70Table 215 feyn Feynman Diagram Symbols 70

5 Dingbats 71Table 216 bbding Arrows 71Table 217 pifont Arrows 71Table 218 universal Arrows 71Table 219 marvosym Scissors 71Table 220 bbding Scissors 71Table 221 pifont Scissors 71Table 222 dingbat Pencils 72Table 223 bbding Pencils and Nibs 72Table 224 pifont Pencils and Nibs 72Table 225 dingbat Fists 72Table 226 bbding Fists 72Table 227 pifont Fists 72Table 228 bbding Crosses and Plusses 72Table 229 pifont Crosses and Plusses 72Table 230 bbding Xs and Check Marks 73Table 231 pifont Xs and Check Marks 73Table 232 wasysym Xs and Check Marks 73Table 233 universal Xs 73Table 234 pifont Circled Numbers 73Table 235 wasysym Stars 73Table 236 bbding Stars Flowers and Similar Shapes 74Table 237 pifont Stars Flowers and Similar Shapes 74Table 238 wasysym Geometric Shapes 74Table 239 MnSymbol Geometric Shapes 74Table 240 ifsym Geometric Shapes 75Table 241 bbding Geometric Shapes 75Table 242 pifont Geometric Shapes 75Table 243 universa Geometric Shapes 76Table 244 universal Geometric Shapes 76Table 245 igo Go Stones 76Table 246 manfnt Dangerous Bend Symbols 76Table 247 skull Symbols 76Table 248 Non-Mathematical mathabx Symbols 76Table 249 marvosym Information Symbols 76Table 250 Miscellaneous dingbat Dingbats 77Table 251 Miscellaneous bbding Dingbats 77

5

Table 252 Miscellaneous pifont Dingbats 77

6 Other symbols 78Table 253 textcomp Genealogical Symbols 78Table 254 wasysym General Symbols 78Table 255 wasysym Circles 78Table 256 wasysym Musical Symbols 78Table 257 arev Musical Symbols 78Table 258 harmony Musical Symbols 79Table 259 harmony Musical Accents 79Table 260 Miscellaneous manfnt Symbols 79Table 261 marvosym Navigation Symbols 79Table 262 marvosym Laundry Symbols 80Table 263 Other marvosym Symbols 80Table 264 Miscellaneous universa Symbols 80Table 265 Miscellaneous universal Symbols 80Table 266 ifsym Weather Symbols 80Table 267 ifsym Alpine Symbols 81Table 268 ifsym Clocks 81Table 269 Other ifsym Symbols 81Table 270 epsdice Dice 81Table 271 skak Chess Informator Symbols 82Table 272 metre Metrical Symbols 82Table 273 metre Small and Large Metrical Symbols 82Table 274 phaistos Symbols from the Phaistos Disk 83Table 275 protosem Proto-Semitic Characters 83Table 276 hieroglf Hieroglyphics 84Table 277 dictsym Dictionary Symbols 84Table 278 simpsons Characters from The Simpsons 85Table 279 staves Magical Staves 85

7 Additional Information 8771 Symbol Name Clashes 8772 Resizing symbols 8773 Where can I find the symbol for 8774 Math-mode spacing 9975 Bold mathematical symbols 10076 ASCII and Latin 1 quick reference 10077 About this document 10478 Copyright and license 106

References 106

Index 107

6

1 Introduction

Welcome to the Comprehensive LATEX Symbol List This document strives to be your primary source of LATEXsymbol information font samples LATEX commands packages usage details caveatsmdasheverything needed toput 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 (httpwwwctanorg)

2 All of their symbols have LATEX 2ε bindings That is a user should be able to access a symbol by namenot just by char〈number〉

These are not particularly limiting criteria the Comprehensive LATEX Symbol List contains samples of 4947symbolsmdashquite a large number Some of these symbols are guaranteed to be available in every LATEX 2ε systemothers require fonts and packages that may not accompany a given distribution and that therefore need tobe installed See httpwwwtexacukcgi-bintexfaq2htmllabel=instpackages+wherefiles for helpwith installing new fonts and packages

11 Document Usage

Each section of this document contains a number of font tables Each table shows a set of symbols with thecorresponding LATEX command to the right of each symbol A tablersquos caption indicates what package needs tobe loaded in order to access that tablersquos symbols For example the symbols in Table 35 ldquotextcomp Old-StyleNumeralsrdquo are made available by putting ldquousepackagetextcomprdquo in your documentrsquos preamble ldquoAMSrdquomeans to use the AMS packages viz amssymb andor amsmath Notes below a table provide additionalinformation 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 certainsymbols do not exist in the OT1 font encoding (Donald Knuthrsquos original 7-bit font encoding which is thedefault 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 ldquousepackage[〈encoding〉]fontencrdquo inyour documentrsquos preamble where 〈encoding〉 is eg T1 or LY1 To limit the change in font encoding to thecurrent group use ldquofontencoding〈encoding〉selectfontrdquo

Section 7 contains some additional information about the symbols in this document It shows which symbolnames are not unique across packages gives examples of how to create new symbols out of existing symbolsexplains how symbols are spaced in math mode presents a LATEX ASCII and Latin 1 tables and providessome information about this document itself The Comprehensive LATEX Symbol List ends with an index ofall the symbols in the document and various additional useful terms

12 Frequently Requested Symbols

There are a number of symbols that are requested over and over again on comptexttex If yoursquore lookingfor such a symbol the following list will help you find it quickly

as in ldquoSpaces are significantrdquo 8

ı ı ı ı etc (versus ı ı i and ı) 13

cent 17

e 17

copy reg and trade 18

permil 19 27

there4 30

B and F 31

and amp 37

62

deg as in ldquo180degrdquo or ldquo15rdquo 64

L F etc 65

N Z R etc 65

minusint

92

acutea è etc (ie several accents per character) 94

lt gt and | (instead of iexcl iquest and mdash) 100

ˆ and ˜ (or sim) 101

7

2 Body-text symbols

This section lists symbols that are intended for use in running text such as punctuation marks accentsligatures and currency symbols

Table 1 LATEX 2ε Escapable ldquoSpecialrdquo Characters

$ $ _ lowast amp amp

lowast The underscore package redefines ldquo_rdquo to produce an underscore in text mode (ie itmakes it unnecessary to escape the underscore character)

Table 2 Predefined LATEX 2ε Text-mode Commands

ˆ textasciicircum lt textless˜ textasciitilde a ordf textordfemininelowast textasteriskcentered o ordm textordmasculine textbackslash para textparagraphlowast

| textbar middot textperiodcentered textbraceleftlowast iquest textquestiondown textbracerightlowast ldquo textquotedblleftbull textbullet rdquo textquotedblright

ccopy copy textcopyrightlowast lsquo textquoteleftdagger textdaggerlowast rsquo textquoterightDagger textdaggerdbllowast rcopy reg textregistered$ textdollarlowast sect textsectionlowast

textellipsislowast pound textsterlinglowast

mdash textemdash TM trade texttrademarkndash textendash textunderscorelowast

iexcl textexclamdown textvisiblespacegt textgreater

Where two symbols are present the left one is the ldquofakedrdquo symbol that LATEX 2εprovides by default and the right one is the ldquotruerdquo symbol that textcomp makesavailable

lowast Itrsquos generally preferable to use the corresponding symbol from Table 3 because thesymbols in that table work properly in both text mode and math mode

Table 3 LATEX 2ε Commands Defined to Work in Both Math and Text Mode

$ $ _ Dagger ddag para P ccopy copy copyright dots sect S dagger dag pound pounds


Table 4 AMS Commands Defined to Work in Both Math and Text Mode

X checkmark r circledR z maltese

8

Table 5 Non-ASCII Letters (Excluding Accented Letters)

a aa ETH DHlowast L L oslash o szlig ss

A AA eth dhlowast l l Oslash O SS SSAElig AE ETH DJlowast Ŋ NGlowast Œ OE THORN THlowast

aelig ae đ djlowast ŋ nglowast œ oe thorn thlowast

lowast Not available in the OT1 font encoding Use the fontenc package to select analternate font encoding such as T1

Table 6 Letters Used to Typeset African Languages

ETH BD deg mc curren mf uml mk raquo Mt mZ Bd mD mF mN MT Acirc TE BH eth Md mG shy mn ordm mt acirc Tesect Bh ETH MD brvbar mg ordf mo mT Aring TOmiddot Bt iexcl md Agrave mI mO reg mulowast aring To BT mE agrave mi mP mUlowast

mb cent me mJ plusmn mp mY mB ME copy mj not ms macr my mC pound Me mK mS para mz

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

lowast mv and mV are synonyms for mu and mU

Table 7 Letters Used to Typeset Vietnamese

Ơ OHORN ơ ohorn Ư UHORN ư uhorn

These characters all need the T5 font encoding which is provided by the vntexpackage

Table 8 Punctuation Marks Not Found in OT1

laquo guillemotleft lsaquo guilsinglleft bdquo quotedblbase textquotedblraquo guillemotright rsaquo guilsinglright sbquo quotesinglbase

To get these symbols use the fontenc package to select an alternate font encodingsuch as T1

Table 9 pifont Decorative Punctuation Marks

ding123 ding125 iexcl ding161 pound ding163| ding124 ~ ding126 cent ding162

9

Table 10 tipa Phonetic Symbols

Egrave textbabygamma P textglotstop iuml textrtailnb textbarb texthalflength oacute textrtailrc textbarc ż texthardsign ugrave textrtailsd textbard texthooktop uacute textrtailteacute textbardotlessj aacute texthtb uuml textrtailzg textbarg ecirc texthtbardotlessj $ textrthookUuml textbarglotstop Aacute texthtc Agrave textsca1 textbari acirc texthtd agrave textscbł textbarl auml texthtg ď textsce8 textbaro H texthth aring textscgYacute textbarrevglotstop Ecirc texththeng Euml textsch0 textbaru Icirc texthtk textschwaigrave textbeltl Ograve texthtp I textsciB textbeta Oacute texthtq ĺ textscjograve textbullseye č texthtrtaild Iuml textscl textceltpal Eacute texthtscg eth textscnX textchi Ouml texthtt Œ textscoeligAring textcloseepsilon szlig texthvlig ś textscomegaNtilde textcloseomega Ucirc textinvglotstop ouml textscrAElig textcloserevepsilon K textinvscr A textscriptaTHORN textcommatailz Igrave textiota g textscriptg^ textcorner ń textlambda V textscriptvă textcrb textlengthmark Uacute textscuą textcrd ş textlhookt Y textscyg textcrg ę textlhtlongi shy textsecstressegrave textcrh ű textlhtlongy ž textsoftsignUcirc textcrinvglotstop Ocirc textlonglegr Acirc textstretchcň textcrlambda iexcl textlptr tC texttctclig2 textcrtwo M textltailm Ugrave textteshligC textctc ntilde textltailn T textthetać textctd euml textltilde thorn textthornćyacute textctdctzlig ETH textlyoghlig pound texttoneletterstemš textctesh Iacute textObardotlessj ţ texttsligJ textctj ŋ textOlyoghlig 5 textturnaő textctn ř textomega ŕ textturnceligť textctt _ textopencorner 4 textturnhťC textcttctclig O textopeno ľ textturnkyuml textctyogh textpalhook Otilde textturnlonglegryacute textctz F textphi W textturnmdyacute textdctzlig | textpipe icirc textturnmrlegS textdoublebaresh textprimstress ocirc textturnr textdoublebarpipe ĳ textraiseglotstop otilde textturnrrtail= textdoublebarslash ğ textraisevibyi 6 textturnscripta textdoublepipe 7 textramshorns Oslash textturntŞ textdoublevertline textrevapostrophe 2 textturnvŤ textdownstep 9 textreve ucirc textturnwAtilde textdyoghlig 3 textrevepsilon L textturnydz textdzlig Q textrevglotstop U textupsilonE textepsilon ź textrevyogh Ţ textupstepS textesh Ccedil textrhookrevepsilon Š textvertline

(continued on next page)

10

(continued from previous page)

R textfishhookr Auml textrhookschwa ğ textvibyiě textg ~ textrhoticity ů textvibyyG textgamma iquest textrptr szlig textwynnŮ textglobfall atilde textrtaild Z textyoghŰ textglobrise iacute textrtaill

tipa defines shortcut characters for many of the above It also defines a commandtone for denoting tone letters (pitches) See the tipa documentation for moreinformation

Table 11 tipx Phonetic Symbols

textaolig 3 texthtbardotlessjvar acute textrthooklongB textbenttailyogh textinvomega q textscaolig textbktailgamma p textinvsca r textscdeltaD textctinvglotstop textinvscripta s textscf2 textctjvar I textlfishhookrlig t textsck textctstretchc textlhookfour w textscmamp textctstretchcvar lt textlhookp x textscp textctturnt 1 textlhti y textscq) textdblig gt textlooptoprevesh ˝ textspleftarrowH textdoublebarpipevar 6 textnrleg $ textstretchcvarG textdoublepipevar 9 textObullseye ˙ textsubdoublearrowˇ textdownfullarrow ˆ textpalhooklong macr textsubrightarrow7 textfemale ˜ textpalhookvar P textthornvari5 textfrbarn F textpipevar Q textthornvariirsquo textfrhookd = textqplig R textthornvariii( textfrhookdvar uml textrectangle S textthornvariv textfrhookt ˚ textretractingvar E textturnglotstop- textfrtailgamma v textrevscl u textturnsckT textglotstopvari z textrevscr textturnscuU textglotstopvarii textrhooka C textturnthreeV textglotstopvariii textrhooke A textturntwo textgrgamma + textrhookepsilon 8 textuncrfemale0 textheng textrhookopeno ˘ textupfullarrow4 texthmlig textrtailhth

Table 13 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


11


lt baro b glotstop nialpha scriptgA barp hookb nibeta Y scriptv+ barsci hookd [ nichi W scuX barscu hookg niepsilon ] scyT baru $ hookh nigamma slashb clickb hookheng ) niiota slashc clickc hookrevepsilon 2 nilambda slashdR clickt hv gt niomega U slashu closedniomega inva C niphi taild closedrevepsilon invf O nisigma H tailinvr crossb d invglotstop S nitheta 0 taill13 crossd amp invh V niupsilon 9 tailn crossh I invlegr 7 nj F tailr3 crossnilambda 5 invm oo L tails curlyc G invr = openo P tailtN curlyesh K invscr reve _ tailza curlyyogh invscripta f reveject Q tesh^ curlyz invv revepsilon B thorn( dlbari Z invw c revglotstop - tildel dz invy scd ` yoghe ejective ipagamma scg

Table 14 wasysym Phonetic Symbols

D DH k dh l openoTHORN Thorn U inve thorn thorn

Table 15 phonetic Phonetic Symbols

j barj f flap i ibar A rotvara i vari barlambda glottal c openo w rotw varomegaM emgma B hausaB h planck y roty C varopenon 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 yoghs esh k hausak m rotm u udescd eth K hausaK rotOmega a varaF fj D hookd r rotr G varg

12

Table 16 t4phonet Phonetic Symbols

textcrd iexcl texthtd | textpipesect textcrh uml texthtk eth textrtaildcent textepsilon plusmn texthtp raquo textrtailtnot textesh ordm texthtt iexcl textschwa textfjlig agrave textiota not textscriptv texthtb copy textltailn textteshligdeg texthtc ordf textopeno para textyogh

The idea behind the t4phonet packagersquos phonetic symbols is to provide an interfaceto some of the characters in the T4 font encoding (Table 6 on page 9) but usingthe same names as the tipa characters presented in Table 10 on page 10

Table 17 semtrans Transliteration Symbols

Alif Ayn

Table 18 Text-mode Accents

Aa Aa Aa lsquoAlsquoa A a dAda Aa rAra

Aa rsquoArsquoa iquestAiquesta |A|aDagger Aa GAGaDagger A a tAta

Aa Aa Aa ~A~a Ảả hAhasect Aa uAua

Aa =A=a Amacr

amacr

bAba Aa HAHa frac14Afrac14a UAUaDagger

Aa Ââ Aa cAca Ąą kAkadagger Aa vAva

Aa newtieAnewtiealowast Acopy acopy textcircledAtextcircleda

lowast Requires the textcomp packagedagger Not available in the OT1 font encoding Use the fontenc package to select an

alternate font encoding such as T1Dagger Requires the T4 font encoding provided by the fc packagesect Requires the T5 font encoding provided by the vntex package

Also note the existence of i and j which produce dotless versions of ldquoirdquo and ldquojrdquo(viz ldquoırdquo and ldquordquo) These are useful when the accent is supposed to replace thedot For example ldquonaiverdquo produces a correct ldquonaıverdquo while ldquonaiverdquowould yield the rather odd-looking ldquonaıverdquo (ldquonaiverdquo does work in encodingsother than OT1 however)

Table 19 tipa Text-mode Accents

acuteAacutea textacutemacronAtextacutemacronaacuteAacutea textacutewedgeAtextacutewedgea


13


Affi affi textadvancingAtextadvancinga

Altalt textbottomtiebarAtextbottomtiebara˘A˘a textbrevemacronAtextbrevemacronaŻAŻa textcircumacuteAtextcircumacuteaÂâ textcircumdotAtextcircumdotasectAsecta textdotacuteAtextdotacutea˙A ˙a textdotbreveAtextdotbrevea˙A ˙a textdotbreveAtextdotbreveasbquoAsbquoa textdoublegraveAtextdoublegraveaİAİa textdoublevbaraccentAtextdoublevbaraccentaŽAŽa textgravecircumAtextgravecircumađAđa textgravedotAtextgravedotaÀà textgravemacronAtextgravemacronaŹAŹa textgravemidAtextgravemida

Abdquoabdquo textinvsubbridgeAtextinvsubbridgea

Afl afl textloweringAtextloweringaŸAŸa textmidacuteAtextmidacuteapermilApermila textovercrossAtextovercrossamdashA

mdasha textoverwAtextoverwa

Aa textpolhookAtextpolhooka

Afi afi textraisingAtextraisinga

Affl affl textretractingAtextretractinga˚Aa textringmacronAtextringmacronaldquoAldquoa textroundcapAtextroundcapa

Aa textseagullAtextseagulla

Arsaquo

arsaquo

textsubacuteAtextsubacutea

Aldquo

aldquo

textsubarchAtextsubarcha

Amacr

amacr

textsubbarAtextsubbara

Ardquoardquo textsubbridgeAtextsubbridgea

Aˆ

aˆ

textsubcircumAtextsubcircuma

A˙a˙

textsubdotAtextsubdota

Alsaquo

alsaquo

textsubgraveAtextsubgravea

Andash andash textsublhalfringAtextsublhalfringa

Aff aff textsubplusAtextsubplusa

Araquo araquo textsubrhalfringAtextsubrhalfringa

A˚

a˚

textsubringAtextsubringa

Alaquoalaquo textsubsquareAtextsubsquarea

A˜

a˜

textsubtildeAtextsubtildea

Auml

auml

textsubumlautAtextsubumlauta

Amdashamdash textsubwAtextsubwa

Aˇ

aˇ

textsubwedgeAtextsubwedgea

Aampaamp textsuperimposetildeAtextsuperimposetildea


14


Aa

textsyllabicAtextsyllabicaÃã texttildedotAtexttildedotagtAgta texttoptiebarAtexttoptiebaraĲAĲa textvbaraccentAtextvbaraccenta

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

Table 20 extraipa Text-mode Accents

rdquoArdquo

rdquoardquo bibridgeAbibridgea Andash raquoandash raquo partvoicelessApartvoicelessa

ŔA Ŕa crtildeAcrtildea Aa slidingAslidingaAa dottedtildeAdottedtildea Aa spreadlipsAspreadlipsaÃã doubletildeAdoubletildea A

â^

subcornerAsubcornera

Araquoaraquo finpartvoiceAfinpartvoicea Amacr

amacr

subdoublebarAsubdoublebara

Araquoaraquo finpartvoicelessAfinpartvoicelessa A

a

subdoublevertAsubdoubleverta

Andash andash inipartvoiceAinipartvoicea Aiexclaiexcl

sublptrAsublptra

Andash andash inipartvoicelessAinipartvoicelessa Aiquestaiquest

subrptrAsubrptrardquoA

rdquoa overbridgeAoverbridgea A

ŢaŢ

whistleAwhistlea

Andash raquoandash raquo partvoiceApartvoicea

Table 21 wsuipa Text-mode Accents

Ag ag dentalAdentala

Aa underarchAunderarcha

Table 22 phonetic Text-mode Accents

Aa

hillAhilla Aa rcArca A˜

a˜

utAuta

A˚

a˚

odAoda Aa sylAsylaA a ohillAohilla Aa tdAtda

The phonetic package provides a few additional macros for linguistic accentsacbar and acarc compose characters with multiple accents for exampleacbarrsquoa produces ldquoacuteardquo and acarce produces ldquoumlerdquo labvel joinstwo characters with an arc labvelmn rarr ldquo_mnrdquo upbar is intended to gobetween characters as in ldquoxupbaryrsquorsquo rarr ldquox yrdquo Lastly uplett behaves liketextsuperscript but uses a smaller font Contrast ldquopupletthrsquorsquo rarr ldquophrdquowith ldquoptextsuperscripthrsquorsquo rarr ldquophrdquo

15

Table 23 metre Text-mode Accents

Aa acutusAacutusa

Aa breveAbreveaAa circumflexusAcircumflexusaAa diaeresisAdiaeresisa

Aa gravisAgravisaAa macronAmacrona

Table 24 t4phonet Text-mode Accents

Aa textdoublegraveAtextdoublegraveaiquestAiquesta textvbaraccentAtextvbaraccentafrac14Afrac14a textdoublevbaraccentAtextdoublevbaraccenta

The idea behind the t4phonet packagersquos text-mode accents is to provide an interfaceto some of the accents in the T4 font encoding (accents marked with ldquoDaggerrdquo in Table 18on page 13) but using the same names as the tipa accents presented in Table 19 onpage 13

Table 25 arcs Text-mode Accents

A_

a_ overarcAoverarca Aa underarcAunderarca

The accents shown above scale only to a few characters wide An optional macroargument alters the effective width of the accented characters See the arcs docu-mentation for more information

Table 26 semtrans Accents

Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast

T is not actually an accent but a command that rotates its argument 180deg usingthe graphicx packagersquos rotatebox command

Table 27 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 accentsHowever it does provide diatop and diaunder commands which are used tocompose diacritics with other characters For example diatop[overring|a]produces ldquoxardquo and diaunder[underdots|a] produces ldquorardquo See the wsuipa doc-umentation for more information

16

Table 28 textcomp Diacritics

˝ textacutedbl ˇ textasciicaron macr textasciimacronacute textasciiacute uml textasciidieresis textgravedbl˘ textasciibreve ` textasciigrave

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

Table 29 textcomp Currency Symbols

฿ textbaht $ textdollarlowast textguarani ₩ textwoncent textcent textdollaroldstyle ₤ textlira yen textyen textcentoldstyle ₫ textdong ₦ textnaira₡ textcolonmonetary euro texteuro textpesocurren textcurrency ƒ textflorin pound textsterlinglowast

lowast Itrsquos generally preferable to use the corresponding symbol from Table 3 on page 8because the symbols in that table work properly in both text mode and math mode

Table 30 marvosym Currency Symbols

cent Denarius e EUR D EURdig e EURtm pound Pfund Ecommerce d EURcr c EURhv brvbar EyesDollar iexcl Shilling

The different euro signs are meant to be visually compatible with different fontsmdashCourier (EURcr) Helvetica (EURhv) Times Roman (EURtm) and the marvosymdigits listed in Table 182 (EURdig) The mathdesign package redefines texteuroto be visually compatible with one of three additional fonts Utopia (euro) Char-ter (euro) or Garamond (euro)

Table 31 wasysym Currency Symbols

cent cent curren currency

Table 32 eurosym Euro Signs

AC geneuro BC geneuronarrow CC geneurowide e officialeuro

euro is automatically mapped to one of the abovemdashby default officialeuromdashbased on a eurosym package option See the eurosym documentation for moreinformation The geneuro characters are generated from the current bodyfontrsquos ldquoCrdquo character and therefore may not appear exactly as shown

17

Table 33 textcomp Legal Symbols

textcircledP ccopy copy textcopyright textservicemarklaquo textcopyleft rcopy reg textregistered TM trade texttrademark


See httpwwwtexacukcgi-bintexfaq2htmllabel=tradesyms for solu-tions to common problems that occur when using these symbols (eg getting a ldquo rcopyrdquowhen you expected to get a ldquoregrdquo)

Table 34 cclicenses Creative Commons License Icons

CCcopy cc BYcopy ccby $copy ccnclowast =copy ccnd

Ccopy ccsalowast

lowast These symbols utilize the rotating package and therefore display improperly in mostDVI viewers

Table 35 textcomp Old-style Numerals

textzerooldstyle textfouroldstyle texteightoldstyle textoneoldstyle textfiveoldstyle textnineoldstyle texttwooldstyle textsixoldstyle textthreeoldstyle textsevenoldstyle

Rather than use the bulky textoneoldstyle texttwooldstyle etc commandsshown above consider using oldstylenums to typeset an old-style number

18

Table 36 Miscellaneous textcomp Symbols

lowast textasteriskcentered a ordf textordfeminine textbardbl o ordm textordmasculine textbigcircle para textparagraphlowast

textblank middot textperiodcenteredbrvbar textbrokenbar textpertenthousandbull textbullet permil textperthousanddagger textdaggerlowast para textpilcrowDagger textdaggerdbllowast textquotesingle- textdblhyphen sbquo textquotestraightbase textdblhyphenchar bdquo textquotestraightdblbase textdiscount textrecipe textestimated textreferencemark textinterrobang sect textsectionlowast

textinterrobangdown textthreequartersemdash textmusicalnote ~ texttildelow textnumero texttwelveudash textopenbullet



Table 37 Miscellaneous wasysym Text-mode Symbols

h permil

19

3 Mathematical symbols

Most but not all of the symbols in this section are math-mode only That is they yield a ldquoMissing $insertedrdquo error message if not used within $ $ [ ] or another math-mode environment Operatorsmarked as ldquovariable-sizedrdquo are taller in displayed formulas shorter in in-text formulas and possibly shorterstill when used in various levels of superscripts or subscripts

Alphanumeric symbols (eg ldquoL rdquo and ldquordquo) are usually produced using one of the math alphabets inTable 196 rather than with an explicit symbol command Look there first if you need a symbol for a transformnumber set or some other alphanumeric

Although there have been many requests on comptexttex for a contradiction symbol the ensuing dis-cussion invariably reveals innumerable ways to represent contradiction in a proof including ldquordquo (blitza)ldquorArrlArrrdquo (RightarrowLeftarrow) ldquoperprdquo (bot) ldquo=rdquo (nleftrightarrow) and ldquordquo (textreferencemark)Because of the lack of notational consensus it is probably better to spell out ldquoContradictionrdquo than to use asymbol for this purpose Similarly discussions on comptexttex have revealed that there are a variety ofways to indicate the mathematical notion of ldquois defined asrdquo Common candidates include ldquordquo (triangleq)ldquoequivrdquo (equiv) ldquoBrdquo (coloneqq) and ldquodef=rdquo (stackreltexttiny def=) See also the example ofequalsfill on page 95 Depending upon the context disjoint union may be represented as ldquo

∐rdquo (coprod)

ldquotrdquo (sqcup) ldquo middotcuprdquo (dotcup) ldquooplusrdquo (oplus) or any of a number of other symbols1 Finally the averagevalue of a variable x is written by some people as ldquoxrdquo (overlinex) by some people as ldquo〈x〉rdquo (langle xrangle) and by some people as ldquoxrdquo or ldquoemptyxrdquo (diameter x or varnothing x) The moral of the story isthat you should be careful always to explain your notation to avoid confusing your readers

Table 38 Math-Mode Versions of Text Symbols

$ mathdollar para mathparagraph pound mathsterling mathellipsis sect mathsection mathunderscore

Itrsquos generally preferable to use the corresponding symbol from Table 3 on page 8because the symbols in that table work properly in both text mode and math mode

Table 39 cmll Unary Operators

oclowast ˆ shneg wnlowast

˜ shift acute shpos

lowast oc and wn differ from ldquordquo and ldquordquo in terms of their math-mode spacing $A=B$produces ldquoA =Brdquo for example while $A=oc B$ produces ldquoA = Brdquo

Table 40 Binary Operators

q amalg cup cup oplus oplus times timeslowast ast dagger dagger oslash triangleleftcopy bigcirc Dagger ddagger otimes otimes triangleright5 bigtriangledown diamond plusmn pm E unlhdlowast

4 bigtriangleup divide div B rhdlowast D unrhdlowast

bull bullet C lhdlowast setminus ] upluscap cap ∓ mp u sqcap or veemiddot cdot odot t sqcup and wedge circ ominus star o wr

lowast Not predefined in LATEX 2ε Use one of the packages latexsym amsfonts amssymbtxfonts pxfonts or wasysym

1Bob Tennent listed these and other disjoint-union symbol possibilities in a November 2007 post to comptexttex

20

Table 41 AMS Binary Operators

Z barwedge circledcirc ᵀ intercal boxdot circleddash h leftthreetimes boxminus d Cup n ltimes boxplus g curlyvee i rightthreetimes boxtimes f curlywedge o rtimese Cap gt divideontimes r smallsetminus centerdot u dotplus Y veebar~ circledast [ doublebarwedge

Table 42 stmaryrd Binary Operators

baro 9 interleave varoast13 bbslash 2 leftslice varobarN binampersand merge varobslashO bindnasrepma minuso varocirclei boxast moo varodotk boxbar ` nplus 5 varogreaterthan boxbox obar 4 varolessthanj boxbslash oblong varominus boxcircle obslash varoplus boxdot = ogreaterthan varoslash boxempty lt olessthan varotimesl boxslash gt ovee 6 varovee curlyveedownarrow owedge 7 varowedge curlyveeuparrow 3 rightslice vartimes curlywedgedownarrow sslash Ydownamp curlywedgeuparrow 8 talloblong Yleft) fatbslash varbigcirc Yright fatsemi varcurlyvee Yup( fatslash varcurlywedge

Table 43 wasysym Binary Operators

C lhd ocircle RHD D unrhd LHD B rhd E unlhd

Table 44 txfontspxfonts Binary Operators

V circledbar T circledwedge medcircW circledbslash M invamp sqcapplusU circledvee medbullet | sqcupplus

21

Table 45 mathabx Binary Operators

ast N curlywedge [ sqcap Asterisk divdot sqcupX barwedge divideontimes ^ sqdoublecap bigstar dotdiv _ sqdoublecup bigvarstar dotplus square blackdiamond dottimes ] squplusX cap Z doublebarwedge udot circplus doublecap Z uplus coasterisk ] doublecup varstar coAsterisk ltimes _ vee convolution pluscirc Y veebarY cup rtimes [ veedoublebarO curlyvee 13 sqbullet ^ wedge

Many of the above glyphs go by multiple names centerdot is equivalent tosqbullet and ast is equivalent to asterisk produces the same glyph asast but as an ordinary symbol not a binary operator Similarly bigast pro-duces a large-operator version of the Asterisk binary operator and bigcoastproduces a large-operator version of the coAsterisk binary operator

22

Table 46 MnSymbol Binary Operators

∐ amalg ⩏ doublesqcup rightthereforelowast ast ⩔ doublevee ⋌ rightthreetimes backslashdiv ⩕ doublewedge ( rightYamp bowtie ∵ downtherefore ⋊ rtimes bullet + downY slashdivcap cap dtimes prod smallprod⩀ capdot fivedots ⊓ sqcap capplus hbipropto E sqcapdotsdot cdot hdotdot G sqcapplus circ lefthalfcap ⊔ sqcupfrac34 closedcurlyvee lefthalfcup D sqcupdotfrac14 closedcurlywedge lefttherefore F sqcuppluscup cup ⋋ leftthreetimes ∷ squaredots⊍ cupdot leftY times times⊎ cupplus ⋉ ltimes udotdot⋎ curlyvee ∖ medbackslash there4 uptherefore5 curlyveedot medcircle ) upY⋏ curlywedge ∕ medslash $ utimes4 curlywedgedot ∣ medvert vbipropto ddotdot medvertdot ∶ vdotdot13 diamonddots minus minus or veedivide div minusdot veedot dotmedvert ∓ mp ⧖ vertbowtie dotminus neswbipropto vertdiv⋒ doublecap nwsebipropto and wedge⋓ doublecup + plus wedgedot7 doublecurlyvee plusmn pm ≀ wreath6 doublecurlywedge righthalfcap⩎ doublesqcap righthalfcup

MnSymbol defines setminus and smallsetminus as synonyms formedbackslash Join as a synonym for bowtie wr as a synonym forwreath shortmid as a synonym for medvert Cap as a synonym fordoublecap Cup as a synonym for doublecup and uplus as a synonym forcupplus

Table 47 mathdesign Binary Operators

_ dtimes ] udtimes ^ utimes

The mathdesign package additionally provides versions of each of the binary oper-ators shown in Table 41 on page 21

Table 48 cmll Binary Operators

` parr amp withlowast

lowast with differs from ldquoamprdquo in terms of its math-mode spacing $A amp B$ producesldquoAampBrdquo for example while $A with B$ produces ldquoAampBrdquo

23

Table 49 ulsy Geometric Binary Operators

odplus

Table 50 mathabx Geometric Binary Operators

blacktriangledown i boxright a ominus blacktriangleleft m boxslash ` oplus blacktriangleright b boxtimes i oright blacktriangleup j boxtop m oslashf boxasterisk o boxtriangleup b otimesn boxbackslash l boxvoid j otopk boxbot f oasterisk o otriangleupe boxcirc n obackslash l ovoidg boxcoasterisk k obot smalltriangledownc boxdiv e ocirc smalltriangleleftd boxdot g ocoasterisk smalltrianglerighth boxleft c odiv smalltriangleupa boxminus d odot` boxplus h oleft

Table 51 MnSymbol Geometric Binary Operators

⧅ boxbackslash filledmedtriangledown ⊚ ocirc⧈ boxbox filledmedtriangleleft ⊙ odot⊡ boxdot filledmedtriangleright ⊖ ominus⊟ boxminus filledmedtriangleup oplus oplus⊞ boxplus ◾ filledsquare ⊘ oslash⧄ boxslash filledstar ostar⊠ boxtimes filledtriangledown otimes otimesq boxvert filledtriangleleft d otriangle diamondbackslash filledtriangleright ⦶ overt diamonddiamond filledtriangleup pentagram⟐ diamonddot meddiamond smalldiamondx diamondminus ◻ medsquare ◽ smallsquare| diamondplus medstar smallstarz diamondslash medtriangledown smalltriangledown diamondtimes ◁ medtriangleleft smalltrianglelefty diamondvert ▷ medtriangleright smalltrianglerightAcirc downslice medtriangleup smalltriangleup filleddiamond ⊛ oast ⋆ thinstar∎ filledmedsquare ⦸ obackslash Agrave upslice

MnSymbol defines blacksquare as a synonym for filledmedsquare squareand Box as synonyms for medsquare diamond as a synonym for smalldiamondDiamond as a synonym for meddiamond star as a synonym for thinstarcircledast as a synonym for oast circledcirc as a synonym for ocircand circleddash as a synonym for ominus

24

Table 52 Variable-sized Math Operators⋂ ⋂bigcap

otimesotimesbigotimes

and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus

int intintoplusoplus

bigoplusor or

bigvee∮ ∮

oint

Table 53 AMS Variable-sized Math Operators

intint intintiint

intintint intintintiiint

intintintint intintintintiiiint

intmiddotmiddot middotint int

middot middot middotint

idotsint

Table 54 stmaryrd Variable-sized Math Operators

embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup

Table 55 wasysym Variable-sized Math Operators

r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint

None of the preceding symbols are defined when wasysym is passed the nointegralsoptionlowast Not defined when wasysym is passed the integrals optiondagger Defined only when wasysym is passed the integrals option Otherwise the default

LATEX int glyph (as shown in Table 52) is used

25

Table 56 mathabx Variable-sized Math Operators

notbigcurlyvee

Yacuteyacutebigboxslash

Eacuteeacutebigoright

brvbarbigsqcap

Ograveogravebigboxtimes

Iacuteiacutebigoslash

laquobigcurlywedge

Uacuteuacutebigboxtop

Ecircecircbigotop

Oumloumlbigboxasterisk

szligyumlbigboxtriangleup

Iumliumlbigotriangleup

THORNthornbigboxbackslash

Uumluumlbigboxvoid

Igraveigravebigovoid

Ucircucircbigboxbot

centbigcomplementop

bigplus

Otildeotildebigboxcirc

AEligaeligbigoasterisk

umlbigsquplus

timesdividebigboxcoasterisk

Icircicircbigobackslash

iexclbigtimes

Oacuteoacutebigboxdiv

Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint

Oslashoslashbigboxleft

Ccedilccedilbigocoasterisk

sup3 raquoint

Ntildentildebigboxminus

Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus

Egraveegravebigoleft

para frac34oint

Ugraveugravebigboxright

Aacuteaacutebigominus

26

Table 57 txfontspxfonts Variable-sized Math Operators

bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint

F Gvaroiiintclockwise

iint

N Ovaroiiintctrclockwise

L Moiiintclockwise

B Cvaroiintclockwise

D Eoiiintctrclockwise

J Kvaroiintctrclockwise

) oiiint

- varointclockwise

H Ioiintclockwise

+ varointctrclockwise

Aoiintctrclockwise

varprod

oiint

27

Table 58 esint Variable-sized Math Operators

macr ˙dotsint

ı ointclockwise

ffl fint

permilointctrclockwise

ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint

ff fivarointclockwise

$landupint

fl ffivarointctrclockwise

sbquo lsaquooiint

28

Table 59 MnSymbol Variable-sized Math Operators

⋂ ⋂ bigcap ⊖ ⊖ bigominus ∁ ∁ complement

⩀ ⩀ bigcapdot oplus oplus bigoplus ∐ ∐ coprod

$ bigcapplus ⊘ ⊘ bigoslash Z [ idotsint

bigcircle bigostar ⨌ ⨌ iiiint

⋃ ⋃ bigcup otimes otimes bigotimes ∭ ∭ iiint

⊍ ⊍ bigcupdot F G bigotriangle ∬ ∬ iint

⊎ ⊎ bigcuppluslowast ⦶ ⦶ bigovert int int int

⋎ ⋎ bigcurlyvee + + bigplus ⨚ ⨚ landdownint

bigcurlyveedot ⊓ ⊓ bigsqcap ⨙ ⨙ landupint

⋏ ⋏ bigcurlywedge - bigsqcapdot ∲ ∲ lcircleleftint

bigcurlywedgedot 0 1 bigsqcapplus ∲ ∲ lcirclerightint

bigdoublecurlyvee ⊔ ⊔ bigsqcup ∯ ∯ oiint

bigdoublecurlywedge bigsqcupdot ∮ ∮ oint

⩔ ⩔ bigdoublevee 2 3 bigsqcupplus prod prod prod

⩕ ⩕ bigdoublewedge ⨉ ⨉ bigtimes ∳ ∳ rcircleleftint

⊛ ⊛ bigoast ⋁ ⋁ bigvee ∳ ∳ rcirclerightint

⦸ ⦸ bigobackslash bigveedot ⨏ ⨏ strokedint

⊚ ⊚ bigocirc ⋀ ⋀ bigwedge sum sum sum

⊙ ⊙ bigodot bigwedgedot ⨋ ⨋ sumint

lowast MnSymbol defines biguplus as a synonym for bigcupplus

Table 60 mathdesign Variable-sized Math Operators

intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint

The mathdesign package provides three versions of each integralmdashin fact of ev-ery symbolmdashto accompany different text fonts Utopia (

int

) Garamond (int

) and

Charter (int

)

29

Table 61 cmll Large Math Operators

˙bigparr

˘bigwith

Table 62 Binary Relations

asymp approx equiv equiv perp perp ^ smile asymp _ frown ≺ prec succ bowtie Z Joinlowast preceq succeq cong | mid prop propto ` vdasha dashv |= models sim sim doteq parallel simeq

lowast Not predefined in LATEX 2ε Use one of the packages latexsym amsfonts amssymbmathabx txfonts pxfonts or wasysym

Table 63 AMS Binary Relations

u approxeq P eqcirc v succapprox backepsilon fallingdotseq lt succcurlyeqv backsim ( multimap succsimw backsimeq t pitchfork there4 therefore∵ because w precapprox asymp thickapproxG between 4 preccurlyeq sim thicksimm Bumpeq - precsim prop varproptol bumpeq risingdotseq 13 Vdash$ circeq p shortmid vDash2 curlyeqprec q shortparallel Vvdash3 curlyeqsucc a smallfrown+ doteqdot ` smallsmile

Table 64 AMS Negated Binary Relations

ncong nshortparallel 3 nVDash- nmid nsim precnapprox∦ nparallel nsucc precnsim⊀ nprec nsucceq succnapprox npreceq 2 nvDash succnsim nshortmid 0 nvdash

Table 65 stmaryrd Binary Relations

A inplus B niplus

Table 66 wasysym Binary Relations

invneg leadsto wasyproptoZ Join logof

30

Table 67 txfontspxfonts Binary Relations

S circledgtr X lJoin ] opentimesR circledless lrtimes y Perp13 colonapprox ( multimap preceqq Colonapprox multimapboth precneqqD coloneq multimapbothvert Y rJoinH Coloneq multimapdot K strictfiF Coloneqq multimapdotboth J strictifB coloneqqlowast multimapdotbothA L strictiff Colonsim multimapdotbothAvert succeqq colonsim multimapdotbothB succneqqI Eqcolon multimapdotbothBvert ∥ varparallelE eqcolon multimapdotbothvert varparallelinvC eqqcolon multimapdotinv VvDashG Eqqcolon multimapinvh eqsim [ openJoin

lowast As an alternative to using txfontspxfonts a ldquo=rdquo symbol can be constructed withldquomathrelmathop=rdquo

Table 68 txfontspxfonts Negated Binary Relations

6 napproxeq $ npreccurlyeq 5 nthickapprox- nasymp 9 npreceqq h ntwoheadleftarrow nbacksim nprecsim g ntwoheadrightarrow+ nbacksimeq nsimeq nvarparallel( nbumpeq 8 nsuccapprox nvarparallelinv) nBumpeq nsucccurlyeq 1 nVdash nequiv nsucceqq7 nprecapprox nsuccsim

Table 69 mathabx Binary Relations

between divides risingdotseq botdoteq dotseq Ccedil succapprox Bumpedeq eqbumped yen succcurlyeq bumpedeq eqcirc Iacute succdot circeq eqcolon Aacute succsim coloneq fallingdotseq 6 therefore corresponds Iuml ggcurly topdoteqpara curlyeqprec Icirc llcurly ( vDashmiddot curlyeqsucc AElig precapprox Vdash) DashV curren preccurlyeq ( VDash) Dashv Igrave precdot Vvdash- dashVv Agrave precsim

31

Table 70 mathabx Negated Binary Relations

napprox M notperp nvDash ncong cent nprec nVDashcedil ncurlyeqprec Egrave nprecapprox nVdashsup1 ncurlyeqsucc brvbar npreccurlyeq amp nvdash+ nDashv ordf npreceq nVvash ndashV Acirc nprecsim Ecirc precnapprox ndashv nsim not precneq+ nDashV nsimeq Auml precnsim ndashVv pound nsucc Euml succnapprox neq Eacute nsuccapprox shy succneq notasymp sect nsucccurlyeq Aring succnsim notdivides laquo nsucceq notequiv Atilde nsuccsim

The changenotsign command toggles the behavior of not to produce either avertical or a diagonal slash through a binary operator Thus ldquo$a not= b$rdquo canbe made to produce either ldquoa = brdquo or ldquoa = brdquo

Table 71 MnSymbol Binary Relations

asymp approx ≖ eqcirc nwfree ∥ shortparallel≊ approxeq ⩦ eqdot aring nwmodels sim sim backapprox ≂ eqsim otilde nwModels ≃ simeq backapproxeq = equal nwsecrossing ≻ succ≌ backcong Yacute equalclosed Oacute nwseline ⪸ succapprox backeqsim equiv equiv times Nwseline ≽ succcurlyeq∽ backsim THORN equivclosed Yacute nwvdash ⪰ succeq⋍ backsimeq ≒ fallingdotseq iacute nwVdash ≿ succsim backtriplesim ≙ hateq ≺ prec ~ swfootline between hcrossing ⪷ precapprox swfree≏ bumpeq z leftfootline ≼ preccurlyeq aelig swmodels≎ Bumpeq leftfree ⪯ preceq ouml swModels≗ circeq acirc leftmodels ≾ precsim THORN swvdashUuml closedequal ograve leftModels x rightfootline icirc swVdashfrac12 closedprec prop leftpropto rightfree ≋ triplesimraquo closedsucc ETH leftrightline ⊧ rightmodels ∣ updownlinecong cong Ocirc Leftrightline ⊫ rightModels ∥ Updownline⋞ curlyeqprec ⪦ leftslice rightpropto y upfootline⋟ curlyeqsucc ⊣ leftvdash ⪧ rightslice upfree≐ doteq ecirc leftVdash ⊢ rightvdash aacute upmodels≑ Doteq | nefootline ⊩ rightVdash ntilde upModels downfootline nefree ≓ risingdotseq uppropto⫝ downfree auml nemodels sefootline perp upvdashatilde downmodels ocirc neModels sefree upVdashoacute downModels Ograve neswline ccedil semodels vcrossing downpropto Ouml Neswline divide seModels ⊪ Vvdash⊤ downvdash Uuml nevdash separated downVdash igrave neVdash szlig sevdash eqbump nwfootline iuml seVdash

32

MnSymbol additionally defines synonyms for some of the preceding symbols

⊣ dashv (same as leftvdash)Oacute diagdown (same as nwseline)Ograve diagup (same as neswline)Ograve divides (same as updownline)≑ doteqdot (same as Doteq)⊧ models (same as rightmodels)∥ parallel (same as Updownline)perp perp (same as upvdash)prop propto (same as leftpropto)ETH relbar (same as leftrightline)Ocirc Relbar (same as Leftrightline)prop varpropto (same as leftpropto)⊧ vDash (same as rightmodels)⊫ VDash (same as rightModels)⊢ vdash (same as rightvdash)⊩ Vdash (same as rightVdash)

Table 72 MnSymbol Negated Binary Relations

≉ napprox neqsim otilde nnwModels ⊁ nsucc napproxeq ne nequal Oacute nnwseline eacute nsuccapprox nbackapprox ecirc nequalclosed times nNwseline ⋡ nsucccurlyeq nbackapproxeq ≢ nequiv Yacute nnwvdash atilde nsucceq nbackcong euml nequivclosed iacute nnwVdash ccedil nsuccsim nbackeqsim neswcrossing ⊀ nprec ~ nswfootline nbacksim nfallingdotseq egrave nprecapprox nswfree nbacksimeq micro nhateq ⋠ npreccurlyeq aelig nswmodels nbacktriplesim z nleftfootline acirc npreceq ouml nswModels nbumpeq nleftfree aelig nprecsim THORN nswvdash nBumpeq acirc nleftmodels x nrightfootline icirc nswVdashsup3 ncirceq ograve nleftModels nrightfree ~ ntriplesimeacute nclosedequal ETH nleftrightline ⊭ nrightmodels ∤ nupdownline≇ ncong Ocirc nLeftrightline ⊯ nrightModels ∦ nUpdownlineograve ncurlyeqprec Uacute nleftvdash ⊬ nrightvdash y nupfootlineoacute ncurlyeqsucc ecirc nleftVdash ⊮ nrightVdash nupfree ndoteq | nnefootline nrisingdotseq aacute nupmodels nDoteq nnefree nsefootline ntilde nupModels ndownfootline auml nnemodels nsefree Ugrave nupvdash⫝̸ ndownfree ocirc nneModels ccedil nsemodels eacute nupVdashatilde ndownmodels Ograve nneswline divide nseModels ⪹ precnapproxoacute ndownModels Ouml nNeswline szlig nsevdash ⋨ precnsimUcirc ndownvdash Uuml nnevdash iuml nseVdash ⪺ succnapproxeuml ndownVdash igrave nneVdash ∤ nshortmid ⋩ succnsim neqbump nnwfootline ∦ nshortparallelsup2 neqcirc nnwfree ≁ nsim neqdot aring nnwmodels ≄ nsimeq


33

Uacute ndashv (same as nleftvdash)Oacute ndiagdown (same as nnwseline)Ograve ndiagup (same as nneswline)∤ ndivides (same as nupdownline)ne ne (same as nequal)ne neq (same as nequal)∤ nmid (same as nupdownline)⊭ nmodels (same as nrightmodels)∦ nparallel (same as nUpdownline)Ugrave nperp (same as nupvdash)ETH nrelbar (same as nleftrightline)Ocirc nRelbar (same as nLeftrightline)⊭ nvDash (same as nrightmodels)⊬ nvdash (same as nrightvdash)⊮ nVdash (same as nrightVdash)⊯ nVDash (same as nrightModels)

Table 73 mathtools Binary Relations

asymp Colonapprox minus coloneq minus Eqcolonasymp colonapprox sim colonsim = eqqcolon= coloneqq sim Colonsim = Eqqcolon= Coloneqq dblcolonminus Coloneq minus eqcolon

Similar symbols can be defined using mathtoolsrsquos vcentcolon which produces acolon centered on the fontrsquos math axis

== vs ==ldquo==rdquo ldquo=vcentcolon=rdquo

Table 74 turnstile Binary Relations

abc

defdddtstileabcdef abc

defnntstileabcdef

abc

def

stdtstileabcdef

abc

defddststileabcdef abc

defnnttstileabcdef

abc

def

stststileabcdef

abc

defddtstileabcdef abc

defnsdtstileabcdef

abc

def

sttstileabcdef

abc

defddttstileabcdef abc

defnsststileabcdef

abc

def

stttstileabcdef

abc

defdndtstileabcdef abc

defnststileabcdef

abc

deftddtstileabcdef

abc

defdnststileabcdef abc

defnsttstileabcdef

abc

deftdststileabcdef

abc

defdntstileabcdef

abc

def

ntdtstileabcdefabc

deftdtstileabcdef


34


abc

defdnttstileabcdef

abc

def

ntststileabcdefabc

deftdttstileabcdef

abc

defdsdtstileabcdef

abc

def

nttstileabcdef abc

deftndtstileabcdef

abc

defdsststileabcdef

abc

def

ntttstileabcdef abc

deftnststileabcdef

abc

defdststileabcdef

abc

defsddtstileabcdef abc

deftntstileabcdef

abc

defdsttstileabcdef

abc

defsdststileabcdef abc

deftnttstileabcdef

abc

def

dtdtstileabcdefabc

defsdtstileabcdef abc

deftsdtstileabcdef

abc

def

dtststileabcdefabc

defsdttstileabcdef abc

deftsststileabcdef

abc

def

dttstileabcdef abc

defsndtstileabcdef abc

deftststileabcdef

abc

def

dtttstileabcdef abc

defsnststileabcdef abc

deftsttstileabcdef

abc

defnddtstileabcdef abc

defsntstileabcdef

abc

def

ttdtstileabcdef

abc

defndststileabcdef abc

defsnttstileabcdef

abc

defttststileabcdef

abc

defndtstileabcdef abc

defssdtstileabcdef

abc

def

tttstileabcdef

abc

defndttstileabcdef abc

defssststileabcdef

abc

def

ttttstileabcdef

abc

defnndtstileabcdef abc

defsststileabcdef

abc

defnnststileabcdef abc

defssttstileabcdef

Each of the above takes an optional argument that controls the size of the upperand lower expressions See the turnstile documentation for more information

Table 75 trsym Binary Relations

InversTransformHoriz TransformHoriz

InversTransformVert TransformVert

Table 76 trfsigns Binary Relationsc dfourier c Dfourierc fourier c Fourierc s laplace s c Laplacec s ztransf s c Ztransf

35

Table 77 cmll Binary Relations

uml coh ˝ scoh˚ incoh ˇ sincoh

Table 78 Subset and Superset Relations

sqsubsetlowast w sqsupseteq sup supsetv sqsubseteq sub subset supe supseteqA sqsupsetlowast sube subseteq


Table 79 AMS Subset and Superset Relations

nsubseteq j subseteqq supsetneqq+ nsupseteq ( subsetneq varsubsetneq nsupseteqq $ subsetneqq amp varsubsetneqq sqsubset c Supset varsupsetneqA sqsupset k supseteqq varsupsetneqqb Subset ) supsetneq

Table 80 stmaryrd Subset and Superset Relations

D subsetplus E supsetplusF subsetpluseq G supsetpluseq

Table 81 wasysym Subset and Superset Relations

sqsubset A sqsupset

Table 82 txfontspxfonts Subset and Superset Relations

a nsqsubset A nsqsupseteq nSupset nsqsubseteq gt nSubsetb nsqsupset nsubseteqq

36

Table 83 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 84 MnSymbol Subset and Superset Relations

Ouml nSqsubset ⊈ nsubseteq ⋤ sqsubsetneq sube subseteqETH nsqsubset Uuml nsubseteqq ouml sqsubsetneqq ⫅ subseteqq⋢ nsqsubseteq szlig nSupset _ Sqsupset ⊊ subsetneqOcirc nsqsubseteqq ⊅ nsupset ⊐ sqsupset ⫋ subsetneqqtimes nSqsupset ⊉ nsupseteq ⊒ sqsupseteq ⋑ SupsetNtilde nsqsupset Yacute nsupseteqq ] sqsupseteqq sup supset⋣ nsqsupseteq ^ Sqsubset ⋥ sqsupsetneq supe supseteqOtilde nsqsupseteqq ⊏ sqsubset divide sqsupsetneqq ⫆ supseteqqTHORN nSubset ⊑ sqsubseteq ⋐ Subset ⊋ supsetneqnsub nsubset sqsubseteqq sub subset ⫌ supsetneqq

MnSymbol additionally defines varsubsetneq as a synonym for subsetneqvarsubsetneqq as a synonym for subsetneqq varsupsetneq as a synonymfor supsetneq and varsupsetneqq as a synonym for supsetneqq

Table 85 Inequalities

ge geq gg le leq ll neq

Table 86 AMS Inequalities

1 eqslantgtr m gtrdot Q lesseqgtr ngeq

0 eqslantless R gtreqless S lesseqqgtr ngeqq

= geqq T gtreqqless ≶ lessgtr ngeqslant

gt geqslant ≷ gtrless lesssim ≯ ngtr

≫ ggg amp gtrsim ≪ lll nleq

gnapprox gvertneqq lnapprox nleqq

13 gneq 5 leqq lneq nleqslant

gneqq 6 leqslant lneqq ≮ nless

gnsim lessapprox lnsim

gtrapprox l lessdot lvertneqq

37

Table 87 wasysym Inequalities

apprge gt apprle

Table 88 txfontspxfonts Inequalities

4 ngg ngtrsim nlesssim ngtrapprox nlessapprox 3 nllamp ngtrless nlessgtr

Table 89 mathabx Inequalities

middot eqslantgtr frac12 gtreqless Agrave lesssim pound ngtr

para eqslantless iquest gtreqqless ll Eacute ngtrapprox

yen geq raquo gtrless Icirc lll Atilde ngtrsim

macr geqq Aacute gtrsim Ecirc lnapprox brvbar nleq

gg micro gvertneqq not lneq deg nleqq

Iuml ggg curren leq sup2 lneqq cent nless

Euml gnapprox reg leqq Auml lnsim Egrave nlessapprox

shy gneq AElig lessapprox acute lvertneqq Acirc nlesssim

sup3 gneqq Igrave lessdot sup1 neqslantgtr laquo nvargeq

Aring gnsim frac14 lesseqgtr cedil neqslantless ordf nvarleq

Ccedil gtrapprox frac34 lesseqqgtr sect ngeq copy vargeq

Iacute gtrdot ordm lessgtr plusmn ngeqq uml varleq

mathabx defines leqslant and le as synonyms for leq geqslant and ge assynonyms for geq nleqslant as a synonym for nleq and ngeqslant as asynonym for ngeq

38

Table 90 MnSymbol Inequalities

⪖ eqslantgtr ⪌ gtreqqless ≲ lesssim Atilde ngtreqless

⪕ eqslantless ≷ gtrless ≪ ll Ccedil ngtreqlessslant

ge geq oacute gtrneqqless ⋘ lll Aring ngtreqqless

⊵ geqclosed ≳ gtrsim ⪉ lnapprox ≹ ngtrless

u geqdot le leq ≨ lneqq ≰ nleq

≧ geqq ⊴ leqclosed ≴ lnsim ⋬ nleqclosed

⩾ geqslant t leqdot ntilde neqslantgtr igrave nleqdot

⪀ geqslantdot ≦ leqq eth neqslantless frac34 nleqq

≫ gg ⩽ leqslant ≱ ngeq ≰ nleqslant

⋙ ggg ⩿ leqslantdot ⋭ ngeqclosed icirc nleqslantdot

⪊ gnapprox lt less iacute ngeqdot ≮ nless

≩ gneqq ⪅ lessapprox iquest ngeqq ⋪ nlessclosed

≵ gnsim ⊲ lessclosed ≱ ngeqslant ecirc nlessdot

gt gtr ⋖ lessdot iuml ngeqslantdot Acirc nlesseqgtr

⪆ gtrapprox ⋚ lesseqgtr Eacute ngg AElig nlesseqgtrslant

⊳ gtrclosed N lesseqgtrslant Euml nggg Auml nlesseqqgtr

⋗ gtrdot ⪋ lesseqqgtr ≯ ngtr ≸ nlessgtr

⋛ gtreqless ≶ lessgtr ⋫ ngtrclosed Egrave nll

O gtreqlessslant ograve lessneqqgtr euml ngtrdot Ecirc nlll


⋙ gggtr (same as ggg)≩ gvertneqq (same as gneqq)⊲ lhd (same as lessclosed)⋘ llless (same as lll)≨ lvertneqq (same as lneqq)⋬ ntrianglelefteq (same as nleqclosed)⋪ ntriangleleft (same as nlessclosed)⋭ ntrianglerighteq (same as ngeqclosed)⋫ ntriangleright (same as ngtrclosed)⊳ rhd (same as gtrclosed)⊴ trianglelefteq (same as leqclosed)⊵ trianglerighteq (same as geqclosed)⊴ unlhd (same as leqclosed)⊵ unrhd (same as geqclosed)⊲ vartriangleleft (same as lessclosed)⊳ vartriangleright (same as gtrclosed)

Table 91 AMS Triangle Relations

J blacktriangleleft 5 ntrianglelefteq E trianglelefteq C vartriangleleftI blacktriangleright 7 ntriangleright triangleq B vartriangleright6 ntriangleleft 4 ntrianglerighteq D trianglerighteq

39

Table 92 stmaryrd Triangle Relations

P trianglelefteqslant Q trianglerighteqslantR ntrianglelefteqslant S ntrianglerighteqslant

Table 93 mathabx Triangle Relations

ntriangleleft ntrianglerighteq triangleright vartriangleright ntrianglelefteq triangleleft trianglerighteq ntriangleright trianglelefteq vartriangleleft

Table 94 MnSymbol Triangle Relations

filledmedtriangledown largetriangleup smalltriangledown filledmedtriangleleft medtriangledown smalltriangleleft filledmedtriangleright ◁ medtriangleleft smalltriangleright filledmedtriangleup ▷ medtriangleright smalltriangleup filledtriangledown medtriangleup ≜ triangleeq filledtriangleleft acute ntriangleeq ⊴ trianglelefteq filledtriangleright ⋪ ntriangleleft ⊵ trianglerighteq filledtriangleup ⋬ ntrianglelefteq ⊲ vartriangleleft largetriangledown ⋫ ntriangleright ⊳ vartriangleright◁ largetriangleleft ⋭ ntrianglerighteq▷ largetriangleright d otriangle

MnSymbol additionally defines synonyms for many of the preceding sym-bols triangleq is a synonym for triangleeq lhd and lessclosedare synonyms for vartriangleleft rhd and gtrclosed are syn-onyms for vartriangleright unlhd and leqclosed are syn-onyms for trianglelefteq unrhd and geqclosed are synonymsfor trianglerighteq blacktriangledown blacktriangleleftblacktriangleright and blacktriangle [sic] are synonyms forrespectively filledmedtriangledown filledmedtriangleleftfilledmedtriangleright and filledmedtriangleup trianglerightis a synonym for medtriangleright triangle vartriangle andbigtriangleup are synonyms for medtriangleup triangleleft is asynonym for medtriangleleft triangledown and bigtriangledown are syn-onyms for medtriangledown nlessclosed is a synonym for ntriangleleftngtrclosed is a synonym for ntriangleright nleqclosed is a synonym forntrianglelefteq and ngeqclosed is a synonym for ntrianglerighteq

The title ldquoTriangle Relationsrdquo is a bit of a misnomer here as only triangleeqand ntriangleeq are defined as TEX relations (class 3 symbols) Thelargetriangle symbols are defined as TEX ldquoordinaryrdquo characters (class 0)and all of the remaining characters are defined as TEX binary operators (class 2)

40

Table 95 Arrows

dArr Downarrow larrminus longleftarrow nwarrowdarr downarrow lArr= Longleftarrow rArr Rightarrowlarr hookleftarrow larrrarr longleftrightarrow rarr rightarrowrarr hookrightarrow lArrrArr Longleftrightarrow searrow leadstolowast 7minusrarr longmapsto swarrowlarr leftarrow =rArr Longrightarrow uarr uparrowlArr Leftarrow minusrarr longrightarrow uArr UparrowhArr Leftrightarrow 7rarr mapsto l updownarrowharr leftrightarrow nearrowdagger m Updownarrow


dagger See the note beneath Table 157 for information about how to put a diagonal arrow

across a mathematical expression (as in ldquo 0

nabla middot ~B rdquo)

Table 96 Harpoons

leftharpoondown rightharpoondown rightleftharpoons leftharpoonup rightharpoonup

Table 97 textcomp Text-mode Arrows

darr textdownarrow rarr textrightarrowlarr textleftarrow uarr textuparrow

Table 98 AMS Arrows

circlearrowleft hArr leftleftarrows rightleftarrows circlearrowright leftrightarrows rArr rightrightarrowsx curvearrowleft leftrightsquigarrow rightsquigarrowy curvearrowright W Lleftarrow Rshc dashleftarrow looparrowleft twoheadleftarrowd dashrightarrow looparrowright twoheadrightarrow downdownarrows Lsh upuparrows leftarrowtail rightarrowtail

Table 99 AMS Negated Arrows

nLeftarrow lt nLeftrightarrow nRightarrow8 nleftarrow = nleftrightarrow 9 nrightarrow

Table 100 AMS Harpoons

downharpoonleft leftrightharpoons upharpoonleft downharpoonright rightleftharpoons upharpoonright

41

Table 101 stmaryrd Arrows

^ leftarrowtriangle lArr Mapsfrom shortleftarrow- leftrightarroweq larr[ mapsfrom shortrightarrow] leftrightarrowtriangle rArr Mapsto shortuparrow lightning 1 nnearrow ssearrowlArr= Longmapsfrom 0 nnwarrow $ sswarrowlarrminus[ longmapsfrom _ rightarrowtriangle=rArr Longmapsto shortdownarrow

Table 102 txfontspxfonts Arrows

boxdotLeft circleddotright Diamondleft boxdotleft circleleft Diamondright boxdotright circleright DiamondRight boxdotRight e dashleftrightarrow f leftsquigarrow boxLeft DiamonddotLeft t Nearrow boxleft Diamonddotleft v Nwarrow boxright Diamonddotright V Rrightarrow boxRight DiamonddotRight u Searrow circleddotleft DiamondLeft w Swarrow

Table 103 mathabx Arrows

ouml circlearrowleft ETH leftarrow Ocirc nwarrowdivide circlearrowright ETH leftleftarrows aelig restrictionoacute curvearrowbotleft Oslash leftrightarrow Ntilde rightarrowotilde curvearrowbotleftright Ocirc leftrightarrows Otilde rightleftarrowsocirc curvearrowbotright uacute leftrightsquigarrow Ntilde rightrightarrowseth curvearrowleft oslash leftsquigarrow ugrave rightsquigarrowograve curvearrowleftright uuml lefttorightarrow yacute righttoleftarrowntilde curvearrowright icirc looparrowdownleft eacute Rshecirc dlsh iuml looparrowdownright times searrowOacute downdownarrows igrave looparrowleft Ouml swarrowyuml downtouparrow iacute looparrowright Ouml updownarrowstimes downuparrows egrave Lsh thorn uptodownarroweuml drsh Otilde nearrow Ograve upuparrows

Table 104 mathabx Negated Arrows

ouml nLeftarrow Uuml nleftrightarrow Ucirc nrightarrowUacute nleftarrow oslash nLeftrightarrow divide nRightarrow

42

Table 105 mathabx Harpoons

THORN barleftharpoon agrave leftharpoonup eacute rightleftharpoonsszlig barrightharpoon Oslash leftleftharpoons Ugrave rightrightharpoonsUcirc downdownharpoons agrave leftrightharpoon ecirc updownharpoonsaring downharpoonleft egrave leftrightharpoons auml upharpoonleftccedil downharpoonright Yacute rightbarharpoon aelig upharpoonrighteuml downupharpoons atilde rightharpoondown Uacute upupharpoonsUuml leftbarharpoon aacute rightharpoonupacirc leftharpoondown aacute rightleftharpoon

Table 106 MnSymbol Arrows

Euml curvearrowdownup larrETH longleftarrow ⤦ rhookswarrowEgrave curvearrowleftright lArrOcirc Longleftarrow 9 rhookuparrowIgrave curvearrownesw larrrarr longleftrightarrow rarr rightarrowIacute curvearrownwse lArrrArr Longleftrightarrow rArr RightarrowEcirc curvearrowrightleft zrarr longmapsto ↣ rightarrowtailIuml curvearrowsenw ETHrarr longrightarrow rightleftarrowsIcirc curvearrowswne OcircrArr Longrightarrow rightlsquigarrowEacute curvearrowupdown looparrowleft ↦ rightmapsto dasheddownarrow looparrowright rightrightarrows dashedleftarrow Lsh uml rightrsquigarrowd dashednearrow nearrow Rrightarrowe dashednwarrow Nearrow Rsh dashedrightarrow $ nearrowtail searrowg dashedsearrow curren nelsquigarrow Searrowf dashedswarrow nemapsto searrowtail dasheduparrow nenearrows sect selsquigarrowdArr Downarrow not nersquigarrow semapstodarr downarrow ⤡ neswarrow senwarrows downarrowtail Neswarrow macr sersquigarrow downdownarrows neswarrows sesearrowspound downlsquigarrow nwarrow sup3 squigarrowdownup downmapsto Nwarrow squigarrowleftrightlaquo downrsquigarrow nwarrowtail acute squigarrownesw downuparrows yen nwlsquigarrow micro squigarrownwseyuml lcirclearrowdown - nwmapsto sup2 squigarrowrightleft⤾ lcirclearrowleft nwnwarrows middot squigarrowsenw⟳ lcirclearrowright shy nwrsquigarrow para squigarrowswne lcirclearrowup ⤢ nwsearrow plusmn squigarrowupdown⤸ lcurvearrowdown Nwsearrow swarrowordm lcurvearrowleft nwsearrows Swarrowfrac14 lcurvearrowne ∲ partialvardlcircleleftintlowast amp swarrowtailfrac12 lcurvearrownw ∲ partialvardlcirclerightintlowast brvbar swlsquigarrow lcurvearrowright ∳ partialvardrcircleleftintlowast swmapstoiquest lcurvearrowse ∳ partialvardrcirclerightintlowast swnearrowsfrac34 lcurvearrowsw ∲ partialvartlcircleleftintlowast reg swrsquigarrowsup1 lcurvearrowup ∲ partialvartlcirclerightintlowast swswarrowslArr Leftarrow ∳ partialvartrcircleleftintlowast twoheaddownarrowlarr leftarrow ∳ partialvartrcirclerightintlowast twoheadleftarrow


43


leftarrowtail ucirc rcirclearrowdown twoheadnearrow leftleftarrows ⟲ rcirclearrowleft twoheadnwarrowcent leftlsquigarrow ⤿ rcirclearrowright ↠ twoheadrightarrow leftmapsto rcirclearrowup twoheadsearrowharr leftrightarrow ⤹ rcurvearrowdown twoheadswarrowhArr Leftrightarrow rcurvearrowleft twoheaduparrow leftrightarrows Auml rcurvearrowne uarr uparrow leftrsquigarrow Aring rcurvearrownw uArr Uparrow3 lhookdownarrow Agrave rcurvearrowright uparrowtail2 lhookleftarrow Ccedil rcurvearrowse updownarrow4 lhooknearrow AElig rcurvearrowsw Updownarrow⤣ lhooknwarrow Aacute rcurvearrowup updownarrows lhookrightarrow rhookdownarrow iexcl uplsquigarrow⤥ lhooksearrow rhookleftarrow upmapsto6 lhookswarrow ⤤ rhooknearrow copy uprsquigarrow1 lhookuparrow = rhooknwarrow upuparrows lightning 8 rhookrightarrow Lleftarrow rhooksearrow


circlearrowleft (same as rcirclearrowup) circlearrowright (same as lcirclearrowup) curvearrowleft (same as rcurvearrowleft) curvearrowright (same as lcurvearrowright) dashleftarrow (same as dashedleftarrow) dashrightarrow (same as dashedrightarrow) hookleftarrow (same as rhookleftarrow) hookrightarrow (same as lhookrightarrow) leadsto (same as rightlsquigarrow) leftrightsquigarrow (same as squigarrowleftright)↦ mapsto (same as rightmapsto) rightsquigarrow (same as rightlsquigarrow)

lowast The partialvar int macros are intended to be used internally by MnSymbolto produce various types of integrals

Table 107 MnSymbol Negated Arrows

Euml ncurvearrowdownup 5 nlhooknwarrow nrightleftarrowsEgrave ncurvearrowleftright 0 nlhookrightarrow nrightlsquigarrowIgrave ncurvearrownesw 7 nlhooksearrow ( nrightmapstoIacute ncurvearrownwse 6 nlhookswarrow nrightrightarrowsEcirc ncurvearrowrightleft 1 nlhookuparrow uml nrightrsquigarrowIuml ncurvearrowsenw otilde nLleftarrow ocirc nRrightarrowIcirc ncurvearrowswne nnearrow nSearrowEacute ncurvearrowupdown nNearrow nsearrowc ndasheddownarrow $ nnearrowtail nsearrowtailb ndashedleftarrow curren nnelsquigarrow sect nselsquigarrow


44


d ndashednearrow nnemapsto nsemapstoe ndashednwarrow nnenearrows nsenwarrows` ndashedrightarrow not nnersquigarrow macr nsersquigarrowg ndashedsearrow nNeswarrow nsesearrowsf ndashedswarrow nneswarrow sup3 nsquigarrowdownupa ndasheduparrow nneswarrows deg nsquigarrowleftright ndownarrow 13 nNwarrow acute nsquigarrownesw nDownarrow nnwarrow micro nsquigarrownwse ndownarrowtail nnwarrowtail sup2 nsquigarrowrightleft ndowndownarrows yen nnwlsquigarrow middot nsquigarrowsenwpound ndownlsquigarrow - nnwmapsto para nsquigarrowswne+ ndownmapsto nnwnwarrows plusmn nsquigarrowupdownlaquo ndownrsquigarrow shy nnwrsquigarrow nswarrow ndownuparrows nnwsearrow nSwarrowyuml nlcirclearrowdown nNwsearrow amp nswarrowtailthorn nlcirclearrowleft nnwsearrows brvbar nswlsquigarrowuuml nlcirclearrowright ucirc nrcirclearrowdown nswmapstoyacute nlcirclearrowup uacute nrcirclearrowleft nswnearrowsraquo nlcurvearrowdown oslash nrcirclearrowright reg nswrsquigarrowordm nlcurvearrowleft ugrave nrcirclearrowup nswswarrowsfrac14 nlcurvearrowne Atilde nrcurvearrowdown ntwoheaddownarrowfrac12 nlcurvearrownw Acirc nrcurvearrowleft ntwoheadleftarrowcedil nlcurvearrowright Auml nrcurvearrowne ntwoheadnearrowiquest nlcurvearrowse Aring nrcurvearrownw ntwoheadnwarrowfrac34 nlcurvearrowsw Agrave nrcurvearrowright ntwoheadrightarrowsup1 nlcurvearrowup Ccedil nrcurvearrowse ntwoheadsearrow nLeftarrow AElig nrcurvearrowsw ntwoheadswarrow↚ nleftarrow Aacute nrcurvearrowup ntwoheaduparrow nleftarrowtail nrhookdownarrow nuparrow nleftleftarrows nrhookleftarrow nUparrowcent nleftlsquigarrow lt nrhooknearrow nuparrowtail nleftmapsto = nrhooknwarrow nupdownarrow↮ nleftrightarrow 8 nrhookrightarrow nUpdownarrow⇎ nLeftrightarrow nrhooksearrow nupdownarrows nleftrightarrows gt nrhookswarrow iexcl nuplsquigarrowordf nleftrsquigarrow 9 nrhookuparrow ) nupmapsto3 nlhookdownarrow ↛ nrightarrow copy nuprsquigarrow2 nlhookleftarrow ⇏ nRightarrow nupuparrows4 nlhooknearrow nrightarrowtail


45

ugrave ncirclearrowleft (same as nrcirclearrowup)yacute ncirclearrowright (same as nlcirclearrowup)Acirc ncurvearrowleft (same as nrcurvearrowleft)cedil ncurvearrowright (same as nlcurvearrowright)` ndasharrow (same as ndashedrightarrow)b ndashleftarrow (same as ndashedleftarrow)` ndashrightarrow (same as ndashedrightarrow)↚ ngets (same as nleftarrow) nhookleftarrow (same as nrhookleftarrow)0 nhookrightarrow (same as nlhookrightarrow) nleadsto (same as nrightlsquigarrow)deg nleftrightsquigarrow (same as nsquigarrowleftright)( nmapsto (same as nrightmapsto) nrightsquigarrow (same as nrightlsquigarrow)↛ nto (same as nrightarrow)

Table 108 MnSymbol Harpoons

downharpoonccwlowast Z neswharpoons O seharpooncw downharpooncwlowast V neswharpoonsenw [ senwharpoons⥯ downupharpoons E nwharpoonccw F swharpoonccw leftharpoonccwlowast M nwharpooncw N swharpooncw leftharpooncwlowast S nwseharpoonnesw ^ swneharpoons⥊ leftrightharpoondownup _ nwseharpoons Q updownharpoonleftright leftrightharpoons W nwseharpoonswne U updownharpoonrightleft⥋ leftrightharpoonupdown rightharpoonccwlowast ⥮ updownharpoonsD neharpoonccw rightharpooncwlowast upharpoonccwlowast

L neharpooncw rightleftharpoons upharpooncwlowast

R neswharpoonnwse G seharpoonccw

lowast Where marked the ldquoccwrdquo suffix can be replaced with ldquouprdquo and the ldquocwrdquo suf-fix can be replaced with ldquodownrdquo (In addition upharpooncw can be written asrestriction)

Table 109 MnSymbol Negated Harpoons

C ndownharpoonccwlowast Z nneswharpoons O nseharpooncwK ndownharpooncwlowast V nneswharpoonsenw [ nsenwharpoons] ndownupharpoons E nnwharpoonccw F nswharpoonccwB nleftharpoonccwlowast M nnwharpooncw N nswharpooncwJ nleftharpooncwlowast S nnwseharpoonnesw ^ nswneharpoonsT nleftrightharpoondownup _ nnwseharpoons Q nupdownharpoonleftright nleftrightharpoons W nnwseharpoonswne U nupdownharpoonrightleftP nleftrightharpoonupdown nrightharpoonccwlowast Y nupdownharpoonsD nneharpoonccw H nrightharpooncwlowast A nupharpoonccwlowast

L nneharpooncw X nrightleftharpoons I nupharpooncwlowast

R nneswharpoonnwse G nseharpoonccw

lowast Where marked the ldquoccwrdquo suffix can be replaced with ldquouprdquo and the ldquocwrdquo suffixcan be replaced with ldquodownrdquo (In addition nupharpooncw can be written asnrestriction)

46

Table 110 chemarrow Arrows

A chemarrow

Table 111 fge Arrows

fgerightarrow fgeuparrow

Table 112 MnSymbol Spoons

s downfilledspoon l nnespoon u nwfilledspoon⫰ downspoon u nnwfilledspoon m nwspoonr leftfilledspoon m nnwspoon p rightfilledspoon⟜ leftspoon p nrightfilledspoon ⊸ rightspoonlowast

s ndownfilledspoon h nrightspoonlowast w sefilledspoonk ndownspoon w nsefilledspoon o sespoont nefilledspoon o nsespoon v swfilledspoonl nespoon v nswfilledspoon n swspoonr nleftfilledspoon n nswspoon q upfilledspoonj nleftspoon q nupfilledspoon ⫯ upspoont nnefilledspoon i nupspoon

lowast MnSymbol defines multimap as a synonym for rightspoon and nmultimap asa synonym for nrightspoon

Table 113 MnSymbol Pitchforks

⫛ downpitchfork nnwpitchfork rightpitchfork leftpitchfork nrightpitchfork sepitchfork ndownpitchfork nsepitchfork swpitchfork nepitchfork nswpitchfork ⋔ uppitchfork nleftpitchfork nuppitchfork nnepitchfork nwpitchfork

lowast MnSymbol defines pitchfork as a synonym for uppitchfork and npitchforkas a synonym for nuppitchfork

47

Table 114 MnSymbol Smiles and Frowns

doublefrown nsmileeq smileeq doublefrowneq nsmileeqfrown amp smileeqfrown doublesmile ≭ nsmilefrown ≍ smilefrown$ doublesmileeq nsmilefrowneq ( smilefrowneq eqfrown yen nsqdoublefrown - sqdoublefrown eqsmile macr nsqdoublefrowneq 7 sqdoublefrowneq frown curren nsqdoublesmile sqdoublesmile frowneq reg nsqdoublesmileeq 6 sqdoublesmileeq frowneqsmile shy nsqeqfrown 5 sqeqfrown frownsmile not nsqeqsmile 4 sqeqsmile) frownsmileeq pound nsqfrown + sqfrown ndoublefrown laquo nsqfrowneq 3 sqfrowneq ndoublefrowneq plusmn nsqfrowneqsmile 9 sqfrowneqsmile ndoublesmile copy nsqfrownsmile 1 sqfrownsmile ndoublesmileeq cent nsqsmile sqsmile neqfrown ordf nsqsmileeq 2 sqsmileeq neqsmile deg nsqsmileeqfrown 8 sqsmileeqfrown nfrown uml nsqsmilefrown 0 sqsmilefrown nfrowneq sect nsqtriplefrown sqtriplefrown nfrowneqsmile brvbar nsqtriplesmile sqtriplesmile nfrownsmile ntriplefrown triplefrowniexcl nfrownsmileeq ntriplesmile triplesmile nsmile smile

lowast MnSymbol defines smallsmile as a synonym for smile smallfrown as a syn-onym for frown asymp as a synonym for smilefrown and nasymp as a syn-onym for nsmilefrown

Table 115 ulsy Contradiction Symbols

blitza blitzb blitzc blitzd 13 blitze

Table 116 Extension Characters

minus relbar = Relbar

Table 117 stmaryrd Extension Characters

Y Arrownot Mapsfromchar MapstocharX arrownot [ mapsfromchar

Table 118 txfontspxfonts Extension Characters

Mappedfromchar Mmappedfromchar Mmapstochar mappedfromchar mmappedfromchar mmapstochar

48

Table 119 mathabx Extension Characters

szlig mapsfromchar THORN mapstocharucirc Mapsfromchar uacute Mapstochar

Table 120 Log-like Symbols

arccos cos csc exp ker limsup min sinharcsin cosh deg gcd lg ln Pr suparctan cot det hom lim log sec tanarg coth dim inf liminf max sin tanh

Calling the above ldquosymbolsrdquo may be a bit misleading2 Each log-like symbol merelyproduces the eponymous textual equivalent but with proper surrounding spac-ing See Section 74 for more information about log-like symbols As bmod andpmod are arguably not symbols we refer the reader to the Short Math Guide forLATEX [Dow00] for samples

Table 121 AMS Log-like Symbols

inj lim injlim limminusrarr varinjlim lim varlimsup

proj lim projlim lim varliminf limlarrminus varprojlim

Load the amsmath package to get these symbols See Section 74 for some additionalcomments regarding log-like symbols As mod and pod are arguably not symbolswe refer the reader to the Short Math Guide for LATEX [Dow00] for samples

Table 122 Greek Letters

α alpha θ theta o o τ tauβ beta ϑ vartheta π pi υ upsilonγ gamma ι iota $ varpi φ phiδ delta κ kappa ρ rho ϕ varphiε epsilon λ lambda varrho χ chiε varepsilon micro mu σ sigma ψ psiζ zeta ν nu ς varsigma ω omegaη eta ξ xi

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

The remaining Greek majuscules can be produced with ordinary Latin letters Thesymbol ldquoMrdquo for instance is used for both an uppercase ldquomrdquo and an uppercase ldquomicrordquoSee Section 75 for examples of how to produce bold Greek letters

Table 123 AMS Greek Letters

z digamma κ varkappa

2Michael J Downes prefers the more general term ldquoatomic math objectsrdquo

49

Table 124 txfontspxfonts Upright Greek Letters

α alphaup θ thetaup π piup φ phiupβ betaup ϑ varthetaup $ varpiup ϕ varphiupγ gammaup ι iotaup ρ rhoup χ chiupδ deltaup κ kappaup varrhoup ψ psiupε epsilonup λ lambdaup σ sigmaup ω omegaupε varepsilonup micro muup ς varsigmaupζ zetaup ν nuup τ tauupη etaup ξ xiup υ upsilonup

Table 125 upgreek Upright Greek Letters

α upalpha θ uptheta π uppi φ upphiβ upbeta ϑ upvartheta ϖ upvarpi ϕ upvarphiγ upgamma ι upiota ρ uprho χ upchiδ updelta κ upkappa ρ upvarrho ψ uppsiε upepsilon λ uplambda σ upsigma ω upomegaε upvarepsilon micro upmu σ upvarsigmaζ upzeta ν upnu τ uptauη upeta ξ upxi υ upupsilon

Γ Upgamma Λ Uplambda Σ Upsigma Ψ Uppsi∆ Updelta Ξ Upxi Υ Upupsilon Ω UpomegaΘ 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 slightlydifferent from the above Contrast for example ldquoΓ∆Θαβγrdquo (Symbol) withldquoΓ∆Θαβγrdquo (Euler)

Table 126 txfontspxfonts Variant Latin Letters

1 varg 3 varv 4 varw 2 vary

Pass the varg option to txfontspxfonts to replace g v w and y with 1 3 4 and 2in every mathematical expression in your document

Table 127 AMS Hebrew Letters

i beth ג gimel k daleth

aleph (alefsym) appears in Table 184 on page 62

Table 128 MnSymbol Hebrew Letters

alefsym aleph ℶ beth ℷ gimel ℸ daleth

50

Table 129 Letter-like Symbols

perp bot forall forall ı imath 3 ni gt top` ell ~ hbar isin in part partial weierp wpexist exists = Im jmath lt Re

Table 130 AMS Letter-like Symbols

k Bbbk complement ~ hbarr circledR ` Finv hslashs circledS a Game nexists

Table 131 txfontspxfonts Letter-like Symbols

cent mathcent pound mathsterlinglowast lt notin = notni


Table 132 mathabx Letter-like Symbols

V barin P in L nottop T varnotinA complement E nexists Q owns U varnotownerD exists M notbot W ownsbarF Finv R notin B partialG Game S notowner C partialslash

Table 133 MnSymbol Letter-like Symbols

bot isin in ∌ nownslowast ⊺ topexist exists ∄ nexists ni owns weierp wpforall forall notin ninlowast weierp powerset

lowast MnSymbol provides synonyms notin for nin ni for owns and intercal fortop

Table 134 trfsigns Letter-like Symbols

e e j im

Table 135 mathdesign Letter-like Symbols

isin in 3 owns6isin notin smallin notsmallin smallowns notsmallowns

The mathdesign package additionally provides versions of each of the letter-likesymbols shown in Table 130

51

Table 136 fge Letter-like Symbols

A fgeA fgeeszett D fgeleftB U fgeUc fgec F fgeF C fgeleftCp fged f fgef B fgerightBe fgee fgelblowast s fges

lowast The fge package defines fgeeta fgeN and fgeoverU as synonyms for fgelb

Table 137 AMS Delimiters

p ulcorner q urcornerx llcorner y lrcorner

Table 138 stmaryrd Delimiters

P Lbag Q Rbag N lbag O rbagV llceil W rrceil T llfloor U rrfloorL llparenthesis M rrparenthesis

Table 139 mathabx Delimiters

v lcorners w rcorners

x ulcorner y urcornerz llcorner lrcorner

Table 140 nath Delimiters

niv vin

52

Table 141 Variable-sized Delimiters

darry downarrow dArr

ww Downarrow [[

[ ]]

]

〈lang

langle 〉rang

rangle |∣∣∣ |

∥∥∥ |

dlceil

lceil erceil

rceil uarrx uparrow uArr

~ww Uparrow

blfloor

lfloor crfloor

rfloor lxy updownarrow m

~w Updownarrow

((

( ))

)

∖

backslash

When used with left and right these symbols expand to the height of theenclosed math expression Note that vert is a synonym for | and Vert is asynonym for |

ε-TEX provides a middle analogue to left and right middle can be used forexample to make an internal ldquo|rdquo expand to the height of the surrounding left andright symbols (This capability is commonly needed when typesetting adjacentbras and kets in Dirac notation ldquo〈φ|ψ〉rdquo) A similar effect can be achieved inconventional LATEX using the braket package

Table 142 Large Variable-sized Delimiters lmoustache rmoustache

lgroup rgroup

arrowvertww wwwww Arrowvert

bracevert

These symbols must be used with left and right The mathabx package how-ever redefines lgroup and rgroup so that those symbols can work without leftand right

Table 143 AMS Variable-sized Delimiters

|∣∣∣ lvert |

∣∣∣ rvert

∥∥∥ lVert

∥∥∥ rVert

According to the amsmath documentation [AMS99] the preceding symbols areintended to be used as delimiters (eg as in ldquo|minusz|rdquo) while the vert and Vertsymbols (Table 141) are intended to be used as operators (eg as in ldquop|qrdquo)

Table 144 stmaryrd Variable-sized Delimiters

~

llbracket

rrbracket

53

Table 145 mathabx Variable-sized Delimiters

v1

ldbrack w9

rdbrack

7 7777 lfilet rfilet

~ thickvert ~

vvvert

Table 146 MnSymbol Variable-sized Delimiters

lceil⎡⎢⎢⎢⎢⎢⎢

lceil rceil⎤⎥⎥⎥⎥⎥⎥

rceil ulcorner urcorner

lfloor⎢⎢⎢⎢⎢⎢⎣

lfloor rfloor⎥⎥⎥⎥⎥⎥⎦

rfloor llcorner lrcorner

^ ^^^

lwavy^ ^

^^

rwavy ⟨ ⟨ langle ⟩ ⟩ rangle

__________

lWavy___

_______rWavy k n langlebar p s ranglebar

( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭

⎫⎪⎪⎪⎪⎪⎭ rgroup

⟦LPPPPPN

lsem ⟧MQQQQQO

rsem ⟪ ⟪ llangle ⟫ ⟫ rrangle

⎧⎪⎭⎧⎪⎪⎪⎪⎪⎭ lmoustache

⎫⎪⎩⎫⎪⎪⎪⎪⎪⎩ rmoustache

⎧⎪⎪⎨⎪⎪⎩lbrace

⎫⎪⎪⎬⎪⎪⎭rbrace

backslash ⟨ ⟨ lt ⟩ ⟩ gt

[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦

] 3 6 ullcorner 8 ulrcorner

∣RRRRRRR | ∥

XXXXXXX | ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪ bracevert

RRRRRRRRRR arrowvert XXX

XXXXXXX Arrowvert

vert is a synonym for | Vert is a synonym for | mid and mvert producethe same symbol as vert but designated as math relations instead of ordinalsdivides produces the same symbol as vert but designated as a binary operatorinstead of an ordinal parallel and mVert produce the same symbol as Vertbut designated as math relations instead of ordinals

54

Table 147 mathdesign Variable-sized Delimiters

ETH

ETH

ETH

ETH

ETH

leftwave ETH

ETH

ETH

ETH

ETH

rightwave

Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

leftevaw Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

rightevaw

The definitions of these symbols include a preceding left or right It is thereforean error to specify left or right explicitly The internal ldquoprimitiverdquo versionsof these symbols are called lwave rwave levaw and revaw

Table 148 nath Variable-sized Delimiters (Double)

〈〈langlang

lAngle 〉〉rangrang

rAngle

[[[[

lBrack ]]]]

rBrack

ddlceillceil

lCeil eerceilrceil

rCeil

bblfloorlfloor

lFloor ccrfloorrfloor

rFloor

||∣∣∣∣∣∣ lVertlowast ||

∣∣∣∣∣∣ rVertlowast

lowast nath redefines all of the above to include implicit left and right commandsHence separate lVert and rVert commands are needed to disambiguate whetherldquo|rdquo is a left or right delimiter

All of the symbols in Table 148 can also be expressed using the double macroSee the nath documentation for examples and additional information

Table 149 nath Variable-sized Delimiters (Triple)

〈〈〈langlanglang

triplelt 〉〉〉rangrangrang

triplegt

[[[[[[

triple[ ]]]]]]

triple]

|||∣∣∣∣∣∣∣∣∣ ltriple|lowast |||

∣∣∣∣∣∣∣∣∣ rtriple|lowast

lowast Similar to lVert and rVert in Table 148 ltriple and rtriple must be usedinstead of triple to disambiguate whether ldquo|rdquo is a left or right delimiter

Note that triplemdashand the corresponding doublemdashis actually a macro thattakes a delimiter as an argument

55

Table 150 textcomp Text-mode Delimiters

lang textlangle rang textrangle〚 textlbrackdbl 〛 textrbrackdbl⁅ textlquill ⁆ textrquill

Table 151 metre Text-mode Delimiters

alad Alad dagger crux dagger Crux alas Alas ]] quadrad ]] Quadrad〉 angud 〉 Angud [[ quadras [[ Quadras〈 angus 〈 Angus

Table 152 Math-mode Accents

a acutea a checka a gravea a tildeaa bara a ddota a hata ~a vecaa brevea a dota a mathringa

Also note the existence of imath and jmath which produce dotless versions ofldquoirdquo and ldquoj rdquo (See Table 184 on page 62) These are useful when the accent issupposed to replace the dot For example ldquohatimathrdquo produces a correctldquo ı rdquo while ldquohatirdquo would yield the rather odd-looking ldquo i rdquo

Table 153 AMS Math-mode Accentsa dddota

a ddddota

These accents are also provided by the mathabx and accents packages and areredefined by the mathdots package if the amsmath and amssymb packages have pre-viously been loaded All of the variations except for the original AMS ones tightenthe space between the dots (from

a to ˙a) The mathabx and mathdots versions also

function properly within subscripts and superscripts (x˙a instead of xa )

Table 154 MnSymbol Math-mode Accents

a veca

Table 155 fge Math-mode Accents

A

a spirituslenisAspirituslenisalowast

lowast When fge is passed the crescent option spirituslenis instead uses a crescentaccent as in ldquo a rdquo

56

Table 156 yhmath Math-mode Accents

a ringa

This symbol is largely obsolete as standard LATEX 2ε has supported mathringsince June 1998 [LAT98]

Table 157 Extensible Accentsrsaquoabc widetildeabclowast rdquoabc widehatabclowast

larrminusabc overleftarrowabcdagger

minusrarrabc overrightarrowabcdagger

abc overlineabc abc underlineabc︷︸︸︷abc overbraceabc abc︸︷︷︸ underbraceabc

radicabc sqrtabcDagger

As demonstrated in a 1997 TUGboat article about typesetting long-division prob-lems [Gib97] an extensible long-division sign (ldquo )abc rdquo) can be faked by putting aldquobig)rdquo in a tabular environment with an hline or cline in the preceding rowThe article also presents a piece of code (uploaded to CTAN as longdivtex) thatautomatically solves and typesetsmdashby putting an overline atop ldquobig)rdquo andthe desired textmdashlong-division problems See also the polynom package which au-tomatically solves and typesets polynomial-division problems in a similar manner

lowast These symbols are made more extensible by the MnSymbol package and even moreextensible by the yhmath package

dagger If yoursquore looking for an extensible diagonal line or arrow to be used for canceling orreducing mathematical subexpressions (eg ldquox+minusxrdquo or ldquo

53 + 2 rdquo) then consider

using the cancel package

Dagger With an optional argument sqrt typesets nth roots For exampleldquosqrt[3]abcrdquo produces ldquo 3radic

abc rdquo and ldquosqrt[n]abcrdquo produces ldquo nradicabc rdquo

Table 158 overrightarrow Extensible Accents=rArrabc Overrightarrowabc

Table 159 yhmath Extensible Accents

abc wideparenabc Egraveabc widetriangleabc

˚abc wideringabc

57

Table 160 AMS Extensible Accents

larrrarrabc overleftrightarrowabc abclarrrarr underleftrightarrowabc

abclarrminus underleftarrowabc abcminusrarr underrightarrowabc

Table 161 MnSymbol Extensible Accentslaquoabc overbraceabc degabc underbraceabc

sup3sup1sup1sup1 sup1sup1sup1microabc overgroupabc abcacutesup1sup1sup1 sup1sup1sup1para undergroupabc

zxabc overlinesegmentabc abczx underlinesegmentabc

ETHabc overleftharpoonabc

ETHabc overrightharpoonabc

abc widehatabc abc widetildeabc

Iacuteabc wideparenabc

Table 162 mathtools Extensible Accents︷︸︸︷abc overbraceabc abc︸︷︷︸ underbraceabc

abc overbracketabclowast abc underbracketabclowast

lowast overbracket and underbracket accept optional arguments that specify thebracket height and thickness See the mathtools documentation for more infor-mation

Table 163 mathabx Extensible Accentshkkikkjabc overbraceabc abc widebarabchkkkkjabc overgroupabc |abc widecheckabc

abcloomoon underbraceabc abc wideparenabc

abcloooon undergroupabc˚abc wideringabc

abc widearrowabc

The braces shown for overbrace and underbrace appear in their minimum sizeThey can expand arbitrarily wide however

58

Table 164 esvect Extensible Accents rdquo

abc vvabc with package option a bdquo

abc vvabc with package option b laquo

abc vvabc with package option c raquo

abc vvabc with package option d ndash

abc vvabc with package option e mdash

abc vvabc with package option f

abc vvabc with package option g permil

abc vvabc with package option h

esvect also defines a vv macro which is used to typeset arrows over vector vari-ables with subscripts See the esvect documentation for more information

Table 165 undertilde Extensible Accents

abcrsaquo utildeabc

Because utilde is based on widetilde it is also made more extensible by theyhmath package

Table 166 AMS Extensible Arrows

abclarrminusminus xleftarrowabcabcminusminusrarr xrightarrowabc

Table 167 mathtools Extensible Arrowsabclarrminusminus xhookleftarrowabc

abcminusminusminusminus xleftrightharpoonsabc

abcminusminusrarr xhookrightarrowabc

abc7minusminusrarr xmapstoabcabclArr== xLeftarrowabc

abc==rArr xRightarrowabcabcminusminus xleftharpoondownabc

abcminusminus xrightharpoondownabcabcminusminus xleftharpoonupabc

abcminusminus xrightharpoonupabcabclarrminusrarr xleftrightarrowabc

abcminusminusminusminus xrightleftharpoonsabc

abclArr=rArr xLeftrightarrowabc

Table 168 chemarr Extensible Arrowsabcminusminusminusminus xrightleftharpoonsabc

59

Table 169 chemarrow Extensible Arrows

abcDGGGGGGG

defautoleftarrowabcdef

abcGGGGGGGA

defautorightarrowabcdef

abcEGGGGGGGGGGGGGGC

defautoleftrightharpoonsabcdef

abcGGGGGGGBFGGGGGGG

defautorightleftharpoonsabcdef

In addition to the symbols shown above chemarrow also provides larrowfillrarrowfill leftrightharpoonsfill and rightleftharpoonsfill macrosEach of these takes a length argument and produces an arrow of the specifiedlength

Table 170 trfsigns Extensible Arrows

a dfta a DFTa

Table 171 extarrows Extensible ArrowsabclArr=rArr xLeftrightarrowabc

abclArr==rArr xLongleftrightarrowabcabclarrminusrarr xleftrightarrowabc

abclarrminusminusrarr xlongleftrightarrowabcabc==== xlongequalabc

abc==rArr xLongrightarrowabcabclArr== xLongleftarrowabc

abcminusminusrarr xlongrightarrowabcabclarrminusminus xlongleftarrowabc

Table 172 extpfeil Extensible Arrows

abc==== xlongequalabcabc7minusminusrarr xmapstoabc

abcminusminusminusminus xtwoheadleftarrowabc

abcminusminusminusminus xtwoheadrightarrowabc

The extpfeil package also provides a newextarrow command to help you defineyour own extensible arrow symbols See the extpfeil documentation for more infor-mation

Table 173 holtpolt Non-commutative Division Symbols

abcdef

holterabcdefabcdef

polterabcdef

60

Table 174 Dots

middot cdotp colonlowast ldotp vdotsdagger

middot middot middot cdots ddotsdagger ldots

lowast While ldquordquo is valid in math mode colon uses different surrounding spacing SeeSection 74 and the Short Math Guide for LATEX [Dow00] for more information onmath-mode spacing

dagger The mathdots package redefines ddots and vdots to make them scale properlywith font size (They normally scale horizontally but not vertically) fixedddotsand fixedvdots provide the original fixed-height functionality of LATEX 2εrsquosddots and vdots macros

Table 175 AMS Dots

∵ becauselowast middot middot middot dotsi there4 thereforelowast

middot middot middot dotsb middot middot middot dotsm dotsc dotso

lowast because and therefore are defined as binary relations and therefore also appearin Table 63 on page 30

The AMS dots symbols are named according to their intended usage dotsbbetween pairs of binary operatorsrelations dotsc between pairs of commasdotsi between pairs of integrals dotsm between pairs of multiplication signsand dotso between other symbol pairs

Table 176 wasysym Dots

there4 wasytherefore

Table 177 MnSymbol Dots

sdot cdot hdotdot ⋰ udots ddotdot ⋯ hdots there4 uptherefore⋱ ddots lefttherefore ∶ vdotdot13 diamonddots righttherefore ⋮ vdots∵ downtherefore ∷ squaredots fivedots udotdot

MnSymbol defines therefore as uptherefore and because asdowntherefore Furthermore cdotp and colon produce the same glyphs ascdot and vdotdot respectively but serve as TEX math punctuation (class 6symbols) instead of TEX binary operators (class 2)

All of the above except hdots and vdots are defined as binary operators andtherefore also appear in Table 46 on page 23 Also unlike most of the other dotsymbols in this document MnSymbolrsquos dots are defined as single characters insteadof as composites of multiple single-dot characters

61

Table 178 mathdots Dots

iddots

Table 179 yhmath Dots

adots

Table 180 mathcomp Math Symbols

tccentigrade Ω tcohm permil tcperthousandmicro tcmu tcpertenthousand

Table 181 mathabx Mayan Digits

0 maya0 2 maya2 4 maya41 maya1 3 maya3 5 maya5

Table 182 marvosym Digits

0 MVZero 2 MVTwo 4 MVFour 6 MVSix 8 MVEight1 MVOne 3 MVThree 5 MVFive 7 MVSeven 9 MVNine

Table 183 fge Digits

0 fgestruckzero 1 fgestruckone

Table 184 Miscellaneous LATEX 2ε Math Symbols

alefsym aleph ^ Diamondlowast infin infty prime prime6 angle diams diamondsuit f mholowast ] sharp backslash empty emptysetDagger nabla nabla spades spadesuit Boxlowastdagger [ flat natural

`surd

clubs clubsuit hearts heartsuit not neg 4 triangle

lowast Not predefined in LATEX 2ε Use one of the packages latexsym amsfonts amssymbtxfonts pxfonts or wasysym Note however that amsfonts and amssymb defineDiamond to produce the same glyph as lozenge (ldquodiamsrdquo) the other packages pro-duce a squarer Diamond as depicted above

dagger To use Boxmdashor any other symbolmdashas an end-of-proof (QED) marker considerusing the ntheorem package which properly juxtaposes a symbol with the end ofthe proof text

Dagger Many people prefer the look of AMSrsquos varnothing (ldquoemptyrdquo Table 185) to that ofLATEXrsquos emptyset

62

Table 185 Miscellaneous AMS Math Symbols

ang angle H blacktriangledown f mho8 backprime diagdown ^ sphericalangleF bigstar diagup square blacklozenge eth eth O triangledown blacksquare diams lozenge empty varnothingN blacktriangle ] measuredangle M vartriangle

Table 186 Miscellaneous wasysym Math Symbols

2 Box 3 Diamond f mholowast varangle

lowast wasysym also defines an agemO symbol which is the same glyph as mho but isintended for use in text mode

Table 187 Miscellaneous txfontspxfonts Math Symbols

_ Diamondblack n lambdaslash r varheartsuit Diamonddot p varclubsuit s varspadesuito lambdabar q vardiamondsuit

Table 188 Miscellaneous mathabx Math Symbols

0 degree 4 fourth gt measuredangle 2 secondaring diagdown hash amp pitchfork sphericalangleauml diagup 8 infty 9 propto 3 thirdI diameter $ leftthreetimes rightthreetimes varhash

Table 189 Miscellaneous MnSymbol Math Symbols

ang angle diamondsuit maltese ♯ sharp backneg flat ∡ measuredangle int smallint backprime heartsuit nabla nabla spades spadesuit checkmark infin infty natural ∢ sphericalangleclubs clubsuit ⨽ invbackneg not negempty diameter ⨼ invneg prime prime

MnSymbol defines emptyset and varnothing as synonyms for diameter lnotand minushookdown as synonyms for neg minushookup as a synonym forinvneg hookdownminus as a synonym for backneg and hookupminus asa synonym for invbackneg

63

Table 190 Miscellaneous Internal MnSymbol Math Symbols

q partialvardint p partialvartint⨚ partialvardlanddownint ⨚ partialvartlanddownint⨙ partialvardlandupint ⨙ partialvartlandupint∲ partialvardlcircleleftint ∲ partialvartlcircleleftint∲ partialvardlcirclerightint ∲ partialvartlcirclerightint∯ partialvardoiint ∯ partialvartoiint∮ partialvardoint ∮ partialvartoint∳ partialvardrcircleleftint ∳ partialvartrcircleleftint∳ partialvardrcirclerightint ∳ partialvartrcirclerightint⨏ partialvardstrokedint ⨏ partialvartstrokedint⨋ partialvardsumint ⨋ partialvartsumint

These symbols are intended to be used internally by MnSymbol to construct theintegrals appearing in Table 59 on page 29 but can nevertheless be used in isolation

Table 191 Miscellaneous textcomp Text-mode Math Symbols

deg textdegreelowast frac12 textonehalfdagger frac34 textthreequartersdagger

divide textdiv frac14 textonequarterdagger sup3 textthreesuperiorfrasl textfractionsolidus sup1 textonesuperior times texttimesnot textlnot plusmn textpm sup2 texttwosuperiorminus textminus radic textsurd

lowast If you prefer a larger degree symbol you might consider defining one asldquoensuremath^circrdquo (ldquordquo)

dagger nicefrac (part of the units package) can be used to construct vulgar fractions likeldquo12rdquo ldquo14rdquo ldquo34rdquo and even ldquocordquo

Table 192 Miscellaneous marvosym Math Symbols

W Anglesign divide Squaredot P Vectorarrowhigh= Corresponds p Vectorarrow

Table 193 Miscellaneous fge Math Symbols

K fgebackslash S fgecap R fgecupacute h fgelangleM fgebaracute Q fgecapbar P fgecupbar L fgeupbracketO fgebarcap N fgecup i fgeinfty

Table 194 Miscellaneous mathdesign Math Symbols∟ rightangle

Table 195 Miscellaneous arev Math Symbols

steaming diams vardiamond varspade varclub hearts varheart

64

Table 196 Math Alphabets

Font sample Generating command Required package

ABCdef123 mathrmABCdef123 noneABCdef123 mathitABCdef123 noneABCdef mathnormalABCdef123 noneABC mathcalABC noneABC mathscrABC mathrsfs

or mathcalABC calrsfsABC mathcalABC euscript with the mathcal option

or mathscrABC euscript with the mathscr optionABCdef123 mathpzcABCdef123 none manually definedlowast

ABC mathbbABC amsfontssect amssymb txfonts or pxfonts varmathbbABC txfonts or pxfontsABCdef123 mathbbABCdef123 bbold or mathbboldagger

ABCdef123 mathbbABCdef123 mbboarddagger

ABCdef12 mathbbmABCdef12 bbmABCdef12 mathbbmssABCdef12 bbmABCdef12 mathbbmttABCdef12 bbmABC1 mathdsABC1 dsfontABC1 mathdsABC1 dsfont with the sans optionABCdef123 mathfrakABCdef123 eufrakABCdef123 textfrakABCdef123 yfontsDagger

ABCdef123 textswabABCdef123 yfontsDagger

ABCˇf123 textgothABCdef123 yfontsDagger

lowast Put ldquoDeclareMathAlphabetmathpzcOT1pzcmitrdquo in your docu-mentrsquos preamble to make mathpzc typeset its argument in Zapf ChanceryAs a similar trick you can typeset the Calligra fontrsquos script ldquo r rdquo (or othercalligraphic symbols) in math mode by loading the calligra package andputting ldquoDeclareMathAlphabetmathcalligraT1calligramnrdquoin your documentrsquos preamble to make mathcalligra typeset itsargument in the Calligra font (You may also want to specifyldquoDeclareFontShapeT1calligramnlt-gts[22]callig15rdquo toset Calligra at 22 times its design size for a better blend with typical body fonts)

dagger The mathbbol package defines some additional blackboard bold charactersparentheses square brackets angle brackets andmdashif the bbgreekl optionis passed to matbbolmdashGreek letters For instance ldquolt[(13)]gtrdquo is pro-duced by ldquomathbbLangleLbrackLparenbbalphabbbetabbgammaRparenRbrackRanglerdquo

mbboard extends the blackboard bold symbol set significantly further Itsupports not only the Greek alphabetmdashincluding ldquoGreek-likerdquo symbols suchas bbnabla (ldquordquo)mdashbut also all punctuation marks various currency sym-bols such as bbdollar (ldquo$rdquo) and bbeuro (ldquoucircrdquo) and the Hebrew alpha-bet (eg ldquobbfinalnunbbyodbbqofbbperdquo rarr ldquoIumlEacutetimesOcircrdquo)

Dagger As their text names imply the fonts provided by the yfonts package areactually text fonts They are included in Table 196 because they are frequentlyused in a mathematical context

65

sect An older (ie prior to 1991) version of the AMSrsquos fonts rendered C N R Sand Z as C N R S and Z As some people prefer the older glyphsmdashmuch tothe AMSrsquos surprisemdashand because those glyphs fail to build under modern versionsof METAFONT Berthold Horn uploaded PostScript fonts for the older blackboard-bold glyphs to CTAN to the fontsmsym10 directory As of this writing howeverthere are no LATEX 2ε packages for utilizing the now-obsolete glyphs

66

4 Science and technology symbols

This section lists symbols that are employed in various branches of science and engineering

Table 197 gensymb Symbols Defined to Work in Both Math and Text Mode

celsius micro micro permil perthousanddeg degree Ω ohm

Table 198 wasysym Electrical and Physical Symbols

AC VHF photon F HF QPPPPPPR gluon

Table 199 ifsym Pulse Diagram Symbols

FallingEdge LongPulseLow PulseLow ShortPulseHighamp LongPulseHigh $ PulseHigh RaisingEdge ShortPulseLow

In addition within textifsym the following codes are valid

l l m m h h d d lt lt gt gt

L L M M H H D D = ltlt gtgt

This enables one to write ldquotextifsymmmltDDDgtmmrdquo to get ldquommltDDDgtmmrdquo orldquotextifsymL|H|L|H|Lrdquo to get ldquoL|H|L|H|Lrdquo See also the timing packagewhich provides a wide variety of pulse-diagram symbols within an environmentdesigned specifically for typesetting pulse diagrams

Finally textifsym supports the display of segmented digits as would appearon an LCD ldquotextifsym-123456rdquo produces ldquo-123456rdquo ldquotextifsymbrdquooutputs a blank with the same width as an ldquo8rdquo

Table 200 ar Aspect Ratio Symbol

A AR

Table 201 textcomp Text-mode Science and Engineering Symbols

textcelsius textmho micro textmu Ω textohm

67

Table 202 wasysym Astronomical Symbols

mercury earth X jupiter Z uranus pluto venus mars Y saturn [ neptune

astrosun fullmoon $ leftmoon newmoon rightmoon

aries _ cancer a libra e aquarius] taurus leo b scorpio d capricornus^ gemini ` virgo c sagittarius f pisces

ascnode descnode V conjunction W opposition vernal

Table 203 marvosym Astronomical Symbols

Acirc Mercury Ecirc Earth Aring Jupiter Ccedil Uranus Eacute PlutoAtilde Venus Auml Mars AElig Saturn Egrave Neptune

Aacute Moon Agrave Sun

agrave Aries atilde Cancer aelig Libra eacute Capricornaacute Taurus auml Leo ccedil Scorpio ecirc Aquariusacirc Gemini aring Virgo egrave Sagittarius euml Pisces

Note that Aries Pisces can also be specified with Zodiac1 Zodiac12

Table 204 mathabx Astronomical Symbols

A Mercury C Earth E Jupiter G Uranus I PlutoB Venus D Mars F Saturn H Neptune J varEarth

M fullmoon K leftmoon N newmoon L rightmoon Sun

P Aries Q Taurus R Gemini

mathabx also defines girl as an alias for Venus boy as an alias for Mars andMoon as an alias for leftmoon

Table 205 wasysym APL Symbols

~ APLbox divide~ APLinv E APLstar APLcomment p APLleftarrowbox APLupF APLdown APLlog n APLuparrowboxo APLdownarrowbox minus APLminus minus notbackslash APLinput q APLrightarrowbox minus notslash

Table 206 wasysym APL Modifiers

APLcirc sim APLnot | APLvert

68

Table 207 marvosym Computer Hardware Symbols

Iacute ComputerMouse Ntilde ParallelPort Icirc SerialInterfaceIuml Keyboard Ograve Printer ETH SerialPort

Table 208 keystroke Computer Keys

Alt Alt Enter Enterlowast PrtSc PrtSclowast

AltGr AltGr Esc Esclowast rarr RArrow

Break Breaklowast Home Homelowast larr Return

7minusrarr BSpacedagger Ins Inslowast Scroll Scrolllowast

Ctrl Ctrllowast larr LArrow Shift uArr Shiftlowast

darr DArrow Num NumLock Spacebar

Del Dellowast Page darr PgDownlowast minusminusrarrminusminusrarr Tabdagger

End Endlowast Page uarr PgUplowast uarr UArrow

lowast Changes based on the language option passed to the keystroke package For exam-ple the german option makes Del produce ldquo Entf rdquo instead of ldquo Del rdquo

dagger These symbols utilize the rotating package and therefore display improperly in mostDVI viewers

The keystroke command draws a key with an arbitrary label For exampleldquokeystrokeF7rdquo produces ldquo F7 rdquo

Table 209 ascii Control Characters (CP437)

SOH BS SI SYN GS STX HT DLE ETB RS ETX LF DCa CAN US EOT VT DCb EM ENQ FF DCc SUB ACK CR DCd ESC BEL SO NAK FS

DEL NBSP NUL brvbar splitvert

Code Page 437 (CP437) which was first utilized by the original IBM PC uses thesymbols SOH through US to depict ASCII characters 1ndash31 and DEL to depictASCII character 127 The NUL symbol not part of CP437 represents ASCIIcharacter 0 NBSP also not part of CP437 represents a nonbreaking spacesplitvert is merely the ldquo|rdquo character drawn as it was on the IBM PC

Table 210 marvosym Communication Symbols

k Email t fax v Faxmachine E Lightning A Pickup

z Emailct u FAX B Letter H Mobilefone T Telefon

69

Table 211 marvosym Engineering Symbols

Beam l Force lsquo Octosteel RoundedTTsteel Bearing rsquo Hexasteel ˜ Rectpipe mdash Squarepipersaquo Circpipe amp Lefttorque rdquo Rectsteel ldquo Squaresteelbull Circsteel L Lineload Righttorque œ Tsteel Fixedbearing $ Loosebearing Ÿ RoundedLsteellowast š TTsteelndash Flatsteel trade Lsteel RoundedTsteellowast

lowast RoundedLsteel and RoundedTsteel seem to be swapped at least in the20000501 version of marvosym

Table 212 wasysym Biological Symbols

female male

Table 213 marvosym Biological Symbols

~ Female hellip FemaleMale MALE Neutral FEMALE Hermaphrodite | Malebdquo FemaleFemale HERMAPHRODITE ƒ MaleMale

Table 214 marvosym Safety-related Symbols

h Biohazard C CEsign ` Explosionsafe j Radioactivityn BSEfree J Estatically a Laserbeam Stopsign

Table 215 feyn Feynman Diagram Symbols

bigbosonloop feynfu feyngvs h feynh

a feyna feynfv feyngv l feynms

c feync f feynf g feyng m feynm

feynfd w feynglu feynhd p feynp

n feynfl o feyngl i feynhs x feynx

e feynfs feyngu feynhu smallbosonloop

All other arguments to the feyn command produce a ldquordquo symbol

The feyn package provides various commands for composing the preceding symbolsinto complete Feynman diagrams See the feyn documentation for examples andadditional information

70

5 Dingbats

Dingbats are symbols such as stars arrows and geometric shapes They are commonly used as bullets initemized 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 LATEXinterface to the Zapf Dingbats font (one of the standard 35 PostScript fonts) However rather than name eachof the dingbats individually pifont merely provides a single ding command which outputs the character thatlies at a given position in the font The consequence is that the pifont symbols canrsquot be listed by name in thisdocumentrsquos index so be mindful of that fact when searching for a particular symbol

Table 216 bbding Arrows

y ArrowBoldDownRight z ArrowBoldRightShort x ArrowBoldUpRight

ArrowBoldRightCircled w ArrowBoldRightStrobe

Table 217 pifont Arrows

Ocirc ding212 Yacute ding221 aelig ding230 iuml ding239 ugrave ding249Otilde ding213 THORN ding222 ccedil ding231 ntilde ding241 uacute ding250Ouml ding214 szlig ding223 egrave ding232 ograve ding242 ucirc ding251times ding215 agrave ding224 eacute ding233 oacute ding243 uuml ding252Oslash ding216 aacute ding225 ecirc ding234 ocirc ding244 yacute ding253Ugrave ding217 acirc ding226 euml ding235 otilde ding245 thorn ding254Uacute ding218 atilde ding227 igrave ding236 ouml ding246Ucirc ding219 auml ding228 iacute ding237 divide ding247Uuml ding220 aring ding229 icirc ding238 oslash ding248

Table 218 universal Arrows

bauarrow bauwhitearrow

Table 219 marvosym Scissors

s Cutleft q Cutright S Leftscissorsr Cutline R Kutline Q Rightscissors

Table 220 bbding Scissors

ScissorHollowLeft ScissorLeftBrokenTop

ScissorHollowRight ScissorRight

ScissorLeft ScissorRightBrokenBottom

ScissorLeftBrokenBottom ScissorRightBrokenTop

Table 221 pifont Scissors

ding33 ding34 ding35 $ ding36

71

Table 222 dingbat Pencils

W largepencil P smallpencil

Table 223 bbding Pencils and Nibs

NibLeft PencilLeft PencilRightDown

NibRight PencilLeftDown PencilRightUp

NibSolidLeft PencilLeftUp

NibSolidRight PencilRight

Table 224 pifont Pencils and Nibs

ding46 ding47 0 ding48 1 ding49 2 ding50

Table 225 dingbat Fists

R leftpointright L rightpointleft N rightpointrightD leftthumbsdown d rightthumbsdownU leftthumbsup u rightthumbsup

Table 226 bbding Fists

HandCuffLeft HandCuffRightUp HandPencilLeft

HandCuffLeftUp HandLeft HandRight

13 HandCuffRight HandLeftUp HandRightUp

Table 227 pifont Fists

ding42 + ding43 ding44 - ding45

Table 228 bbding Crosses and Plusses

Cross + CrossOpenShadow amp PlusOutline

- CrossBoldOutline CrossOutline ) PlusThinCenterOpen

4 CrossClowerTips Plus

CrossMaltese ( PlusCenterOpen

Table 229 pifont Crosses and Plusses

9 ding57 ding59 = ding61 ding63 ding58 lt ding60 gt ding62 ding64

72

Table 230 bbding Xs and Check Marks

Checkmark XSolid XSolidBrush

CheckmarkBold $ XSolidBold

Table 231 pifont Xs and Check Marks

3 ding51 5 ding53 7 ding554 ding52 6 ding54 8 ding56

Table 232 wasysym Xs and Check Marks

2 CheckedBox Square 4 XBox

Table 233 universal Xs

baucross

Table 234 pifont Circled Numbers

not ding172 para ding182 Agrave ding192 Ecirc ding202shy ding173 middot ding183 Aacute ding193 Euml ding203reg ding174 cedil ding184 Acirc ding194 Igrave ding204macr ding175 sup1 ding185 Atilde ding195 Iacute ding205deg ding176 ordm ding186 Auml ding196 Icirc ding206plusmn ding177 raquo ding187 Aring ding197 Iuml ding207sup2 ding178 frac14 ding188 AElig ding198 ETH ding208sup3 ding179 frac12 ding189 Ccedil ding199 Ntilde ding209acute ding180 frac34 ding190 Egrave ding200 Ograve ding210micro ding181 iquest ding191 Eacute ding201 Oacute ding211

pifont (part of the psnfss package) provides a dingautolist environment whichresembles enumerate but uses circled numbers as bullets3 See the psnfss docu-mentation for more information

Table 235 wasysym Stars

C davidsstar A hexstar B varhexstar

3In fact dingautolist can use any set of consecutive Zapf Dingbats symbols

73

Table 236 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 lt FiveStarOpenDotted [ SixFlowerRemovedOpenPetal

Z EightAsterisk = FiveStarOutline G SixStar

S EightFlowerPetal gt 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 237 pifont Stars Flowers and Similar Shapes

A ding65 J ding74 S ding83 ding92 e ding101B ding66 K ding75 T ding84 ] ding93 f ding102C ding67 L ding76 U ding85 ^ ding94 g ding103D ding68 M ding77 V ding86 _ ding95 h ding104E ding69 N ding78 W ding87 ` ding96 i ding105F ding70 O ding79 X ding88 a ding97 j ding106G ding71 P ding80 Y ding89 b ding98 k ding107H ding72 Q ding81 Z ding90 c ding99I ding73 R ding82 [ ding91 d ding100

Table 238 wasysym Geometric Shapes

7 hexagon 8 octagon D pentagon 9 varhexagon

Table 239 MnSymbol Geometric Shapes

filledlargestar largediamond largestar loz smalllozenge⧫ filledlozenge loz largelozenge largestarofdavid⧫ filledmedlozenge largepentagram loz medlozenge largecircle ◻ largesquare medstarofdavid

MnSymbol defines bigcirc as a synonym for largecircle bigstar as a syn-onym for filledlargestar lozenge as a synonym for medlozenge andblacklozenge as a synonym for filledmedlozenge

74

Table 240 ifsym Geometric Shapes

BigCircle T FilledBigTriangleRight E SmallCircle

13 BigCross Q FilledBigTriangleUp SmallCross

amp 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 combinesome of the above into useful new symbols For example BigCircle andFilledSmallCircle combine to give ldquou rdquo Likewise Square and Cross com-bine to give ldquo0rdquo See Section 73 for more information about constructing newsymbols out of existing symbols

Table 241 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

Table 242 pifont Geometric Shapes

l ding108 o ding111 r ding114 u ding117 y ding121m ding109 p ding112 s ding115 w ding119 z ding122n ding110 q ding113 t ding116 x ding120

75

Table 243 universa Geometric Shapes

baucircle bausquare bautriangle

Table 244 universal Geometric Shapes

baucircle bauhole bausquare baueclipse baupunct bautriangle

Table 245 igo Go Stones

blackstone[igocircle] whitestone[igocircle]

| blackstone[igocross] | whitestone[igocross]

blackstone[igonone] whitestone[igonone]

~ blackstone[igosquare] ~ whitestone[igosquare]

blackstone[igotriangle] whitestone[igotriangle]

In addition to the symbols shown above igorsquos blackstone and whitestonecommands accept numbers from 1 to 99 and display them circled as c and c respectively

The igo package is intended to typeset Go boards (goban) See the igo documen-tation for more information

Table 246 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 textlhdbendand textreversedvideodbend

Table 247 skull Symbols

A skull

Table 248 Non-Mathematical mathabx Symbols

O rip

Table 249 marvosym Information Symbols

reg Bicycle o Football Z PointinghandV Checkedbox x Gentsroom w WheelchairU Clocklogo I Industry b WritinghandK Coffeecup i InfoX Crossedbox y Ladiesroom

76

Table 250 Miscellaneous dingbat Dingbats

O anchor E eye S SborderC carriagereturn C filledsquarewithdots B squarewithdots

D checkmark I satellitedish Z Zborder

Table 251 Miscellaneous bbding Dingbats

Envelope Peace PhoneHandset T SunshineOpenCircled

q OrnamentDiamondSolid Phone Plane Tape

Table 252 Miscellaneous pifont Dingbats

ding37 ( ding40 curren ding164 sect ding167 laquo ding171amp ding38 ) ding41 yen ding165 uml ding168 copy ding169 ding39 v ding118 brvbar ding166 ordf ding170

77

6 Other symbols

The following are all the symbols that didnrsquot fit neatly or unambiguously into any of the previous sections(Do weather symbols belong under ldquoScience and technologyrdquo Should dice be considered ldquomathematicsrdquo)While some of the tables contain clearly related groups of symbols (eg musical notes) others represent motleyassortments of whatever the font designer felt like drawing

Table 253 textcomp Genealogical Symbols

b textborn c textdivorced m textmarriedd textdied l textleaf

Table 254 wasysym General Symbols

m ataribox clock LEFTarrow smiley bell diameter lightning sun- blacksmiley L DOWNarrow phone K UParrow1 Bowtie frownie pointer loz wasylozenge| brokenvert invdiameter recorder checked 6 kreuz RIGHTarrow

Table 255 wasysym Circles

CIRCLE G LEFTcircle H RIGHTcircle rightturn Circle I Leftcircle J RightcircleG LEFTCIRCLE H RIGHTCIRCLE leftturn

Table 256 wasysym Musical Symbols

eighthnote 13 halfnote twonotes fullnote quarternote

See also flat sharp and natural (Table 184 on page 62)

Table 257 arev Musical Symbols

quarternote eighthnote sixteenthnote


78

Table 258 harmony Musical Symbols

ˇ ldquo ˇ ldquo== AAcht DD DDohne ˘ ldquo Halb ˇ ldquo==== SechBR gt VM

ˇ ldquo( Acht D Dohne lt HaPa ˇ ldquo=== SechBr ˇ ldquo Zwdrˇ ldquo== AchtBL ss Ds permil Pu SePa A ZwPaˇ ldquo== AchtBR SS DS ˇ ldquo) Sech lt UB

AcPa macr Ganz ˇ ldquo==== SechBL ˇ ldquo Vier

DD DD lt GaPa ˇ ldquo=== SechBl gt ViPa

The musixtex package must be installed to use harmony

Table 259 harmony Musical Accents

Aa

aa

FerliAFerlialowast Aa OhneAOhnealowast

Aa

aa

FermiAFermia A a UmdAUmdalowast

Alal KrAKra

lowast These symbols take an optional argument which shifts the accent either horizontallyor vertically (depending on the command) by the given distance

In addition to the accents shown above HH is a special accent commandwhich accepts five period-separated characters and typesets them such thatldquoHHXabcdrdquo produces ldquoX

a

bcdrdquo All arguments except the first can be omit-

ted ldquoHHXrdquo produces ldquoXrdquo Takt takes two arguments and composes theminto a musical time signature For example ldquoTakt128rdquo produces ldquo 8

12rdquo Astwo special cases ldquoTaktc0rdquo produces ldquoSrdquo and ldquoTaktc1rdquo produces ldquoRrdquo


Table 260 Miscellaneous manfnt Symbols

manboldkidney manpenkidney

$ manconcentriccircles amp manquadrifolium manconcentricdiamond manquartercircle

mancone manrotatedquadrifolium mancube manrotatedquartercircley manerrarrow manstar manfilledquartercircle mantiltpennib manhpennib 7 mantriangledown manimpossiblecube x mantriangleright mankidney 6 mantriangleup manlhpenkidney manvpennib

Table 261 marvosym Navigation Symbols

middot Forward raquo MoveDown acute RewindToIndex frac14 ToTopcedil ForwardToEnd ordm MoveUp micro RewindToStartsup1 ForwardToIndex para Rewind frac12 ToBottom

79

Table 262 marvosym Laundry Symbols

Oslash AtForty Uuml Handwash Ocirc ShortNinetyFiveOacute AtNinetyFive macr IroningI Ouml ShortSixtyOtilde AtSixty deg IroningII Ucirc ShortThirtyEuml Bleech plusmn IroningIII Uacute SpecialFortylaquo CleaningA Igrave NoBleech Tumblerfrac34 CleaningF uml NoChemicalCleaning permil WashCottoniquest CleaningFF sup2 NoIroning Š WashSyntheticsnot CleaningP NoTumbler lsaquo WashWoolshy CleaningPP times ShortFiftyYacute Dontwash Ugrave ShortForty

Table 263 Other marvosym Symbols

ˆ Ankh dagger Cross Œ Heart copy Smileyyacute Bat F FHBOlogo yuml MartinVogel thorn Womanfaceyen Bouquet f FHBOLOGO m Mundus Y YinyangDagger Celtcross sect Frowny MVAtordf CircledA FullFHBO MVRightarrow

Table 264 Miscellaneous universa Symbols

bauforms bauhead

Table 265 Miscellaneous universal Symbols

baudash bauforms bauquarter varQ bauequal bauhead bauquestion13 bauface bauplus bauwindow

Table 266 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 Thermo0 Thermo6 produce thermometers that are between06 and 66 full of mercury

Similarly wind〈sun〉〈angle〉〈strength〉 will draw wind symbols with a givenamount of sun (0ndash4) a given angle (in degrees) and a given strength in kmh (0ndash100) For example wind000 produces ldquo 0 rdquo wind200 producesldquo 0 rdquo and wind40100 produces ldquo rdquo

80

Table 267 ifsym Alpine Symbols

SummitSign Summit SurveySign HalfFilledHut

StoneMan Mountain Joch VarSummit

Hut IceMountain Flag

FilledHut VarMountain VarFlag

Village VarIceMountain Tent

Table 268 ifsym Clocks

Interval StopWatchStart VarClock Wecker

StopWatchEnd Taschenuhr VarTaschenuhr

ifsym also exports a showclock macro showclock〈hours〉〈minutes〉 outputsa clock displaying the corresponding time For instance ldquoshowclock540rdquoproduces ldquo rdquo 〈hours〉 must be an integer from 0 to 11 and 〈minutes〉 must be aninteger multiple of 5 from 0 to 55

Table 269 Other ifsym Symbols

FilledSectioningDiamond Letter Radiation

Fire PaperLandscape SectioningDiamond

Irritant PaperPortrait Telephone

StrokeOne StrokeThree StrokeFive

StrokeTwo StrokeFour

In addition Cube1 Cube6 produce dice with the corresponding number ofspots

Table 270 epsdice Dice

epsdice1 epsdice3 epsdice5epsdice2 epsdice4 epsdice6

The epsdice package does not provide a font but rather an interface to a set ofgraphics drawn in Encapsulated PostScript Consequently epsdice does not workwith pdfLATEX

81

Table 271 skak Chess Informator Symbols

g bbetter d doublepawns N novelty R variousi bdecisive L ending F onlymove f wbetterb betteris j equal o opposbishops h wdecisivea bishoppair P etc r passedpawn J weakpte bupperhand H file M qside w withI centre O kside s samebishops A withattackRR comment x markera l see E withidean compensation y markerb q seppawns C withinitV counterplay m mate T timelimit v withoutt devadvantage S morepawns k unclear c wupperhandG diagonal U moreroom u unitedpawns D zugzwang

The preceding symbols are merely the named informator symbol skak cantypeset many more chess-related symbols including those for all of the pieces(KQRBNPkqrbnp) but only in the context of moves and boards notas individual named LATEX symbols

Table 272 metre Metrical Symbols

times

amacr

bBm cc ˘ Mbb ˙˙

Pppp otimes

t

˘ Bmacr

bbm Ccc ˘ macrmbbx ˙

˙pppp tsbm

˘ bmacr

Bbmmacr

m oo ˙˙

Ppppp tsmb

˘ Bb ˘ bbmbmacr

M˙

p ˙˙

ppppp tsmm

˘ BBmacr ˘ bbmx timesmacr ma

macrpm ps

macrvppm

˘ bbmacr

bm ˘ Mb ˙ pp ˙ pxpmacr

vpppm

˘ bBmacr

Bm ˘ mb ˙ Pp ˙ Pxp ˙˙ xtimes bba c ˘ mBb

macrppm sim

R

˘ bbb C ˘ mbB ˙˙

ppp sim

r

macrBBm Cc ˘ mbb ˙

˙Ppp otimes

T

The preceding symbols are valid only within the argument to the metre command

Table 273 metre Small and Large Metrical Symbols

divide anaclasis divide Anaclasislt antidiple lt Antidipleltmiddotmiddot antidiple ltmiddotmiddot Antidiplesup antisigma sup Antisigmatimesmiddotmiddotmiddotmiddot asteriscus timesmiddotmiddotmiddotmiddot Asteriscus

and catalexis and Catalexisgt diple gt Diplegtmiddotmiddot diple gtmiddotmiddot Diple

obelus Obelusmiddotmiddot obelus middotmiddot Obelussim respondens sim Respondensotimes terminus otimes Terminusoplus terminus oplus Terminus

82

Table 274 phaistos Symbols from the Phaistos Disk

J PHarrow e PHeagle B PHplumedHead

h PHbee o PHflute d PHram

X PHbeehive H PHgaunlet l PHrosette

R PHboomerang p PHgrater P PHsaw

K PHbow G PHhelmet L PHshield

b PHbullLeg a PHhide Y PHship

D PHcaptive Z PHhorn V PHsling

S PHcarpentryPlane Q PHlid r PHsmallAxe

c PHcat m PHlily q PHstrainer

E PHchild N PHmanacles C PHtattooedHead

M PHclub O PHmattock I PHtiara

W PHcolumn n PHoxBack g PHtunny

U PHcomb k PHpapyrus j PHvine

T PHdolium A PHpedestrian s PHwavyBand

f PHdove i PHplaneTree F PHwoman

Table 275 protosem Proto-Semitic Characters

a Aaleph E AAhe k Akaph s Asamekh R AAreshA AAaleph z Azayin K AAkaph p Ape S Ashinb Abeth w Avav l Alamed P AApe v AhelmetB AAbeth H Aheth L AAlamed x Asade V AAhelmetg Agimel h AAheth m Amem X AAsade t Atavd Adaleth T Ateth n Anun q AqophD AAdaleth y Ayod o Aayin Q AAqophe Ahe Y AAyod O AAayin r Aresh

The protosem package defines abbreviated control sequences for each of the aboveIn addition single-letter shortcuts can be used within the argument to thetextproto command (eg ldquotextprotoPakynrdquo produces ldquoPakynrdquo) Seethe protosem documentation for more information

83

Table 276 hieroglf Hieroglyphics

A HA I HI n Hn T HT

a Ha i Hi O HO t Ht

B HB ˝ Hibl o Ho ˘ Htongue

b Hb ˆ Hibp p Hp U HU

c Hc uml Hibs P HP u Hu

C HC ˜ Hibw ˙ Hplural V HV

D HD J HJ + Hplus v Hv

d Hd j Hj Q HQ | Hvbar

cedil Hdual k Hk q Hq w Hw

e He K HK Hquery W HWE HE L HL R HR X HX

f Hf l Hl r Hr x Hx

F HF m Hm s Hs Y HY

G HG M HM S HS y Hy

g Hg ˇ Hman macr Hscribe z Hz

h Hh acute Hms Hslash Z HZ

H HH N HN ˚ Hsv

| Hone 3 Hhundred 5 HXthousand 7 Hmillion

2 Hten 4 Hthousand 6 HCthousand

The hieroglf package defines alternate control sequences and single-letter shortcutsfor each of the above which can be used within the argument to the textpmhg

command (eg ldquotextpmhgPakinrdquo produces ldquoPakinrdquo) See the hieroglfdocumentation for more information

Table 277 dictsym Dictionary Symbols

a dsaeronautical c dscommercial m dsmedicalG dsagricultural H dsheraldical X dsmilitaryA dsarchitectural J dsjuridical R dsrailwaysB dsbiological L dsliterary T dstechnicalC dschemical M dsmathematical

84

Table 278 simpsons Characters from The Simpsons

Bart

Homer Maggie SNPP

Burns

Lisa

Marge

The location of the charactersrsquo pupils can be controlled with the Goofy commandSee A METAFONT of lsquoSimpsonsrsquo characters [Che97] for more information Alsoeach of the above can be prefixed with Left to make the character face left insteadof right

LeftBart

Table 279 staves Magical Staves

staveI staveXXIV staveXLVII

staveII staveXXV staveXLVIII

staveIII staveXXVI 0 staveXLIX

staveIV staveXXVII 1 staveL

staveV staveXXVIII 2 staveLI

staveVI staveXXIX 3 staveLII

staveVII staveXXX 4 staveLIII

staveVIII staveXXXI 5 staveLIV

staveIX staveXXXII 6 staveLV

staveX staveXXXIII 7 staveLVI

staveXI staveXXXIV 8 staveLVII

staveXII staveXXXV 9 staveLVIII

staveXIII staveXXXVI staveLIX

13 staveXIV $ staveXXXVII staveLX

staveXV staveXXXVIII lt staveLXI

staveXVI amp staveXXXIX = staveLXII


85


staveXVII staveXL gt staveLXIII

staveXVIII ( staveXLI staveLXIV

staveXIX ) staveXLII staveLXV

staveXX staveXLIII A staveLXVI

staveXXI + staveXLIV B staveLXVII

staveXXII staveXLV C staveLXVIII

staveXXIII - staveXLVI

The meanings of these symbols are described on the Web site for the Mu-seum of Icelandic Sorcery and Witchcraft at httpwwwgaldrasyningisindexphpoption=com contentamptask=categoryampsectionid=5ampid=18ampItemid=

60 (TinyURL httptinyurlcom25979m) For example staveL (ldquo1rdquo) isintended to ward off ghosts and evil spirits

86

7 Additional Information

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

71 Symbol Name Clashes

Unfortunately a number of symbol names are not unique they appear in more than one package Dependingon how the symbols are defined in each package LATEX will either output an error message or replace anearlier-defined symbol with a later-defined symbol Table 280 presents a selection of name clashes that appearin this document

Using multiple symbols with the same name in the same documentmdashor even merely loading conflictingsymbol packagesmdashcan be tricky but as evidenced by the existence of Table 280 not impossible The generalprocedure is to load the first package rename the conflicting symbols and then load the second packageExamine the LATEX source for this document (symbolstex) for examples of this and other techniques forhandling symbol conflicts Note that symbolstexrsquos savesymbol and restoresymbol macros have beenextracted into the savesym package which can be downloaded from CTAN

txfonts and pxfonts redefine a huge number of symbolsmdashessentially all of the symbols defined by latexsymtextcomp the various AMS symbol sets and LATEX 2ε itself Similarly mathabx redefines a vast number ofmath symbols in an attempt to improve their look The txfonts pxfonts and mathabx conflicts are not listedin Table 280 because they are designed to be compatible with the symbols they replace Table 281 on page 89illustrates what ldquocompatiblerdquo means in this context

To use the new txfontspxfonts symbols without altering the documentrsquos main font merely reset the defaultfont families back to their original values after loading one of those packages

renewcommandrmdefaultcmrrenewcommandsfdefaultcmssrenewcommandttdefaultcmtt

72 Resizing symbols

Mathematical symbols listed in this document as ldquovariable-sizedrdquo are designed to stretch vertically Eachvariable-sized symbol comes in one or more basic sizes plus a variation comprising both stretchable andnonstretchable segments Table 282 on page 89 presents the symbols and uparrow in their default sizein their big Big bigg and Bigg sizes in an even larger size achieved using leftright andmdashforcontrastmdashin a large size achieved by changing the font size using LATEX 2εrsquos fontsize command Becausethe symbols shown belong to the Computer Modern family the type1cm package needs to be loaded to supportfont sizes larger than 2488 pt

Note how fontsize makes the symbol wider and thicker (The graphicx packagersquos scalebox orresizebox commands would produce a similar effect) Also the fontsize-enlarged symbol is verticallycentered relative to correspondingly large text unlike the symbols enlarged using big et al or leftrightwhich all use the same math axis regardless of symbol size However fontsize is not limited to mathematicaldelimiters Also scalebox and resizebox are more robust to poorly composed symbols (eg two symbolsmade to overlap by backspacing a fixed distance) but do not work with every TEX backend and will producejagged symbols when scaling a bitmapped font

All variable-sized delimiters are defined (by the corresponding tfm file) in terms of up to five segments asillustrated by Figure 1 on page 89 The top middle and bottom segments are of a fixed size The top-middleand middle-bottom segments (which are constrained to be the same character) are repeated as many times asnecessary to achieve the desired height

73 Where can I find the symbol for

If you canrsquot find some symbol yoursquore looking for in this document there are a few possible explanations

87

Table

280

Sym

bol

Nam

eC

lash

es

Sym

bol

LAT E

X2 ε

AMS

stm

aryr

dw

asys

ymm

ath

abx

mar

vosy

mb

bd

ing

ifsy

md

ingb

atw

suip

a

baro

lt

bigtriangledown

5`

bigtriangleup

4a

checkmark

XD

Circle

5

Cross

dagger

ggg

≫Iuml

Letter

B

lightning

Lightning

E

lll

≪Icirc

Square

f

0Sun

Agrave

TriangleDown

o3

TriangleUp

n1

88

Table 281 Example of a Benign Name Clash

Default txfontsSymbol (Computer Modern) (Times Roman)

R R Rtextrecipe

Table 282 Sample resized delimiters

Symbol Default size big Big bigg Bigg left right fontsize

trade

uparrow uarrx x x

xxuarr

minusrarr

top

top-middle (extensible)

middle

middle-bottom (extensible)

bottom

Figure 1 Implementation of variable-sized delimiters

89

bull The symbol isnrsquot intuitively named As a few examples the ifsym command to draw dice is ldquoCuberdquo aplus sign with a circle around it (ldquoexclusive orrdquo to computer engineers) is ldquooplusrdquo and lightning boltsin fonts designed by German speakers may have ldquoblitzrdquo in their names as in the ulsy package The moralof the story is to be creative with synonyms when searching the index

bull The symbol is defined by some package that I overlooked (or deemed unimportant) If therersquos somesymbol package that you think should be included in the Comprehensive LATEX Symbol List please sendme e-mail at the address listed on the title page

bull The symbol isnrsquot 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 bindingfor it For example the PostScript Symbol font contains a ldquocrarrrdquo symbol which may be useful for representinga carriage return but there is no package (as far as I know) for accessing that symbol To produce anunnamed symbol you need to switch to the font explicitly with LATEX 2εrsquos low-level font commands [LAT00]and use TEXrsquos primitive char command [Knu86a] to request a specific character number in the font4 In factchar is not strictly necesssary the character can often be entered symbolically For example the symbolfor an impulse train or Tate-Shafarevich group (ldquoXrdquo) 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 asldquofontencodingOT2selectfontchar88rdquo it may be more intuitive to use the OT2 font encodingrsquos ldquoSHrdquoligature ldquofontencodingOT2selectfont SHrdquo

Reflecting and rotating existing symbols

A common request on comptexttex is for a reversed or rotated version of an existing symbolAs a last resort these effects can be achieved with the graphicx (or graphics) packagersquos reflectbox androtatebox macros For example textsuperscriptreflectbox produces an irony mark (ldquo rdquocf httpenwikipediaorgwikiIrony mark) and rotatebox[origin=c]180$iota$ produces thedefinite-description operator (ldquo ιrdquo) The disadvantage of the graphicxgraphics approach is that not every TEXbackend handles graphical transformations5 Far better is to find a suitable font that contains the desiredsymbol in the correct orientation For instance if the phonetic package is available then textitriotawill yield a backend-independent ldquordquo Similarly tiparsquos textrevepsilon (ldquo3rdquo) or wsuiparsquos revepsilon (ldquordquo)may be used to express the mathematical notion of ldquosuch thatrdquo in a cleaner manner than with reflectboxor rotatebox6

Joining and overlapping existing symbols

Symbols that do not exist in any font can sometimes be fabricated out of existing symbols The LATEX 2ε sourcefile fontdefdtx contains a number of such definitions For example models (see Table 62 on page 30) isdefined in that file with

defmodelsmathrel|joinrel=

where mathrel and joinrel are used to control the horizontal spacing def is the TEX primitive uponwhich LATEXrsquos newcommand is based See The TEXbook [Knu86a] for more information on all three of thosecommands

With some simple pattern-matching one can easily define a backward models sign (ldquo=|rdquo)

defismodeledby=joinrelmathrel|

In general arrowsharpoons horizontal lines (ldquo=rdquo ldquo-rdquo ldquorelbarrdquo and ldquoRelbarrdquo) and the various math-extension characters can be combined creatively with miscellaneous other characters to produce a variety ofnew symbols Of course new symbols can be composed from any set of existing characters For instance LATEXdefines hbar (ldquo~rdquo) as a ldquomacrrdquo character (mathcharrsquo26) followed by a backspace of 9 math units (mkern-9mu)followed by the letter ldquohrdquo

defhbarmathcharrsquo26mkern-9muh

4pifont defines a convenient Pisymbol command for accessing symbols in PostScript fonts by number For exampleldquoPisymbolpsy191rdquo produces ldquocrarrrdquo

5As an example Xdvi ignores both reflectbox and rotatebox6More common symbols for representing ldquosuch thatrdquo include ldquo|rdquo ldquordquo and ldquostrdquo

90

We can just as easily define other barred letters

defbbarmathcharrsquo26mkern-9mu bdefdbarmathcharrsquo26mkern-12mu d

(The space after the ldquomurdquo is optional but is added for clarity) bbar and dbar define ldquobrdquo and ldquodrdquo respectivelyNote that dbar requires a greater backward math kern than bbar a minus9 mu kern would have produced theless-attractive ldquodrdquo glyph

The amsmath package provides overset and underset commands for placing one symbol respectivelyabove or below another For example oversetGsim7 produces ldquoGsimrdquo (sometimes used for ldquoequidecom-posable with respect to Grdquo)

Sometimes an ordinary tabular environment can be co-opted into juxtaposing existing symbols into a newsymbol Consider the following definition of asterism (ldquo rdquo) from a June 2007 post to comptexttex byPeter Flynn

newcommandasterismsmashraisebox-5exsetlengthtabcolsep-5ptbegintabularccmulticolumn2c[-2ex]amp

endtabular

Note how the space between columns (tabcolsep) and rows ([ ]) is made negative to squeeze theasterisks closer together

There is a TEX primitive called mathaccent that centers one mathematical symbol atop another Forexample one can define dotcup (ldquo middotcuprdquo)mdashthe composition of a cup and a cdotmdashas follows

newcommanddotcupensuremathmathaccentcdotcup

The catch is that mathaccent requires the accent to be a ldquomath characterrdquo That is it must be a characterin a math font as opposed to a symbol defined in terms of other symbols See The TEXbook [Knu86a] for moreinformation

Another TEX primitive that is useful for composing symbols is vcenter vcenter is conceptually similarto ldquobegintabularlrdquo in LATEX but takes a list of vertical material instead of -separated rows Alsoit vertically centers the result on the math axis (Many operators such as ldquo+rdquo and ldquominusrdquo are also verticallycentered on the math axis) Enrico Gregorio posted the following symbol definition to comptexttex inMarch 2004 in response to a query about an alternate way to denote equivalence

newcommandthreesimmathrelvcenteroffinterlineskiphbox$sim$vskip-35exhbox$sim$vskip-35exhbox$sim$

The threesim symbol which vertically centers three sim (ldquosimrdquo) symbols with 035 x-heights of space betweenthem is rendered as ldquosimsimsimrdquo offinterlineskip is a macro that disables implicit interline spacing Withoutit threesim would have a full line of vertical spacing between each sim Because of vcenter threesimaligns properly with other math operators adivide b simsimsim ctimes d

A related LATEX command borrowed from Plain TEX is ooalign ooalign vertically overlaps symbolsand works both within and outside of math mode Essentially it creates a single-column tabular environmentwith zero vertical distance between rows However because it is based directly on TEXrsquos ialign primitiveooalign uses TEXrsquos tabular syntax instead of LATEXrsquos (ie with cr as the row terminator instead of ) Thefollowing example of ooalign a macro that defines a standard-state symbol (stst ldquominus rdquo) as a superscriptedPlimsoll line (barcirc ldquominusrdquo)8 is due to an October 2007 comptexttex post by Donald Arseneau

makeatletterprovidecommandbarcircmathpalettebarredcircdefbarred12ooalignhfil$1-$hfilcrhfil$12$hfilcrnewcommandstst^protectbarcircmakeatother

7LATEXrsquos stackrel command is similar but is limited to placing a symbol above a binary relation8While barcirc illustrates how to combine symbols using ooalign the stmaryrd packagersquos minuso command (Table 42 on

page 21) provides a similar glyph (ldquordquo) as a single indivisible symbol

91

In the preceding code note the ooalign callrsquos use of hfil to horizontally center a minus sign (ldquominusrdquo) anda circ (ldquordquo)

As another example of ooalign consider the following code (due to Enrico Gregorio in a June 2007 postto comptexttex) that overlaps a ni (ldquo3rdquo) and two minus signs (ldquominusminusrdquo) to produce ldquo3minusminusrdquo an obscure variationon the infrequently used ldquo3rdquo symbol for ldquosuch thatrdquodiscussed on page 90

newcommandsuchthatmathrelooalign$ni$crkern-1pt$-$kern-65pt$-$

The slashed package although originally designed for producing Feynman slashed-character notation infact facilitates the production of arbitrary overlapped symbols The default behavior is to overwrite a givencharacter with ldquordquo For example slashedD produces ldquo Drdquo However the declareslashed commandprovides the flexibility to specify the mathematical context of the composite character (operator relationpunctuation etc as will be discussed in Section 74) the overlapping symbol horizontal and vertical adjust-ments in symbol-relative units and the character to be overlapped Consider for example the symbol forreduced quadrupole moment (ldquo-Irdquo) This can be declared as follows

newcommandrqmdeclareslashedtext-0040IslashedI

declareslashedmiddotmiddotmiddotmiddotI affects the meaning of all subsequent slashedI commands in the samescope The preceding definition of rqm therefore uses an extra set of curly braces to limit that scope toa single slashedI In addition rqm uses amstextrsquos text macro (described on the next page) to makedeclareslashed use a text-mode hyphen (ldquo-rdquo) instead of a math-mode minus sign (ldquominusrdquo) and to ensure thatthe hyphen scales properly in size in subscripts and superscripts See slashedrsquos documentation (located inslashedsty itself) for a detailed usage description of the slashed and declareslashed commands

Somewhat simpler than slashed is the centernot package centernot provides a single command centernotwhich like not puts a slash over the subsequent mathematical symbol However instead of putting the slashat a fixed location centernot centers the slash over its argument

6minusrarr notlongrightarrow

vs6minusrarr centernotlongrightarrow

See the centernot documentation for more information

Making new symbols work in superscripts and subscripts

To make composite symbols work properly within subscripts and superscripts you may need to use TEXrsquosmathchoice primitive mathchoice evaluates one of four expressions based on whether the current mathstyle is display text script or scriptscript (See The TEXbook [Knu86a] for a more complete descrip-tion) For example the following LATEX codemdashposted to comptexttex by Torsten Brongermdashcomposesa subsuperscriptable ldquoperpgtrdquo symbol out of top and bot (ldquogtrdquo and ldquoperprdquo)

deftopbotatom1hboxhbox to 0pt$1bot$hss$1top$newcommandtopbotmathrelmathchoicetopbotatomdisplaystyle

topbotatomtextstyletopbotatomscriptstyletopbotatomscriptscriptstyle

The following is another example that uses mathchoice to construct symbols in different math modesThe code defines a principal value integral symbol which is an integral sign with a line through it

defXint1mathchoiceXXintdisplaystyletextstyle1XXinttextstylescriptstyle1XXintscriptstylescriptscriptstyle1XXintscriptscriptstylescriptscriptstyle1int

92

defXXint123setbox0=hbox$123int$vcenterhbox$23$kern-5wd0

defddashintXint=defdashintXint-

(The preceding code was taken verbatim from the UK TEX Usersrsquo Group FAQ at httpwwwtexacukfaq) dashint produces a single-dashed integral sign (ldquominus

intrdquo) while ddashint produces a double-dashed

one (ldquo=int

rdquo) The Xint macro defined above can also be used to generate a wealth of new integrals ldquoint

rdquo(Xintcirclearrowright) ldquo

intrdquo (Xintcirclearrowleft) ldquosub

intrdquo (Xintsubset) ldquoinfin

intrdquo (Xintinfty) and

so forthLATEX 2ε provides a simple wrapper for mathchoice that sometimes helps produce terser symbol def-

initions The macro is called mathpalette and it takes two arguments mathpalette invokes the firstargument passing it one of ldquodisplaystylerdquo ldquotextstylerdquo ldquoscriptstylerdquo or ldquoscriptscriptstylerdquofollowed by the second argument mathpalette is useful when a symbol macro must know which mathstyle is currently in use (eg to set it explicitly within an mbox) Donald Arseneau posted the followingmathpalette-based definition of a probabilistic-independence symbol (ldquoperpperprdquo) to comptexttex in June 2000

newcommandindependentprotectmathpaletteprotectindependenTperpdefindependenT12mathrelrlap$12$mkern2mu12

The independent macro uses mathpalette to pass the independenT helper macro both the current mathstyle and the perp symbol independenT typesets perp in the current math style moves two math units tothe right and finally typesets a secondmdashoverlappingmdashcopy of perp again in the current math style rlapwhich enables text overlap is described later on this page

Some people like their square-root signs with a trailing ldquohookrdquo (ie ldquoradic rdquo) as this helps visually distinguishexpressions like ldquo

radic3x rdquo from those like ldquo

radic3xrdquo In March 2002 Dan Luecking posted a mathpalette-based

definition of a hooked square-root symbol to comptexttex

defhksqrtmathpaletteDHLhksqrtdefDHLhksqrt12setbox0=hbox$1sqrt2$dimen0=ht0advancedimen0-02ht0setbox2=hboxvrule heightht0 depth -dimen0box0lower04ptbox2

Notice how DHLhksqrt uses mathpalette to recover the outer math style (argument 1) from within anhbox The rest of the code is simply using TEX primitives to position a hook of height 02 times the sqrtheight at the right of the sqrt See The TEXbook [Knu86a] for more understanding of TEX ldquoboxesrdquo andldquodimensrdquo

Sometimes however amstextrsquos text macro is all that is necessary to make composite symbols appearcorrectly in subscripts and superscripts as in the following definitions of neswarrow (ldquordquo) and nwsearrow(ldquordquo)9

newcommandneswarrowmathreltext$nearrow$llap$swarrow$newcommandnwsearrowmathreltext$nwarrow$llap$searrow$

text resembles LATEXrsquos mbox command but shrinks its argument appropriately when used within a subscriptor superscript llap (ldquoleft overlaprdquo) and its counterpart rlap (ldquoright overlaprdquo) appear frequently whencreating composite characters llap outputs its argument to the left of the current position overlappingwhatever text is already there Similarly rlap overlaps whatever text would normally appear to the rightof its argument For example ldquoAllapBrdquo and ldquorlapABrdquo each produce ldquoABrdquo However the result of theformer is the width of ldquoArdquo and the result of the latter is the width of ldquoBrdquomdashllap and rlap takeup zero space

In a June 2002 post to comptexttex Donald Arseneau presented a general macro for aligning an arbitrarynumber of symbols on their horizontal centers and vertical baselines

makeatletterdefmoverlaymathpalettemovrlay

9Note that if your goal is to typeset commutative diagrams then you should probably be using XY-pic

93

defmovrlay12leavevmodevtopbaselineskipzskip lineskiplimit-maxdimenialignhfil$1$hfilcr2crcr

makeatother

The makeatletter and makeatother commands are needed to coerce LATEX into accepting ldquordquo aspart of a macro name moverlay takes a list of symbols separated by cr (TEXrsquos equivalent ofLATEXrsquos ) For example the topbot command defined on page 92 could have been expressed asldquomoverlaytopcrbotrdquo and the neswarrow command defined on the previous page could have beenexpressed as ldquomoverlaynearrowcrswarrowrdquo

The basic concept behind moverlayrsquos implementation is that moverlay typesets the given symbols in atable that utilizes a zero baselineskip This causes every row to be typeset at the same vertical positionSee The TEXbook [Knu86a] for explanations of the TEX primitives used by moverlay

Modifying LATEX-generated symbols

Oftentimes symbols composed in the LATEX 2ε source code can be modified with minimal effort to produceuseful variations For example fontdefdtx composes the ddots symbol (see Table 174 on page 61) out ofthree periods raised 7 pt 4 pt and 1 pt respectively

defddotsmathinnermkern1muraise7pvboxkern7phboxmkern2muraise4phboxmkern2muraisephboxmkern1mu

p is a LATEX 2ε shortcut for ldquoptrdquo or ldquo10ptrdquo The remaining commands are defined in TheTEXbook [Knu86a] To draw a version of ddots with the dots going along the opposite diagonal we merelyhave to reorder the raise7p raise4p and raisep

makeatletterdefrevddotsmathinnermkern1muraisepvboxkern7phboxmkern2muraise4phboxmkern2muraise7phboxmkern1mu

makeatother

revddots is essentially identical to the mathdots packagersquos iddots command or the yhmath packagersquos adotscommand

Producing complex accents

Accents are a special case of combining existing symbols to make new symbols While various tables inthis document show how to add an accent to an existing symbol some applications such as translitera-tions from non-Latin alphabets require multiple accents per character For instance the creator of pdfTEXwrites his name as ldquoHan Thacutee Thanhrdquo The dblaccnt package enables LATEX to stack accents as in ldquoHlsquoanThrsquoê Thlsquoanhrdquo (albeit not in the OT1 font encoding) In addition the wsuipa package defines diatopand diaunder macros for putting one or more diacritics or accents above or below a given character Forexample diaunder[diatop[rsquo|=]|textsubdotr] produces ldquoacuter

˙rdquo See the wsuipa documentation for

more informationThe accents package facilitates the fabrication of accents in math mode Its accentset command en-

ables any character to be used as an accent For instance accentsetstarf produces ldquo

f rdquo andaccentseteX produces ldquo

e

Xrdquo underaccent does the same thing but places the accent beneath thecharacter This enables constructs like underaccenttildeV which produces ldquo

˜V rdquo accents provides

other accent-related features as well see the documentation for more information

Creating extensible symbols

A relatively simple example of creating extensible symbols stems from a comptexttex post by DonaldArseneau (June 2003) The following code defines an equals sign that extends as far to the right as possiblejust like LATEXrsquos hrulefill command

94

makeatletterdefequalsfill$mthmathord=mkern-7mucleadershbox$mathord=$hfillmkern-7mumathord=$

makeatother

TEXrsquos cleaders and hfill primitives are the key to understanding equalsfillrsquos extensibility Essen-tially equalsfill repeats a box containing ldquo=rdquo plus some negative space until it fills the maximum avail-able horizontal space equalsfill is intended to be used with LATEXrsquos stackrel command which stacksone mathematical expression (slightly reduced in size) atop another Hence ldquostackrelarightarrowrdquoproduces ldquo ararrrdquo and ldquoX stackreltextdefinitionhboxequalsfill Yrdquo produces ldquoX definition======= Y rdquo

If all that needs to extend are horizontal and vertical linesmdashas opposed to repeated symbols such as theldquo=rdquo in the previous examplemdashLATEXrsquos array or tabular environments may suffice Consider the followingcode (due to a February 1999 comptexttex post by Donald Arseneau) for typesetting annuities

DeclareRobustCommandannu[1]_defarraystretch0setlengtharraycolsep1pt adjust thesesetlengtharrayrulewidth2pt two settingsbeginarray[b]c|hline[arraycolsep]scriptstyle 1endarray

One can then use eg ldquo$Aannuxn$rdquo to produce ldquoAxn rdquoA more complex example of composing accents is the following definition of extensible overbracket

underbracket overparenthesis and underparenthesis symbols taken from a May 2002comptexttex post by Donald Arseneau

makeatletterdefoverbracket1mathopvboxialigncrcrnoalignkern3p

downbracketfillcrcrnoalignkern3pnointerlineskip$hfildisplaystyle1hfil$crcrlimits

defunderbracket1mathopvtopialigncrcr$hfildisplaystyle1hfil$crcrnoalignkern3pnointerlineskipupbracketfillcrcrnoalignkern3plimits

defoverparenthesis1mathopvboxialigncrcrnoalignkern3pdownparenthfillcrcrnoalignkern3pnointerlineskip$hfildisplaystyle1hfil$crcrlimits

defunderparenthesis1mathopvtopialigncrcr$hfildisplaystyle1hfil$crcrnoalignkern3pnointerlineskipupparenthfillcrcrnoalignkern3plimits

defdownparenthfill$mthbraceldleadersvrulehfillbracerd$defupparenthfill$mthbraceluleadersvrulehfillbraceru$defupbracketfill$mthmakesmshllapvruleheight3pwidth7pleadersvruleheight7phfillmakesmshrlapvruleheight3pwidth7p$

defdownbracketfill$mthmakesmshllapvruleheight7pdepth23pwidth7pleadersvruleheight7phfillmakesmshrlapvruleheight7pdepth23pwidth7p$

makeatother

Table 283 showcases these accents The TEXbook [Knu86a] or another book on TEX primitives is indispensiblefor understanding how the preceding code works The basic idea is that downparenthfill upparenthfilldownbracketfill and upbracketfill do all of the work they output a left symbol (eg braceld [ldquo︷rdquo]for downparenthfill) a horizontal rule that stretches as wide as possible and a right symbol (eg bracerd[ldquo︷rdquo] for downparenthfill) overbracket underbracket overparenthesis and underparenthesis

95

merely create a table whose width is determined by the given text thereby constraining the width of thehorizontal rules

Table 283 Manually Composed Extensible Accents

abc overbracketabc︷︷abc overparenthesisabc

abc underbracketabc abc︸︸ underparenthesisabc

Note that the simplewick package provides mechanisms for typesetting Wick contractions which uti-lize overbracket- and underbracket-like brackets of variable width and height (or depth) For ex-ample ldquoacontractionABCacontraction[2ex]ABCDbcontractionABCDABCDrdquoproduces

ABCD

See the simplewick documentation for more information

Developing new symbols from scratch

Sometimes is it simply not possible to define a new symbol in terms of existing symbols Fortunately most ifnot all TEX distributions are shipped with a tool called METAFONT which is designed specifically for creatingfonts to be used with TEX The METAFONTbook [Knu86b] is the authoritative text on METAFONT If youplan to design your own symbols with METAFONT The METAFONTbook is essential reading Nevertheless thefollowing is an extremely brief tutorial on how to create a new LATEX symbol using METAFONT Its primarypurpose is to cover the LATEX-specific operations not mentioned in The METAFONTbook and to demonstratethat symbol-font creation is not necessarily a difficult task

Suppose we need a symbol to represent a light bulb (ldquoArdquo)10 The first step is to draw this in METAFONTIt is common to separate the font into two files a size-dependent file which specifies the design size andvarious font-specific parameters that are a function of the design size and a size-independent file which drawscharacters in the given size Figure 2 shows the METAFONT code for lightbulb10mf lightbulb10mfspecifies various parameters that produce a 10 pt light bulb then loads lightbulbmf Ideally one shouldproduce lightbulb〈size〉mf files for a variety of 〈size〉s This is called ldquooptical scalingrdquo It enables forexample the lines that make up the light bulb to retain the same thickness at different font sizes which looksmuch nicer than the alternativemdashand defaultmdashldquomechanical scalingrdquo When a lightbulb〈size〉mf file doesnot exist for a given size 〈size〉 the computer mechanically produces a wider taller thicker symbol

A vs A vs A vs A vs A vs A vs A10 pt 20 pt 30 pt 40 pt 50 pt 60 pt 70 pt

font identifier = LightBulb10 Name the fontfont size 10pt Specify the design size

em = 10pt ldquoMrdquo width is 10 pointscap = 7pt Capital letter height is 7 points above the baselinesb = 14pt Leave this much space on the side of each charactero = 116pt Amount that curves overshoot borders

input lightbulb Load the file that draws the actual glyph

Figure 2 Sample METAFONT size-specific file (lightbulb10mf)

lightbulbmf shown in Figure 3 draws a light bulb using the parameters defined in lightbulb10mfNote that the the filenames ldquolightbulb10mfrdquo and ldquolightbulbmfrdquo do not follow the Berry font-naming

10Irsquom not a very good artist yoursquoll have to pretend that ldquoArdquo looks like a light bulb

96

scheme [Ber01] the Berry font-naming scheme is largely irrelevant for symbol fonts which generally lack bolditalic small-caps slanted and other such variants

mode setup Target a given printer

define pixels(em cap sb) Convert to device-specific unitsdefine corrected pixels(o) Same but add a device-specific fudge factor

Define a light bulb at the character position for ldquoArdquo with width 12em height cap and depth 1ptbeginchar(A 12em cap 1pt) A light bulb

pickup pencircle scaled 12pt Use a pen with a small circular tip

Define the points we needtop z1 = (w2 h+ o) z1 is at the top of a circlert z2 = (w + sb + ominus x4 y4) z2 is at the same height as z4 but the opposite sidebot z3 = (z1 minus (0 w minus sbminus o)) z3 is at the bottom of the circlelft z4 = (sbminus o 12[y1 y3]) z4 is on the left of the circlepath bulb Define a path for the bulb itselfbulb = z1 z2 z3 z4 cycle The bulb is a closed path

z5 = point 2minus 13 of bulb z5 lies on the bulb a little to the right of z3z6 = (x5 0) z6 is at the bottom directly under z5z7 = (x8 0) z7 is at the bottom directly under z8z8 = point 2 + 13 of bulb z8 lies on the bulb a little to the left of z3bot z67 = (12[x6 x7] pen botminus ominus 18pt) z67 lies halfway between z6 and z7 but a jot lower

Draw the bulb and the basedraw bulb Draw the bulb properdraw z5 - - z6 z67 z7 - - z8 Draw the base of the bulb

Display key positions and points to help us debugmakegrid(0 sb w2 w minus sb)(0minus1pt y2 h) Label ldquointerestingrdquo x and y coordinatespenlabels(1 2 3 4 5 6 67 7 8) Label control points for debugging

endcharend

Figure 3 Sample METAFONT size-independent file (lightbulbmf)

The code in Figures 2 and 3 is heavily commented and should demonstrate some of the basic conceptsbehind METAFONT usage declaring variables defining points drawing lines and curves and preparing todebug or fine-tune the output Again The METAFONTbook [Knu86b] is the definitive reference on META-FONT programming

METAFONT can produce ldquoproofsrdquo of fontsmdashlarge labeled versions that showcase the logical structure ofeach character In fact proof mode is METAFONTrsquos default mode To produce a proof of lightbulb10mfissue the following commands at the operating-system prompt

promptgt mf lightbulb10mf lArr Produces lightbulb102602gfpromptgt gftodvi lightbulb102602gf lArr Produces lightbulb10dvi

You can then view lightbulb10dvi with any DVI viewer The result is shown in Figure 4 Observe how thegrid defined with makegrid at the bottom of Figure 3 draws vertical lines at positions 0 sb w2 and w minus sband horizontal lines at positions 0 minus1pt y2 and h Similarly observe how the penlabels command labels allof the important coordinates z1 z2 z8 and z67 which lightbulbmf defines to lie between z6 and z7

Most if not all TEX distributions include a Plain TEX file called testfonttex which is useful for testingnew fonts in a variety of ways One useful routine produces a table of all of the characters in the font

promptgt tex testfontThis is TeX Version 314159 (Web2C 731)(usrsharetexmftexplainbasetestfonttexName of the font to test = lightbulb10

97

1

2

3

4

5

6677

8

Figure 4 Proof diagram of lightbulb10mf

Now type a test command (help for help))table

bye[1]Output written on testfontdvi (1 page 1516 bytes)Transcript written on testfontlog

The resulting table stored in testfontdvi and illustrated in Figure 5 shows every character in the fontTo understand how to read the table note that the character code for ldquoArdquomdashthe only character defined bylightbulb10mfmdashis 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 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F

Figure 5 Font table produced by testfonttex

The LightBulb10 font is now usable by TEX LATEX 2ε however needs more information before documentscan use the font First we create a font-description file that tells LATEX 2ε how to map fonts in a given fontfamily and encoding to a particular font in a particular font size For symbol fonts this mapping is fairly simpleSymbol fonts almost always use the ldquoUrdquo (ldquoUnknownrdquo) font encoding and frequently occur in only one variantnormal weight and non-italicized The filename for a font-description file important it must be of the formldquo〈encoding〉〈family〉fdrdquo where 〈encoding〉 is the lowercase version of the encoding name (typically ldquourdquo forsymbol fonts) and 〈family〉 is the name of the font family For LightBulb10 letrsquos call this ldquobulbrdquo Figure 6 liststhe contents of ubulbfd The document ldquoLATEX 2ε Font Selectionrdquo [LAT00] describes DeclareFontFamilyand DeclareFontShape in detail but the gist of ubulbfd is first to declare a U-encoded version of the bulbfont family and then to specify that a LATEX 2ε request for a U-encoded version of bulb with a (m)edium fontseries (as opposed to eg bold) and a (n)ormal font shape (as opposed to eg italic) should translate into aTEX request for lightbulb10tfm mechanically scaled to the current font size

The final step is to write a LATEX 2ε style file that defines a name for each symbol in the font Becausewe have only one symbol our style file lightbulbsty (Figure 7) is rather trivial Note that instead oftypesetting ldquoArdquo we could have had lightbulb typeset ldquochar65rdquo ldquochar41rdquo or ldquocharrsquo101rdquo (respectivelydecimal hexadecimal and octal character offsets into the font) For a simple one-character symbol font

98

DeclareFontFamilyUbulbDeclareFontShapeUbulbmnlt-gt lightbulb10

Figure 6 LATEX 2ε font-description file (ubulbfd)

such as LightBulb10 it would be reasonable to merge ubulbfd into lightbulbsty instead of maintainingtwo separate files In either case a document need only include ldquousepackagelightbulbrdquo to make thelightbulb symbol available

newcommandlightbulbusefontUbulbmnA

Figure 7 LATEX 2ε style file (lightbulbsty)

METAFONT normally produces bitmapped fonts However it is also possible with the help of someexternal tools to produce PostScript Type 1 fonts These have the advantages of rendering better in Adobereg

Acrobatreg (at least in versions prior to 60) and of being more memory-efficient when handled by a PostScriptinterpreter See httpwwwtexacukcgi-bintexfaq2htmllabel=textrace for pointers to tools that canproduce Type 1 fonts from METAFONT

74 Math-mode spacing

Terms such as ldquobinary operatorsrdquo ldquorelationsrdquo and ldquopunctuationrdquo in Section 3 primarily regard the surroundingspacing (See the Short Math Guide for LATEX [Dow00] for a nice exposition on the subject) To use a symbolfor a different purpose you can use the TEX commands mathord mathop mathbin mathrel mathopenmathclose and mathpunct For example if you want to use downarrow as a variable (an ldquoordinaryrdquosymbol) instead of a delimiter you can write ldquo$3 x + mathorddownarrow$rdquo to get the properly spacedldquo3x + darrrdquo rather than the awkward-looking ldquo3x+ darrrdquo Similarly to create a dotted-union symbol (ldquocuprdquo) thatspaces like the ordinary set-union symbol (cup) it must be defined with mathbin just as cup is Contrastldquo$A dotcup B$rdquo (ldquoAcupBrdquo) with ldquo$A mathbindotcup B$rdquo (ldquoAcupBrdquo) See The TEXbook [Knu86a]for the definitive description of math-mode spacing

The purpose of the ldquolog-like symbolsrdquo in Tables 120 and 121 is to provide the correct amount of spacingaround and within multiletter function names Table 284 contrasts the output of the log-like symbols withvarious naıve alternatives In addition to spacing the log-like symbols also handle subscripts properly Forexample ldquomax_p in Prdquo produces ldquomaxpisinP rdquo in text but ldquomax

pisinPrdquo as part of a displayed formula

Table 284 Spacing AroundWithin Log-like Symbols

LATEX expression Output

$r sin theta$ r sin θ (best)$r sin theta$ rsinθ$r mboxsin theta$ rsinθ$r mathrmsin theta$ rsinθ

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

DeclareMathOperatoratanatanDeclareMathOperatorlcmlcm

The difference between DeclareMathOperator and DeclareMathOperator involves the handling of sub-scripts With DeclareMathOperator subscripts are written beneath log-like symbols in display style andto the right in text style This is useful for limit operators (eg lim) and functions that tend to map overa set (eg min) In contrast DeclareMathOperator tells TEX that subscripts should always be displayedto the right of the operator as is common for functions that take a single parameter (eg log and cos)Table 285 contrasts symbols declared with DeclareMathOperator and DeclareMathOperator in both textstyle ($ $) and display style ([ ])11

11Note that displaystyle can be used to force display style within $ $ and textstyle can be used to force text stylewithin [ ]

99

Table 285 Defining new log-like symbols

Declaration function $newlogsym p in P$ [ newlogsym p in P ]

DeclareMathOperator newlogsympisinP newlogsympisinP


It is common to use a thin space () between the words of a multiword operators as inldquoDeclareMathOperatorargmaxargmaxrdquo liminf limsup and all of the log-like symbols shownin Table 121 utilize this spacing convention

75 Bold mathematical symbols

LATEX does not normally use bold symbols when typesetting mathematics However bold symbols are occa-sionally needed for example when naming vectors Any of the approaches described at httpwwwtexacukcgi-bintexfaq2htmllabel=boldgreek can be used to produce bold mathematical symbols Table 286contrasts the output produced by these various techniques As the table illustrates these techniques exhibitvariation 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 286 Producing bold mathematical symbols

Package Code Output

none $alpha + b = Gamma div D$ α+ b = ΓdivideD (no bold)none $mathbfalpha + b = Gamma div D$ α+ b = ΓdivideDnone boldmath$alpha + b = Gamma div D$ α+ b = ΓdivideDamsbsy $pmbalpha + b = Gamma div D$ α+ b = ΓdivideDα+ b = ΓdivideDα+ b = ΓdivideD (faked bold)amsbsy $boldsymbolalpha + b = Gamma div D$ α+ b = ΓdivideDbm $bmalpha + b = Gamma div D$ α+ b = ΓdivideDfixmath $mathboldalpha + b = Gamma div D$ α+ b = Γ divideD

76 ASCII and Latin 1 quick reference

Table 287 on the next page amalgamates data from various other tables in this document into a convenientreference for LATEX 2ε typesetting of ASCII characters ie the characters available on a typical US computerkeyboard The first two columns list the characterrsquos ASCII code in decimal and hexadecimal The thirdcolumn shows what the character looks like The fourth column lists the LATEX 2ε command to typeset thecharacter as a text character And the fourth column lists the LATEX 2ε command to typeset the characterwithin a texttt command (or more generally when ttfamily is in effect)

The following are some additional notes about the contents of Table 287

bull ldquordquo is not available in the OT1 font encoding

bull The characters ldquoltrdquo ldquogtrdquo and ldquo|rdquo do work as expected in math mode although they produce respectivelyldquoiexclrdquo ldquoiquestrdquo and ldquomdashrdquo in text mode when using the OT1 font encoding12 The following are some alternativesfor typesetting ldquoltrdquo ldquogtrdquo and ldquo|rdquo

ndash Specify a document font encoding other than OT1 (as described on page 7)

ndash Use the appropriate symbol commands from Table 2 on page 8 viz textless textgreaterand textbar

ndash Enter the symbols in math mode instead of text mode ie $lt$ $gt$ and $|$12Donald Knuth didnrsquot think such symbols were important outside of mathematics so he omitted them from his text fonts

100

Table 287 LATEX 2ε ASCII Table

Dec Hex Char Body text texttt

33 21 34 22 textquotedbl 35 23 36 24 $ $ $37 25 38 26 amp amp amp39 27 rsquo rsquo rsquo40 28 ( ( (41 29 ) ) )42 2A 43 2B + + +44 2C 45 2D - - -46 2E 47 2F 48 30 0 0 049 31 1 1 150 32 2 2 2

57 39 9 9 958 3A 59 3B 60 3C lt textless lt61 3D = = =


62 3E gt textgreater gt63 3F 64 40 65 41 A A A66 42 B B B67 43 C C C

90 5A Z Z Z91 5B [ [ [92 5C textbackslash charlsquo93 5D ] ] ]94 5E ˆ ^ ^95 5F _ charlsquo_96 60 lsquo lsquo lsquo97 61 a a a98 62 b b b99 63 c c c

122 7A z z z123 7B charlsquo124 7C | textbar |125 7D charlsquo126 7E ˜ ~ ~

Note that for typesetting metavariables many people prefer textlangle and textrangle to textlessand textgreater ie ldquo〈filename〉rdquo instead of ldquoltfilenamegtrdquo

bull Although ldquordquo does not require any special treatment LATEX additionally defines a slash commandwhich outputs the same glyph but permits a line break afterwards That is ldquoincreasedecreaserdquo isalways typeset as a single entity while ldquoincreaseslashdecreaserdquo may be typeset with ldquoincreaserdquoon one line and ldquodecreaserdquo on the next

bull textasciicircum can be used instead of ^ and textasciitilde can be used instead of ~Note that textasciitilde and ~ produce raised diacritic tildes ldquoTextrdquo (ie vertically centered)tildes can be generated with either the math-mode sim command (shown in Table 62 on page 30)which produces a somewhat wide ldquosimrdquo or the textcomp packagersquos texttildelow (shown in Table 36on page 19) which produces a vertically centered ldquo~rdquo in most fonts but a baseline-oriented ldquo~rdquo inComputer Modern txfonts pxfonts and various other fonts originating from the TEX world If yourgoal is to typeset tildes in URLs or Unix filenames your best bet is to use the url package which has anumber of nice features such as proper line-breaking of such names

bull The various char commands within texttt are necessary only in the OT1 font encoding In otherencodings (eg T1) commands such as _ and textbackslash all work properly

bull The code page 437 (IBM PC) version of ASCII characters 1 to 31 can be typeset using the ascii packageSee Table 209 on page 69

bull To replace ldquolsquordquo and ldquorsquordquo with the more computer-like (and more visibly distinct) ldquo`rdquo and ldquordquo withina verbatim environment use the upquote package Outside of verbatim you can use char18 andchar13 to get the modified quote characters (The former is actually a grave accent)

Similar to Table 287 Table 288 on the next page is an amalgamation of data from other tables in thisdocument While Table 287 shows how to typeset the 7-bit ASCII character set Table 288 shows the Latin 1(Western European) character set also known as ISO-8859-1

101

Table 288 LATEX 2ε Latin 1 Table

Dec Hex Char LATEX 2ε

161 A1 iexcl lsquo162 A2 cent textcent (tc)163 A3 pound pounds164 A4 curren textcurrency (tc)165 A5 yen textyen (tc)166 A6 brvbar textbrokenbar (tc)167 A7 sect S168 A8 uml textasciidieresis (tc)169 A9 copy textcopyright170 AA ordf textordfeminine171 AB laquo guillemotleft (T1)172 AC not textlnot (tc)173 AD - -174 AE reg textregistered175 AF macr textasciimacron (tc)176 B0 deg textdegree (tc)177 B1 plusmn textpm (tc)178 B2 sup2 texttwosuperior (tc)179 B3 sup3 textthreesuperior (tc)180 B4 acute textasciiacute (tc)181 B5 micro textmu (tc)182 B6 para P183 B7 middot textperiodcentered184 B8 cedil c185 B9 sup1 textonesuperior (tc)186 BA ordm textordmasculine187 BB raquo guillemotright (T1)188 BC frac14 textonequarter (tc)189 BD frac12 textonehalf (tc)190 BE frac34 textthreequarters (tc)191 BF iquest lsquo

192 C0 A lsquoA

193 C1 A rsquoA

194 C2 A Â195 C3 A ~A196 C4 A A

197 C5 A AA198 C6 AElig AE199 C7 C cC

200 C8 E lsquoE

201 C9 E rsquoE

202 CA E Ê203 CB E E

204 CC I lsquoI

205 CD I rsquoI

206 CE I Î207 CF I I208 D0 ETH DH (T1)


209 D1 N ~N

210 D2 O lsquoO

211 D3 O rsquoO

212 D4 O Ô213 D5 O ~O214 D6 O O215 D7 times texttimes (tc)216 D8 Oslash O

217 D9 U lsquoU

218 DA U rsquoU

219 DB U Û220 DC U U

221 DD Y rsquoY222 DE THORN TH (T1)223 DF szlig ss224 E0 a lsquoa225 E1 a rsquoa226 E2 a â227 E3 a ~a228 E4 a a229 E5 a aa230 E6 aelig ae231 E7 c cc232 E8 e lsquoe233 E9 e rsquoe234 EA e ê235 EB e e236 EC ı lsquoı237 ED ı rsquoı238 EE ı ^ı239 EF ı ı240 F0 eth dh (T1)241 F1 n ~n242 F2 o lsquoo243 F3 o rsquoo244 F4 o ô245 F5 o ~o246 F6 o o247 F7 divide textdiv (tc)248 F8 oslash o249 F9 u lsquou250 FA u rsquou251 FB u û252 FC u u253 FD y rsquoy254 FE thorn th (T1)255 FF y y

102


bull A ldquo(tc)rdquo after a symbol name means that the textcomp package must be loaded to access that symbolA ldquo(T1)rdquo means that the symbol requires the T1 font encoding The fontenc package can change thefont encoding document-wide

bull Many of the text accents can also be produced using the accent commands shown in Table 18 onpage 13 plus an empty argument For instance = is essentially the same as textasciimacron

bull The commands in the ldquoLATEX 2εrdquo columns work both in body text and within a texttt command(or more generally when ttfamily is in effect)

bull The ldquopoundrdquo and ldquo$rdquo glyphs occupy the same slot (36) of the OT1 font encoding with ldquopoundrdquo appearing in italicfonts and ldquo$rdquo appearing in roman fonts A problem with LATEXrsquos default handling of this double-mappingis that ldquosffamilyslshapepoundsrdquo produces ldquo$rdquo not ldquopoundrdquo Other font encodings use separate slotsfor the two characters and are therefore robust to the problem of ldquopoundrdquordquo$rdquo conflicts Authors who usepounds should select a font encoding other than OT1 (as explained on page 7) or use the textcomppackage which redefines pounds to use the TS1 font encoding

bull Character 173 - is shown as ldquo-rdquo but is actually a discretionary hyphen it appears only at the end ofa line

Microsoftreg Windowsreg normally uses a superset of Latin 1 called ldquoCode 252rdquo or ldquoCP1252rdquo forshort CP1252 introduces symbols in the Latin 1 ldquoinvalidrdquo range (characters 128ndash159) Table 289 presents thecharacters with which CP1252 augments the standard Latin 1 table

Table 289 LATEX 2ε Code Page 1252 Table


128 80 euro texteuro (tc)130 82 sbquo quotesinglbase (T1)131 83 f textitf132 84 bdquo quotedblbase (T1)133 85 dots134 86 dagger dag135 87 Dagger ddag136 88 ˆ textasciicircum137 89 permil textperthousand (tc)138 8A S vS139 8B lsaquo guilsinglleft (T1)140 8C Œ OE142 8E Z vZ


145 91 lsquo lsquo146 92 rsquo rsquo147 93 ldquo lsquolsquo148 94 rdquo rsquorsquo149 95 bull textbullet150 96 ndash --151 97 mdash ---152 98 ˜ textasciitilde153 99 trade texttrademark154 9A s vs155 9B rsaquo guilsinglright (T1)156 9C œ oe158 9E z vz159 9F Y Y


bull As in Table 288 a ldquo(tc)rdquo after a symbol name means that the textcomp package must be loaded to accessthat symbol A ldquo(T1)rdquo means that the symbol requires the T1 font encoding The fontenc package canchange the font encoding document-wide

bull Not all characters in the 128ndash159 range are defined

bull Look up ldquoeuro signsrdquo in the index for alternatives to texteuro

While too large to incorporate into this document a listing of ISO 88791986 SGMLXML character entitiesand their LATEX equivalents is available from httpwwwbitjunglecom~isoent Some of the characterspresented there make use of isoent a LATEX 2ε package (available from the same URL) that fakes some of themissing ISO glyphs using the LATEX picture environment13

13isoent is not featured in this document because it is not available from CTAN and because the faked symbols are not ldquotruerdquocharacters they exist in only one size regardless of the body textrsquos font size

103

77 About this document

History David Carlisle wrote the first version of this document in October 1994 It originally contained allof the native LATEX symbols (Tables 40 52 62 95 120 122 141 142 152 157 184 and a few tables that havesince been reorganized) and was designed to be nearly identical to the tables in Chapter 3 of Leslie Lamportrsquosbook [Lam86] Even the table captions and the order of the symbols within each table matched The AMSsymbols (Tables 41 63 64 98 99 123 127 137 and 185) and an initial Math Alphabets table (Table 196)were added thereafter Later Alexander Holt provided the stmaryrd tables (Tables 42 54 65 101 117 and138)

In January 2001 Scott Pakin took responsibility for maintaining the symbol list and has since implementeda complete overhaul of the document The result now called ldquoThe Comprehensive LATEX Symbol Listrdquoincludes the following new features

bull the addition of a handful of new math alphabets dozens of new font tables and thousands of newsymbols

bull the categorization of the symbol tables into body-text symbols mathematical symbols science andtechnology symbols dingbats and other symbols to provide a more user-friendly document structure

bull an index table of contents and a frequently-requested symbol list to help users quickly locate symbols

bull symbol tables rewritten to list the symbols in alphabetical order

bull appendices to provide additional information relevant to using symbols in LATEX

bull 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 Davidrsquos original versionMost of the changes are geared towards making the document easier to extend modify and reformat

Build characteristics Table 290 lists some of this documentrsquos build characteristics Most important isthe list of packages that LATEX couldnrsquot find but that symbolstex otherwise would have been able to takeadvantage of Complete prebuilt versions of this document are available from CTAN (httpwwwctanorgor one of its many mirror sites) in the directory tex-archiveinfosymbolscomprehensive Table 291shows the package date (specified in the sty file with ProvidesPackage) for each package that was used tobuild this document and that specifies a package date Packages are not listed in any particular order in eitherTable 290 or 291

Table 290 Document Characteristics

Characteristic Value

Source file symbolstexBuild date January 3 2008Symbols documented 4947Packages included textcomp latexsym amssymb stmaryrd euscript wasysym

pifont manfnt bbding undertilde ifsym tipa tipx extraipawsuipa phonetic ulsy ar metre txfonts mathabx fclfontskak ascii dingbat skull eurosym esvect yfonts yhmathesint mathdots trsym universa upgreek overrightarrowchemarr chemarrow nath trfsigns mathtools phaistos arcsvietnam t4phonet holtpolt semtrans dictsym extarrowsprotosem harmony hieroglf cclicenses mathdesign arevMnSymbol cmll extpfeil keystroke fge turnstile simpsonsepsdice feyn universal staves igo accents nicefrac bmmathrsfs chancery calligra bbold mbboard dsfont bbm

Packages omitted none

104

Table 291 Package versions used in the preparation of this document

Name Date

textcomp 20050927latexsym 19980817amssymb 20020122stmaryrd 19940303euscript 20011001wasysym 20031030pifont 20050412manfnt 19990701bbding 19960621undertilde 20000808ifsym 20000418tipa 20020808tipx 20030101wsuipa 19940716metre 20011205txfonts 20050103mathabx 20030729skak 20030927ascii 20060530dingbat 20010427skull 20020123eurosym 19980806yfonts 20030108mathdots 20060316trsym 20000625universa 980801upgreek 20030212chemarr 20060220mathtools 20041010phaistos 20040423arcs 20040509t4phonet 20040601semtrans 19980210dictsym 20040726extarrows 20020330protosem 20050318harmony 20070503hieroglf 20000923cclicenses 20050520arev 20050614MnSymbol 20070121extpfeil 20060727keystroke 20030815fge 20070603turnstile 20070623epsdice 20010215feyn 20020423universal 971224accents 20060512nicefrac 19980804bm 20040226calligra 19960718

105

78 Copyright and license

The Comprehensive LATEX Symbol ListCopyright copy 2008 Scott Pakin

This work may be distributed andor modified under the conditions of the LATEX Project Public License eitherversion 13c of this license or (at your option) any later version The latest version of this license is in

httpwwwlatex-projectorglppltxt

and version 13c or later is part of all distributions of LATEX version 20060520 or laterThis work has the LPPL maintenance status ldquomaintainedrdquoThe current maintainer of this work is Scott Pakin

References

[AMS99] American Mathematical Society Userrsquos Guide for the amsmath Package (Version 20) December 131999 Available from ftpftpamsorgpubtexdocamsmathamsldocpdf

[Ber01] Karl Berry Fontname Filenames for TEX fonts June 2001 Available from httpwwwctanorgtex-archiveinfofontname

[Che97] Raymond Chen A METAFONT of lsquoSimpsonsrsquo characters Baskerville 4(4)19 September1997 ISSN 1354-5930 Available from httptugctanorgusergrpsuktugbaskervi4 4bask4 4ps

[Dow00] Michael Downes Short math guide for LATEX July 19 2000 Version 107 Available from httpwwwamsorgtexshort-math-guidehtml

[Gib97] Jeremy Gibbons Heymdashit works TUGboat 18(2)75ndash78 June 1997 Available from httpwwwtugorgTUGboatArticlestb18-2tb55workspdf

[Knu86a] Donald E Knuth The TEXbook volume A of Computers and Typesetting Addison-Wesley ReadingMA USA 1986

[Knu86b] Donald E Knuth The METAFONTbook volume C of Computers and Typesetting Addison-WesleyReading 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 fromhttpwwwctanorgtex-archivemacroslatexdocltnews09pdf (also included in many TEXdistributions)

[LAT00] LATEX3 Project Team LATEX 2ε font selection January 30 2000 Available from httpwwwctanorgtex-archivemacroslatexdocfntguideps (also included in many TEX distri-butions)

106

Index

If yoursquore having trouble locating a symbol try looking under ldquoTrdquo for ldquotext rdquo Many text-mode commands beginwith that prefix Also accents are shown overunder a gray box eg ldquo a rdquo for ldquorsquordquo

Some symbol entries appear to be listed repeatedly This happens when multiple packages define identical (or nearlyidentical) glyphs with the same symbol name14

Symbols (a) 13 () 8 101$ ($) 8 101 () 8 101amp (amp) 8 101rsquo (a) 13( (() 53

( (() 54

) ()) 53

) ()) 54

() 22 100- (-) 102 103 (a) 13 () 53

() 54

lt (⟨) 54

[ ([) 53

[ (⎡⎢⎢⎢⎢⎢⎣) 54

91] (]) 53

] (⎤⎥⎥⎥⎥⎥⎦) 54

^ (a) 13^ (ˆ) 101| () 53| (iquesta) 13= (a) 13= (macr) 103| (|) 53_ ( ) 8 101 () 8 53 101 () 8 53 101lsquo (a) 13~ (a) 13~ (˜) 101

Aa (esvect package option) 59a ( times

) 82

AA (A) 9aa (a) 9AAaleph (A) 83AAayin (O) 83AAbeth (B) 83

AAcht ( ˇ ldquo ˇ ldquo==

) 79AAdaleth (D) 83

AAhe (E) 83AAhelmet (V) 83AAheth (h) 83AAkaph (K) 83AAlamed (L) 83Aaleph (a) 83AApe (P) 83AAqoph (Q) 83AAresh (R) 83AAsade (X) 83Aayin (o) 83AAyod (Y) 83Abeth (b) 83absolute value see lvert and

rvert

abzuglich see textdiscount

AC () 67acarc 15acbar 15accents 13ndash17 33ndash35 44 46

56ndash60 68 79 86 94ndash96any character as 94extensible 57ndash60 95ndash96multiple per character 94

accents (package) 56 94 104 105accentset 94

Acht ( ˇ ldquo( ) 79

AchtBL ( ˇ ldquo==

) 79

AchtBR ( ˇ ldquo==) 79

ACK () 69acontraction 96

AcPa ( ) 79actuarial symbols 95acute (acute) 56acutus (a) 16Adaleth (d) 83adjoint (dagger) see dag

Adobe Acrobat 99

adots ( ) 62 94

advancing see textadvancing

AE (AElig) 9ae (aelig) 9agemO (0) 63Agimel (g) 83Ahe (e) 83Ahelmet (v) 83Aheth (H) 83ain (s) 16Akaph (k) 83

Alad () 56alad () 56Alamed (l) 83

Alas () 56alas () 56aleph (alefsym) 50 62aleph (alefsym) 50Alif () 13alpha (α) 49alphabets

African 9Cyrillic 90Greek 49 50 65Hebrew 50 65hieroglyphic 84math 65phonetic 10ndash13proto-Semitic 83Vietnamese 9

alphaup (α) 50alpine symbols 81Alt ( Alt ) 69

AltGr ( AltGr ) 69

amalg (q) 20amalg (∐) 23Amem (m) 83ampersand see amp

AMS 7 8 21 25 30 36 37 3941 49ndash53 56 58 59 61ndash6366 87 104

amsbsy (package) 100amsfonts (package) 20 30 36 41

62 65amsmath (package) 7 49 56 91

99amssymb (package) 7 20 30 36

41 56 62 65 104 105 107amstext (package) 92 93Anaclasis (divide) 82anaclasis (divide) 82

anchor (O) 77and see wedge

angle (ang) 63angle ( 6 ) 62angle (ang) 63angles 62ndash64Anglesign (W) 64

Angstrom unitmath mode see mathring

text mode see AA

Angud (〉) 56angud (〉) 56angular minutes see prime

angular seconds see second

Angus (〈) 56angus (〈) 56

14This occurs frequently between amssymb and mathabx for example

107

Ankh (ˆ) 80annu ( ) 95annuity 95Antidiple (lt) 82antidiple (lt) 82Antidiple (ltmiddotmiddot ) 82antidiple (ltmiddotmiddot ) 82Antisigma (sup) 82antisigma (sup) 82Anun (n) 83Ape (p) 83APL

modifiers 68symbols 68

APLbox (~) 68APLcirc () 68APLcomment () 68APLdown (F) 68APLdownarrowbox (o) 68APLinput () 68APLinv (divide~) 68APLleftarrowbox (p) 68APLlog () 68

APLminus (minus) 68APLnot (sim) 68APLrightarrowbox (q) 68APLstar (E) 68APLup () 68APLuparrowbox (n) 68APLvert ( | ) 68apprge () 38apprle (gt) 38approx (asymp) 30approx (asymp) 32approxeq (u) 30approxeq (≊) 32Aqoph (q) 83Aquarius (ecirc) 68aquarius (e) 68AR (A) 67ar (package) 67 104arc see accentsarccos (arccos) 49arcminutes see prime

arcs (package) 16 104 105arcseconds see second

arcsin (arcsin) 49arctan (arctan) 49Aresh (r) 83arev (package) 64 78 104 105arg (arg) 49Aries (P) 68Aries (agrave) 68aries () 68

ArrowBoldDownRight (y) 71

ArrowBoldRightCircled () 71

ArrowBoldRightShort (z) 71

ArrowBoldRightStrobe (w) 71

ArrowBoldUpRight (x) 71Arrownot (Y) 48arrownot (X) 48

arrows 41ndash43 47 69 71 90diagonal for reducing subex-pressions 57

double-headed diagonal 93extensible 57ndash60fletched 47 71negated 41 42 44

Arrowvert (ww) 53

Arrowvert (

XXXXXXX) 54

arrowvert () 53

arrowvert (

RRRRRRR) 54Arseneau Donald 91 93ndash95Asade (x) 83Asamekh (s) 83ASCII 7 9 69 100ndash101 104

table 101ascii (package) 69 101 104 105ascnode () 68Ashin (S) 83aspect ratio 67ast () 22ast (lowast) 20ast (lowast) 23Asteriscus (timesmiddotmiddotmiddotmiddot ) 82asteriscus (timesmiddotmiddotmiddotmiddot ) 82Asterisk () 22

Asterisk (N) 74asterisk () 22

AsteriskBold (A) 74

AsteriskCenterOpen (B) 74

AsteriskRoundedEnds (X) 74asterisks 22 74

AsteriskThin (C) 74

AsteriskThinCenterOpen (D) 74

asterism ( ) 91astrological symbols 68astronomical symbols 68astrosun () 68asymp () 30asymp (≍) 48atan (atan) 99ataribox (m) 78Atav (t) 83Ateth (T) 83AtForty (Oslash) 80AtNinetyFive (Oacute) 80atomic math objects 49 100AtSixty (Otilde) 80

autoleftarrow (DGGGGG) 60

autoleftrightharpoons

(EGGGGGGGGGGC) 60

autorightarrow (GGGGGA) 60

autorightleftharpoons

(GGGGGBFGGGGG) 60

Avav (w) 83average 20Ayn () 13Ayod (y) 83Azayin (z) 83

BB 9B ( ˘) 82b (esvect package option) 59b (a

macr) 13

b ( ˘) 82babygamma () 11backapprox () 32backapproxeq () 32backcong (≌) 32backepsilon () 30backeqsim () 32backneg () 63backprime (8) 63backprime () 63backsim (v) 30backsim (∽) 32backsimeq (w) 30backsimeq (⋍) 32backslash () 53 62

backslash () 54

backslashdiv () 23backtriplesim () 32banana brackets

see llparenthesis andrrparenthesis

bar (macr) 56barb () 11barcirc (minus ) 91bard () 11bari () 11barin (V) 51barj (j) 12barl () 11barlambda () 12barleftharpoon (THORN) 43baro () 21baro ( vs lt) 88baro (lt) 12barp (A) 12barred letters 91barrightharpoon (szlig) 43barsci (+) 12barscu (X) 12

Bart (

) 85baru (T) 12barwedge (X) 22barwedge (Z) 21Bat (yacute) 80bauarrow () 71baucircle () 76baucircle () 76baucross () 73

108

baudash () 80baueclipse () 76bauequal () 80bauface (13) 80bauforms () 80

bauforms () 80bauhead () 80

bauhead () 80bauhole () 76bauplus () 80baupunct () 76bauquarter () 80bauquestion () 80bausquare () 76bausquare () 76bautriangle () 76bautriangle () 76bauwhitearrow () 71bauwindow () 80BB ( ˘ ) 82Bb ( ˘ ) 82bB ( ˘ ) 82bb ( ˘ ) 82bba ( times) 82bbalpha () 65bbar (b) 91bbb ( ˘) 82bbbeta () 65Bbbk (k) 51bbding (package) 71ndash75 77 88

104 105bbdollar ($) 65bbetter (g) 82bbeuro (ucirc) 65bbfinalnun (Iuml) 65bbgamma (13) 65bbgreekl (mathbbol package op-

tion) 65BBm (

macr) 82

Bbm (macr

) 82bBm (

macr) 82

bbm (package) 65 104bbm (

macr) 82

bbmb ( ˘) 82bbmx (

macr ˘) 82bbnabla () 65bbold (package) 65 104bbpe (Ocirc) 65bbqof (times) 65bbslash (13) 21bbyod (Eacute) 65bcontraction 96bdecisive (i) 82Beam () 70Bearing () 70because (∵) 30 61because (∵) 61BEL () 69bell () 78Berry Karl 106beta (β) 49

betaup (β) 50beth (i) 50beth (ℶ) 50betteris (b) 82between ( ) 31between (G) 30between () 32bibridge (

rdquoardquo) 15

Bicycle (reg) 76Big 87 89big 87 89bigast () 22

bigbosonloop () 70bigbox (

e) 25

bigboxasterisk (Ouml

) 26bigboxbackslash (

THORN) 26

bigboxbot (Ucirc

) 26bigboxcirc (

Otilde) 26

bigboxcoasterisk (times

) 26bigboxdiv (

Oacute) 26

bigboxdot (Ocirc

) 26bigboxleft (

Oslash) 26

bigboxminus (Ntilde

) 26bigboxplus (

ETH) 26

bigboxright (Ugrave

) 26bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26

bigboxtriangleup (szlig

) 26bigboxvoid (

Uuml) 26

bigcap (⋂

) 25bigcap (⋂) 29bigcapdot (⩀) 29bigcapplus ($) 29bigcirc (copy) 20bigcirc () 74

BigCircle () 75bigcircle () 29bigcoast () 22bigcomplementop (

) 26

BigCross (13) 75bigcup (

⋃) 25

bigcup (⋃) 29bigcupdot (⊍) 29

bigcupplus (⊎) 29bigcupplus (⊎) 29bigcurlyvee (

) 26

bigcurlyvee (b

) 25bigcurlyvee (⋎) 29bigcurlyveedot () 29bigcurlywedge (

) 26

bigcurlywedge (c

) 25bigcurlywedge (⋏) 29bigcurlywedgedot () 29

BigDiamondshape (amp) 75bigdoublecurlyvee () 29bigdoublecurlywedge () 29bigdoublevee (⩔) 29bigdoublewedge (⩕) 29Bigg 87 89bigg 87 89

BigHBar () 75biginterleave (

g) 25

BigLowerDiamond (_) 75bignplus (

) 25

bigoast (⊛) 29bigoasterisk (

AElig) 26

bigobackslash (Icirc

) 26bigobackslash (⦸) 29bigobot (

Euml) 26

bigocirc (Aring

) 26bigocirc (⊚) 29bigocoasterisk (

Ccedil) 26

bigodiv (Atilde

) 26bigodot (

⊙) 25

bigodot (⊙) 29bigoleft (

Egrave) 26

bigominus (Aacute

) 26bigominus (⊖) 29bigoplus (

oplus) 25

bigoplus (oplus) 29bigoright (

Eacute) 26

bigoslash (Iacute

) 26bigoslash (⊘) 29bigostar () 29bigotimes (

otimes) 25

bigotimes (otimes) 29bigotop (

Ecirc) 26

bigotriangle (F) 29bigotriangleup (

Iuml) 26

bigovert (⦶) 29bigovoid (

Igrave) 26

bigparallel (f) 25

bigparr (˙

) 30bigplus (

) 26

bigplus (+) 29

BigRightDiamond () 75bigsqcap (

) 26

bigsqcap (

) 25bigsqcap (⊓) 29bigsqcapdot () 29bigsqcapplus (

) 27

bigsqcapplus (0) 29bigsqcup (

⊔) 25

bigsqcup (⊔) 29bigsqcupdot () 29bigsqcupplus (

) 27

bigsqcupplus (2) 29

BigSquare ( ) 75bigsquplus (

) 26

bigstar () 22bigstar (F) 63bigstar () 74bigtimes (

) 26

bigtimes (⨉) 29

BigTriangleDown () 75bigtriangledown (

`) 25

bigtriangledown (5 vs`

) 88bigtriangledown (5) 20bigtriangledown () 40

BigTriangleLeft () 75

BigTriangleRight ($) 75

109

BigTriangleUp () 75bigtriangleup (

a) 25

bigtriangleup (4 vsa

) 88bigtriangleup (4) 20bigtriangleup () 40biguplus (

⊎) 25

biguplus (⊎) 29bigvarstar () 22

BigVBar () 75bigvee (

or) 25

bigvee (⋁) 29bigveedot () 29bigwedge (

and) 25

bigwedge (⋀) 29bigwedgedot () 29

bigwith (˘

) 30binampersand (N) 21binary operators 20ndash24binary relations 30ndash32 34ndash39

47 48negated 30ndash33

bindnasrepma (O) 21Biohazard (h) 70biological symbols 70bishop see chess symbolsbishoppair (a) 82blackboard bold see alphabets

mathblackdiamond () 22blacklozenge () 63blacklozenge (⧫) 74blacksmiley (-) 78blacksquare () 63blacksquare (∎) 24blackstone 76blacktriangle (N) 63blacktriangle () 40blacktriangledown () 24blacktriangledown (H) 63blacktriangledown () 40blacktriangleleft () 24blacktriangleleft (J) 39blacktriangleleft () 40blacktriangleright () 24blacktriangleright (I) 39blacktriangleright () 40blacktriangleup () 24blank see textblank

Bleech (Euml) 80blitza () 20 48blitzb () 48blitzc () 48blitzd () 48blitze (13) 48Bm (

macr) 82

bm (package) 100 104 105bm 100bm (

macr) 82

bmod 49body-text symbols 8ndash19bold symbols 100boldmath 100

boldsymbol 100born see textborn

bosons 70bot (perp) 20 51 92bot () 51botdoteq () 31Bouquet (yen) 80Bowtie (1) 78bowtie () 30bowtie (amp) 23Box () 62Box (2) 63Box (◻) 24boxast (i) 21boxasterisk (f) 24boxbackslash (n) 24boxbackslash (⧅) 24boxbar (k) 21boxbot (k) 24boxbox () 21boxbox (⧈) 24boxbslash (j) 21boxcirc (e) 24boxcircle () 21boxcoasterisk (g) 24boxdiv (c) 24boxdot (d) 24boxdot () 21boxdot (⊡) 24boxdotLeft () 42boxdotleft () 42boxdotRight () 42boxdotright () 42boxempty () 21boxLeft () 42boxleft (h) 24boxleft () 42boxminus (a) 24boxminus () 21boxminus (⊟) 24boxplus (`) 24boxplus () 21boxplus (⊞) 24boxRight () 42boxright (i) 24boxright () 42boxslash (m) 24boxslash (l) 21boxslash (⧄) 24boxtimes (b) 24boxtimes () 21boxtimes (⊠) 24boxtop (j) 24boxtriangleup (o) 24boxvert (q) 24boxvoid (l) 24boy (D) 68bra 53braceld (︷) 95bracerd (︷) 95

bracevert () 53

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 54

brackets see delimitersbraket (package) 53Break ( Break ) 69

breve see accentsbreve (˘) 56breve (a) 16brokenvert (|) 78Bronger Torsten 92BS () 69BSEfree (n) 70BSpace ( 7minusrarr ) 69

bullet (bull) 20bullet () 23bullseye see textbullseye

Bumpedeq () 31bumpedeq () 31Bumpeq (m) 30Bumpeq (≎) 32bumpeq (l) 30bumpeq (≏) 32bupperhand (e) 82

Burns (

) 85

CC ( ) 82c (esvect package option) 59c (a) 13 102c ( ) 82calligra (package) 65 104 105Calligra (font) 65calrsfs (package) 65CAN () 69cancel (package) 57Cancer (atilde) 68cancer (_) 68Cap (e) 21Cap (⋒) 23cap (X) 22cap (cap) 20cap (cap) 23capdot (⩀) 23capplus () 23Capricorn (eacute) 68capricornus (d) 68card suits 62ndash64 77cardinality see aleph

care of (co) 64caret see ^

Carlisle David 1 104caron see accentscarriage return 69 77 90 see

also hookleftarrow

carriagereturn (C) 77castle see chess symbolsCatalexis (and) 82catalexis (and) 82catamorphism


Cc ( ) 82

110

cc ( CCcopy ) 18cc ( ) 82ccby ( BYcopy ) 18Ccc ( ) 82cclicenses (package) 18 104 105ccnc ( $copy ) 18ccnd ( =copy ) 18ccsa (

Ccopy ) 18cdot (middot) 20 91cdot (sdot) 23 61cdotp (middot) 61cdotp (sdot) 61cdots (middot middot middot ) 61Cedi see textcolonmonetary

cedilla see accentscelestial bodies 68celsius () 67Celtcross (Dagger) 80cent (cent) 17centerdot (13) 22centerdot () 21centernot (package) 92centernot 92centre (I) 82cents see textcent

CEsign (C) 70chancery (package) 104changenotsign 32char 7 90Charter (font) 17 29check (ˇ) 56check marks 73 76 77checked () 78CheckedBox (2) 73Checkedbox (V) 76

Checkmark () 73checkmark (X) 8checkmark () 63

checkmark (X vs D) 88

checkmark (D) 77

CheckmarkBold () 73chemarr (package) 59 104 105chemarrow (package) 47 60 104chemarrow (A) 47Chen Raymond 106chess symbols 82chi (χ) 49chiup (χ) 50circ () 20 64 92circ () 23circeq () 31circeq ($) 30circeq (≗) 32CIRCLE ( ) 78

Circle (5) 75

Circle ( vs 5) 88Circle () 78circlearrowleft (ouml) 42circlearrowleft () 41circlearrowleft () 44circlearrowright (divide) 42

circlearrowright () 41circlearrowright () 44circled numbers 73 76CircledA (ordf) 80circledast (~) 21circledast (⊛) 24circledbar (V) 21circledbslash (W) 21circledcirc () 21circledcirc (⊚) 24circleddash () 21circleddash (⊖) 24circleddot see odot

circleddotleft () 42circleddotright () 42circledgtr (S) 31circledless (R) 31circledminus see ominus

circledotleft seecircleddotleft

circledotright seecircleddotright

circledplus see oplus

circledR (r) 8 51circledS (s) 51circledslash see oslash

circledtimes see otimes

circledvee (U) 21circledwedge (T) 21circleleft () 42circleright () 42circles 75 76 78

CircleShadow (d) 75

CircleSolid (a) 75Circpipe (rsaquo) 70circplus () 22Circsteel (bull) 70circumflex see accentscircumflexus (a) 16CleaningA (laquo) 80CleaningF (frac34) 80CleaningFF (iquest) 80CleaningP (not) 80CleaningPP (shy) 80clickb () 12clickc () 12clickt (R) 12clock () 78clock symbols 81Clocklogo (U) 76closedcurlyvee (frac34) 23closedcurlywedge (frac14) 23closedequal (Uuml) 32closedniomega () 12closedprec (frac12) 32closedrevepsilon () 12closedsucc (raquo) 32Cloud () 80clovers 74clubs (suit) 62ndash64 77clubsuit (clubs) 62clubsuit (clubs) 63

cmll (package) 20 23 30 36 104coAsterisk () 22coasterisk () 22code page 1252 103

table 103code page 437 69 101Coffeecup (K) 76coh (uml) 36colon 61colon ( ) 61colon (∶) 61Colonapprox () 31Colonapprox (asymp) 34colonapprox (asymp) 34colonapprox (13) 31Coloneq (H) 31Coloneq (minus) 34coloneq () 31coloneq (minus) 34coloneq (D) 31Coloneqq (F) 31Coloneqq (=) 34coloneqq (=) 34coloneqq (B) 20 31Colonsim () 31Colonsim (sim) 34colonsim (sim) 34colonsim () 31comment (RR) 82communication symbols 69comptexttex (newsgroup) 7

20 90ndash95compensation (n) 82complement (A) 51complement () 51complement (∁) 29complex numbers (C) see

alphabets mathComprehensive TEX Archive Net-

work 1 7 57 66 87 103104

computer hardware symbols 69computer keys 69Computer Modern (font) 87 89

101ComputerMouse (Iacute) 69cong () 30cong (cong) 32conjunction see wedge

conjunction (V) 68consequence relations 34contradiction symbols 20 48control characters 69convolution () 22coprod (

∐) 20 25

coprod (∐) 29copyright 8 18 102copyright (copy) 8corner (k) 16Corresponds (=) 64corresponds () 31cos (cos) 49 99cosh (cosh) 49

111

cot (cot) 49coth (coth) 49counterplay (V) 82Courier (font) 17CP1252 see code page 1252CP437 see code page 437CR () 69cr 91Creative Commons licenses 18crescent (fge package option) 56

Cross () 75

Cross (dagger vs vs ) 88

Cross () 72Cross (dagger) 80crossb () 12

CrossBoldOutline (-) 72

CrossClowerTips (4) 72crossd (13) 12Crossedbox (X) 76crosses 72 76 80crossh () 12

CrossMaltese () 72crossnilambda (3) 12

CrossOpenShadow (+) 72

CrossOutline () 72crotchet see musical symbolscrtilde (

Ŕa) 15

crucifixes 72 80Crux (dagger) 56crux (dagger) 56csc (csc) 49CTAN see Comprehensive TEX

Archive NetworkCtrl ( Ctrl ) 69

Cube 81 90cube root see sqrt

Cup (d) 21Cup (⋓) 23cup (Y) 22cup (cup) 20 91 99cup (cup) 23cupdot (⊍) 23cupplus (⊎) 23curlyc () 12curlyeqprec (para) 31curlyeqprec (2) 30curlyeqprec (⋞) 32curlyeqsucc (middot) 31curlyeqsucc (3) 30curlyeqsucc (⋟) 32curlyesh (N) 12curlyvee (O) 22curlyvee (g) 21curlyvee (⋎) 23curlyveedot (5) 23curlyveedownarrow () 21curlyveeuparrow () 21curlywedge (N) 22curlywedge (f) 21curlywedge (⋏) 23curlywedgedot (4) 23

curlywedgedownarrow () 21curlywedgeuparrow (amp) 21curlyyogh (a) 12curlyz (^) 12currency (curren) 17currency symbols 17 65curvearrowbotleft (oacute) 42curvearrowbotleftright (otilde)

42curvearrowbotright (ocirc) 42curvearrowdownup (Euml) 43curvearrowleft (eth) 42curvearrowleft (x) 41curvearrowleft () 44curvearrowleftright (ograve) 42curvearrowleftright (Egrave) 43curvearrownesw (Igrave) 43curvearrownwse (Iacute) 43curvearrowright (ntilde) 42curvearrowright (y) 41curvearrowright () 44curvearrowrightleft (Ecirc) 43curvearrowsenw (Iuml) 43curvearrowswne (Icirc) 43curvearrowupdown (Eacute) 43Cutleft (s) 71Cutline (r) 71cutoff subtraction see dotdiv

Cutright (q) 71

DD (a

uml) 16

d (esvect package option) 59d (a) 13dag (dagger) 8 103dagger (dagger) 20daleth (k) 50daleth (ℸ) 50dangerous bend symbols 76DArrow ( darr ) 69

dasharrow seedashrightarrow

dasheddownarrow () 43dashedleftarrow () 43dashednearrow (d) 43dashednwarrow (e) 43dashedrightarrow () 43dashedsearrow (g) 43dashedswarrow (f) 43dasheduparrow () 43

dashint (minusint

) 93

dashleftarrow (c) 41dashleftarrow () 44dashleftrightarrow (e) 42dashrightarrow (d) 41dashrightarrow () 44DashV ()) 31Dashv ()) 31dashv (a) 30dashv (⊣) 33dashVv (-) 31davidsstar (C) 73

DavidStar (0) 74

DavidStarSolid () 74dbar (d) 91dbend () 76dblaccnt (package) 94dblcolon () 34DCa () 69DCb () 69DCc () 69DCd () 69DD (DD) 79ddag (Dagger) 8 103ddagger (Dagger) 20

ddashint (=int

) 93

ddddot (

) 56dddot (

) 56

dddtstile ( ) 34

DDohne (DD) 79ddot (uml) 56ddotdot () 23 61

ddots ( ) 61 94

ddots (⋱) 61

ddststile ( ) 34

ddtstile ( ) 34

ddttstile ( ) 34

DeclareFontFamily 98DeclareFontShape 98DeclareMathOperator 99DeclareMathOperator 99declareslashed 92definite-description operator ( ι)

90definition symbols 20 95deg (deg) 49degree (0) 63degree (deg) 67degrees see textdegree

DEL () 69Del ( Del ) 69

Deleatur see Denarius

delimiters 52ndash56text-mode 56variable-sized 53ndash55wavy-line 54 55

Delta (∆) 49delta (δ) 49deltaup (δ) 50demisemiquaver see musical

symbolsDenarius (cent) 17dental (ag) 15derivitive partial see partial

descnode () 68det (det) 49devadvantage (t) 82

Dfourier ( c) 35

dfourier ( c ) 35

DFT ( ) 60

dft ( ) 60

112

DH (ETH) 9 102DH ( D) 12dh (eth) 9 102dh (k) 12diacritics see accentsdiaeresis (a) 16diaeligresis see accentsdiagdown (aring) 63diagdown () 63diagdown (Oacute) 33diagonal (G) 82diagup (auml) 63diagup () 63diagup (Ograve) 33diameter (I) 63diameter () 20diameter (empty) 63diameter () 78Diamond (^) 62Diamond (3) 63Diamond () 24diamond () 20diamond () 24diamondbackslash () 24Diamondblack (_) 63diamonddiamond () 24Diamonddot () 63diamonddot (⟐) 24DiamonddotLeft () 42Diamonddotleft () 42DiamonddotRight () 42Diamonddotright () 42diamonddots (13) 23 61DiamondLeft () 42Diamondleft () 42diamondminus (x) 24diamondplus (|) 24DiamondRight () 42Diamondright () 42diamonds 75diamonds (suit) 62ndash64 77

DiamondShadowA () 75

DiamondShadowB () 75

DiamondShadowC () 75

Diamondshape (6) 75diamondslash (z) 24

DiamondSolid (p) 75diamondsuit (diams) 62diamondsuit () 63diamondtimes () 24diamondvert (y) 24diatop 16 94diaunder 16 94dice 81 90dictionary symbols 10ndash13 84dictsym (package) 84 104 105died see textdied

differential inexact see dbar

digamma (z) 49digits 62

LCD 67Mayan 62

old-style 18segmented 67

dim (dim) 49ding 9 71ndash75 77dingautolist 73dingbat (package) 72 77 88 104

105dingbat symbols 71ndash77Diple (gt) 82diple (gt) 82Diple (gtmiddotmiddot ) 82diple (gtmiddotmiddot ) 82Dirac notation 53discount see textdiscount

discretionary hyphen 103disjoint union 20disjunction see vee

displaystyle 92 93 95 99ditto marks see textquotedbl

div (divide) 20div (divide) 23divdot () 22divideontimes () 22divideontimes (gt) 21divides () 31divides (Ograve) 33division 20 57

non-commutative 60division times see

divideontimes

divorced see textdivorced

DJ (ETH) 9dj (đ) 9dlbari (() 12DLE () 69dlsh (ecirc) 42

dndtstile ( ) 34

dnststile ( ) 34

dntstile ( ) 34

dnttstile ( ) 35does not divide see nmid

does not exist see nexists

Dohne (D) 79dollar see textdollar

dollar sign see $

Dontwash (Yacute) 80dot ( ˙ ) 56dot symbols 8 61 62 94dotcup ( middotcup) 20 91dotdiv () 22Doteq see doteqdot

Doteq (≑) 32doteq () 30doteq (≐) 32doteqdot (+) 30doteqdot (≑) 33dotless i (ı)

math mode 56 62text mode 13

dotless j ()math mode 56 62text mode 13

dotmedvert () 23dotminus () 23dotplus () 22dotplus (u) 21dots ( ) 8 103dots (ellipses) 8 61 62 94dotsb (middot middot middot ) 61dotsc ( ) 61dotseq () 31dotsi (middot middot middot ) 61dotsint (

macr) 28

dotsm (middot middot middot ) 61dotso ( ) 61dotted union (cup) 99

dottedtilde (a) 15

dottimes () 22double 55doublebarwedge (Z) 22doublebarwedge ([) 21doublecap see Cap

doublecap () 22doublecap (⋒) 23doublecup see Cup

doublecup (]) 22doublecup (⋓) 23doublecurlyvee (7) 23doublecurlywedge (6) 23doublefrown () 48doublefrowneq () 48doublepawns (d) 82doublesmile () 48doublesmileeq ($) 48doublesqcap (⩎) 23doublesqcup (⩏) 23doubletilde (ã) 15doublevee (⩔) 23doublewedge (⩕) 23DOWNarrow (L) 78Downarrow (dArr) 41 53Downarrow (dArr) 43downarrow 99downarrow (darr) 41 53downarrow (darr) 43downarrowtail () 43downbracketfill 95downdownarrows (Oacute) 42downdownarrows () 41downdownarrows () 43downdownharpoons (Ucirc) 43Downes Michael J 49 106downfilledspoon (s) 47downfootline () 32downfree (⫝) 32downharpoonccw () 46downharpooncw () 46downharpoonleft (aring) 43downharpoonleft () 41downharpoonright (ccedil) 43downharpoonright () 41downlsquigarrow (pound) 43downmapsto () 43downModels (oacute) 32downmodels (atilde) 32

113

downp ( ) 16

downparenthfill 95

downpitchfork (⫛) 47

downpropto () 32

downrsquigarrow () 43

downslice () 24

downspoon (⫰) 47

downt ( ) 16

downtherefore (∵) 23 61

downtouparrow ( ) 42

downuparrows ( ) 42

downuparrows () 43

downupharpoons ( ) 43

downupharpoons (⥯) 46

downVdash () 32

downvdash (⊤) 32

downY () 23

drsh ( ) 42

DS (SS) 79

Ds (ss) 79

dsaeronautical (a) 84

dsagricultural (G) 84

dsarchitectural (A) 84

dsbiological (B) 84

dschemical (C) 84

dscommercial (c) 84

dsdtstile ( ) 35

dsfont (package) 65 104

dsheraldical (H) 84

dsjuridical (J) 84

dsliterary (L) 84

dsmathematical (M) 84

dsmedical (m) 84

dsmilitary (X) 84

dsrailways (R) 84

dsststile ( ) 35

dstechnical (T) 84

dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35

dtimes () 23

dtimes (13) 23

dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35

DVI 18 69 97

dz ( ) 12

E

e (esvect package option) 59

e (e) 51

ε-TEX 53

Earth ( ) 68

Earth (Ecirc) 68

earth () 68

Ecommerce () 17

EightAsterisk ( ) 74

EightFlowerPetal ( ) 74

EightFlowerPetalRemoved ( ) 74

eighth note see musical symbolseighthnote () 78eighthnote () 78

EightStar ( ) 74

EightStarBold ( ) 74

EightStarConvex ( ) 74

EightStarTaper ( ) 74ejective ( ) 12electrical symbols 67electromotive force (E) see

alphabets mathell () 51

Ellipse ( ) 75ellipses (dots) 8 61 62 94ellipses (ovals) 75

EllipseShadow ( ) 75

EllipseSolid ( ) 75EM () 69Email (k) 69Emailct (z) 69emgma ( ) 12emptyset (empty) 62emptyset (empty) 63End ( End ) 69

end of proof 62ending (L) 82eng ( ) 11engineering symbols 67 70engma ( ) 12ENQ () 69entails see models

Enter ( Enter ) 69

Envelope ( ) 77enya ( ) 12EOT () 69epsdice (package) 81 104 105epsdice ( ) 81epsi ( ) 12epsilon (ε) 49epsilonup (ε) 50eqbump () 32eqbumped ( ) 31eqcirc ( ) 31eqcirc () 30eqcirc (≖) 32Eqcolon () 31Eqcolon (minus) 34eqcolon ( ) 31eqcolon (minus) 34eqcolon () 31eqdot (⩦) 32eqfrown () 48Eqqcolon () 31Eqqcolon (=) 34eqqcolon (=) 34eqqcolon () 31eqsim () 31eqsim (≂) 32eqslantgtr ( ) 38

eqslantgtr () 37

eqslantgtr (⪖) 39

eqslantless ( ) 38

eqslantless () 37

eqslantless (⪕) 39

eqsmile () 48

equal (=) 32

equal (j) 82

equalclosed () 32

equalsfill 20 95

equidecomposable 91

equilibrium seerightleftharpoons

equiv (equiv) 20 30

equiv (equiv) 32

equivalence seeequiv leftrightarrowand threesim

equivclosed () 32

er ( ) 11

es-zet see ss

ESC () 69

Esc ( Esc ) 69

escapable characters 8

esh ( ) 11

esh ( ) 12

esint (package) 28 104

Estatically (J) 70

estimated see textestimated

esvect (package) 59 104

eta (η) 49

etaup (η) 50

ETB () 69

etc (P) 82

eth (eth) 63

eth ( ) 11

eth ( ) 12

ETX () 69

eufrak (package) 65

Euler Roman 50

EUR (e ) 17

EURcr (d) 17

EURdig (D) 17

EURhv (c) 17

euro 17

euro signs 17

blackboard bold 65

eurosym (package) 17 104 105

EURtm (e) 17

euscript (package) 65 104 105

evaluated at see vert

evil spirits 86

exclusive or 90

exists ( ) 51

exists (exist) 51

exists (exist) 51

exp (exp) 49

Explosionsafe (`) 70

extarrows (package) 60 104 105

extensible accents 57ndash60 95ndash96

extensible arrows 57ndash60

114

extensible symbols creating 94ndash96

extensible tildes 57 59extension characters 48 49extpfeil (package) 60 104 105extraipa (package) 15 104eye (E) 77EyesDollar (brvbar) 17

Ff (esvect package option) 59faces 69 78 80 85fallingdotseq () 31fallingdotseq () 30fallingdotseq (≒) 32FallingEdge () 67fatbslash ()) 21fatsemi () 21fatslash (() 21FAX (u) 69fax (t) 69Faxmachine (v) 69fc (package) 9 13fclfont (package) 104feet see prime and

textquotesingle

FEMALE () 70Female (~) 70female () 70FemaleFemale (bdquo) 70FemaleMale (hellip) 70

Ferli (aa) 79

Fermi (aa

) 79fermions 70feyn (package) 70 104 105Feynman slashed character nota-

tion 92Feynman-diagram symbols 70feyna (a) 70feync (c) 70feynfd () 70feynfl (n) 70

feynfs (e) 70feynfu () 70

feynfv () 70feynf (f) 70feynglu (w) 70

feyngl (o) 70feyngu () 70feyngvs () 70

feyngv () 70feyng (g) 70feynhd () 70feynhs (i) 70feynhu () 70feynh (h) 70feynms (l) 70feynm (m) 70feynp (p) 70feynx (x) 70

FF () 69fge (package) 47 52 56 62 64

104 105fge-digits 62fgeA (A) 52fgebackslash (K) 64fgebaracute (M) 64fgebarcap (O) 64fgec (c) 52fgecap (S) 64fgecapbar (Q) 64fgecup (N) 64fgecupacute (R) 64fgecupbar (P) 64fged (p) 52fgee (e) 52fgeeszett () 52fgeeta () 52fgeF (F) 52fgef (f) 52fgeinfty (i) 64fgelangle (h) 64fgelb 52fgelb () 52fgeleftB (D) 52fgeleftC (C) 52fgeN () 52fgeoverU () 52fgerightarrow () 47fgerightB (B) 52fges (s) 52fgestruckone (1) 62fgestruckzero (0) 62fgeU (U) 52fgeuparrow () 47fgeupbracket (L) 64FHBOLOGO (f) 80FHBOlogo (F) 80file (H) 82

FilledBigCircle (U) 75

FilledBigDiamondshape (V) 75

FilledBigSquare (P) 75

FilledBigTriangleDown (S) 75

FilledBigTriangleLeft (R) 75

FilledBigTriangleRight (T) 75

FilledBigTriangleUp (Q) 75

FilledCircle (e) 75FilledCloud ( ) 80filleddiamond () 24

FilledDiamondShadowA () 75

FilledDiamondShadowC () 75

FilledDiamondshape (f) 75

FilledHut () 81filledlargestar () 74filledlozenge (⧫) 74filledmedlozenge (⧫) 74filledmedsquare (∎) 24filledmedtriangledown () 24

40

filledmedtriangleleft () 2440

filledmedtriangleright () 24 40

filledmedtriangleup () 2440

FilledRainCloud () 80

FilledSectioningDiamond () 81

FilledSmallCircle (u) 75

FilledSmallDiamondshape (v) 75

FilledSmallSquare (p) 75

FilledSmallTriangleDown (s) 75

FilledSmallTriangleLeft (r) 75

FilledSmallTriangleRight

(t) 75

FilledSmallTriangleUp (q) 75

FilledSnowCloud ($) 80

FilledSquare (`) 75filledsquare (◾) 24

FilledSquareShadowA () 75

FilledSquareShadowC () 75

filledsquarewithdots (C) 77filledstar () 24

FilledSunCloud () 80

FilledTriangleDown (c) 75filledtriangledown () 24 40

FilledTriangleLeft (b) 75filledtriangleleft () 24 40

FilledTriangleRight (d) 75filledtriangleright () 24

40FilledTriangleUp (a) 75filledtriangleup () 24 40FilledWeakRainCloud () 80finger pointing see fistsfinpartvoice (araquo) 15finpartvoiceless (araquo) 15

fint (gt

) 27

fint (ffl) 28

Finv (F) 51Finv (`) 51

Fire () 81fish hook see strictif

fists 72fivedots () 23 61

FiveFlowerOpen (R) 74

FiveFlowerPetal (P) 74

FiveStar (8) 74

FiveStarCenterOpen () 74

FiveStarConvex () 74

FiveStarLines (7) 74

FiveStarOpen (9) 74

FiveStarOpenCircled () 74

115

FiveStarOpenDotted (lt) 74

FiveStarOutline (=) 74

FiveStarOutlineHeavy (gt) 74

FiveStarShadow () 74Fixedbearing () 70

fixedddots ( ) 61

fixedvdots () 61

fixmath (package) 100fj (F) 12

Flag () 81flap (f) 12flapr (D) 11flat ([) 62 78flat () 63Flatsteel (ndash) 70fletched arrows 47 71florin see textflorin

flowers 74Flynn Peter 91

Fog () 80font encodings 7 100 103

7-bit 78-bit 7ASCII 104document 103Latin 1 104limiting scope of 7LY1 7OT1 7 9 13 94 100 101103

OT2 90T1 7 9 13 101 103T4 9 13 16T5 9 13TS1 103

fontdefdtx (file) 90 94fontenc (package) 7 9 13 103fontencoding 7fonts

Calligra 65Charter 17 29Computer Modern 87 89101

Courier 17Garamond 17 29Helvetica 17Symbol 50 90Times Roman 17 89Type 1 99Utopia 17 29Zapf Chancery 65Zapf Dingbats 71 73

fontsize 87 89Football (o) 76forall (forall) 51forall (forall) 51Force (l) 70Forward (middot) 79ForwardToEnd (cedil) 79ForwardToIndex (sup1) 79

FourAsterisk (1) 74

FourClowerOpen (V) 74

FourClowerSolid (W) 74

Fourier ( c) 35

fourier ( c ) 35Fourier transform (F) see

alphabets mathFourStar (5) 74

FourStarOpen (6) 74fourth (4) 63fractions 64fraktur see alphabets mathFrege logic symbols 47 52 62 64frown (_) 30frown () 48frown symbols 48frowneq () 48frowneqsmile () 48frownie () 78frownsmile () 48frownsmileeq ()) 48Frowny (sect) 80FS () 69FullFHBO () 80fullmoon (M) 68fullmoon () 68fullnote () 78

GG (a) 13g (esvect package option) 59Game (G) 51Game (a) 51Gamma (Γ) 49gamma (γ) 49gammaup (γ) 50Ganz ( macr ) 79GaPa (lt) 79Garamond (font) 17 29gcd (gcd) 49ge see geq

Gemini (R) 68Gemini (acirc) 68gemini (^) 68genealogical symbols 78geneuro (AC) 17geneuronarrow (BC) 17geneurowide (CC) 17gensymb (package) 67Gentsroom (x) 76geometric shapes 74ndash76geq (yen) 38geq (ge) 37 38geq (ge) 39geqclosed (⊵) 39 40geqdot (u) 39geqq (macr) 38geqq (=) 37geqq (≧) 39geqslant (gt) 37geqslant (⩾) 39geqslantdot (⪀) 39

german (keystroke package option) 69

gets see leftarrow

gg () 38gg () 37gg (≫) 39ggcurly (Iuml) 31ggg (Iuml) 38ggg (≫) 37ggg (≫ vs Iuml) 88ggg (⋙) 39gggtr see ggg

gggtr (⋙) 39ghosts 86Gibbons Jeremy 106gimel (ג) 50gimel (ℷ) 50girl (B) 68glotstop (b) 12glottal () 12gluon (QPPPPPPR) 67gluons 70gnapprox (Euml) 38gnapprox () 37gnapprox (⪊) 39gneq (shy) 38gneq (13) 37gneqq (sup3) 38gneqq () 37gneqq (≩) 39gnsim (Aring) 38gnsim () 37gnsim (≵) 39Go boards 76Go stones 76goban 76Goofy 85graphics (package) 90graphicx (package) 16 87 90grave (`) 56gravis (a) 16greater-than signs see

inequalitiesGreek 49 50

blackboard bold 65bold 49 100upright 50

Gregorio Enrico 91 92GS () 69gtr (gt) 39gtrapprox (Ccedil) 38gtrapprox () 37gtrapprox (⪆) 39gtrclosed (⊳) 39 40gtrdot (Iacute) 38gtrdot (m) 37gtrdot (⋗) 39gtreqless (frac12) 38

gtreqless (R) 37

gtreqless (⋛) 39gtreqlessslant (O) 39

gtreqqless (iquest) 38

116

gtreqqless (T) 37

gtreqqless (⪌) 39

gtrless (raquo) 38gtrless (≷) 37gtrless (≷) 39

gtrneqqless (oacute) 39

gtrsim (Aacute) 38gtrsim (amp) 37gtrsim (≳) 39guillemotleft (laquo) 9 102guillemotright (raquo) 9 102guilsinglleft (lsaquo) 9 103guilsinglright (rsaquo) 9 103gvertneqq (micro) 38gvertneqq () 37gvertneqq (≩) 39

HH (a) 13h (esvect package option) 59

h (ả) 13HA (A) 84

Ha (a) 84hacek see accents

Hail () 80Halb ( ˘ ldquo) 79half note see musical symbols

HalfCircleLeft (s) 75

HalfCircleRight (r) 75

HalfFilledHut () 81halflength (p) 16halfnote (13) 78

HalfSun () 80Hamiltonian (H) see alphabets

mathHandCuffLeft () 72

HandCuffLeftUp () 72

HandCuffRight (13) 72

HandCuffRightUp () 72

HandLeft () 72

HandLeftUp () 72

HandPencilLeft () 72

HandRight () 72

HandRightUp () 72hands see fistsHandwash (Uuml) 80HaPa (lt) 79harmony (package) 79 104 105harpoons 41 43 46hash () 63hash mark see

hat (ˆ) 56hateq (≙) 32hausaB (B) 12hausab (b) 12hausaD (T) 12hausad (D) 12hausaK (K) 12hausak (k) 12

HB (B) 84

Hb (b) 84

HBar () 75hbar (~) 51 90hbipropto () 23HC (C) 84

Hc (c) 84hcrossing () 32

HCthousand (6) 84HD (D) 84

Hd (d) 84hdotdot () 23 61hdots (⋯) 61Hdual (cedil) 84HE (E) 84He (e) 84heads see facesHeart (Œ) 80hearts (suit) 62ndash64 77heartsuit (hearts) 62heartsuit () 63Hebrew 50 65Helvetica (font) 17HERMAPHRODITE () 70Hermaphrodite () 70hexagon (7) 74Hexasteel (rsquo) 70hexstar (A) 73HF (F) 67HF (F) 84Hf (f) 84hfil 92HG (G) 84Hg (g) 84HH 79

HH (H) 84Hh (h) 84Hhundred (3) 84

HI (I) 84

Hi (i) 84Hibl (˝) 84

Hibp (ˆ) 84

Hibs (uml) 84

Hibw (˜) 84hieroglf (package) 84 104 105hieroglyphics 84Hilbert space (H) see alphabets

mathhill (a

) 15

HJ (J) 84Hj (j) 84HK (K) 84Hk (k) 84hksqrt (

radic) 93

HL (L) 84Hl (l) 84HM (M) 84

Hm (m) 84

Hman (ˇ) 84

Hmillion (7) 84

Hms (acute) 84HN (N) 84Hn (n) 84HO (O) 84

Ho (o) 84Holt Alexander 1 104

holter ( ) 60

holtpolt (package) 60 104hom (hom) 49Home ( Home ) 69

Homer (

) 85Hone (|) 84hookb () 12hookd () 12hookd (D) 12hookdownminus () 63hookg () 12hookh ($) 12hookheng () 12hookleftarrow (larr) 41hookleftarrow () 44hookrevepsilon () 12hookrightarrow (rarr) 41hookrightarrow () 44hookupminus (⨽) 63Horn Berthold 66HP (P) 84Hp (p) 84Hplural (˙) 84

Hplus (+) 84HQ (Q) 84Hq (q) 84

Hquery () 84HR (R) 84Hr (r) 84HS (S) 84

Hs (s) 84

Hscribe (macr) 84

Hslash () 84hslash () 51Hsv (˚) 84HT (T) 84HT () 69Ht (t) 84Hten (2) 84

Hthousand (4) 84

Htongue (˘) 84

HU (U) 84

Hu (u) 84Hungarian umlaut see accents

Hut () 81

HV (V) 84

117

Hv (v) 84hv () 12Hvbar (|) 84HW (W) 84

Hw (w) 84HX (X) 84

Hx (x) 84

HXthousand (5) 84

HY (Y) 84

Hy (y) 84hyphen discretionary 103

HZ (Z) 84Hz (z) 84

Ii (ı) 13ialign 91 93 95ibar ( i ) 12IBM PC 69 101Icelandic staves 85IceMountain () 81

iddots ( ) 62

iddots () 94

idotsint (intmiddot middotmiddotint

) 25

idotsint (

) 27

idotsint (Z) 29iff see Longleftrightarrow

ifsym (package) 67 75 80 8188 90 104 105

igo (package) 76 104igocircle () 76igocircle () 76igocross (|) 76igocross (|) 76igonone () 76igonone () 76igosquare (~) 76igosquare (~) 76igotriangle () 76igotriangle () 76

iiiint (intintintint

) 25

iiiint (

) 27

iiiint (ˇ

) 28

iiiint (⨌) 29iiint (

micro) 26

iiint (intintint

) 25

iiint (

) 25 27

iiint (˝

) 28

iiint (∭) 29iint (

acute) 26

iint (intint

) 25

iint (

) 25 27

iint (˜

) 28

iint (∬) 29Im (=) 51im (j) 51imath (ı) 51 56impliedby see Longleftarrow

implies see Longrightarrow

and vdash

impulse train see shain (P) 51in (isin) 51in (isin) 51in (isin) 51inches see second and

textquotedbl

incoh (˚) 36independence

probabilistic 93statistical 93stochastic see bot

independent (perpperp) 93Industry (I) 76inequalities 8 37ndash39inexact differential see dbar

inf (inf) 49infinity (infin) see infty

Info (i) 76information symbols 76informator symbols 82infty (8) 63infty (infin) 62infty (infin) 63inipartvoice (andash ) 15inipartvoiceless (andash ) 15

injlim (inj lim) 49inplus (A) 30Ins ( Ins ) 69

int (sup3) 26

int (int

) 25

int (r

) 25

int (int) 29

intclockwise () 29

integers (Z) see alphabets mathintegrals 25ndash29 63 92ndash93integrals (wasysym package op-

tion) 25intercal (ᵀ) 21intercal (⊺) 51interleave (9) 21intersection see cap

Interval () 81inva () 12invamp (M) 21invbackneg (⨽) 63invdiameter () 78inve (U) 12InversTransformHoriz () 35

InversTransformVert () 35inverted symbols 10ndash12 16 90invf () 12invglotstop (d) 12invh (amp) 12invlegr (I) 12invm (5) 12invneg () 30invneg (⨼) 63invr (G) 12

invscr (K) 12invscripta () 12invv () 12invw (Z) 12invy () 12iota (ι) 49iotaup (ι) 50ipagamma ( ) 12IroningI (macr) 80IroningII (deg) 80IroningIII (plusmn) 80

irony mark ( ) 90

Irritant () 81ismodeledby (=|) 90ISO character entities 103isoent (package) 103

Jj () 13

JackStar (2) 74

JackStarBold (3) 74Jewish star 73 74jmath () 51 56Joch () 81Join (Z) 30Join (amp) 23joinrel 90Jupiter (E) 68Jupiter (Aring) 68jupiter (X) 68

Kk ( ˛) 13kappa (κ) 49kappaup (κ) 50ker (ker) 49ket 53Keyboard (Iuml) 69keyboard symbols 69keys computer 69keystroke (package) 69 104 105keystroke ( ) 69

king see chess symbolsknight see chess symbolsKnuth Donald E 7 100 106

symbols by 76 79Kr ( l) 79kreuz (6) 78kside (O) 82Kutline (R) 71

LL ( L) 9l ( l) 9labdentalnas (4) 11labvel 15Ladiesroom (y) 76Lagrangian (L) see alphabets

mathLambda (Λ) 49lambda (λ) 49lambdabar (o) 63

118

lambdaslash (n) 63

lambdaup (λ) 50

Lamport Leslie 104 106

land see wedge

landdownint () 28

landdownint (⨚) 29

landupint () 28

landupint (⨙) 29

Langle (lt) 65

lAngle (〈〈) 55

langle (〈) 20 53

langle (⟨) 54

langlebar (n) 54

Laplace ( s c) 35

laplace ( c s) 35

Laplace transform (L) seealphabets math

Laplacian (∆) see Delta

Laplacian (nabla2) see nabla

largecircle () 74

largediamond () 74

largelozenge (loz) 74

largepencil (W) 72

largepentagram () 74

largesquare (◻) 74

largestar () 74

largestarofdavid () 74

largetriangledown () 40

largetriangleleft (◁) 40

largetriangleright (▷) 40

largetriangleup () 40

LArrow ( larr ) 69

larrowfill 60

Laserbeam (a) 70

LATEX 17 25 49 53 61 62 71 8287 90ndash96 99ndash101 103 104106

LATEX 2ε 1 7 8 18ndash20 30 3641 57 61 62 66 87 88 9093 94 98ndash103 106

latexsym (package) 20 30 36 4162 87 104 105

latfric () 11

Latin 1 7 101 103 104

table 102

laundry symbols 80

Lbag (P) 52

lbag (N) 52

lbrace (⎧⎪⎪⎨⎪⎪⎩

) 54

Lbrack ([) 65

lBrack ([[) 55

LCD digits 67

lCeil (dd) 55

lceil (d) 53

lceil (⎡⎢⎢⎢⎢⎢⎢) 54

lcirclearrowdown (yuml) 43lcirclearrowleft (⤾) 43lcirclearrowright (⟳) 43lcirclearrowup () 43

lcircleleftint (∲) 29

lcirclerightint (∲) 29lcm (lcm) 99lcorners (v) 52lcurvearrowdown (⤸) 43lcurvearrowleft (ordm) 43lcurvearrowne (frac14) 43lcurvearrownw (frac12) 43lcurvearrowright () 43lcurvearrowse (iquest) 43lcurvearrowsw (frac34) 43lcurvearrowup (sup1) 43ldbrack (v) 54ldotp () 61ldots ( ) 61le see leq

leadsto () 30 41leadsto () 44leaf see textleaf

Left 85left 53 55 87 89LEFTarrow () 78Leftarrow (lArr) 20 41Leftarrow (lArr) 43leftarrow (ETH) 42leftarrow (larr) 41leftarrow (larr) 43leftarrowtail () 41leftarrowtail () 44leftarrowtriangle (^) 42leftbarharpoon (Uuml) 43LEFTCIRCLE (G) 78LEFTcircle (G) 78Leftcircle (I) 78

leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

leftfilledspoon (r) 47leftfootline (z) 32leftfree () 32lefthalfcap () 23lefthalfcup () 23leftharpoonccw () 46leftharpooncw () 46leftharpoondown (acirc) 43leftharpoondown () 41leftharpoonup (agrave) 43leftharpoonup () 41leftleftarrows (ETH) 42leftleftarrows (hArr) 41leftleftarrows () 44leftleftharpoons (Oslash) 43leftlsquigarrow (cent) 44leftmapsto () 44leftModels (ograve) 32leftmodels (acirc) 32leftmoon (K) 68

leftmoon ($) 68leftp (v) 16leftpitchfork () 47leftpointright (R) 72leftpropto (prop) 32Leftrightarrow (hArr) 41Leftrightarrow (hArr) 44leftrightarrow (Oslash) 42leftrightarrow (harr) 41leftrightarrow (harr) 44leftrightarroweq (-) 42leftrightarrows (Ocirc) 42leftrightarrows () 41leftrightarrows () 44leftrightarrowtriangle (])

42leftrightharpoon (agrave) 43leftrightharpoondownup (⥊)

46leftrightharpoons (egrave) 43leftrightharpoons () 41leftrightharpoons () 46leftrightharpoonsfill 60leftrightharpoonupdown (⥋)

46Leftrightline (Ocirc) 32leftrightline (ETH) 32leftrightsquigarrow (uacute) 42leftrightsquigarrow () 41leftrightsquigarrow () 44leftrsquigarrow () 44Leftscissors (S) 71leftslice (2) 21leftslice (⪦) 32leftspoon (⟜) 47leftsquigarrow (oslash) 42leftsquigarrow (f) 42leftt (n) 16lefttherefore () 23 61leftthreetimes ($) 63leftthreetimes (h) 21leftthreetimes (⋋) 23leftthumbsdown (D) 72leftthumbsup (U) 72lefttorightarrow (uuml) 42Lefttorque (amp) 70leftturn () 78leftVdash (ecirc) 32leftvdash (⊣) 32

leftwave (

ETH

ETH

ETH

ETH

) 55

leftY () 23legal symbols 8 18 102legm (6) 11legr (E) 11length (q) 16Leo (auml) 68leo () 68leq (curren) 38leq (le) 37 38leq (le) 39leqclosed (⊴) 39 40

119

leqdot (t) 39leqq (reg) 38leqq (5) 37leqq (≦) 39leqslant (6) 37leqslant (⩽) 39leqslantdot (⩿) 39less (lt) 39less-than signs see inequalitieslessapprox (AElig) 38lessapprox () 37lessapprox (⪅) 39lessclosed (⊲) 39 40lessdot (Igrave) 38lessdot (l) 37lessdot (⋖) 39lesseqgtr (frac14) 38

lesseqgtr (Q) 37

lesseqgtr (⋚) 39lesseqgtrslant (N) 39

lesseqqgtr (frac34) 38

lesseqqgtr (S) 37

lesseqqgtr (⪋) 39

lessgtr (ordm) 38lessgtr (≶) 37lessgtr (≶) 39

lessneqqgtr (ograve) 39

lesssim (Agrave) 38lesssim () 37lesssim (≲) 39Letter () 81Letter (B vs ) 88Letter (B) 69letter-like symbols 51 52letters see alphabets

barred 91non-ASCII 9slashed 92variant Latin 50

levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

LF () 69

lfilet (

7777) 54

lFloor (bb) 55lfloor (b) 53

lfloor (⎢⎢⎢⎢⎢⎢⎣) 54

lg (lg) 49

lgroup (

) 53

lgroup (⎧⎪⎪⎪⎪⎪⎩) 54

LHD () 21lhd (C) 20 21lhd (⊲) 39 40lhdbend (~) 76lhookdownarrow (3) 44lhookleftarrow (2) 44lhooknearrow (4) 44lhooknwarrow (⤣) 44

lhookrightarrow () 44lhooksearrow (⤥) 44lhookswarrow (6) 44lhookuparrow (1) 44Libra (aelig) 68libra (a) 68Lie derivative (L) see alphabets

mathlife-insurance symbols 95lightbulb (A) 98lightbulbmf (file) 96 97lightbulbsty (file) 98 99lightbulb102602gf (file) 97lightbulb10dvi (file) 97lightbulb10mf (file) 96ndash98lightbulb10tfm (file) 98

Lightning (E vs ) 88

Lightning () 80Lightning (E) 69lightning ( ) 42lightning ( vs ) 88lightning () 44lightning () 78lim (lim) 49 99liminf (lim inf) 49 100limits 49limsup (lim sup) 49 100linear implication see multimap

linear logic symbols 20 30 36Lineload (L) 70linguistic symbols 10ndash13

Lisa (

) 85lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 54

llap 93llbracket (~) 53llceil (V) 52llcorner (z) 52llcorner (x) 52

llcorner () 54

llcurly (Icirc) 31Lleftarrow (W) 41Lleftarrow () 44llfloor (T) 52lll (Icirc) 38lll (≪) 37lll (≪ vs Icirc) 88lll (⋘) 39llless see lll

llless (⋘) 39llparenthesis (L) 52

lmoustache (

) 53

lmoustache (⎧⎪⎪⎪⎪⎪⎭) 54

ln (ln) 49lnapprox (Ecirc) 38lnapprox () 37lnapprox (⪉) 39lneq (not) 38lneq () 37lneqq (sup2) 38lneqq () 37lneqq (≨) 39lnot see neg

lnot (not) 63lnsim (Auml) 38lnsim () 37lnsim (≴) 39local ring (O) see alphabets

mathlog (log) 49 99log-like symbols 49 100logical operators

and see wedge

not see neg and sim

or see vee

logof () 30lollipop see multimap

long division 57longdiv (package) 57Longleftarrow (lArr=) 41Longleftarrow (lArrOcirc) 43longleftarrow (larrETH) 43longleftarrow (larrminus) 41Longleftrightarrow (lArrrArr) 41Longleftrightarrow (lArrrArr) 43longleftrightarrow (larrrarr) 43longleftrightarrow (larrrarr) 41Longmapsfrom (lArr=) 42longmapsfrom (larrminus[) 42Longmapsto (=rArr) 42longmapsto (zrarr) 43longmapsto (7minusrarr) 41LongPulseHigh (amp) 67LongPulseLow () 67Longrightarrow (=rArr) 41Longrightarrow (OcircrArr) 43longrightarrow (ETHrarr) 43longrightarrow (minusrarr) 41looparrowdownleft (icirc) 42looparrowdownright (iuml) 42looparrowleft (igrave) 42looparrowleft () 41looparrowleft () 43looparrowright (iacute) 42looparrowright () 41looparrowright () 43Loosebearing ($) 70lor see vee

LowerDiamond (o) 75lowering see textlowering

lozenge (diams) 62 63lozenge (loz) 74Lparen (() 65lrcorner () 52lrcorner (y) 52

120

lrcorner () 54

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 54

lsemantic see ldbrack

Lsh (egrave) 42Lsh () 41Lsh () 43Lsteel (trade) 70ltimes () 22ltimes (n) 21ltimes (⋉) 23ltriple 55Luecking Dan 93lVert () 53lVert (||) 55lvert (|) 53lvertneqq (acute) 38lvertneqq () 37lvertneqq (≨) 39

lwave (

ETH

ETH

ETH

ETH

) 55

lWavy (_______

) 54

lwavy (^^^) 54

lz (1) 11

MM 9M (

macr) 82

m 9m (

macr) 82

ma ( times) 82macron see accentsmacron (a) 16

Maggie ( ) 85

magical signs 85majuscules 49makeatletter 94makeatother 94MALE () 70Male (|) 70male () 70MaleMale (ƒ) 70maltese (z) 8maltese () 63manboldkidney () 79manconcentriccircles ($) 79manconcentricdiamond () 79mancone () 79mancube () 79manerrarrow (y) 79manfilledquartercircle () 79manfnt (package) 76 79 104 105manhpennib () 79manimpossiblecube () 79mankidney () 79manlhpenkidney () 79

manpenkidney () 79

manquadrifolium (amp) 79manquartercircle ( ) 79

manrotatedquadrifolium () 79

manrotatedquartercircle () 79

manstar () 79mantiltpennib () 79mantriangledown (7) 79mantriangleright (x) 79mantriangleup (6) 79manvpennib () 79Mappedfromchar () 48mappedfromchar () 48Mapsfrom (lArr) 42mapsfrom (larr[) 42Mapsfromchar (ucirc) 49Mapsfromchar () 48mapsfromchar (szlig) 49mapsfromchar ([) 48Mapsto (rArr) 42mapsto (7rarr) 41mapsto (↦) 44Mapstochar (uacute) 49Mapstochar () 48mapstochar (THORN) 49

Marge (

) 85markera (x) 82markerb (y) 82married see textmarried

Mars (D) 68Mars (Auml) 68mars () 68MartinVogel (yuml) 80marvosym (package) 17 62 64

68ndash71 76 79 80 88matbbol (package) 65mate (m) 82material biconditional

see leftrightarrow andequiv

material conditional seerightarrow and supset

material equivalence see leftrightarrow andequiv

material implication seerightarrow and supset

math alphabets 65math-text 20mathabx (package) 22 24 26

30ndash32 36ndash38 40 42 43 4951ndash54 56 58 62 63 68 7687 88 104 105 107

mathaccent 91mathbb 65mathbbm 65

mathbbmss 65mathbbmtt 65mathbbol (package) 65mathbf 100mathbin 99mathbold 100mathcal (euscript package option)

65mathcal 65mathcent (cent) 51mathchoice 92 93mathclose 99mathcomp (package) 62mathdesign (package) 17 23 29

51 55 64 104mathdollar ($) 20mathdots (package) 56 61 62

94 104 105mathds 65mathellipsis ( ) 20mathematical symbols 20ndash66mathfrak 65mathit 65mathnormal 65mathop 99mathopen 99mathord 99mathpalette 93mathparagraph (para) 20mathpunct 99mathpzc 65mathrel 90 99mathring ( ) 56 57mathrm 65mathrsfs (package) 65 104mathscr (euscript package option)

65mathscr 65mathsection (sect) 20mathsterling (pound) 20 51mathtools (package) 34 58 59

104 105mathunderscore ( ) 20max (max) 49Maxwell-Stefan diffusion coeffi-

cient seeDH

maya 62Mb ( ˘) 82mb ( ˘) 82Mbb ( ˘ ) 82mBb ( ˘ ) 82mbB ( ˘ ) 82mbb ( ˘ ) 82mbboard (package) 65 104mbbx ( ˘ macr

) 82mbox 93measuredangle (gt) 63measuredangle (]) 63measuredangle (∡) 63mechanical scaling 96 98medbackslash (∖) 23medbullet () 21

121

medcirc () 21medcircle () 23meddiamond () 24medlozenge (loz) 74medslash (∕) 23medsquare (◻) 24medstar () 24medstarofdavid () 74medtriangledown () 24 40medtriangleleft (◁) 24 40medtriangleright (▷) 24 40medtriangleup () 24 40medvert (∣) 23medvertdot () 23Mercury (A) 68Mercury (Acirc) 68mercury () 68merge () 21METAFONT 66 96 97 99METAFONTbook symbols 79metre (package) 16 56 82 104

105metre 82metrical symbols 82mho (f) 62 63micro see textmu

micro (micro) 67

Microsoftreg Windowsreg 103mid (|) 30 54middle 53midtilde () 16millesimal sign see

textperthousand

min (min) 49 99minim see musical symbolsminus see textminus

minus (minus) 23minusdot () 23minushookdown (not) 63minushookup (⨼) 63minuso () 21 91minutes angular see prime

miscellaneous symbols 62ndash6477ndash86

ldquoMissing $ insertedrdquo 20Mmappedfromchar () 48mmappedfromchar () 48Mmapstochar () 48mmapstochar () 48MnSymbol (package) 23 24 29

32 33 37 39 40 43ndash48 5051 54 56ndash58 61 63 64 74104 105

Mobilefone (H) 69mod 49models (|=) 30 90models (⊧) 33moduli space see alphabets

mathmonetary symbols 17 65moo () 21Moon (K) 68

Moon (Aacute) 68morepawns (S) 82moreroom (U) 82Mountain () 81mouse see ComputerMouse

MoveDown (raquo) 79moverlay 94MoveUp (ordm) 79mp (∓) 20mp (∓) 23mu (micro) 49multimap (() 30 31multimap (⊸) 47multimapboth () 31multimapbothvert () 31multimapdot () 31multimapdotboth () 31multimapdotbothA () 31multimapdotbothAvert () 31multimapdotbothB () 31multimapdotbothBvert () 31multimapdotbothvert () 31multimapdotinv () 31multimapinv () 31multiple accents per character 94Mundus (m) 80Museum of Icelandic Sorcery and

Witchcraft 86musical symbols 19 62 63 78

79musixtex (package) 79muup (micro) 50MVAt () 80MVEight (8) 62MVFive (5) 62MVFour (4) 62MVNine (9) 62MVOne (1) 62MVRightarrow () 80MVSeven (7) 62MVSix (6) 62MVThree (3) 62MVTwo (2) 62MVZero (0) 62

Nnabla (nabla) 62nabla (nabla) 63NAK () 69napprox () 32napprox (≉) 33napproxeq (6) 31napproxeq () 33nasymp (-) 31nasymp (≭) 48nath (package) 52 55 104natural () 62 78natural () 63natural numbers (N) see

alphabets mathnavigation symbols 79nbackapprox () 33nbackapproxeq () 33

nbackcong () 33nbackeqsim () 33nbacksim () 31nbacksim () 33nbacksimeq (+) 31nbacksimeq () 33nbacktriplesim () 33NBSP ( ) 69nBumpeq ()) 31nBumpeq () 33nbumpeq (() 31nbumpeq () 33ncirceq (sup3) 33ncirclearrowleft (ugrave) 46ncirclearrowright (yacute) 46nclosedequal (eacute) 33ncong () 32

ncong () 30

ncong (≇) 33ncurlyeqprec (cedil) 32ncurlyeqprec (ograve) 33ncurlyeqsucc (sup1) 32ncurlyeqsucc (oacute) 33ncurvearrowdownup (Euml) 44ncurvearrowleft (Acirc) 46ncurvearrowleftright (Egrave) 44ncurvearrownesw (Igrave) 44ncurvearrownwse (Iacute) 44ncurvearrowright (cedil) 46ncurvearrowrightleft (Ecirc) 44ncurvearrowsenw (Iuml) 44ncurvearrowswne (Icirc) 44ncurvearrowupdown (Eacute) 44ndasharrow (`) 46ndasheddownarrow (c) 44ndashedleftarrow (b) 44ndashednearrow (d) 45ndashednwarrow (e) 45ndashedrightarrow (`) 45ndashedsearrow (g) 45ndashedswarrow (f) 45ndasheduparrow (a) 45ndashleftarrow (b) 46ndashrightarrow (`) 46nDashV (+) 32nDashv (+) 32ndashV () 32ndashv () 32ndashv (Uacute) 34ndashVv () 32

nddtstile ( ) 35

ndiagdown (Oacute) 34ndiagup (Ograve) 34ndivides (∤) 34nDoteq () 33ndoteq () 33ndoublefrown () 48ndoublefrowneq () 48ndoublesmile () 48ndoublesmileeq () 48nDownarrow () 45ndownarrow () 45

122

ndownarrowtail () 45ndowndownarrows () 45ndownfilledspoon (s) 47ndownfootline () 33ndownfree (⫝̸) 33ndownharpoonccw (C) 46ndownharpooncw (K) 46ndownlsquigarrow (pound) 45ndownmapsto (+) 45ndownModels (oacute) 33ndownmodels (atilde) 33ndownpitchfork () 47ndownrsquigarrow (laquo) 45ndownspoon (k) 47ndownuparrows () 45ndownupharpoons (]) 46ndownVdash (euml) 33ndownvdash (Ucirc) 33

ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq

ne (ne) 34Nearrow (t) 42Nearrow () 43nearrow (Otilde) 42nearrow () 41 93 94nearrow () 43nearrowtail ($) 43nefilledspoon (t) 47nefootline (|) 32nefree () 32neg (not) 62neg (not) 63negation see neg and sim

neharpoonccw (D) 46neharpooncw (L) 46nelsquigarrow (curren) 43nemapsto () 43neModels (ocirc) 32nemodels (auml) 32nenearrows () 43nepitchfork () 47Neptune (H) 68Neptune (Egrave) 68neptune ([) 68neq () 32neq () 37neq (ne) 34neqbump () 33neqcirc (sup2) 33neqdot () 33neqfrown () 48neqsim () 33neqslantgtr (sup1) 38neqslantgtr (ntilde) 39neqslantless (cedil) 38neqslantless (eth) 39neqsmile () 48nequal (ne) 33nequalclosed (ecirc) 33

nequiv () 31nequiv (≢) 33nequivclosed (euml) 33nersquigarrow (not) 43nespoon (l) 47Neswarrow () 43neswarrow () 93 94neswarrow (⤡) 43neswarrows () 43neswbipropto () 23neswcrossing () 33neswharpoonnwse (R) 46neswharpoons (Z) 46neswharpoonsenw (V) 46Neswline (Ouml) 32neswline (Ograve) 32Neutral () 70neVdash (igrave) 32nevdash (Uuml) 32newextarrow 60newmoon (N) 68newmoon ( ) 68newtie (a) 13nexists (E) 51nexists () 51nexists (∄) 51nfallingdotseq () 33nfrown () 48nfrowneq () 48nfrowneqsmile () 48nfrownsmile () 48nfrownsmileeq (iexcl) 48NG (Ŋ) 9ng (ŋ) 9ngeq (sect) 38

ngeq () 37 38

ngeq (≱) 39ngeqclosed (⋭) 39 40ngeqdot (iacute) 39ngeqq (plusmn) 38

ngeqq () 37

ngeqq (iquest) 39

ngeqslant () 37

ngeqslant (≱) 39ngeqslantdot (iuml) 39ngets (↚) 46ngg (4) 38ngg (Eacute) 39nggg (Euml) 39ngtr (pound) 38ngtr (≯) 37ngtr (≯) 39ngtrapprox (Eacute) 38ngtrapprox () 38ngtrclosed (⋫) 39 40ngtrdot (euml) 39

ngtreqless (Atilde) 39

ngtreqlessslant (Ccedil) 39

ngtreqqless (Aring) 39

ngtrless (amp) 38

ngtrless (≹) 39

ngtrsim (Atilde) 38ngtrsim () 38nhateq (micro) 33nhookleftarrow () 46nhookrightarrow (0) 46ni (3) 51 92ni (ni) 51nialpha () 12nibar see ownsbar

nibeta () 12

NibLeft () 72

NibRight () 72nibs 72

NibSolidLeft ( ) 72

NibSolidRight () 72nicefrac (package) 64 104 105nichi ([) 12niepsilon () 12nigamma () 12niiota ()) 12nilambda (2) 12nin (notin) 51niomega (gt) 12niphi (C) 12niplus (B) 30nisigma (O) 12nitheta (S) 12niupsilon (V) 12niv ( ) 52nj (7) 12nlcirclearrowdown (yuml) 45nlcirclearrowleft (thorn) 45nlcirclearrowright (uuml) 45nlcirclearrowup (yacute) 45nlcurvearrowdown (raquo) 45nlcurvearrowleft (ordm) 45nlcurvearrowne (frac14) 45nlcurvearrownw (frac12) 45nlcurvearrowright (cedil) 45nlcurvearrowse (iquest) 45nlcurvearrowsw (frac34) 45nlcurvearrowup (sup1) 45nleadsto ( ) 46nLeftarrow (ouml) 42nLeftarrow () 41nLeftarrow () 45nleftarrow (Uacute) 42nleftarrow (8) 41nleftarrow (↚) 45nleftarrowtail () 45nleftfilledspoon (r) 47nleftfootline (z) 33nleftfree () 33nleftharpoonccw (B) 46nleftharpooncw (J) 46nleftleftarrows () 45nleftlsquigarrow (cent) 45nleftmapsto () 45nleftModels (ograve) 33nleftmodels (acirc) 33nleftpitchfork () 47nLeftrightarrow (oslash) 42

123

nLeftrightarrow (lt) 41nLeftrightarrow (⇎) 45nleftrightarrow (Uuml) 42nleftrightarrow (=) 20 41nleftrightarrow (↮) 45nleftrightarrows () 45nleftrightharpoondownup (T)

46nleftrightharpoons () 46nleftrightharpoonupdown (P)

46nLeftrightline (Ocirc) 33nleftrightline (ETH) 33nleftrightsquigarrow (deg) 46nleftrsquigarrow (ordf) 45nleftspoon (j) 47nleftVdash (ecirc) 33nleftvdash (Uacute) 33nleq (brvbar) 38

nleq () 37 38

nleq (≰) 39nleqclosed (⋬) 39 40nleqdot (igrave) 39nleqq (deg) 38

nleqq () 37

nleqq (frac34) 39

nleqslant () 37

nleqslant (≰) 39nleqslantdot (icirc) 39nless (cent) 38nless (≮) 37nless (≮) 39nlessapprox (Egrave) 38nlessapprox () 38nlessclosed (⋪) 39 40nlessdot (ecirc) 39

nlesseqgtr (Acirc) 39

nlesseqgtrslant (AElig) 39

nlesseqqgtr (Auml) 39

nlessgtr () 38

nlessgtr (≸) 39

nlesssim (Acirc) 38nlesssim ( ) 38nlhookdownarrow (3) 45nlhookleftarrow (2) 45nlhooknearrow (4) 45nlhooknwarrow (5) 44nlhookrightarrow (0) 44nlhooksearrow (7) 44nlhookswarrow (6) 44nlhookuparrow (1) 44nll (3) 38nll (Egrave) 39nLleftarrow (otilde) 44nlll (Ecirc) 39nmapsto (() 46nmid (-) 30nmid (∤) 34nmodels (⊭) 34nmultimap (h) 47

nndtstile ( ) 35nNearrow () 44nnearrow (1) 42nnearrow () 44nnearrowtail ($) 44nnefilledspoon (t) 47nnefootline (|) 33nnefree () 33nneharpoonccw (D) 46nneharpooncw (L) 46nnelsquigarrow (curren) 44nnemapsto () 45nneModels (ocirc) 33nnemodels (auml) 33nnenearrows () 45nnepitchfork () 47nnersquigarrow (not) 45nnespoon (l) 47nNeswarrow () 45nneswarrow () 45nneswarrows () 45nneswharpoonnwse (R) 46nneswharpoons (Z) 46nneswharpoonsenw (V) 46nNeswline (Ouml) 33nneswline (Ograve) 33nneVdash (igrave) 33nnevdash (Uuml) 33

nnststile ( ) 35

nntstile ( ) 34

nnttstile ( ) 34nNwarrow (13) 45nnwarrow (0) 42nnwarrow () 45nnwarrowtail () 45nnwfilledspoon (u) 47nnwfootline () 33nnwfree () 33nnwharpoonccw (E) 46nnwharpooncw (M) 46nnwlsquigarrow (yen) 45nnwmapsto (-) 45nnwModels (otilde) 33nnwmodels (aring) 33nnwnwarrows () 45nnwpitchfork () 47nnwrsquigarrow (shy) 45nNwsearrow () 45nnwsearrow () 45nnwsearrows () 45nnwseharpoonnesw (S) 46nnwseharpoons (_) 46nnwseharpoonswne (W) 46nNwseline (times) 33nnwseline (Oacute) 33nnwspoon (m) 47nnwVdash (iacute) 33nnwvdash (Yacute) 33NoBleech (Igrave) 80NoChemicalCleaning (uml) 80nointegrals (wasysym package op-

tion) 25

NoIroning (sup2) 80non-commutative division 60nonbreaking space 69norm see lVert and rVert

NoSun () 80not see neg

not 32 92not equal (= vs =) 32notasymp () 32notbackslash (minus) 68notbot (M) 51notdivides () 32notequiv () 32notin (R) 51notin (lt) 51notin (6isin) 51notin (notin) 51notni (=) 51notowner (S) 51notowns see notowner and

notni

notperp (M) 32notslash (minus) 68notsmallin () 51notsmallowns () 51nottop (L) 51NoTumbler () 80novelty (N) 82nowns (∌) 51nparallel (∦) 30nparallel (∦) 34nperp (Ugrave) 34npitchfork () 47nplus (`) 21nprec (cent) 32nprec (⊀) 30nprec (⊀) 33nprecapprox (Egrave) 32nprecapprox (7) 31nprecapprox (egrave) 33npreccurlyeq (brvbar) 32npreccurlyeq ($) 31npreccurlyeq (⋠) 33npreceq (ordf) 32

npreceq () 30

npreceq (acirc) 33npreceqq (9) 31nprecsim (Acirc) 32nprecsim () 31nprecsim (aelig) 33nrcirclearrowdown (ucirc) 45nrcirclearrowleft (uacute) 45nrcirclearrowright (oslash) 45nrcirclearrowup (ugrave) 45nrcurvearrowdown (Atilde) 45nrcurvearrowleft (Acirc) 45nrcurvearrowne (Auml) 45nrcurvearrownw (Aring) 45nrcurvearrowright (Agrave) 45nrcurvearrowse (Ccedil) 45nrcurvearrowsw (AElig) 45nrcurvearrowup (Aacute) 45

124

nRelbar (Ocirc) 34nrelbar (ETH) 34nrestriction (I) 46nrhookdownarrow () 45nrhookleftarrow () 45nrhooknearrow (lt) 45nrhooknwarrow (=) 45nrhookrightarrow (8) 45nrhooksearrow () 45nrhookswarrow (gt) 45nrhookuparrow (9) 45nRightarrow (divide) 42nRightarrow () 41nRightarrow (⇏) 45nrightarrow (Ucirc) 42nrightarrow (9) 41nrightarrow (↛) 45nrightarrowtail ( ) 45nrightfilledspoon (p) 47nrightfootline (x) 33nrightfree () 33nrightharpoonccw () 46nrightharpooncw (H) 46nrightleftarrows () 44nrightleftharpoons (X) 46nrightlsquigarrow ( ) 44nrightmapsto (() 44nrightModels (⊯) 33nrightmodels (⊭) 33nrightpitchfork () 47nrightrightarrows () 44nrightrsquigarrow (uml) 44nrightspoon (h) 47nrightsquigarrow ( ) 46nrightVdash (⊮) 33nrightvdash (⊬) 33nrisingdotseq () 33nRrightarrow (ocirc) 44

nsdtstile ( ) 34nSearrow () 44nsearrow () 44nsearrowtail () 44nsefilledspoon (w) 47nsefootline () 33nsefree () 33nseharpoonccw (G) 46nseharpooncw (O) 46nselsquigarrow (sect) 44nsemapsto () 45nseModels (divide) 33nsemodels (ccedil) 33nsenwarrows () 45nsenwharpoons ([) 46nsepitchfork () 47nsersquigarrow (macr) 45nsesearrows () 45nsespoon (o) 47nseVdash (iuml) 33nsevdash (szlig) 33nshortmid () 30nshortmid (∤) 33nshortparallel () 30

nshortparallel (∦) 33nsim () 32nsim () 30nsim (≁) 33nsimeq () 32nsimeq () 31nsimeq (≄) 33nsmile () 48nsmileeq () 48nsmileeqfrown () 48nsmilefrown (≭) 48nsmilefrowneq ( ) 48nsqdoublefrown (yen) 48nsqdoublefrowneq (macr) 48nsqdoublesmile (curren) 48nsqdoublesmileeq (reg) 48nsqeqfrown (shy) 48nsqeqsmile (not) 48nsqfrown (pound) 48nsqfrowneq (laquo) 48nsqfrowneqsmile (plusmn) 48nsqfrownsmile (copy) 48nsqsmile (cent) 48nsqsmileeq (ordf) 48nsqsmileeqfrown (deg) 48nsqsmilefrown (uml) 48nSqsubset (Ouml) 37nsqSubset () 37nsqsubset () 37nsqsubset (a) 36nsqsubset (ETH) 37nsqsubseteq () 37nsqsubseteq () 36nsqsubseteq (⋢) 37nsqsubseteqq () 37nsqsubseteqq (Ocirc) 37nSqsupset (times) 37nsqSupset () 37nsqsupset () 37nsqsupset (b) 36nsqsupset (Ntilde) 37nsqsupseteq () 37nsqsupseteq (A) 36nsqsupseteq (⋣) 37nsqsupseteqq () 37nsqsupseteqq (Otilde) 37nsqtriplefrown (sect) 48nsqtriplesmile (brvbar) 48nsquigarrowdownup (sup3) 45nsquigarrowleftright (deg) 45nsquigarrownesw (acute) 45nsquigarrownwse (micro) 45nsquigarrowrightleft (sup2) 45nsquigarrowsenw (middot) 45nsquigarrowswne (para) 45nsquigarrowupdown (plusmn) 45

nsststile ( ) 34

nststile ( ) 34

nsttstile ( ) 34nSubset () 37nSubset (gt) 36nSubset (THORN) 37

nsubset () 37nsubset (nsub) 37nsubseteq () 37

nsubseteq () 36

nsubseteq (⊈) 37nsubseteqq () 37nsubseteqq () 36nsubseteqq (Uuml) 37nsucc (pound) 32nsucc () 30nsucc (⊁) 33nsuccapprox (Eacute) 32nsuccapprox (8) 31nsuccapprox (eacute) 33nsucccurlyeq (sect) 32nsucccurlyeq () 31nsucccurlyeq (⋡) 33nsucceq (laquo) 32

nsucceq () 30

nsucceq (atilde) 33nsucceqq () 31nsuccsim (Atilde) 32nsuccsim () 31nsuccsim (ccedil) 33nSupset () 37nSupset () 36nSupset (szlig) 37nsupset () 37nsupset (⊅) 37nsupseteq () 37

nsupseteq (+) 36

nsupseteq (⊉) 37nsupseteqq () 37nsupseteqq () 36nsupseteqq (Yacute) 37nSwarrow () 45nswarrow () 45nswarrowtail (amp) 45nswfilledspoon (v) 47nswfootline (~) 33nswfree () 33nswharpoonccw (F) 46nswharpooncw (N) 46nswlsquigarrow (brvbar) 45nswmapsto () 45nswModels (ouml) 33nswmodels (aelig) 33nswnearrows () 45nswneharpoons (^) 46nswpitchfork () 47nswrsquigarrow (reg) 45nswspoon (n) 47nswswarrows () 45nswVdash (icirc) 33nswvdash (THORN) 33

ntdtstile ( ) 34

ntheorem (package) 62nthickapprox (5) 31nto (↛) 46ntriangleeq (acute) 40ntriangleleft () 40

125

ntriangleleft (6) 39ntriangleleft (⋪) 39 40ntrianglelefteq () 40

ntrianglelefteq (5) 39

ntrianglelefteq (⋬) 39 40ntrianglelefteqslant (R) 40ntriangleright () 40ntriangleright (7) 39ntriangleright (⋫) 39 40ntrianglerighteq () 40

ntrianglerighteq (4) 39

ntrianglerighteq (⋭) 39 40ntrianglerighteqslant (S) 40ntriplefrown () 48ntriplesim (~) 33ntriplesmile () 48

ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35

ntwoheaddownarrow () 45ntwoheadleftarrow (h) 31ntwoheadleftarrow () 45ntwoheadnearrow () 45ntwoheadnwarrow () 45ntwoheadrightarrow (g) 31ntwoheadrightarrow () 45ntwoheadsearrow () 45ntwoheadswarrow () 45ntwoheaduparrow () 45nu (ν) 49nuclear power plant see SNPP

NUL () 69null set 62 63number see textnumero

number sets see alphabets mathnumbers see digits

circled 73 76NumLock ( Num ) 69

nUparrow () 45nuparrow () 45nuparrowtail () 45nUpdownarrow () 45nupdownarrow () 45nupdownarrows () 45nupdownharpoonleftright (Q)

46nupdownharpoonrightleft (U)

46nupdownharpoons (Y) 46nUpdownline (∦) 33nupdownline (∤) 33nupfilledspoon (q) 47nupfootline (y) 33nupfree () 33nupharpoonccw (A) 46nupharpooncw (I) 46nuplsquigarrow (iexcl) 45nupmapsto ()) 45nupModels (ntilde) 33nupmodels (aacute) 33

nuppitchfork () 47nuprsquigarrow (copy) 45nupspoon (i) 47nupuparrows () 45nupVdash (eacute) 33nupvdash (Ugrave) 33nuup (ν) 50nvargeq (laquo) 38nvarleq (ordf) 38nvarparallel () 31nvarparallelinv () 31nVDash () 32nVDash (3) 30nVDash (⊯) 34nVdash () 32nVdash (1) 31nVdash (⊮) 34nvDash () 32nvDash (2) 30nvDash (⊭) 34nvdash (amp) 32nvdash (0) 30nvdash (⊬) 34nVvash () 32Nwarrow (v) 42Nwarrow () 43nwarrow (Ocirc) 42nwarrow () 41 93nwarrow () 43nwarrowtail () 43nwfilledspoon (u) 47nwfootline () 32nwfree () 32nwharpoonccw (E) 46nwharpooncw (M) 46nwlsquigarrow (yen) 43nwmapsto (-) 43nwModels (otilde) 32nwmodels (aring) 32nwnwarrows () 43nwpitchfork () 47nwrsquigarrow (shy) 43Nwsearrow () 43nwsearrow () 93nwsearrow (⤢) 43nwsearrows () 43nwsebipropto () 23nwsecrossing () 32nwseharpoonnesw (S) 46nwseharpoons (_) 46nwseharpoonswne (W) 46Nwseline (times) 32nwseline (Oacute) 32nwspoon (m) 47nwVdash (iacute) 32nwvdash (Yacute) 32

OO (Oslash) 9o (oslash) 9o (o) 49oast (⊛) 24oasterisk (f) 24

obackslash (n) 24obackslash (⦸) 24obar () 21Obelus ( ) 82obelus ( ) 82Obelus ( middotmiddot ) 82obelus ( middotmiddot ) 82oblong () 21obot (k) 24obslash () 21oc () 20ocirc (e) 24ocirc (⊚) 24ocircle () 21ocoasterisk (g) 24octagon (8) 74Octosteel (lsquo) 70od (a

˚) 15

odiv (c) 24odot (d) 24odot () 20odot (⊙) 24odplus () 24OE (Œ) 9 103oe (œ) 9 103officialeuro (e) 17offinterlineskip 91ogonek see accentsogreaterthan (=) 21ohill ( a) 15ohm see textohm

ohm (Ω) 67

Ohne (a) 79

OHORN (Ơ) 9ohorn (ơ) 9

oiiint ()

) 27

oiiint (

) 29

oiiintclockwise (L

) 27

oiiintctrclockwise (D

) 27

oiint (middot

) 26

oiint (

) 25 27

oiint (sbquo

) 28

oiint (

) 29

oiint (∯) 29

oiintclockwise (H

) 27

oiintctrclockwise (

) 27

oint (para) 26

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27

ointclockwise (ı) 28

ointclockwise () 29

ointctrclockwise (

) 27

ointctrclockwise () 28


old-style digits 18oldstylenums 18oleft (h) 24olessthan (lt) 21

126

Omega (Ω) 49omega (ω) 49omegaup (ω) 50ominus (a) 24ominus () 20ominus (⊖) 24onlymove (F) 82oo ( ) 82oo () 12ooalign 91 92open (z) 16open unit disk (D) see

alphabets mathopenJoin ([) 31openo (=) 12openo (c) 12openo (l) 12opentimes (]) 31operators

binary 20ndash24logical see logical operatorsset see set operatorsunary 20

oplus (`) 24oplus (oplus) 20 90oplus (oplus) 24opposbishops (o) 82opposition (W) 68optical scaling 96options see package optionsor see vee

oright (i) 24

OrnamentDiamondSolid (q) 77orthogonal to see bot

oslash (m) 24oslash () 20oslash (⊘) 24ostar () 24otimes (b) 24otimes (otimes) 20otimes (otimes) 24otop (j) 24otriangle (d) 24 40otriangleup (o) 24ovals 75ovee (gt) 21overarc (a_) 16

overbrace (hkkikkj

) 58

overbrace (copy

) 58

overbrace (︷︸︸︷

) 58


) 57

overbracket ( ) 58

overbracket ( ) 95 96overbridge (

rdquoa) 15

overgroup (hkkkkj

) 58

overgroup (sup3micro

) 58overleftarrow (larrminus) 57

overleftharpoon (ETH) 58overleftrightarrow (larrrarr) 58

overline ( ) 20 57

overlinesegment (zx) 58

overparenthesis (︷︷

) 95 96Overrightarrow (=rArr) 57overrightarrow (package) 57 104overrightarrow (minusrarr) 57

overrightharpoon (ETH) 58overring (x) 16overset 91overt (⦶) 24ovoid (l) 24owedge () 21owns see ni

owns (Q) 51owns (3) 51owns (ni) 51ownsbar (W) 51

PP (para) 8 102p (

˙) 82

p 94package options

a (esvect) 59b (esvect) 59bbgreekl (mathbbol) 65c (esvect) 59crescent (fge) 56d (esvect) 59e (esvect) 59f (esvect) 59g (esvect) 59german (keystroke) 69h (esvect) 59integrals (wasysym) 25mathcal (euscript) 65mathscr (euscript) 65nointegrals (wasysym) 25sans (dsfont) 65varg (txfontspxfonts) 50

packageslongdiv 57accents 56 94 104 105amsbsy 100amsfonts 20 30 36 41 6265

amsmath 7 49 56 91 99amssymb 7 20 30 36 4156 62 65 104 105 107

amstext 92 93ar 67 104arcs 16 104 105arev 64 78 104 105ascii 69 101 104 105bbding 71ndash75 77 88 104105

bbm 65 104bbold 65 104bm 100 104 105braket 53calligra 65 104 105calrsfs 65

cancel 57cclicenses 18 104 105centernot 92chancery 104chemarr 59 104 105chemarrow 47 60 104cmll 20 23 30 36 104dblaccnt 94dictsym 84 104 105dingbat 72 77 88 104 105dsfont 65 104epsdice 81 104 105esint 28 104esvect 59 104eufrak 65eurosym 17 104 105euscript 65 104 105extarrows 60 104 105extpfeil 60 104 105extraipa 15 104fc 9 13fclfont 104feyn 70 104 105fge 47 52 56 62 64 104105

fixmath 100fontenc 7 9 13 103gensymb 67graphics 90graphicx 16 87 90harmony 79 104 105hieroglf 84 104 105holtpolt 60 104ifsym 67 75 80 81 88 90104 105

igo 76 104isoent 103keystroke 69 104 105latexsym 20 30 36 41 6287 104 105

manfnt 76 79 104 105marvosym 17 62 64 68ndash7176 79 80 88

matbbol 65mathabx 22 24 2630ndash32 36ndash38 40 42 43 4951ndash54 56 58 62 63 68 7687 88 104 105 107

mathbbol 65mathcomp 62mathdesign 17 23 29 5155 64 104

mathdots 56 61 62 94 104105

mathrsfs 65 104mathtools 34 58 59 104105

mbboard 65 104metre 16 56 82 104 105MnSymbol 23 24 2932 33 37 39 40 43ndash48 5051 54 56ndash58 61 63 64 74104 105

127

musixtex 79nath 52 55 104nicefrac 64 104 105ntheorem 62overrightarrow 57 104phaistos 83 104 105phonetic 12 15 90 104pifont 9 71ndash75 77 90 104105

polynom 57protosem 83 104 105psnfss 73pxfonts 20 21 27 30 3136 38 41 42 48 50 51 6263 65 87 101

rotating 18 69savesym 87semtrans 13 16 104 105simplewick 96simpsons 85 104skak 82 104 105skull 76 104 105slashed 92staves 85 104stmaryrd 21 25 3036 40 42 48 52 53 88 91104 105

t4phonet 13 16 104 105textcomp 78 13 17ndash19 41 56 64 6778 87 101 103ndash105

timing 67tipa 10 11 13 15 16 90104 105

tipx 11 104 105trfsigns 35 51 60 104trsym 35 104 105turnstile 34 35 104 105txfonts 20 21 27 30 31 3638 41 42 48 50 51 62 6365 87 89 101 104 105

type1cm 87ulsy 24 48 90 104underscore 8undertilde 59 104 105units 64universa 76 80 104 105universal 71 73 76 80 104105

upgreek 50 104 105upquote 101url 101vietnam 104vntex 9 13wasysym 12 17 19ndash21 2530 36 38 41 61ndash63 67 6870 73 74 78 88 104 105

wsuipa 11 15 16 88 90 94104 105

yfonts 65 104 105yhmath 57 59 62 94 104

Pakin Scott 1 104PaperLandscape () 81

PaperPortrait () 81par see invamp

paragraph mark see P

parallel see also varparallel

parallel () 30 54parallel (∥) 33ParallelPort (Ntilde) 69parr (`) 23partial (B) 51partial (part) 51partialslash (C) 51partialvardint (q) 64partialvardlanddownint (⨚) 64partialvardlandupint (⨙) 64partialvardlcircleleftint

(∲) 43partialvardlcircleleftint

(∲) 64partialvardlcirclerightint


(∲) 64partialvardoiint (∯) 64partialvardoint (∮) 64partialvardrcircleleftint

(∳) 43partialvardrcircleleftint

(∳) 64partialvardrcirclerightint


(∳) 64partialvardstrokedint (⨏) 64partialvardsumint (⨋) 64partialvartint (p) 64partialvartlanddownint (⨚) 64partialvartlandupint (⨙) 64partialvartlcircleleftint

(∲) 43partialvartlcircleleftint

(∲) 64partialvartlcirclerightint


(∲) 64partialvartoiint (∯) 64partialvartoint (∮) 64partialvartrcircleleftint

(∳) 43partialvartrcircleleftint

(∳) 64partialvartrcirclerightint


(∳) 64partialvartstrokedint (⨏) 64partialvartsumint (⨋) 64particle-physics symbols 70parts per thousand see

textperthousand

partvoice (andash raquo) 15partvoiceless (andash raquo) 15

passedpawn (r) 82

pawn see chess symbols

Peace () 77

PencilLeft () 72

PencilLeftDown () 72

PencilLeftUp () 72

PencilRight () 72

PencilRightDown () 72

PencilRightUp () 72

pencils 72

pentagon (D) 74

pentagram () 24

people see faces

percent sign see

permil (h) 19

Perp (y) 31

perp (perp) 30 93

perp (perp) 33

perthousand (permil) 67

Pfund (pound) 17

PgDown ( Page darr ) 69

PgUp ( Page uarr ) 69

phaistos (package) 83 104 105

Phaistos disk 83

pharmaceutical prescription seetextrecipe

PHarrow (J) 83

PHbee (h) 83

PHbeehive (X) 83

PHboomerang (R) 83

PHbow (K) 83

PHbullLeg (b) 83

PHcaptive (D) 83

PHcarpentryPlane (S) 83

PHcat (c) 83

PHchild (E) 83

PHclub (M) 83

PHcolumn (W) 83

PHcomb (U) 83

PHdolium (T) 83

PHdove (f) 83

PHeagle (e) 83

PHflute (o) 83

PHgaunlet (H) 83

PHgrater (p) 83

PHhelmet (G) 83

PHhide (a) 83

128

PHhorn (Z) 83Phi (Φ) 49phi (φ) 49phiup (φ) 50

PHlid (Q) 83

PHlily (m) 83

PHmanacles (N) 83

PHmattock (O) 83

Phone () 77phone () 78

PhoneHandset () 77phonetic (package) 12 15 90 104phonetic symbols 10ndash13photon () 67photons 70

PHoxBack (n) 83

PHpapyrus (k) 83

PHpedestrian (A) 83

PHplaneTree (i) 83

PHplumedHead (B) 83

PHram (d) 83

PHrosette (l) 83

PHsaw (P) 83

PHshield (L) 83

PHship (Y) 83

PHsling (V) 83

PHsmallAxe (r) 83

PHstrainer (q) 83

PHtattooedHead (C) 83

PHtiara (I) 83PHtunny (g) 83

PHvine (j) 83

PHwavyBand (s) 83

PHwoman (F) 83physical symbols 67Pi (Π) 49pi (π) 49Pickup (A) 69pifont (package) 9 71ndash75 77 90

104 105pilcrow see P

pipe see textpipe

Pisces (euml) 68pisces (f) 68Pisymbol 90pitchfork (amp) 63pitchfork (t) 30pitchfork (⋔) 47

pitchfork symbols 47piup (π) 50planck ( h) 12

Plane () 77planets 68playing cards see card suitsPlimsoll line 91 see also minuso

Plus () 72plus (+) 23plus-or-minus sign see pm

PlusCenterOpen (() 72pluscirc () 22

PlusOutline (amp) 72plusses 72

PlusThinCenterOpen ()) 72Pluto (I) 68Pluto (Eacute) 68pluto () 68pm (plusmn) 20pm (plusmn) 23pm (

macr) 82

pmb 100pmod 49pod 49pointer () 78pointing finger see fistsPointinghand (Z) 76polishhook (~) 16

polter ( ) 60

polygons 74polynom (package) 57polynomial division 57PostScript 50 66 71 81 90 99PostScript fonts 71 90pounds (pound) 8 102 103power set (P) see alphabets

mathpowerset (weierp) 51Pp ( ˙) 82pp ( ˙ ) 82ppm (

macr) 82

Ppp ( ˙˙) 82

ppp ( ˙˙

) 82Pppp ( ˙

˙) 82

pppp ( ˙˙

) 82Ppppp ( ˙

˙) 82

ppppp ( ˙˙

) 82Pr (Pr) 49prec (≺) 30prec (≺) 32precapprox (AElig) 31precapprox (w) 30precapprox (⪷) 32preccurlyeq (curren) 31preccurlyeq (4) 30preccurlyeq (≼) 32precdot (Igrave) 31preceq () 30preceq (⪯) 32preceqq () 31

precnapprox (Ecirc) 32precnapprox () 30precnapprox (⪹) 33precneq (not) 32precneqq () 31precnsim (Auml) 32precnsim () 30precnsim (⋨) 33precsim (Agrave) 31precsim (-) 30precsim (≾) 32prescription see textrecipe

prime (prime) 62prime (prime) 63Printer (Ograve) 69printerrsquos fist see fistsprobabilistic independence 93prod (

prod) 25

prod (prod) 29projlim (proj lim) 49pronunciation symbols see

phonetic symbolsproof end of 62propto (9) 63propto (prop) 30propto (prop) 33proto-Semitic symbols 83protosem (package) 83 104 105ProvidesPackage 104PrtSc ( PrtSc ) 69

ps ( ) 82Psi (Ψ) 49psi (ψ) 49psiup (ψ) 50psnfss (package) 73Pu (permil ) 79pulse diagram symbols 67PulseHigh ($) 67PulseLow () 67punctuation 9pwedge (U) 12pxfonts (package) 20 21 27 30

31 36 38 41 42 48 50 5162 63 65 87 101

Pxp ( ˙) 82pxp ( ˙ ) 82

QQED 62qside (M) 82Quadrad (]]) 56quadrad (]]) 56Quadras ([[) 56quadras ([[) 56quarter note see musical symbolsquarternote () 78quarternote () 78quaternions (H) see alphabets

mathquaver see musical symbolsqueen see chess symbolsquotedblbase (bdquo) 9 103quotesinglbase (sbquo) 9 103

129

RR ( sim

) 82r (a) 13r ( sim

) 82

Radiation () 81radicals see sqrt and surd

Radioactivity (j) 70

Rain () 80

RainCloud () 80raising see textraising

RaisingEdge ( ) 67Rangle (gt) 65rAngle (〉〉) 55rangle (〉) 20 53

rangle (⟩) 54

ranglebar (s) 54

RArrow ( rarr ) 69

rarrowfill 60rational numbers (Q) see

alphabets mathrationalized Planck constant see

hbar

Rbag (Q) 52rbag (O) 52

rbrace (⎫⎪⎪⎬⎪⎪⎭

) 54Rbrack (]) 65rBrack (]]) 55rc (a) 15rCeil (ee) 55rceil (e) 53

rceil (⎤⎥⎥⎥⎥⎥⎥) 54

rcirclearrowdown (ucirc) 44rcirclearrowleft (⟲) 44rcirclearrowright (⤿) 44rcirclearrowup () 44

rcircleleftint (∳) 29

rcirclerightint (∳) 29rcorners (w) 52rcurvearrowdown (⤹) 44rcurvearrowleft () 44rcurvearrowne (Auml) 44rcurvearrownw (Aring) 44rcurvearrowright (Agrave) 44rcurvearrowse (Ccedil) 44rcurvearrowsw (AElig) 44rcurvearrowup (Aacute) 44rdbrack (w) 54Re (lt) 51real numbers (R) see alphabets

mathrecipe see textrecipe

recorder () 78

Rectangle (u) 75

RectangleBold (v) 75rectangles 75

RectangleThin (t) 75Rectpipe (˜) 70

Rectsteel (rdquo) 70reduced quadrupole moment see

rqm

reflectbox 90registered trademark see

textregistered

relational symbols 30binary 30ndash32 34ndash39 47 48negated binary 30ndash33triangle 39 40

Relbar (=) 48 90Relbar (Ocirc) 33relbar (minus) 48 90relbar (ETH) 33resizebox 87Respondens (sim) 82respondens (sim) 82restoresymbol 87restriction see

upharpoonright

restriction (aelig) 42restriction () 46retracting see textretracting

Return ( larr ) 69

return see carriage return

revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

revD () 12

revddots ( ) 94

reve () 12reveject (f) 12revepsilon () 12 90reverse solidus see

textbackslash

reversed symbols 90reversedvideodbend () 76revglotstop (c) 12Rewind (para) 79RewindToIndex (acute) 79RewindToStart (micro) 79

rfilet (

) 54

rFloor (cc) 55rfloor (c) 53

rfloor (⎥⎥⎥⎥⎥⎥⎦) 54

rgroup (

) 53

rgroup (⎫⎪⎪⎪⎪⎪⎭) 54

RHD () 21rhd (B) 20 21rhd (⊳) 39 40rho (ρ) 49rhookdownarrow () 44rhookleftarrow () 44rhooknearrow (⤤) 44rhooknwarrow (=) 44rhookrightarrow (8) 44rhooksearrow () 44rhookswarrow (⤦) 43rhookuparrow (9) 43

rhoup (ρ) 50right 53 55 87 89rightangle (∟) 64RIGHTarrow () 78Rightarrow (rArr) 20 41Rightarrow (rArr) 43rightarrow (Ntilde) 42rightarrow (rarr) 41rightarrow (rarr) 43rightarrowtail () 41rightarrowtail (↣) 43rightarrowtriangle (_) 42rightbarharpoon (Yacute) 43RIGHTCIRCLE (H) 78RIGHTcircle (H) 78Rightcircle (J) 78

RightDiamond () 75

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

rightfilledspoon (p) 47rightfootline (x) 32rightfree () 32righthalfcap () 23righthalfcup () 23rightharpoonccw () 46rightharpooncw () 46rightharpoondown (atilde) 43rightharpoondown () 41rightharpoonup (aacute) 43rightharpoonup () 41rightleftarrows (Otilde) 42rightleftarrows () 41rightleftarrows () 43rightleftharpoon (aacute) 43rightleftharpoons (eacute) 43rightleftharpoons () 41rightleftharpoons () 41rightleftharpoons () 46rightleftharpoonsfill 60rightlsquigarrow () 43rightmapsto (↦) 43rightModels (⊫) 32rightmodels (⊧) 32rightmoon (L) 68rightmoon () 68rightp (w) 16rightpitchfork () 47rightpointleft (L) 72

rightpointright (N) 72rightpropto () 32rightrightarrows (Ntilde) 42rightrightarrows (rArr) 41rightrightarrows () 43rightrightharpoons (Ugrave) 43rightrsquigarrow (uml) 43Rightscissors (Q) 71rightslice (3) 21rightslice (⪧) 32rightspoon (⊸) 47rightsquigarrow (ugrave) 42rightsquigarrow ( ) 41rightsquigarrow () 44

130

rightt (o) 16righttherefore () 23 61rightthreetimes () 63rightthreetimes (i) 21rightthreetimes (⋌) 23rightthumbsdown (d) 72rightthumbsup (u) 72righttoleftarrow (yacute) 42Righttorque () 70rightturn () 78rightVdash (⊩) 32rightvdash (⊢) 32

rightwave (

ETH

ETH

ETH

ETH

) 55

rightY (() 23ring ( ) 57ring equal to see circeq

ring in equal to see eqcirc

riota () 12rip (O) 76risingdotseq () 31risingdotseq () 30risingdotseq (≓) 32rJoin (Y) 31rlap 75 93

rmoustache (

) 53

rmoustache (⎫⎪⎪⎪⎪⎪⎩) 54

rook see chess symbolsroots see sqrt

rotatebox 16 90rotated symbols 10ndash12 16 90rotating (package) 18 69rotm (m) 12rotOmega () 12rotr (r) 12rotvara (A) 12rotw (w) 12roty (y) 12RoundedLsteel (Ÿ) 70RoundedTsteel () 70RoundedTTsteel () 70Rparen ()) 65rqm ( -I) 92

rrangle (⟫) 54

rrbracket () 53rrceil (W) 52rrfloor (U) 52Rrightarrow (V) 42Rrightarrow () 43rrparenthesis (M) 52RS () 69

rsem (MQQQQQO) 54

rsemantic see rdbrack

Rsh (eacute) 42Rsh () 41Rsh () 43rtimes () 22rtimes (o) 21rtimes (⋊) 23

rtriple 55rVert (||) 55rVert () 53rvert (|) 53

rwave (

ETH

ETH

ETH

ETH

) 55

rWavy (_______

) 54

rwavy (^^^) 54

SS (sect) 8 102safety-related symbols 70Sagittarius (egrave) 68sagittarius (c) 68samebishops (s) 82sans (dsfont package option) 65

satellitedish (I) 77Saturn (F) 68Saturn (AElig) 68saturn (Y) 68savesym (package) 87savesymbol 87Sborder (S) 77scalebox 87scaling

mechanical 96 98optical 96

scd () 12scg () 12schwa () 11schwa (e) 12Schwartz distribution spaces see

alphabets mathsci () 11scientific symbols 67ndash70

ScissorHollowLeft () 71

ScissorHollowRight () 71

ScissorLeft () 71

ScissorLeftBrokenBottom () 71

ScissorLeftBrokenTop () 71

ScissorRight () 71ScissorRightBrokenBottom

() 71

ScissorRightBrokenTop () 71scissors 71scn () 11scoh (˝) 36Scorpio (ccedil) 68scorpio (b) 68scr (J) 11script letters see alphabets mathscripta () 11scriptg () 12scriptscriptstyle 92 93scriptstyle 92 93scriptv (Y) 12Scroll ( Scroll ) 69

scu (W) 12

scy (]) 12

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35

seagull see textseagull

Searrow (u) 42Searrow () 43searrow (times) 42searrow () 41 93searrow () 43searrowtail () 43sec (sec) 49

Sech ( ˇ ldquo) ) 79

SechBL ( ˇ ldquo====

) 79

SechBl ( ˇ ldquo===

) 79

SechBR ( ˇ ldquo====) 79

SechBr ( ˇ ldquo===) 79

second (2) 63seconds angular see second

secstress (i) 16section mark see S

SectioningDiamond () 81see (l) 82sefilledspoon (w) 47sefootline () 32sefree () 32segmented digits 67seharpoonccw (G) 46seharpooncw (O) 46selectfont 7selsquigarrow (sect) 43semantic valuation see

llbracketrrbracketand ldbrackrdbrack

semapsto () 43semibreve see musical symbolssemidirect products 21 22 63semiquaver see musical symbolssemitic transliteration 13 16seModels (divide) 32semodels (ccedil) 32semtrans (package) 13 16 104

105senwarrows () 43senwharpoons ([) 46

SePa ( ) 79separated () 32sepitchfork () 47seppawns (q) 82SerialInterface (Icirc) 69SerialPort (ETH) 69sersquigarrow (macr) 43sesearrows () 43sespoon (o) 47set operators

intersection see cap

union see cup

setminus () 20

131

setminus (∖) 23seVdash (iuml) 32sevdash (szlig) 32SGML 103sha (X) 90sharp (]) 62 78sharp (♯) 63Shift ( Shift uArr ) 69

shift (˜) 20Shilling (iexcl) 17shneg (ˆ) 20shortdownarrow () 42ShortFifty (times) 80ShortForty (Ugrave) 80shortleftarrow () 42shortmid (p) 30shortmid (∣) 23ShortNinetyFive (Ocirc) 80shortparallel (q) 30shortparallel (∥) 32ShortPulseHigh () 67ShortPulseLow () 67shortrightarrow () 42ShortSixty (Ouml) 80ShortThirty (Ucirc) 80shortuparrow () 42showclock 81shpos (acute) 20SI () 69Sigma (Σ) 49sigma (σ) 49sigmaup (σ) 50sim (sim) 30 91 101sim (sim) 32simeq () 30simeq (≃) 32simplewick (package) 96simpsons (package) 85 104Simpsons characters 85sin (sin) 49sincoh (ˇ) 36sinh (sinh) 49

SixFlowerAlternate (O) 74

SixFlowerAltPetal (U) 74

SixFlowerOpenCenter (M) 74

SixFlowerPetalDotted (Q) 74

SixFlowerPetalRemoved (L) 74SixFlowerRemovedOpenPetal

([) 74

SixStar (G) 74

SixteenStarLight (K) 74sixteenth note see musical

symbolssixteenthnote () 78skak (package) 82 104 105skull (package) 76 104 105

skull (A) 76slash () 101slashb () 12slashc () 12slashd () 12

slashdiv () 23slashed (package) 92slashed 92slashed letters 92slashedsty (file) 92slashu (U) 12

Sleet () 80sliding (a) 15

smallbosonloop ( ) 70

SmallCircle (E) 75

SmallCross () 75smalldiamond () 24

SmallDiamondshape (F) 75smallfrown (a) 30smallfrown () 48

SmallHBar () 75smallin () 51smallint (int) 63

SmallLowerDiamond () 75smalllozenge (loz) 74smallowns () 51smallpencil (P) 72smallprod (prod) 23

SmallRightDiamond (O) 75smallsetminus (r) 21smallsetminus (∖) 23smallsmile (`) 30smallsmile () 48

SmallSquare () 75smallsquare (◽) 24smallstar () 24

SmallTriangleDown (C) 75smalltriangledown () 24smalltriangledown () 24 40

SmallTriangleLeft (B) 75smalltriangleleft () 24smalltriangleleft () 24 40

SmallTriangleRight (D) 75smalltriangleright () 24smalltriangleright () 24 40

SmallTriangleUp (A) 75smalltriangleup () 24smalltriangleup () 24 40

SmallVBar () 75smile (^) 30smile () 48smile symbols 48smileeq ( ) 48smileeqfrown (amp) 48smilefrown (≍) 48smilefrowneq (() 48Smiley (copy) 80smiley () 78smiley faces 69 78 80

sndtstile ( ) 35

Snow () 80

SnowCloud () 80

Snowflake (`) 74

SnowflakeChevron (^) 74

SnowflakeChevronBold (_) 74snowflakes 74

SNPP () 85

snststile ( ) 35

sntstile ( ) 35

snttstile ( ) 35SO () 69SOH () 69space

thin 100space visible 8Spacebar ( ) 69

spades (suit) 62ndash64 77spadesuit (spades) 62spadesuit (spades) 63

Sparkle (]) 74

SparkleBold () 74sparkles 74ldquospecialrdquo characters 8SpecialForty (Uacute) 80sphericalangle () 63sphericalangle (^) 63sphericalangle (∢) 63

SpinDown () 75

SpinUp ()) 75spirituslenis (a) 56spirituslenis () 56splitvert (brvbar) 69spoon symbols 47spreadlips (a) 15sqbullet (13) 22sqcap ([) 22sqcap (u) 20sqcap (⊓) 23sqcapdot (E) 23sqcapplus () 21sqcapplus (G) 23sqcup () 22sqcup (t) 20sqcup (⊔) 23sqcupdot (D) 23sqcupplus (|) 21sqcupplus (F) 23sqdoublecap (^) 22sqdoublecup (_) 22sqdoublefrown (-) 48sqdoublefrowneq (7) 48sqdoublesmile () 48sqdoublesmileeq (6) 48sqeqfrown (5) 48sqeqsmile (4) 48sqfrown (+) 48sqfrowneq (3) 48sqfrowneqsmile (9) 48sqfrownsmile (1) 48

sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

132

sqrt (radic

) 57 93sqsmile () 48sqsmileeq (2) 48sqsmileeqfrown (8) 48sqsmilefrown (0) 48Sqsubset (^) 37sqSubset () 37sqsubset () 37sqsubset () 36sqsubset (⊏) 37sqsubseteq () 37sqsubseteq (v) 36sqsubseteq (⊑) 37sqsubseteqq () 37sqsubseteqq () 37sqsubsetneq () 37sqsubsetneq (⋤) 37sqsubsetneqq () 37sqsubsetneqq (ouml) 37Sqsupset (_) 37sqSupset () 37sqsupset () 37sqsupset (A) 36sqsupset (⊐) 37sqsupseteq () 37sqsupseteq (w) 36sqsupseteq (⊒) 37sqsupseteqq () 37sqsupseteqq (]) 37sqsupsetneq () 37sqsupsetneq (⋥) 37sqsupsetneqq () 37sqsupsetneqq (divide) 37sqtriplefrown () 48sqtriplesmile () 48

Square (0) 75

Square ( vs f vs 0) 88Square () 73

Square (f) 75square () 22square () 63square (◻) 24square root see sqrt

hooked see hksqrt

SquareCastShadowBottomRight

(k) 75

SquareCastShadowTopLeft (m) 75

SquareCastShadowTopRight

(l) 75Squaredot (divide) 64squaredots (∷) 23 61Squarepipe (mdash) 70squares 75 76

SquareShadowA () 75

SquareShadowB () 75

SquareShadowBottomRight (h) 75

SquareShadowC () 75

SquareShadowTopLeft (j) 75

SquareShadowTopRight (i) 75

SquareSolid (g) 75

Squaresteel (ldquo) 70

squarewithdots (B) 77

squigarrowdownup (sup3) 43

squigarrowleftright () 43

squigarrownesw (acute) 43

squigarrownwse (micro) 43

squigarrowrightleft (sup2) 43

squigarrowsenw (middot) 43

squigarrowswne (para) 43

squigarrowupdown (plusmn) 43

squplus (]) 22

SS (SS) 9

ss (szlig) 9

ssdtstile ( ) 35

ssearrow () 42

sslash () 21

ssststile ( ) 35

sststile ( ) 35

ssttstile ( ) 35

sswarrow ($) 42

stackrel 20 91 95

standard state 91

star () 20 94

star (⋆) 24

Star of David 73 74

stars 63 73 74

statistical independence 93

staveI () 85

staveII () 85

staveIII () 85

staveIV () 85

staveIX () 85

staveL (1) 85 86

staveLI (2) 85

staveLII (3) 85

staveLIII (4) 85

staveLIV (5) 85

staveLIX () 85

staveLV (6) 85

staveLVI (7) 85

staveLVII (8) 85

staveLVIII (9) 85

staveLX () 85

staveLXI (lt) 85

staveLXII (=) 85

staveLXIII (gt) 86

staveLXIV () 86

staveLXV () 86

staveLXVI (A) 86

staveLXVII (B) 86

staveLXVIII (C) 86

staves 85

staves (package) 85 104

staveV () 85

staveVI () 85

staveVII () 85

staveVIII () 85

staveX () 85

staveXI () 85

staveXII () 85

staveXIII () 85

staveXIV (13) 85

staveXIX () 86

staveXL () 86

staveXLI (() 86

staveXLII ()) 86

staveXLIII () 86

staveXLIV (+) 86

staveXLIX (0) 85

staveXLV () 86

staveXLVI (-) 86

staveXLVII () 85

staveXLVIII () 85

staveXV () 85

staveXVI () 85

staveXVII () 86

staveXVIII () 86

staveXX () 86

staveXXI () 86

staveXXII () 86

staveXXIII () 86

staveXXIV () 85

staveXXIX () 85

staveXXV () 85

staveXXVI () 85

staveXXVII () 85

133

staveXXVIII () 85

staveXXX () 85

staveXXXI () 85

staveXXXII () 85

staveXXXIII ( ) 85

staveXXXIV () 85

staveXXXIX (amp) 85

staveXXXV () 85

staveXXXVI () 85staveXXXVII ($) 85staveXXXVIII () 85

stdtstile ( ) 34

steaming () 64sterling see pounds

stmaryrd (package) 21 25 3036 40 42 48 52 53 88 91104 105

stochastic independence see bot

StoneMan () 81Stopsign () 70

StopWatchEnd () 81

StopWatchStart () 81stress (h) 16strictfi (K) 31strictif (J) 31strictiff (L) 31

strokedint (⨏) 29

StrokeFive () 81

StrokeFour () 81

StrokeOne () 81

StrokeThree () 81

StrokeTwo () 81stst (minus ) 91

stststile ( ) 34

sttstile ( ) 34

stttstile ( ) 34

STX () 69SUB () 69subatomic particles 70subcorner (a

^) 15

subdoublebar (amacr) 15

subdoublevert (a) 15

sublptr (aiexcl) 15

subrptr (aiquest) 15

subscriptsnew symbols used in 92

Subset () 37Subset (b) 36Subset (⋐) 37subset () 37subset (sub) 36subset (sub) 37

subseteq () 37subseteq (sube) 36subseteq (sube) 37subseteqq () 37subseteqq (j) 36subseteqq (⫅) 37subsetneq () 37subsetneq (() 36subsetneq (⊊) 37subsetneqq () 37

subsetneqq ($) 36subsetneqq (⫋) 37subsetplus (D) 36subsetpluseq (F) 36subsets 36 37succ () 30succ (≻) 32succapprox (Ccedil) 31succapprox (v) 30succapprox (⪸) 32succcurlyeq (yen) 31succcurlyeq (lt) 30succcurlyeq (≽) 32succdot (Iacute) 31succeq () 30succeq (⪰) 32succeqq () 31succnapprox (Euml) 32succnapprox () 30succnapprox (⪺) 33succneq (shy) 32succneqq () 31succnsim (Aring) 32succnsim () 30succnsim (⋩) 33succsim (Aacute) 31succsim () 30succsim (≿) 32such that 90 92suchthat (3minusminus) 92sum (

sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 81

SummitSign () 81Sun () 68

Sun (Agrave vs vs ) 88

Sun () 80Sun (Agrave) 68sun () 78

SunCloud () 80

SunshineOpenCircled (T) 77sup (sup) 49superscripts

new symbols used in 92supersets 36 37Supset () 37Supset (c) 36Supset (⋑) 37supset () 37supset (sup) 36

supset (sup) 37supseteq () 37supseteq (supe) 36supseteq (supe) 37supseteqq () 37supseteqq (k) 36supseteqq (⫆) 37supsetneq () 37supsetneq ()) 36supsetneq (⊋) 37supsetneqq () 37

supsetneqq () 36supsetneqq (⫌) 37supsetplus (E) 36supsetpluseq (G) 36surd (

`) 62

SurveySign () 81Swarrow (w) 42Swarrow () 43swarrow (Ouml) 42swarrow () 41 93 94swarrow () 43swarrowtail (amp) 43swfilledspoon (v) 47swfootline (~) 32swfree () 32swharpoonccw (F) 46swharpooncw (N) 46swlsquigarrow (brvbar) 43swmapsto () 43swModels (ouml) 32swmodels (aelig) 32swnearrows () 43swneharpoons (^) 46swpitchfork () 47swrsquigarrow (reg) 43swspoon (n) 47swswarrows () 43swung dash see sim

swVdash (icirc) 32swvdash (THORN) 32syl (a) 15syllabic (j) 16Symbol (font) 50 90symbols

actuarial 95alpine 81APL 68astrological 68astronomical 68biological 70body-text 8ndash19bold 100chess 82clock 81communication 69computer hardware 69contradiction 20 48currency 17 65dangerous bend 76definition 20 95dictionary 10ndash13 84dingbat 71ndash77

134

dot 8 61 62 94electrical 67engineering 67 70extensible 57ndash60 89 94ndash96Feynman diagram 70Frege logic 47 52 62 64frown 48genealogical 78general 78Go stones 76information 76informator 82inverted 10ndash12 16 90keyboard 69Knuthrsquos 76 79laundry 80legal 8 18 102letter-like 51 52life insurance 95linear logic 20 30 36linguistic 10ndash13log-like 49 100magical signs 85mathematical 20ndash66METAFONTbook 79metrical 82miscellaneous 62ndash64 77ndash86monetary 17 65musical 19 62 63 78 79navigation 79non-commutative division 60particle physics 70Phaistos disk 83phonetic 10ndash13physical 67pitchfork 47proto-Semitic 83pulse diagram 67relational 30reversed 90rotated 10ndash12 16 90safety-related 70scientific 67ndash70Simpsons characters 85smile 48spoon 47staves 85subset and superset 36 37technological 67ndash70TEXbook 76 79transliteration 13upside-down 10ndash12 16 90100ndash101

variable-sized 25ndash29 87 89weather 80zodiacal 68

symbolstex (file) 87 104SYN () 69

TT 9T ( a) 16T ( otimes

) 82

t ( a) 13t ( otimes

) 82t4phonet (package) 13 16 104

105Tab ( minusminusrarrminusminusrarr ) 69

tabcolsep 91tacks 30 51taild () 12tailinvr (H) 12taill (0) 12tailn (9) 12tailr (F) 12tails (L) 12tailt (P) 12tailz (_) 12Takt 79talloblong (8) 21tally markers 81tan (tan) 49tanh (tanh) 49

Tape () 77

Taschenuhr () 81Tate-Shafarevich group see shatau (τ) 49Taurus (Q) 68Taurus (aacute) 68taurus (]) 68tauup (τ) 50tccentigrade () 62tcmu (micro) 62tcohm (Ω) 62tcpertenthousand () 62tcperthousand (permil) 62td (a) 15

tddtstile ( ) 34

tdststile ( ) 34

tdtstile ( ) 34

tdttstile ( ) 35

technological symbols 67ndash70Telefon (T) 69

Telephone (() 81Tennent Bob 20

Tent () 81Terminus (otimes) 82terminus (otimes) 82Terminus (oplus) 82terminus (oplus) 82tesh (Q) 12testfontdvi (file) 98testfonttex (file) 97 98TEX 40 61 87 90ndash99 101 106TEXbook The 90ndash95 99

symbols from 76 79text 20 92 93textacutedbl (˝) 17textacutemacron (acutea) 13textacutewedge (acutea) 13textadvancing (affi) 14textaolig () 11textasciiacute (acute) 17 102

textasciibreve (˘) 17textasciicaron (ˇ) 17textasciicircum (ˆ) 8 101

103textasciidieresis (uml) 17 102textasciigrave (`) 17textasciimacron 103textasciimacron (macr) 17 102textasciitilde (˜) 8 101 103textasteriskcentered (lowast) 8

19textbabygamma (Egrave) 10textbackslash () 8 101textbaht (฿) 17textbar (|) 8 100 101textbarb (b) 10textbarc (c) 10textbard (d) 10textbardbl () 19textbardotlessj (eacute) 10textbarg (g) 10textbarglotstop (Uuml) 10textbari (1) 10textbarl (ł) 10textbaro (8) 10textbarrevglotstop (Yacute) 10textbaru (0) 10textbeltl (igrave) 10textbenttailyogh (B) 11textbeta (B) 10textbigcircle () 19textbktailgamma () 11textblank () 19textborn (b) 78textbottomtiebar (alt) 14

textbraceleft () 8textbraceright () 8textbrevemacron (˘a) 14textbrokenbar (brvbar) 19 102textbullet (bull) 8 19 103textbullseye (ograve) 10textcelsius () 67textceltpal ( ) 10textcent (cent) 17 102textcentoldstyle () 17textchi (X) 10textcircled (copy) 13textcircledP () 18textcircumacute (Ża) 14textcircumdot (â) 14textcloseepsilon (Aring) 10textcloseomega (Ntilde) 10textcloserevepsilon (AElig) 10textcolonmonetary (₡) 17textcommatailz (THORN) 10textcomp (package) 7

8 13 17ndash19 41 56 64 6778 87 101 103ndash105

textcopyleft (laquo) 18textcopyright (copy) 8 18 102textcorner (^) 10textcrb (ă) 10

135

textcrd (ą) 10textcrd () 13textcrg (g) 10textcrh (egrave) 10textcrh (sect) 13textcrinvglotstop (Ucirc) 10textcrlambda (ň) 10textcrtwo (2) 10textctc (C) 10textctd (ć) 10textctdctzlig (ćyacute) 10textctesh (š) 10textctinvglotstop (D) 11textctj (J) 10textctjvar (2) 11textctn (ő) 10textctstretchc () 11textctstretchcvar (amp) 11textctt (ť) 10textcttctclig (ťC) 10textctturnt () 11textctyogh (yuml) 10textctz (yacute) 10textcurrency (curren) 17 102textdagger (dagger) 8 19textdaggerdbl (Dagger) 8 19

textdbend (

) 76textdblhyphen (-) 19textdblhyphenchar () 19textdblig ()) 11textdctzlig (dyacute) 10textdegree (deg) 64 102textdied (d) 78textdiscount () 19textdiv (divide) 64textdivorced (c) 78textdollar ($) 8 17textdollaroldstyle () 17textdong (₫) 17textdotacute (secta) 14textdotbreve ( ˙a) 14textdoublebaresh (S) 10textdoublebarpipe () 10textdoublebarpipevar (H) 11textdoublebarslash (= ) 10textdoublegrave (sbquoa) 14textdoublegrave (a) 16textdoublepipe () 10textdoublepipevar (G) 11textdoublevbaraccent (İa) 14textdoublevbaraccent (frac14a) 16textdoublevertline (Ş) 10textdownarrow (darr) 41textdownfullarrow (ˇ) 11textdownstep (Ť) 10textdyoghlig (Atilde) 10textdzlig (dz) 10texteightoldstyle () 18textellipsis ( ) 8textemdash (mdash) 8textendash (ndash) 8textepsilon (E) 10

textepsilon (cent) 13textesh (S) 10textesh (not) 13textestimated () 19texteuro (euro) 17texteuro (euro) 17 103textexclamdown (iexcl) 8textfemale (7) 11textfishhookr (R) 11textfiveoldstyle () 18textfjlig () 13textflorin (ƒ) 17textfouroldstyle () 18textfractionsolidus (frasl) 64textfrak 65textfrbarn (5) 11textfrhookd (rsquo) 11textfrhookdvar (() 11textfrhookt () 11textfrtailgamma (-) 11textg (ě) 11textgamma (G) 11textglobfall (Ů) 11textglobrise (Ű) 11textglotstop (P) 10textglotstopvari (T) 11textglotstopvarii (U) 11textglotstopvariii (V) 11textgoth 65textgravecircum (Ža) 14textgravedbl () 17textgravedot (đa) 14textgravemacron (à) 14textgravemid (Źa) 14textgreater (gt) 8 100 101textgrgamma () 11textguarani () 17texthalflength () 10texthardsign (ż) 10textheng (0) 11texthmlig (4) 11texthooktop () 10texthtb (aacute) 10texthtb ( ) 13texthtbardotlessj (ecirc) 10texthtbardotlessjvar (3) 11texthtc (Aacute) 10texthtc (deg) 13texthtd (acirc) 10texthtd (iexcl) 13texthtg (auml) 10texthth (H) 10texththeng (Ecirc) 10texthtk (Icirc) 10texthtk (uml) 13texthtp (Ograve) 10texthtp (plusmn) 13texthtq (Oacute) 10texthtrtaild (č) 10texthtscg (Eacute) 10texthtt (Ouml) 10texthtt (ordm) 13texthvlig (szlig) 10

textifsym 67textinterrobang () 19textinterrobangdown () 19textinvglotstop (Ucirc) 10textinvomega () 11textinvsca (p) 11textinvscr (K) 10textinvscripta () 11textinvsubbridge (abdquo) 14textiota (Igrave) 10textiota (agrave) 13textlambda (ń) 10textlangle (lang) 56 101textlbrackdbl (〚) 56textleaf (l) 78textleftarrow (larr) 41textlengthmark () 10textless (lt) 8 100 101textlfishhookrlig (I) 11

textlhdbend (~

) 76textlhookfour () 11textlhookp (lt) 11textlhookt (ş) 10textlhti (1) 11textlhtlongi (ę) 10textlhtlongy (ű) 10textlira (₤) 17textlnot (not) 64 102textlonglegr (Ocirc) 10textlooptoprevesh (gt) 11textlowering (afl) 14textlptr (iexcl) 10textlquill (⁅) 56textltailm (M) 10textltailn (ntilde) 10textltailn (copy) 13textltilde (euml) 10textlyoghlig (ETH) 10textmarried (m) 78textmho () 67textmidacute (Ÿa) 14textminus (minus) 64textmu (micro) 67 102textmusicalnote () 19textnaira (₦) 17textnineoldstyle () 18textnrleg (6) 11textnumero () 19textObardotlessj (Iacute) 10textObullseye (9) 11textohm (Ω) 67textOlyoghlig (ŋ) 10textomega (ř) 10textonehalf (frac12) 64 102textoneoldstyle 18textoneoldstyle () 18textonequarter (frac14) 64 102textonesuperior (sup1) 64 102textopenbullet () 19textopencorner (_) 10textopeno (O) 10textopeno (ordf) 13

136

textordfeminine (ordf) 8 19 102textordmasculine (ordm) 8 19

102textovercross (permila) 14textoverw (

mdasha) 14

textpalhook () 10textpalhooklong (ˆ) 11textpalhookvar (˜) 11textparagraph (para) 8 19textperiodcentered (middot) 8 19

102textpertenthousand () 19textperthousand (permil) 19 103textpeso () 17textphi (F) 10textpilcrow (para) 19textpipe (|) 10textpipe (|) 13textpipevar (F) 11textpm (plusmn) 64 102textpmhg 84textpolhook (a) 14textprimstress () 10textproto 83textqplig (=) 11textquestiondown (iquest) 8textquotedbl () 9 100textquotedblleft (ldquo) 8textquotedblright (rdquo) 8textquoteleft (lsquo) 8textquoteright (rsquo) 8textquotesingle () 19textquotestraightbase (sbquo) 19textquotestraightdblbase (bdquo)

19textraiseglotstop (ĳ) 10textraisevibyi (ğ) 10textraising (afi) 14textramshorns (7) 10textrangle (rang) 56 101textrbrackdbl (〛) 56textrecipe () 19 89textrectangle (uml) 11textreferencemark () 19 20textregistered (reg) 8 18 102textretracting (affl) 14textretractingvar (˚) 11textrevapostrophe () 10textreve (9) 10textrevepsilon (3) 10 90

textreversedvideodbend (

) 76

textrevglotstop (Q) 10textrevscl (v) 11textrevscr (z) 11textrevyogh (ź) 10textrhooka ( ) 11textrhooke () 11textrhookepsilon (+) 11textrhookopeno () 11textrhookrevepsilon (Ccedil) 10textrhookschwa (Auml) 11

textrhoticity (~) 11textrightarrow (rarr) 41textringmacron (a) 14textroundcap (ldquoa) 14textrptr (iquest) 11textrquill (⁆) 56textrtaild (atilde) 11textrtaild (eth) 13textrtailhth () 11textrtaill (iacute) 11textrtailn (iuml) 10textrtailr (oacute) 10textrtails (ugrave) 10textrtailt (uacute) 10textrtailt (raquo) 13textrtailz (uuml) 10textrthook ($) 10textrthooklong (acute) 11textsca (Agrave) 10textscaolig (q) 11textscb (agrave) 10textscdelta (r) 11textsce (ď) 10textscf (s) 11textscg (aring) 10textsch (Euml) 10textschwa () 10textschwa (iexcl) 13textsci (I) 10textscj (ĺ) 10textsck (t) 11textscl (Iuml) 10textscm (w) 11textscn (eth) 10textscoelig (Œ) 10textscomega (ś) 10textscp (x) 11textscq (y) 11textscr (ouml) 10textscripta (A) 10textscriptg (g) 10textscriptv (V) 10textscriptv (not) 13textscu (Uacute) 10textscy (Y) 10textseagull (a) 14textsecstress (shy) 10textsection (sect) 8 19textservicemark () 18textsevenoldstyle () 18textsixoldstyle () 18textsoftsign (ž) 10textspleftarrow (˝) 11textsterling (pound) 8 17textstretchc (Acirc) 10textstretchcvar ($) 11textstyle 92 93 99textsubacute (a

rsaquo) 14

textsubarch (aldquo) 14

textsubbar (amacr) 14

textsubbridge (ardquo) 14textsubcircum (a

ˆ) 14

textsubdot (a˙) 14

textsubdoublearrow (˙) 11textsubgrave (a

lsaquo) 14

textsublhalfring (andash) 14textsubplus (aff) 14textsubrhalfring (araquo) 14textsubrightarrow (macr) 11textsubring (a

˚) 14

textsubsquare (alaquo) 14textsubtilde (a

˜) 14

textsubumlaut (auml) 14

textsubw (amdash) 14textsubwedge (a

ˇ) 14

textsuperimposetilde (aamp) 14

textsuperscript 15textsurd (radic) 64textswab 65textsyllabic (a

) 15

texttctclig (tC) 10textteshlig (Ugrave) 10textteshlig () 13texttheta (T) 10textthorn (thorn) 10textthornvari (P) 11textthornvarii (Q) 11textthornvariii (R) 11textthornvariv (S) 11textthreeoldstyle () 18textthreequarters (frac34) 64 102textthreequartersemdash ()

19textthreesuperior (sup3) 64 102texttildedot (ã) 15texttildelow (~) 19 101texttimes (times) 64texttoneletterstem (pound) 10texttoptiebar (gta) 15texttrademark (trade) 8 18 103texttslig (ţ) 10textturna (5) 10textturncelig (ŕ) 10textturnglotstop (E) 11textturnh (4) 10textturnk (ľ) 10textturnlonglegr (Otilde) 10textturnm (W) 10textturnmrleg (icirc) 10textturnr (ocirc) 10textturnrrtail (otilde) 10textturnsck (u) 11textturnscripta (6) 10textturnscu () 11textturnt (Oslash) 10textturnthree (C) 11textturntwo (A) 11textturnv (2) 10textturnw (ucirc) 10textturny (L) 10texttwelveudash () 19texttwooldstyle 18texttwooldstyle () 18texttwosuperior (sup2) 64 102textuncrfemale (8) 11

137

textunderscore ( ) 8textuparrow (uarr) 41textupfullarrow (˘) 11textupsilon (U) 10textupstep (Ţ) 10textvbaraccent (Ĳa) 15textvbaraccent (iquesta) 16textvertline (Š) 10textvibyi (ğ) 11textvibyy (ů) 11textvisiblespace ( ) 8textwon (₩) 17textwynn (szlig) 11textyen (yen) 17 102textyogh (Z) 11textyogh (para) 13textzerooldstyle () 18TH (THORN) 9 102th (thorn) 9 102

Thanh Han Thacutee 94therefore (6) 31therefore (there4) 30 61therefore (there4) 61Thermo 80Theta (Θ) 49theta (θ) 49thetaup (θ) 50thickapprox (asymp) 30thicksim (sim) 30thickvert (~) 54thin space 100

ThinFog () 80thinstar (⋆) 24third (3) 63thirty-second note see musical

symbolsThorn (THORN) 12thorn (B) 12thorn (p) 12thorn (thorn) 12thousandths see

textperthousand

threesim (simsimsim) 91tilde 8 10 11 13 16 19 56 57

59 94 101extensible 57 59vertically centered 101

tilde (˜) 56 94tildel (-) 12time of day 81timelimit (T) 82times (times) 20times (times) 23Times Roman (font) 17 89timing (package) 67tipa (package) 10 11 13 15 16

90 104 105tipx (package) 11 104 105

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35

tnttstile ( ) 35to see rightarrow

ToBottom (frac12) 79tone 11top (gt) 51 92top (⊺) 51topbot (perpgt) 92 94topdoteq () 31torus (T) see alphabets mathToTop (frac14) 79trademark see texttrademark

TransformHoriz () 35transforms 35 60 see also

alphabets math

TransformVert () 35transliteration

semitic 13 16transliteration symbols 13transversality see pitchfork

trfsigns (package) 35 51 60 104triangle (4) 62triangle () 40triangle relations 39 40

TriangleDown (3) 75

TriangleDown (o vs 3) 88

TriangleDown (o) 75triangledown (O) 63triangledown () 40triangleeq (≜) 40

TriangleLeft (2) 75triangleleft () 40triangleleft () 20triangleleft (◁) 40trianglelefteq () 40trianglelefteq (E) 39trianglelefteq (⊴) 39 40trianglelefteqslant (P) 40

triangleq () 20 39triangleq (≜) 40

TriangleRight (4) 75triangleright () 40triangleright () 20triangleright (▷) 40trianglerighteq () 40trianglerighteq (D) 39trianglerighteq (⊵) 39 40trianglerighteqslant (Q) 40triangles 63 75 76

TriangleUp (1) 75

TriangleUp (n vs 1) 88

TriangleUp (n) 75triple 55triplefrown () 48triplesim (≋) 32triplesmile () 48trsym (package) 35 104 105tsbm ( ) 82

tsdtstile ( ) 35tsmb ( ) 82tsmm ( ) 82

tsststile ( ) 35Tsteel (œ) 70

tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 70

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35

TUGboat 57Tumbler () 80turnstile (package) 34 35 104

105TwelweStar (J) 74twoheaddownarrow () 43twoheadleftarrow () 41twoheadleftarrow () 43twoheadnearrow () 44twoheadnwarrow () 44twoheadrightarrow () 41twoheadrightarrow (↠) 44twoheadsearrow () 44twoheadswarrow () 44twoheaduparrow () 44twonotes () 78txfonts (package) 20 21 27 30

31 36 38 41 42 48 50 5162 63 65 87 89 101 104105

type1cm (package) 87Type 1 (font) 99

UU (a

˘) 16

U (frac14a) 13u (a) 13UArrow ( uarr ) 69

UB (lt) 79ubar (u) 12ubulbfd (file) 98 99udesc (u) 12udot () 22udotdot () 23 61udots (⋰) 61udtimes (]) 23

UHORN (Ư) 9uhorn (ư) 9ulcorner (x) 52ulcorner (p) 52

ulcorner () 54

ullcorner (6) 54

ulrcorner () 54

ulsy (package) 24 48 90 104

Umd ( a) 79umlaut see accentsunary operators 20

138

unclear (k) 82underaccent 94underarc (a) 16underarch (a) 15underbrace (loomoon) 58

underbrace (reg) 58

underbrace (︸︷︷︸) 58


underbracket ( ) 58

underbracket ( ) 95 96

underdots (r) 16undergroup (loooon) 58

undergroup (acutepara) 58

underleftarrow (larrminus) 58

underleftrightarrow (larrrarr) 58

underline ( ) 57underlinesegment (zx) 58

underparenthesis (︸︸) 95 96

underrightarrow (minusrarr) 58

underring (y) 16underscore see _

underscore (package) 8underset 91undertilde (package) 59 104 105undertilde (|) 16underwedge () 16union see cup

unit disk (D) see alphabetsmath

unitedpawns (u) 82units (package) 64unity (1) see alphabets mathuniversa (package) 76 80 104

105universal (package) 71 73 76 80

104 105unlhd (E) 20 21unlhd (⊴) 39 40unrhd (D) 20 21unrhd (⊵) 39 40upalpha (α) 50UParrow (K) 78Uparrow (uArr) 41 53Uparrow (uArr) 44uparrow (uarr) 41 53 87uparrow (uarr) 44uparrowtail () 44upbar 15upbeta (β) 50upbracketfill 95upchi (χ) 50Updelta (∆) 50updelta (δ) 50Updownarrow (m) 41 53Updownarrow () 44updownarrow (l) 41 53updownarrow () 44updownarrows (Ouml) 42

updownarrows () 44updownharpoonleftright (Q) 46updownharpoonrightleft (U) 46updownharpoons (ecirc) 43updownharpoons (⥮) 46Updownline (∥) 32updownline (∣) 32upepsilon (ε) 50upeta (η) 50upfilledspoon (q) 47upfootline (y) 32upfree () 32Upgamma (Γ) 50upgamma (γ) 50upgreek (package) 50 104 105upharpoonccw () 46upharpooncw () 46upharpoonleft (auml) 43upharpoonleft () 41upharpoonright (aelig) 43upharpoonright () 41upiota (ι) 50upkappa (κ) 50Uplambda (Λ) 50uplambda (λ) 50uplett 15uplsquigarrow (iexcl) 44uplus (Z) 22uplus (]) 20uplus (⊎) 23upmapsto () 44upModels (ntilde) 32upmodels (aacute) 32upmu (micro) 50upnu (ν) 50Upomega (Ω) 50upomega (ω) 50upp (t) 16upparenthfill 95Upphi (Φ) 50upphi (φ) 50Uppi (Π) 50uppi (π) 50uppitchfork (⋔) 47uppropto () 32Uppsi (Ψ) 50uppsi (ψ) 50upquote (package) 101uprho (ρ) 50upright Greek letters 50uprsquigarrow (copy) 44upside-down symbols 100ndash101upside-down symbols 10ndash12 16

90Upsigma (Σ) 50upsigma (σ) 50Upsilon (Υ) 49upsilon (υ) 49upsilonup (υ) 50upslice (Agrave) 24upspoon (⫯) 47upt (l) 16uptau (τ) 50

uptherefore (there4) 23 61Uptheta (Θ) 50uptheta (θ) 50uptodownarrow (thorn) 42upuparrows (Ograve) 42upuparrows () 41upuparrows () 44upupharpoons (Uacute) 43Upupsilon (Υ) 50upupsilon (υ) 50upvarepsilon (ε) 50upvarphi (ϕ) 50upvarpi (ϖ) 50upvarrho (ρ) 50upvarsigma (σ) 50upvartheta (ϑ) 50upVdash () 32upvdash (perp) 32Upxi (Ξ) 50upxi (ξ) 50upY ()) 23upzeta (ζ) 50Uranus (G) 68Uranus (Ccedil) 68uranus (Z) 68urcorner (y) 52urcorner (q) 52

urcorner () 54

url (package) 101US () 69usepackage 7ut (a

˜) 15

utilde (˜) 59

utimes (^) 23utimes ($) 23Utopia (font) 17 29

Vv (a) 13vara (a) 12varangle () 63varbigcirc () 21

VarClock () 81varclub () 64varclubsuit (p) 63varcurlyvee () 21varcurlywedge () 21vardiamond (diams) 64vardiamondsuit (q) 63varEarth (J) 68varepsilon (ε) 49varepsilonup (ε) 50

VarFlag () 81varg (txfontspxfonts package op-

tion) 50varg (1) 50varg (G) 12vargeq (copy) 38varhash () 63varheart (hearts) 64varheartsuit (r) 63

139

varhexagon (9) 74varhexstar (B) 73vari (i) 12variable-sized symbols 25ndash29 87

89VarIceMountain () 81varinjlim (limminusrarr) 49

varint (r

) 25various (R) 82varkappa (κ) 49varleq (uml) 38varliminf (lim) 49

varlimsup (lim) 49varmathbb 65VarMountain () 81varnothing (empty) 20 62 63varnothing (empty) 63varnotin (T) 51varnotowner (U) 51varoast () 21varobar () 21varobslash () 21varocircle () 21varodot () 21varogreaterthan (5) 21

varoiiintclockwise (F

) 27

varoiiintctrclockwise (N

)

27varoiint (

) 28

varoiintclockwise (B

) 27

varoiintctrclockwise (J

) 27

varoint (u

) 25

varointclockwise (-

) 27

varointclockwise (ff) 28

varointctrclockwise (+

) 27

varointctrclockwise (fl) 28

varolessthan (4) 21varomega () 12varominus () 21varopeno (C) 12varoplus () 21varoslash () 21varotimes () 21varovee (6) 21varowedge (7) 21varparallel (∥) 31varparallelinv () 31varphi (ϕ) 49varphiup (ϕ) 50varpi ($) 49varpiup ($) 50varprod (

) 27

varprojlim (limlarrminus) 49

varpropto (prop) 30varpropto (prop) 33varQ () 80varrho () 49varrhoup () 50varsigma (ς) 49varsigmaup (ς) 50varspade () 64

varspadesuit (s) 63varsqsubsetneq () 37varsqsubsetneqq () 37varsqsupsetneq () 37varsqsupsetneqq () 37varstar () 22varsubsetneq () 37varsubsetneq ( ) 36varsubsetneq (⊊) 37varsubsetneqq () 37varsubsetneqq (amp) 36varsubsetneqq (⫋) 37

VarSummit () 81varsupsetneq () 37varsupsetneq () 36varsupsetneq (⊋) 37varsupsetneqq () 37varsupsetneqq () 36varsupsetneqq (⫌) 37

VarTaschenuhr () 81vartheta (ϑ) 49varthetaup (ϑ) 50vartimes () 21vartriangle (M) 63vartriangle () 40vartriangleleft () 40vartriangleleft (C) 39vartriangleleft (⊲) 39 40vartriangleright () 40vartriangleright (B) 39vartriangleright (⊳) 39 40varv (3) 50varw (4) 50vary (2) 50

VBar () 75vbipropto () 23vcentcolon () 34vcenter 91vcrossing () 32VDash (() 31VDash (⊫) 33Vdash () 31Vdash (13) 30Vdash (⊩) 33vDash (() 31vDash () 30vDash (⊧) 33vdash (`) 30vdash (⊢) 33vdotdot (∶) 23 61

vdots () 61

vdots (⋮) 61vec () 56vec (~) 56Vectorarrow (p) 64

Vectorarrowhigh (P) 64vee (_) 22vee (or) 20vee (or) 23veebar (Y) 22veebar (Y) 21

veedot () 23veedoublebar ([) 22Venus (B) 68Venus (Atilde) 68venus () 68vernal () 68Vert () 53 54vert (|) 53 54vertbowtie (⧖) 23vertdiv () 23VHF () 67Vier ( ˇ ldquo) 79vietnam (package) 104

Village () 81

vin ( ) 52vinculum see overline

ViPa ( gt ) 79Virgo (aring) 68virgo (`) 68VM (gt) 79vntex (package) 9 13vod (v

˚) 12

voicedh (h) 12vppm (

macr) 82

vpppm (macr

) 82VT () 69vv ( raquo) 59VvDash () 31Vvdash () 31Vvdash () 30Vvdash (⊪) 32vvvert (~) 54

WWashCotton (permil) 80WashSynthetics (Š) 80WashWool (lsaquo) 80wasylozenge (loz) 78wasypropto () 30wasysym (package) 12

17 19ndash21 25 30 36 38 4161ndash63 67 68 70 73 74 7888 104 105

wasytherefore (there4) 61wavy-line delimiters 54 55wbetter (f) 82wdecisive (h) 82weakpt (J) 82

WeakRain () 80WeakRainCloud () 80weather symbols 80

Wecker () 81wedge (^) 22wedge (and) 20wedge (and) 23wedgedot () 23Weierstrass weierp function see wp

Wheelchair (w) 76whistle (a

Ţ) 15

whitestone 76whole note see musical symbols

140

Wick contractions 96widearrow (t) 58widebar (s) 58widecheck (q) 58widehat () 58widehat () 57wideparen (u) 58wideparen (Igrave) 58wideparen (Ucirc) 57

widering (Ucirc) 58

widering (Ucirc) 57widetilde () 58widetilde (˜) 57 59widetriangle (Ecirc) 57wind 80window 80

Windowsreg 103with (amp) 23with (w) 82withattack (A) 82withidea (E) 82withinit (C) 82without (v) 82wn () 20Womanface (thorn) 80won see textwon

wp (weierp) 51wp (weierp) 51wr (o) 20wr (≀) 23wreath (≀) 23wreath product see wr

Writinghand (b) 76wsuipa (package) 11 15 16 88

90 94 104 105wupperhand (c) 82

Xx ( ˙˙) 82XBox (4) 73

Xdvi 90

xhookleftarrow (larrminus) 59

xhookrightarrow (minusrarr) 59

Xi (Ξ) 49

xi (ξ) 49

xiup (ξ) 50

xLeftarrow (lArr=) 59

xleftarrow (larrminus) 59

xleftharpoondown (minus) 59

xleftharpoonup (minus) 59

xLeftrightarrow (lArrrArr) 60


xleftrightarrow (larrrarr) 60


xleftrightharpoons (minusminus) 59

xlongequal (===) 60

xlongequal (===) 60

xLongleftarrow (lArr==) 60

xlongleftarrow (larrminusminus) 60

xLongleftrightarrow (lArr==rArr) 60

xlongleftrightarrow (larrminusminusrarr) 60

xLongrightarrow (==rArr) 60

xlongrightarrow (minusminusrarr) 60

xmapsto ( 7minusrarr) 59


XML 103

xRightarrow (=rArr) 59

xrightarrow (minusrarr) 59

xrightharpoondown (minus) 59

xrightharpoonup (minus) 59

xrightleftharpoons (minusminus) 59


Xs 73 76

XSolid () 73

XSolidBold ($) 73

XSolidBrush () 73

xtwoheadleftarrow (minusminusminus) 60

xtwoheadrightarrow (minusminusminus) 60XY-pic 93

YYdown () 21yen see textyen

yfonts (package) 65 104 105yhmath (package) 57 59 62 94

104Yinyang (Y) 80Yleft () 21yogh (`) 12yogh (x) 12Yright () 21Yup () 21

ZZapf Chancery (font) 65Zapf Dingbats (font) 71 73Zborder (Z) 77zeta (ζ) 49zetaup (ζ) 50Zodiac 68zodiacal symbols 68

Ztransf ( s c) 35

ztransf ( c s) 35zugzwang (D) 82

Zwdr ( ˇ ldquo ) 79

ZwPa ( A ) 79

141

Table 31 wasysym Currency Symbols 17Table 32 eurosym Euro Signs 17Table 33 textcomp Legal Symbols 18Table 34 cclicenses Creative Commons License Icons 18Table 35 textcomp Old-style Numerals 18Table 36 Miscellaneous textcomp Symbols 19Table 37 Miscellaneous wasysym Text-mode Symbols 19

3 Mathematical symbols 20Table 38 Math-Mode Versions of Text Symbols 20Table 39 cmll Unary Operators 20Table 40 Binary Operators 20Table 41 AMS Binary Operators 21Table 42 stmaryrd Binary Operators 21Table 43 wasysym Binary Operators 21Table 44 txfontspxfonts Binary Operators 21Table 45 mathabx Binary Operators 22Table 46 MnSymbol Binary Operators 23Table 47 mathdesign Binary Operators 23Table 48 cmll Binary Operators 23Table 49 ulsy Geometric Binary Operators 24Table 50 mathabx Geometric Binary Operators 24Table 51 MnSymbol Geometric Binary Operators 24Table 52 Variable-sized Math Operators 25Table 53 AMS Variable-sized Math Operators 25Table 54 stmaryrd Variable-sized Math Operators 25Table 55 wasysym Variable-sized Math Operators 25Table 56 mathabx Variable-sized Math Operators 26Table 57 txfontspxfonts Variable-sized Math Operators 27Table 58 esint Variable-sized Math Operators 28Table 59 MnSymbol Variable-sized Math Operators 29Table 60 mathdesign Variable-sized Math Operators 29Table 61 cmll Large Math Operators 30Table 62 Binary Relations 30Table 63 AMS Binary Relations 30Table 64 AMS Negated Binary Relations 30Table 65 stmaryrd Binary Relations 30Table 66 wasysym Binary Relations 30Table 67 txfontspxfonts Binary Relations 31Table 68 txfontspxfonts Negated Binary Relations 31Table 69 mathabx Binary Relations 31Table 70 mathabx Negated Binary Relations 32Table 71 MnSymbol Binary Relations 32Table 72 MnSymbol Negated Binary Relations 33Table 73 mathtools Binary Relations 34Table 74 turnstile Binary Relations 34Table 75 trsym Binary Relations 35Table 76 trfsigns Binary Relations 35Table 77 cmll Binary Relations 36Table 78 Subset and Superset Relations 36Table 79 AMS Subset and Superset Relations 36Table 80 stmaryrd Subset and Superset Relations 36Table 81 wasysym Subset and Superset Relations 36Table 82 txfontspxfonts Subset and Superset Relations 36Table 83 mathabx Subset and Superset Relations 37Table 84 MnSymbol Subset and Superset Relations 37Table 85 Inequalities 37Table 86 AMS Inequalities 37

2


3


4



5




References 106

Index 107

6

1 Introduction





11 Document Usage








cent 17

e 17


permil 19 27

there4 30

B and F 31

and amp 37

62


L F etc 65

N Z R etc 65

minusint

92




7

2 Body-text symbols



















8



















9




10









11







˚vod


12





Alif Ayn





Aa =A=a Amacr

amacr










13











Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



Aˇ

aˇ




14


Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



15


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast









16















17







Ccopy ccsalowast





18








h permil

19





∐rdquo (coprod)















20









21




22










23


odplus






24



and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint



25


notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint



26


bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint

27


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28























intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)

29


˙bigparr

˘bigwith









A inplus B niplus



30








31






32






33







abc


defnntstileabcdef

abc

def

stdtstileabcdef

abc


defnnttstileabcdef

abc

def

stststileabcdef

abc


defnsdtstileabcdef

abc

def

sttstileabcdef

abc


defnsststileabcdef

abc

def

stttstileabcdef

abc


defnststileabcdef

abc

deftddtstileabcdef

abc


defnsttstileabcdef

abc

deftdststileabcdef

abc

defdntstileabcdef

abc

def

ntdtstileabcdefabc

deftdtstileabcdef


34


abc

defdnttstileabcdef

abc

def

ntststileabcdefabc

deftdttstileabcdef

abc

defdsdtstileabcdef

abc

def

nttstileabcdef abc

deftndtstileabcdef

abc

defdsststileabcdef

abc

def

ntttstileabcdef abc

deftnststileabcdef

abc

defdststileabcdef

abc


deftntstileabcdef

abc

defdsttstileabcdef

abc


deftnttstileabcdef

abc

def

dtdtstileabcdefabc


deftsdtstileabcdef

abc

def

dtststileabcdefabc


deftsststileabcdef

abc

def

dttstileabcdef abc


deftststileabcdef

abc

def

dtttstileabcdef abc


deftsttstileabcdef

abc


defsntstileabcdef

abc

def

ttdtstileabcdef

abc


defsnttstileabcdef

abc

defttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef






35











sqsubset A sqsupset



36



















37


apprge gt apprle

















38

























39









40

Table 95 Arrows






Table 96 Harpoons




Table 98 AMS Arrows






41









42






43









44




45












46


A chemarrow










47












48

















49















50














e e j im




51












niv vin

52



ww Downarrow [[

[ ]]

]

〈lang

langle 〉rang

rangle |∣∣∣ |

∥∥∥ |

dlceil

lceil erceil


~ww Uparrow

blfloor

lfloor crfloor


~w Updownarrow

((

( ))

)

∖

backslash




lgroup rgroup


bracevert



|∣∣∣ lvert |

∣∣∣ rvert

∥∥∥ lVert

∥∥∥ rVert



~

llbracket

rrbracket

53


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert


54


ETH

ETH

ETH

ETH

ETH

leftwave ETH

ETH

ETH

ETH

ETH

rightwave

Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

leftevaw Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

rightevaw



〈〈langlang


rAngle

[[[[

lBrack ]]]]

rBrack

ddlceillceil

lCeil eerceilrceil

rCeil

bblfloorlfloor


rFloor








triplegt

[[[[[[

triple[ ]]]]]]

triple]





55









a ddddota





a veca


A



56


a ringa

















˚abc wideringabc

57

















abc widearrowabc


58












abcrsaquo utildeabc














59


abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG




a dfta a DFTa












abcdef

holterabcdefabcdef

polterabcdef

60

Table 174 Dots





Table 175 AMS Dots











61


iddots


adots











`surd





62













63
















64















65


66















A AR



67




















68






















69





female male














70

5 Dingbats



















71

























72









baucross







73

























74





































75

















A skull


O rip



76









77

6 Other symbols














78








Aa

aa


Aa

aa


Alal KrAKra



a











79






bauforms bauhead












80





















81





times

amacr

bBm cc ˘ Mbb ˙˙

Pppp otimes

t

˘ Bmacr


˙pppp tsbm

˘ bmacr

Bbmmacr

m oo ˙˙

Ppppp tsmb

˘ Bb ˘ bbmbmacr

M˙

p ˙˙

ppppp tsmm


macrpm ps

macrvppm

˘ bbmacr


vpppm

˘ bBmacr


macrppm sim

R


ppp sim

r


˙Ppp otimes

T






82




















83


A HA I HI n Hn T HT

a Ha i Hi O HO t Ht









f Hf l Hl r Hr x Hx

F HF m Hm s Hs Y HY

G HG M HM S HS y Hy



H HH N HN ˚ Hsv







84


Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart



















85











86









72 Resizing symbols






87

Table

280

Sym

bol

Nam

eC

lash

es

Sym

bol

LAT E

X2 ε

AMS

stm

aryr

dw

asys

ymm

ath

abx

mar

vosy

mb

bd

ing

ifsy

md

ingb

atw

suip

a

baro

lt

bigtriangledown

5`

bigtriangleup

4a

checkmark

XD

Circle

5

Cross

dagger

ggg

≫Iuml

Letter

B

lightning

Lightning

E

lll

≪Icirc

Square

f

0Sun

Agrave

TriangleDown

o3

TriangleUp

n1

88



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


89

















90







endtabular












91

















92





one (ldquo=int






















93


makeatother








makeatother








e






94


makeatother













makeatother


95






ABCD












96










endcharend








97

1

2

3

4

5

6677

8






0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F




98



















99









Package Code Output










100
















101




192 C0 A lsquoA

193 C1 A rsquoA

194 C2 A Â195 C3 A ~A196 C4 A A


200 C8 E lsquoE

201 C9 E rsquoE

202 CA E Ê203 CB E E

204 CC I lsquoI

205 CD I rsquoI



209 D1 N ~N

210 D2 O lsquoO

211 D3 O rsquoO


217 D9 U lsquoU

218 DA U rsquoU

219 DB U Û220 DC U U


102







Microsoftreg Windowsreg normally uses a superset of Latin 1 called ldquoCode Page 1252rdquo or ldquoCP1252rdquo forshort CP1252 introduces symbols in the Latin 1 ldquoinvalidrdquo range (characters 128ndash159) Table 289 presents thecharacters with which CP1252 augments the standard Latin 1 table












103

















104


Name Date


105






References











106

Index




( (() 54

) ()) 53

) ()) 54

() 22 100- (-) 102 103 (a) 13 () 53

() 54

lt (⟨) 54

[ ([) 53

[ (⎡⎢⎢⎢⎢⎢⎣) 54

91] (]) 53

] (⎤⎥⎥⎥⎥⎥⎦) 54



) 82



) 79AAdaleth (D) 83


rvert






AchtBL ( ˇ ldquo==

) 79




Adobe Acrobat 99

adots ( ) 62 94







AltGr ( AltGr ) 69


AMS 7 8 21 25 30 36 37 3941 49ndash53 56 58 59 61ndash6366 87 104








text mode see AA





107














Arrowvert (ww) 53

Arrowvert (

XXXXXXX) 54

arrowvert () 53

arrowvert (




AsteriskBold (A) 74



AsteriskThin (C) 74





(EGGGGGGGGGGC) 60



(GGGGGBFGGGGG) 60



macr) 13


backslash () 54




Bart (


108





tion) 65BBm (

macr) 82

Bbm (macr

) 82bBm (

macr) 82


macr) 82

bbmb ( ˘) 82bbmx (



rdquoardquo) 15



e) 25



THORN) 26

bigboxbot (Ucirc

) 26bigboxcirc (

Otilde) 26


) 26bigboxdiv (

Oacute) 26

bigboxdot (Ocirc

) 26bigboxleft (

Oslash) 26

bigboxminus (Ntilde

) 26bigboxplus (

ETH) 26

bigboxright (Ugrave

) 26bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 26

bigcap (⋂



) 26


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 25


) 25


AElig) 26



Euml) 26

bigocirc (Aring


Ccedil) 26

bigodiv (Atilde

) 26bigodot (

⊙) 25


Egrave) 26

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


otimes) 25


Ecirc) 26


Iuml) 26


Igrave) 26

bigparallel (f) 25

bigparr (˙

) 30bigplus (

) 26

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 26


) 26

bigtimes (⨉) 29


`) 25





109


a) 25



⊎) 25



or) 25


and) 25


bigwith (˘






macr) 82

bm (package) 100 104 105bm 100bm (

macr) 82




bracevert () 53

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 54





Burns (

) 85




also hookleftarrow



Cc ( ) 82

110







checkmark (D) 77


Circle (5) 75










CircleShadow (d) 75






work 1 7 57 66 87 103104




∐) 20 25


111


Cross () 75








Ŕa) 15







Cutright (q) 71

DD (a

uml) 16




dashint (minusint

) 93


DavidStar (0) 74


ddashint (=int

) 93

ddddot (

) 56dddot (

) 56

dddtstile ( ) 34


ddots ( ) 61 94

ddots (⋱) 61

ddststile ( ) 34

ddtstile ( ) 34

ddttstile ( ) 34



DEL () 69Del ( Del ) 69






Dfourier ( c) 35

dfourier ( c ) 35

DFT ( ) 60

dft ( ) 60

112









LCD 67Mayan 62








divideontimes



dndtstile ( ) 34

dnststile ( ) 34

dntstile ( ) 34




dollar sign see $






macr) 28


dottedtilde (a) 15




113

downp ( ) 16

downparenthfill 95


downpropto () 32


downslice () 24

downspoon (⫰) 47

downt ( ) 16



downuparrows ( ) 42

downuparrows () 43



downVdash () 32

downvdash (⊤) 32

downY () 23

drsh ( ) 42

DS (SS) 79

Ds (ss) 79




dsbiological (B) 84

dschemical (C) 84

dscommercial (c) 84

dsdtstile ( ) 35


dsheraldical (H) 84

dsjuridical (J) 84

dsliterary (L) 84


dsmedical (m) 84

dsmilitary (X) 84

dsrailways (R) 84

dsststile ( ) 35

dstechnical (T) 84

dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35

dtimes () 23

dtimes (13) 23

dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35

DVI 18 69 97

dz ( ) 12

E


e (e) 51

ε-TEX 53

Earth ( ) 68

Earth (Ecirc) 68

earth () 68

Ecommerce () 17





EightStar ( ) 74









Enter ( Enter ) 69


eqslantgtr () 37

eqslantgtr (⪖) 39

eqslantless ( ) 38

eqslantless () 37


eqsmile () 48

equal (=) 32

equal (j) 82

equalclosed () 32

equalsfill 20 95

equidecomposable 91


equiv (equiv) 20 30

equiv (equiv) 32


equivclosed () 32

er ( ) 11

es-zet see ss

ESC () 69

Esc ( Esc ) 69


esh ( ) 11

esh ( ) 12


Estatically (J) 70



eta (η) 49

etaup (η) 50

ETB () 69

etc (P) 82

eth (eth) 63

eth ( ) 11

eth ( ) 12

ETX () 69

eufrak (package) 65

Euler Roman 50

EUR (e ) 17

EURcr (d) 17

EURdig (D) 17

EURhv (c) 17

euro 17

euro signs 17

blackboard bold 65


EURtm (e) 17



evil spirits 86

exclusive or 90

exists ( ) 51

exists (exist) 51

exists (exist) 51

exp (exp) 49





114




textquotesingle


Ferli (aa) 79

Fermi (aa







FF () 69fge (package) 47 52 56 62 64














40












(t) 75












fint (gt

) 27

fint (ffl) 28






FiveStar (8) 74




FiveStarOpen (9) 74


115





fixedddots ( ) 61

fixedvdots () 61






OT2 90T1 7 9 13 101 103T4 9 13 16T5 9 13TS1 103





FourAsterisk (1) 74



Fourier ( c) 35







gets see leftarrow






gtreqless (R) 37



116

gtreqqless (T) 37

gtreqqless (⪌) 39





h (ả) 13HA (A) 84











HandLeft () 72

HandLeftUp () 72


HandRight () 72



HB (B) 84

Hb (b) 84






HI (I) 84

Hi (i) 84Hibl (˝) 84

Hibp (ˆ) 84

Hibs (uml) 84


mathhill (a

) 15


radic) 93

HL (L) 84Hl (l) 84HM (M) 84

Hm (m) 84

Hman (ˇ) 84

Hmillion (7) 84



holter ( ) 60


Homer (


Hplus (+) 84HQ (Q) 84Hq (q) 84


Hs (s) 84

Hscribe (macr) 84


Hthousand (4) 84

Htongue (˘) 84

HU (U) 84


Hut () 81

HV (V) 84

117

Hv (v) 84hv () 12Hvbar (|) 84HW (W) 84

Hw (w) 84HX (X) 84

Hx (x) 84

HXthousand (5) 84

HY (Y) 84


HZ (Z) 84Hz (z) 84


iddots ( ) 62

iddots () 94


) 25

idotsint (

) 27


ifsym (package) 67 75 80 8188 90 104 105



) 25

iiiint (

) 27

iiiint (ˇ

) 28


micro) 26

iiint (intintint

) 25

iiint (

) 25 27

iiint (˝

) 28


acute) 26

iint (intint

) 25

iint (

) 25 27

iint (˜

) 28



and vdash


textquotedbl







int (sup3) 26

int (int

) 25

int (r

) 25

int (int) 29

intclockwise () 29






irony mark ( ) 90


Jj () 13

JackStar (2) 74







118

lambdaslash (n) 63

lambdaup (λ) 50


land see wedge

landdownint () 28


landupint () 28

landupint (⨙) 29

Langle (lt) 65

lAngle (〈〈) 55

langle (〈) 20 53

langle (⟨) 54

langlebar (n) 54

Laplace ( s c) 35

laplace ( c s) 35




largecircle () 74

largediamond () 74


largepencil (W) 72



largestar () 74






LArrow ( larr ) 69

larrowfill 60

Laserbeam (a) 70




latfric () 11

Latin 1 7 101 103 104

table 102

laundry symbols 80

Lbag (P) 52

lbag (N) 52


) 54

Lbrack ([) 65

lBrack ([[) 55

LCD digits 67

lCeil (dd) 55

lceil (d) 53

lceil (⎡⎢⎢⎢⎢⎢⎢) 54






leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55






leftwave (

ETH

ETH

ETH

ETH

) 55


119


lesseqgtr (Q) 37



lesseqqgtr (S) 37

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

LF () 69

lfilet (

7777) 54


lfloor (⎢⎢⎢⎢⎢⎢⎣) 54

lg (lg) 49

lgroup (

) 53

lgroup (⎧⎪⎪⎪⎪⎪⎩) 54







Lisa (

) 85lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 54


llcorner () 54



lmoustache (

) 53





and see wedge

not see neg and sim

or see vee





120

lrcorner () 54

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 54



lwave (

ETH

ETH

ETH

ETH

) 55

lWavy (_______

) 54

lwavy (^^^) 54

lz (1) 11

MM 9M (

macr) 82

m 9m (

macr) 82


Maggie ( ) 85


manpenkidney () 79





Marge (

















cient seeDH



121



micro (micro) 67


textperthousand





32 33 37 39 40 43ndash48 5051 54 56ndash58 61 63 64 74104 105










ncong () 30


nddtstile ( ) 35


122


ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 37 38


ngeqq () 37

ngeqq (iquest) 39

ngeqslant () 37





ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 12

NibLeft () 72


NibSolidLeft ( ) 72


123




nleq () 37 38


nleqq () 37

nleqq (frac34) 39

nleqslant () 37





nlessgtr () 38

nlessgtr (≸) 39



nnststile ( ) 35

nntstile ( ) 34


tion) 25




notni


npreceq () 30


124




nsststile ( ) 34

nststile ( ) 34



nsubseteq () 36


nsucceq () 30


nsupseteq (+) 36


ntdtstile ( ) 34


125






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35











˚) 15


ohm (Ω) 67

Ohne (a) 79


oiiint ()

) 27

oiiint (

) 29

oiiintclockwise (L

) 27


) 27

oiint (middot

) 26

oiint (

) 25 27

oiint (sbquo

) 28

oiint (

) 29

oiint (∯) 29

oiintclockwise (H

) 27

oiintctrclockwise (

) 27

oint (para) 26

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 29

ointctrclockwise (

) 27




126





oright (i) 24



overbrace (hkkikkj

) 58

overbrace (copy

) 58


) 58


) 57

overbracket ( ) 58


rdquoa) 15

overgroup (hkkkkj

) 58




overline ( ) 20 57






PP (para) 8 102p (

˙) 82

p 94package options



amsmath 7 49 56 91 99amssymb 7 20 30 36 4156 62 65 104 105 107









mathdots 56 61 62 94 104105



127





timing 67tipa 10 11 13 15 16 90104 105




wsuipa 11 15 16 88 90 94104 105

yfonts 65 104 105yhmath 57 59 62 94 104






















textperthousand


passedpawn (r) 82


Peace () 77

PencilLeft () 72


PencilLeftUp () 72

PencilRight () 72


PencilRightUp () 72

pencils 72

pentagon (D) 74

pentagram () 24

people see faces

percent sign see

permil (h) 19

Perp (y) 31

perp (perp) 30 93

perp (perp) 33


Pfund (pound) 17




Phaistos disk 83


PHarrow (J) 83

PHbee (h) 83

PHbeehive (X) 83

PHboomerang (R) 83

PHbow (K) 83

PHbullLeg (b) 83

PHcaptive (D) 83


PHcat (c) 83

PHchild (E) 83

PHclub (M) 83

PHcolumn (W) 83

PHcomb (U) 83

PHdolium (T) 83

PHdove (f) 83

PHeagle (e) 83

PHflute (o) 83

PHgaunlet (H) 83

PHgrater (p) 83

PHhelmet (G) 83

PHhide (a) 83

128


PHlid (Q) 83

PHlily (m) 83

PHmanacles (N) 83

PHmattock (O) 83



PHoxBack (n) 83

PHpapyrus (k) 83

PHpedestrian (A) 83

PHplaneTree (i) 83

PHplumedHead (B) 83

PHram (d) 83

PHrosette (l) 83

PHsaw (P) 83

PHshield (L) 83

PHship (Y) 83

PHsling (V) 83

PHsmallAxe (r) 83

PHstrainer (q) 83



PHvine (j) 83

PHwavyBand (s) 83



pipe see textpipe








macr) 82


polter ( ) 60



macr) 82

Ppp ( ˙˙) 82

ppp ( ˙˙

) 82Pppp ( ˙

˙) 82

pppp ( ˙˙

) 82Ppppp ( ˙

˙) 82

ppppp ( ˙˙




prod) 25




31 36 38 41 42 48 50 5162 63 65 87 101

Pxp ( ˙) 82pxp ( ˙ ) 82



129

RR ( sim

) 82r (a) 13r ( sim

) 82



Rain () 80



rangle (⟩) 54

ranglebar (s) 54

RArrow ( rarr ) 69



hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 54





recorder () 78

Rectangle (u) 75




rqm


textregistered



upharpoonright


Return ( larr ) 69


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

revD () 12

revddots ( ) 94


textbackslash


rfilet (

) 54


rfloor (⎥⎥⎥⎥⎥⎥⎦) 54

rgroup (

) 53

rgroup (⎫⎪⎪⎪⎪⎪⎭) 54



RightDiamond () 75

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55



130


rightwave (

ETH

ETH

ETH

ETH

) 55




rmoustache (

) 53




rrangle (⟫) 54


rsem (MQQQQQO) 54




rwave (

ETH

ETH

ETH

ETH

) 55

rWavy (_______

) 54

rwavy (^^^) 54








ScissorLeft () 71




() 71


scu (W) 12

scy (]) 12

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 79


) 79











union see cup

setminus () 20

131








([) 74

SixStar (G) 74







SmallCircle (E) 75












sndtstile ( ) 35

Snow () 80

SnowCloud () 80

Snowflake (`) 74



SNPP () 85

snststile ( ) 35

sntstile ( ) 35




Sparkle (]) 74


SpinDown () 75


sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

132

sqrt (radic


Square (0) 75



hooked see hksqrt


(k) 75




SquareShadowA () 75

SquareShadowB () 75


SquareShadowC () 75



SquareSolid (g) 75











squplus (]) 22

SS (SS) 9

ss (szlig) 9

ssdtstile ( ) 35

ssearrow () 42

sslash () 21

ssststile ( ) 35

sststile ( ) 35

ssttstile ( ) 35

sswarrow ($) 42

stackrel 20 91 95

standard state 91

star () 20 94

star (⋆) 24

Star of David 73 74

stars 63 73 74


staveI () 85

staveII () 85

staveIII () 85

staveIV () 85

staveIX () 85

staveL (1) 85 86

staveLI (2) 85

staveLII (3) 85

staveLIII (4) 85

staveLIV (5) 85

staveLIX () 85

staveLV (6) 85

staveLVI (7) 85

staveLVII (8) 85

staveLVIII (9) 85

staveLX () 85

staveLXI (lt) 85

staveLXII (=) 85

staveLXIII (gt) 86

staveLXIV () 86

staveLXV () 86

staveLXVI (A) 86

staveLXVII (B) 86

staveLXVIII (C) 86

staves 85


staveV () 85

staveVI () 85

staveVII () 85

staveVIII () 85

staveX () 85

staveXI () 85

staveXII () 85

staveXIII () 85

staveXIV (13) 85

staveXIX () 86

staveXL () 86

staveXLI (() 86

staveXLII ()) 86

staveXLIII () 86

staveXLIV (+) 86

staveXLIX (0) 85

staveXLV () 86

staveXLVI (-) 86

staveXLVII () 85

staveXLVIII () 85

staveXV () 85

staveXVI () 85

staveXVII () 86

staveXVIII () 86

staveXX () 86

staveXXI () 86

staveXXII () 86

staveXXIII () 86

staveXXIV () 85

staveXXIX () 85

staveXXV () 85

staveXXVI () 85

staveXXVII () 85

133

staveXXVIII () 85

staveXXX () 85

staveXXXI () 85

staveXXXII () 85

staveXXXIII ( ) 85

staveXXXIV () 85

staveXXXIX (amp) 85

staveXXXV () 85


stdtstile ( ) 34





StopWatchEnd () 81


strokedint (⨏) 29

StrokeFive () 81

StrokeFour () 81

StrokeOne () 81

StrokeThree () 81


stststile ( ) 34

sttstile ( ) 34

stttstile ( ) 34


^) 15



sublptr (aiexcl) 15






sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 81




SunCloud () 80





`) 62




134





) 82

t ( a) 13t ( otimes




Tape () 77


tddtstile ( ) 34

tdststile ( ) 34

tdtstile ( ) 34

tdttstile ( ) 35









8 13 17ndash19 41 56 64 6778 87 101 103ndash105


135


textdbend (




textlhdbend (~


136



mdasha) 14





) 76



rsaquo) 14




ˆ) 14

textsubdot (a˙) 14


lsaquo) 14


˚) 14


˜) 14



ˇ) 14



) 15



137





textperthousand




90 104 105tipx (package) 11 104 105

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35




alphabets math




TriangleDown (3) 75






TriangleUp (1) 75





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 70

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



31 36 38 41 42 48 50 5162 63 65 87 89 101 104105


UU (a

˘) 16




ulcorner () 54

ullcorner (6) 54

ulrcorner () 54



138


underbrace (reg) 58



underbracket ( ) 58


















urcorner () 54


˜) 15

utilde (˜) 59






139



varint (r




) 27


)

27varoiint (

) 28


) 27


) 27

varoint (u

) 25

varointclockwise (-

) 27



) 27



) 27







vdots () 61




Village () 81



˚) 12


macr) 82

vpppm (macr



17 19ndash21 25 30 36 38 4161ndash63 67 68 70 73 74 7888 104 105





Ţ) 15


140


widering (Ucirc) 58





90 94 104 105wupperhand (c) 82

Xx ( ˙˙) 82XBox (4) 73

Xdvi 90



Xi (Ξ) 49

xi (ξ) 49

xiup (ξ) 50










xlongequal (===) 60

xlongequal (===) 60









XML 103







Xs 73 76

XSolid () 73

XSolidBold ($) 73

XSolidBrush () 73







Ztransf ( s c) 35



ZwPa ( A ) 79

141


3


4



5




References 106

Index 107

6

1 Introduction





11 Document Usage








cent 17

e 17


permil 19 27

there4 30

B and F 31

and amp 37

62


L F etc 65

N Z R etc 65

minusint

92




7

2 Body-text symbols



















8



















9




10









11







˚vod


12





Alif Ayn





Aa =A=a Amacr

amacr










13











Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



Aˇ

aˇ




14


Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



15


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast









16















17







Ccopy ccsalowast





18








h permil

19





∐rdquo (coprod)















20









21




22










23


odplus






24



and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint



25


notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint



26


bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint

27


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28























intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)

29


˙bigparr

˘bigwith









A inplus B niplus



30








31






32






33







abc


defnntstileabcdef

abc

def

stdtstileabcdef

abc


defnnttstileabcdef

abc

def

stststileabcdef

abc


defnsdtstileabcdef

abc

def

sttstileabcdef

abc


defnsststileabcdef

abc

def

stttstileabcdef

abc


defnststileabcdef

abc

deftddtstileabcdef

abc


defnsttstileabcdef

abc

deftdststileabcdef

abc

defdntstileabcdef

abc

def

ntdtstileabcdefabc

deftdtstileabcdef


34


abc

defdnttstileabcdef

abc

def

ntststileabcdefabc

deftdttstileabcdef

abc

defdsdtstileabcdef

abc

def

nttstileabcdef abc

deftndtstileabcdef

abc

defdsststileabcdef

abc

def

ntttstileabcdef abc

deftnststileabcdef

abc

defdststileabcdef

abc


deftntstileabcdef

abc

defdsttstileabcdef

abc


deftnttstileabcdef

abc

def

dtdtstileabcdefabc


deftsdtstileabcdef

abc

def

dtststileabcdefabc


deftsststileabcdef

abc

def

dttstileabcdef abc


deftststileabcdef

abc

def

dtttstileabcdef abc


deftsttstileabcdef

abc


defsntstileabcdef

abc

def

ttdtstileabcdef

abc


defsnttstileabcdef

abc

defttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef






35











sqsubset A sqsupset



36



















37


apprge gt apprle

















38

























39









40

Table 95 Arrows






Table 96 Harpoons




Table 98 AMS Arrows






41









42






43









44




45












46


A chemarrow










47












48

















49















50














e e j im




51












niv vin

52



ww Downarrow [[

[ ]]

]

〈lang

langle 〉rang

rangle |∣∣∣ |

∥∥∥ |

dlceil

lceil erceil


~ww Uparrow

blfloor

lfloor crfloor


~w Updownarrow

((

( ))

)

∖

backslash




lgroup rgroup


bracevert



|∣∣∣ lvert |

∣∣∣ rvert

∥∥∥ lVert

∥∥∥ rVert



~

llbracket

rrbracket

53


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert


54


ETH

ETH

ETH

ETH

ETH

leftwave ETH

ETH

ETH

ETH

ETH

rightwave

Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

leftevaw Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

rightevaw



〈〈langlang


rAngle

[[[[

lBrack ]]]]

rBrack

ddlceillceil

lCeil eerceilrceil

rCeil

bblfloorlfloor


rFloor








triplegt

[[[[[[

triple[ ]]]]]]

triple]





55









a ddddota





a veca


A



56


a ringa

















˚abc wideringabc

57

















abc widearrowabc


58












abcrsaquo utildeabc














59


abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG




a dfta a DFTa












abcdef

holterabcdefabcdef

polterabcdef

60

Table 174 Dots





Table 175 AMS Dots











61


iddots


adots











`surd





62













63
















64















65


66















A AR



67




















68






















69





female male














70

5 Dingbats



















71

























72









baucross







73

























74





































75

















A skull


O rip



76









77

6 Other symbols














78








Aa

aa


Aa

aa


Alal KrAKra



a











79






bauforms bauhead












80





















81





times

amacr

bBm cc ˘ Mbb ˙˙

Pppp otimes

t

˘ Bmacr


˙pppp tsbm

˘ bmacr

Bbmmacr

m oo ˙˙

Ppppp tsmb

˘ Bb ˘ bbmbmacr

M˙

p ˙˙

ppppp tsmm


macrpm ps

macrvppm

˘ bbmacr


vpppm

˘ bBmacr


macrppm sim

R


ppp sim

r


˙Ppp otimes

T






82




















83


A HA I HI n Hn T HT

a Ha i Hi O HO t Ht









f Hf l Hl r Hr x Hx

F HF m Hm s Hs Y HY

G HG M HM S HS y Hy



H HH N HN ˚ Hsv







84


Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart



















85











86









72 Resizing symbols






87

Table

280

Sym

bol

Nam

eC

lash

es

Sym

bol

LAT E

X2 ε

AMS

stm

aryr

dw

asys

ymm

ath

abx

mar

vosy

mb

bd

ing

ifsy

md

ingb

atw

suip

a

baro

lt

bigtriangledown

5`

bigtriangleup

4a

checkmark

XD

Circle

5

Cross

dagger

ggg

≫Iuml

Letter

B

lightning

Lightning

E

lll

≪Icirc

Square

f

0Sun

Agrave

TriangleDown

o3

TriangleUp

n1

88



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


89

















90







endtabular












91

















92





one (ldquo=int






















93


makeatother








makeatother








e






94


makeatother













makeatother


95






ABCD












96










endcharend








97

1

2

3

4

5

6677

8






0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F




98



















99









Package Code Output










100
















101




192 C0 A lsquoA

193 C1 A rsquoA

194 C2 A Â195 C3 A ~A196 C4 A A


200 C8 E lsquoE

201 C9 E rsquoE

202 CA E Ê203 CB E E

204 CC I lsquoI

205 CD I rsquoI



209 D1 N ~N

210 D2 O lsquoO

211 D3 O rsquoO


217 D9 U lsquoU

218 DA U rsquoU

219 DB U Û220 DC U U


102



















103

















104


Name Date


105






References











106

Index




( (() 54

) ()) 53

) ()) 54

() 22 100- (-) 102 103 (a) 13 () 53

() 54

lt (⟨) 54

[ ([) 53

[ (⎡⎢⎢⎢⎢⎢⎣) 54

91] (]) 53

] (⎤⎥⎥⎥⎥⎥⎦) 54



) 82



) 79AAdaleth (D) 83


rvert






AchtBL ( ˇ ldquo==

) 79




Adobe Acrobat 99

adots ( ) 62 94







AltGr ( AltGr ) 69


AMS 7 8 21 25 30 36 37 3941 49ndash53 56 58 59 61ndash6366 87 104








text mode see AA





107














Arrowvert (ww) 53

Arrowvert (

XXXXXXX) 54

arrowvert () 53

arrowvert (




AsteriskBold (A) 74



AsteriskThin (C) 74





(EGGGGGGGGGGC) 60



(GGGGGBFGGGGG) 60



macr) 13


backslash () 54




Bart (


108





tion) 65BBm (

macr) 82

Bbm (macr

) 82bBm (

macr) 82


macr) 82

bbmb ( ˘) 82bbmx (



rdquoardquo) 15



e) 25



THORN) 26

bigboxbot (Ucirc

) 26bigboxcirc (

Otilde) 26


) 26bigboxdiv (

Oacute) 26

bigboxdot (Ocirc

) 26bigboxleft (

Oslash) 26

bigboxminus (Ntilde

) 26bigboxplus (

ETH) 26

bigboxright (Ugrave

) 26bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 26

bigcap (⋂



) 26


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 25


) 25


AElig) 26



Euml) 26

bigocirc (Aring


Ccedil) 26

bigodiv (Atilde

) 26bigodot (

⊙) 25


Egrave) 26

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


otimes) 25


Ecirc) 26


Iuml) 26


Igrave) 26

bigparallel (f) 25

bigparr (˙

) 30bigplus (

) 26

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 26


) 26

bigtimes (⨉) 29


`) 25





109


a) 25



⊎) 25



or) 25


and) 25


bigwith (˘






macr) 82

bm (package) 100 104 105bm 100bm (

macr) 82




bracevert () 53

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 54





Burns (

) 85




also hookleftarrow



Cc ( ) 82

110







checkmark (D) 77


Circle (5) 75










CircleShadow (d) 75






work 1 7 57 66 87 103104




∐) 20 25


111


Cross () 75








Ŕa) 15







Cutright (q) 71

DD (a

uml) 16




dashint (minusint

) 93


DavidStar (0) 74


ddashint (=int

) 93

ddddot (

) 56dddot (

) 56

dddtstile ( ) 34


ddots ( ) 61 94

ddots (⋱) 61

ddststile ( ) 34

ddtstile ( ) 34

ddttstile ( ) 34



DEL () 69Del ( Del ) 69






Dfourier ( c) 35

dfourier ( c ) 35

DFT ( ) 60

dft ( ) 60

112









LCD 67Mayan 62








divideontimes



dndtstile ( ) 34

dnststile ( ) 34

dntstile ( ) 34




dollar sign see $






macr) 28


dottedtilde (a) 15




113

downp ( ) 16

downparenthfill 95


downpropto () 32


downslice () 24

downspoon (⫰) 47

downt ( ) 16



downuparrows ( ) 42

downuparrows () 43



downVdash () 32

downvdash (⊤) 32

downY () 23

drsh ( ) 42

DS (SS) 79

Ds (ss) 79




dsbiological (B) 84

dschemical (C) 84

dscommercial (c) 84

dsdtstile ( ) 35


dsheraldical (H) 84

dsjuridical (J) 84

dsliterary (L) 84


dsmedical (m) 84

dsmilitary (X) 84

dsrailways (R) 84

dsststile ( ) 35

dstechnical (T) 84

dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35

dtimes () 23

dtimes (13) 23

dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35

DVI 18 69 97

dz ( ) 12

E


e (e) 51

ε-TEX 53

Earth ( ) 68

Earth (Ecirc) 68

earth () 68

Ecommerce () 17





EightStar ( ) 74









Enter ( Enter ) 69


eqslantgtr () 37

eqslantgtr (⪖) 39

eqslantless ( ) 38

eqslantless () 37


eqsmile () 48

equal (=) 32

equal (j) 82

equalclosed () 32

equalsfill 20 95

equidecomposable 91


equiv (equiv) 20 30

equiv (equiv) 32


equivclosed () 32

er ( ) 11

es-zet see ss

ESC () 69

Esc ( Esc ) 69


esh ( ) 11

esh ( ) 12


Estatically (J) 70



eta (η) 49

etaup (η) 50

ETB () 69

etc (P) 82

eth (eth) 63

eth ( ) 11

eth ( ) 12

ETX () 69

eufrak (package) 65

Euler Roman 50

EUR (e ) 17

EURcr (d) 17

EURdig (D) 17

EURhv (c) 17

euro 17

euro signs 17

blackboard bold 65


EURtm (e) 17



evil spirits 86

exclusive or 90

exists ( ) 51

exists (exist) 51

exists (exist) 51

exp (exp) 49





114




textquotesingle


Ferli (aa) 79

Fermi (aa







FF () 69fge (package) 47 52 56 62 64














40












(t) 75












fint (gt

) 27

fint (ffl) 28






FiveStar (8) 74




FiveStarOpen (9) 74


115





fixedddots ( ) 61

fixedvdots () 61






OT2 90T1 7 9 13 101 103T4 9 13 16T5 9 13TS1 103





FourAsterisk (1) 74



Fourier ( c) 35







gets see leftarrow






gtreqless (R) 37



116

gtreqqless (T) 37

gtreqqless (⪌) 39





h (ả) 13HA (A) 84











HandLeft () 72

HandLeftUp () 72


HandRight () 72



HB (B) 84

Hb (b) 84






HI (I) 84

Hi (i) 84Hibl (˝) 84

Hibp (ˆ) 84

Hibs (uml) 84


mathhill (a

) 15


radic) 93

HL (L) 84Hl (l) 84HM (M) 84

Hm (m) 84

Hman (ˇ) 84

Hmillion (7) 84



holter ( ) 60


Homer (


Hplus (+) 84HQ (Q) 84Hq (q) 84


Hs (s) 84

Hscribe (macr) 84


Hthousand (4) 84

Htongue (˘) 84

HU (U) 84


Hut () 81

HV (V) 84

117

Hv (v) 84hv () 12Hvbar (|) 84HW (W) 84

Hw (w) 84HX (X) 84

Hx (x) 84

HXthousand (5) 84

HY (Y) 84


HZ (Z) 84Hz (z) 84


iddots ( ) 62

iddots () 94


) 25

idotsint (

) 27


ifsym (package) 67 75 80 8188 90 104 105



) 25

iiiint (

) 27

iiiint (ˇ

) 28


micro) 26

iiint (intintint

) 25

iiint (

) 25 27

iiint (˝

) 28


acute) 26

iint (intint

) 25

iint (

) 25 27

iint (˜

) 28



and vdash


textquotedbl







int (sup3) 26

int (int

) 25

int (r

) 25

int (int) 29

intclockwise () 29






irony mark ( ) 90


Jj () 13

JackStar (2) 74







118

lambdaslash (n) 63

lambdaup (λ) 50


land see wedge

landdownint () 28


landupint () 28

landupint (⨙) 29

Langle (lt) 65

lAngle (〈〈) 55

langle (〈) 20 53

langle (⟨) 54

langlebar (n) 54

Laplace ( s c) 35

laplace ( c s) 35




largecircle () 74

largediamond () 74


largepencil (W) 72



largestar () 74






LArrow ( larr ) 69

larrowfill 60

Laserbeam (a) 70




latfric () 11

Latin 1 7 101 103 104

table 102

laundry symbols 80

Lbag (P) 52

lbag (N) 52


) 54

Lbrack ([) 65

lBrack ([[) 55

LCD digits 67

lCeil (dd) 55

lceil (d) 53

lceil (⎡⎢⎢⎢⎢⎢⎢) 54






leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55






leftwave (

ETH

ETH

ETH

ETH

) 55


119


lesseqgtr (Q) 37



lesseqqgtr (S) 37

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

LF () 69

lfilet (

7777) 54


lfloor (⎢⎢⎢⎢⎢⎢⎣) 54

lg (lg) 49

lgroup (

) 53

lgroup (⎧⎪⎪⎪⎪⎪⎩) 54







Lisa (

) 85lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 54


llcorner () 54



lmoustache (

) 53





and see wedge

not see neg and sim

or see vee





120

lrcorner () 54

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 54



lwave (

ETH

ETH

ETH

ETH

) 55

lWavy (_______

) 54

lwavy (^^^) 54

lz (1) 11

MM 9M (

macr) 82

m 9m (

macr) 82


Maggie ( ) 85


manpenkidney () 79





Marge (

















cient seeDH



121



micro (micro) 67


textperthousand





32 33 37 39 40 43ndash48 5051 54 56ndash58 61 63 64 74104 105










ncong () 30


nddtstile ( ) 35


122


ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 37 38


ngeqq () 37

ngeqq (iquest) 39

ngeqslant () 37





ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 12

NibLeft () 72


NibSolidLeft ( ) 72


123




nleq () 37 38


nleqq () 37

nleqq (frac34) 39

nleqslant () 37





nlessgtr () 38

nlessgtr (≸) 39



nnststile ( ) 35

nntstile ( ) 34


tion) 25




notni


npreceq () 30


124




nsststile ( ) 34

nststile ( ) 34



nsubseteq () 36


nsucceq () 30


nsupseteq (+) 36


ntdtstile ( ) 34


125






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35











˚) 15


ohm (Ω) 67

Ohne (a) 79


oiiint ()

) 27

oiiint (

) 29

oiiintclockwise (L

) 27


) 27

oiint (middot

) 26

oiint (

) 25 27

oiint (sbquo

) 28

oiint (

) 29

oiint (∯) 29

oiintclockwise (H

) 27

oiintctrclockwise (

) 27

oint (para) 26

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 29

ointctrclockwise (

) 27




126





oright (i) 24



overbrace (hkkikkj

) 58

overbrace (copy

) 58


) 58


) 57

overbracket ( ) 58


rdquoa) 15

overgroup (hkkkkj

) 58




overline ( ) 20 57






PP (para) 8 102p (

˙) 82

p 94package options



amsmath 7 49 56 91 99amssymb 7 20 30 36 4156 62 65 104 105 107









mathdots 56 61 62 94 104105



127





timing 67tipa 10 11 13 15 16 90104 105




wsuipa 11 15 16 88 90 94104 105

yfonts 65 104 105yhmath 57 59 62 94 104






















textperthousand


passedpawn (r) 82


Peace () 77

PencilLeft () 72


PencilLeftUp () 72

PencilRight () 72


PencilRightUp () 72

pencils 72

pentagon (D) 74

pentagram () 24

people see faces

percent sign see

permil (h) 19

Perp (y) 31

perp (perp) 30 93

perp (perp) 33


Pfund (pound) 17




Phaistos disk 83


PHarrow (J) 83

PHbee (h) 83

PHbeehive (X) 83

PHboomerang (R) 83

PHbow (K) 83

PHbullLeg (b) 83

PHcaptive (D) 83


PHcat (c) 83

PHchild (E) 83

PHclub (M) 83

PHcolumn (W) 83

PHcomb (U) 83

PHdolium (T) 83

PHdove (f) 83

PHeagle (e) 83

PHflute (o) 83

PHgaunlet (H) 83

PHgrater (p) 83

PHhelmet (G) 83

PHhide (a) 83

128


PHlid (Q) 83

PHlily (m) 83

PHmanacles (N) 83

PHmattock (O) 83



PHoxBack (n) 83

PHpapyrus (k) 83

PHpedestrian (A) 83

PHplaneTree (i) 83

PHplumedHead (B) 83

PHram (d) 83

PHrosette (l) 83

PHsaw (P) 83

PHshield (L) 83

PHship (Y) 83

PHsling (V) 83

PHsmallAxe (r) 83

PHstrainer (q) 83



PHvine (j) 83

PHwavyBand (s) 83



pipe see textpipe








macr) 82


polter ( ) 60



macr) 82

Ppp ( ˙˙) 82

ppp ( ˙˙

) 82Pppp ( ˙

˙) 82

pppp ( ˙˙

) 82Ppppp ( ˙

˙) 82

ppppp ( ˙˙




prod) 25




31 36 38 41 42 48 50 5162 63 65 87 101

Pxp ( ˙) 82pxp ( ˙ ) 82



129

RR ( sim

) 82r (a) 13r ( sim

) 82



Rain () 80



rangle (⟩) 54

ranglebar (s) 54

RArrow ( rarr ) 69



hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 54





recorder () 78

Rectangle (u) 75




rqm


textregistered



upharpoonright


Return ( larr ) 69


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

revD () 12

revddots ( ) 94


textbackslash


rfilet (

) 54


rfloor (⎥⎥⎥⎥⎥⎥⎦) 54

rgroup (

) 53

rgroup (⎫⎪⎪⎪⎪⎪⎭) 54



RightDiamond () 75

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55



130


rightwave (

ETH

ETH

ETH

ETH

) 55




rmoustache (

) 53




rrangle (⟫) 54


rsem (MQQQQQO) 54




rwave (

ETH

ETH

ETH

ETH

) 55

rWavy (_______

) 54

rwavy (^^^) 54








ScissorLeft () 71




() 71


scu (W) 12

scy (]) 12

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 79


) 79











union see cup

setminus () 20

131








([) 74

SixStar (G) 74







SmallCircle (E) 75












sndtstile ( ) 35

Snow () 80

SnowCloud () 80

Snowflake (`) 74



SNPP () 85

snststile ( ) 35

sntstile ( ) 35




Sparkle (]) 74


SpinDown () 75


sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

132

sqrt (radic


Square (0) 75



hooked see hksqrt


(k) 75




SquareShadowA () 75

SquareShadowB () 75


SquareShadowC () 75



SquareSolid (g) 75











squplus (]) 22

SS (SS) 9

ss (szlig) 9

ssdtstile ( ) 35

ssearrow () 42

sslash () 21

ssststile ( ) 35

sststile ( ) 35

ssttstile ( ) 35

sswarrow ($) 42

stackrel 20 91 95

standard state 91

star () 20 94

star (⋆) 24

Star of David 73 74

stars 63 73 74


staveI () 85

staveII () 85

staveIII () 85

staveIV () 85

staveIX () 85

staveL (1) 85 86

staveLI (2) 85

staveLII (3) 85

staveLIII (4) 85

staveLIV (5) 85

staveLIX () 85

staveLV (6) 85

staveLVI (7) 85

staveLVII (8) 85

staveLVIII (9) 85

staveLX () 85

staveLXI (lt) 85

staveLXII (=) 85

staveLXIII (gt) 86

staveLXIV () 86

staveLXV () 86

staveLXVI (A) 86

staveLXVII (B) 86

staveLXVIII (C) 86

staves 85


staveV () 85

staveVI () 85

staveVII () 85

staveVIII () 85

staveX () 85

staveXI () 85

staveXII () 85

staveXIII () 85

staveXIV (13) 85

staveXIX () 86

staveXL () 86

staveXLI (() 86

staveXLII ()) 86

staveXLIII () 86

staveXLIV (+) 86

staveXLIX (0) 85

staveXLV () 86

staveXLVI (-) 86

staveXLVII () 85

staveXLVIII () 85

staveXV () 85

staveXVI () 85

staveXVII () 86

staveXVIII () 86

staveXX () 86

staveXXI () 86

staveXXII () 86

staveXXIII () 86

staveXXIV () 85

staveXXIX () 85

staveXXV () 85

staveXXVI () 85

staveXXVII () 85

133

staveXXVIII () 85

staveXXX () 85

staveXXXI () 85

staveXXXII () 85

staveXXXIII ( ) 85

staveXXXIV () 85

staveXXXIX (amp) 85

staveXXXV () 85


stdtstile ( ) 34





StopWatchEnd () 81


strokedint (⨏) 29

StrokeFive () 81

StrokeFour () 81

StrokeOne () 81

StrokeThree () 81


stststile ( ) 34

sttstile ( ) 34

stttstile ( ) 34


^) 15



sublptr (aiexcl) 15






sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 81




SunCloud () 80





`) 62




134





) 82

t ( a) 13t ( otimes




Tape () 77


tddtstile ( ) 34

tdststile ( ) 34

tdtstile ( ) 34

tdttstile ( ) 35









8 13 17ndash19 41 56 64 6778 87 101 103ndash105


135


textdbend (




textlhdbend (~


136



mdasha) 14





) 76



rsaquo) 14




ˆ) 14

textsubdot (a˙) 14


lsaquo) 14


˚) 14


˜) 14



ˇ) 14



) 15



137





textperthousand




90 104 105tipx (package) 11 104 105

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35




alphabets math




TriangleDown (3) 75






TriangleUp (1) 75





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 70

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



31 36 38 41 42 48 50 5162 63 65 87 89 101 104105


UU (a

˘) 16




ulcorner () 54

ullcorner (6) 54

ulrcorner () 54



138


underbrace (reg) 58



underbracket ( ) 58


















urcorner () 54


˜) 15

utilde (˜) 59






139



varint (r




) 27


)

27varoiint (

) 28


) 27


) 27

varoint (u

) 25

varointclockwise (-

) 27



) 27



) 27







vdots () 61




Village () 81



˚) 12


macr) 82

vpppm (macr



17 19ndash21 25 30 36 38 4161ndash63 67 68 70 73 74 7888 104 105





Ţ) 15


140


widering (Ucirc) 58





90 94 104 105wupperhand (c) 82

Xx ( ˙˙) 82XBox (4) 73

Xdvi 90



Xi (Ξ) 49

xi (ξ) 49

xiup (ξ) 50










xlongequal (===) 60

xlongequal (===) 60









XML 103







Xs 73 76

XSolid () 73

XSolidBold ($) 73

XSolidBrush () 73







Ztransf ( s c) 35



ZwPa ( A ) 79

141


4



5




References 106

Index 107

6

1 Introduction





11 Document Usage








cent 17

e 17


permil 19 27

there4 30

B and F 31

and amp 37

62


L F etc 65

N Z R etc 65

minusint

92




7

2 Body-text symbols



















8



















9




10









11







˚vod


12





Alif Ayn





Aa =A=a Amacr

amacr










13











Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



Aˇ

aˇ




14


Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



15


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast









16















17







Ccopy ccsalowast





18








h permil

19





∐rdquo (coprod)















20









21




22










23


odplus






24



and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint



25


notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint



26


bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint

27


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28























intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)

29


˙bigparr

˘bigwith









A inplus B niplus



30








31






32






33







abc


defnntstileabcdef

abc

def

stdtstileabcdef

abc


defnnttstileabcdef

abc

def

stststileabcdef

abc


defnsdtstileabcdef

abc

def

sttstileabcdef

abc


defnsststileabcdef

abc

def

stttstileabcdef

abc


defnststileabcdef

abc

deftddtstileabcdef

abc


defnsttstileabcdef

abc

deftdststileabcdef

abc

defdntstileabcdef

abc

def

ntdtstileabcdefabc

deftdtstileabcdef


34


abc

defdnttstileabcdef

abc

def

ntststileabcdefabc

deftdttstileabcdef

abc

defdsdtstileabcdef

abc

def

nttstileabcdef abc

deftndtstileabcdef

abc

defdsststileabcdef

abc

def

ntttstileabcdef abc

deftnststileabcdef

abc

defdststileabcdef

abc


deftntstileabcdef

abc

defdsttstileabcdef

abc


deftnttstileabcdef

abc

def

dtdtstileabcdefabc


deftsdtstileabcdef

abc

def

dtststileabcdefabc


deftsststileabcdef

abc

def

dttstileabcdef abc


deftststileabcdef

abc

def

dtttstileabcdef abc


deftsttstileabcdef

abc


defsntstileabcdef

abc

def

ttdtstileabcdef

abc


defsnttstileabcdef

abc

defttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef






35











sqsubset A sqsupset



36



















37


apprge gt apprle

















38

























39









40

Table 95 Arrows






Table 96 Harpoons




Table 98 AMS Arrows






41









42






43









44




45












46


A chemarrow










47












48

















49















50














e e j im




51












niv vin

52



ww Downarrow [[

[ ]]

]

〈lang

langle 〉rang

rangle |∣∣∣ |

∥∥∥ |

dlceil

lceil erceil


~ww Uparrow

blfloor

lfloor crfloor


~w Updownarrow

((

( ))

)

∖

backslash




lgroup rgroup


bracevert



|∣∣∣ lvert |

∣∣∣ rvert

∥∥∥ lVert

∥∥∥ rVert



~

llbracket

rrbracket

53


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert


54


ETH

ETH

ETH

ETH

ETH

leftwave ETH

ETH

ETH

ETH

ETH

rightwave

Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

leftevaw Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

rightevaw



〈〈langlang


rAngle

[[[[

lBrack ]]]]

rBrack

ddlceillceil

lCeil eerceilrceil

rCeil

bblfloorlfloor


rFloor








triplegt

[[[[[[

triple[ ]]]]]]

triple]





55









a ddddota





a veca


A



56


a ringa

















˚abc wideringabc

57

















abc widearrowabc


58












abcrsaquo utildeabc














59


abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG




a dfta a DFTa












abcdef

holterabcdefabcdef

polterabcdef

60

Table 174 Dots





Table 175 AMS Dots











61


iddots


adots











`surd





62













63
















64















65


66















A AR



67




















68


















Code 37 (CP437) which was first utilized by the original IBM PC uses thesymbols SOH through US to depict ASCII characters 1ndash31 and DEL to depictASCII character 127 The NUL symbol not part of CP437 represents ASCIIcharacter 0 NBSP also not part of CP437 represents a nonbreaking spacesplitvert is merely the ldquo|rdquo character drawn as it was on the IBM PC




69





female male














70

5 Dingbats



















71

























72









baucross







73

























74





































75

















A skull


O rip



76









77

6 Other symbols














78








Aa

aa


Aa

aa


Alal KrAKra



a











79






bauforms bauhead












80





















81





times

amacr

bBm cc ˘ Mbb ˙˙

Pppp otimes

t

˘ Bmacr


˙pppp tsbm

˘ bmacr

Bbmmacr

m oo ˙˙

Ppppp tsmb

˘ Bb ˘ bbmbmacr

M˙

p ˙˙

ppppp tsmm


macrpm ps

macrvppm

˘ bbmacr


vpppm

˘ bBmacr


macrppm sim

R


ppp sim

r


˙Ppp otimes

T






82




















83


A HA I HI n Hn T HT

a Ha i Hi O HO t Ht









f Hf l Hl r Hr x Hx

F HF m Hm s Hs Y HY

G HG M HM S HS y Hy



H HH N HN ˚ Hsv







84


Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart



















85











86









72 Resizing symbols






87

Table

280

Sym

bol

Nam

eC

lash

es

Sym

bol

LAT E

X2 ε

AMS

stm

aryr

dw

asys

ymm

ath

abx

mar

vosy

mb

bd

ing

ifsy

md

ingb

atw

suip

a

baro

lt

bigtriangledown

5`

bigtriangleup

4a

checkmark

XD

Circle

5

Cross

dagger

ggg

≫Iuml

Letter

B

lightning

Lightning

E

lll

≪Icirc

Square

f

0Sun

Agrave

TriangleDown

o3

TriangleUp

n1

88



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


89

















90







endtabular












91

















92





one (ldquo=int






















93


makeatother








makeatother








e






94


makeatother













makeatother


95






ABCD












96










endcharend








97

1

2

3

4

5

6677

8






0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F




98



















99









Package Code Output










100
















101




192 C0 A lsquoA

193 C1 A rsquoA

194 C2 A Â195 C3 A ~A196 C4 A A


200 C8 E lsquoE

201 C9 E rsquoE

202 CA E Ê203 CB E E

204 CC I lsquoI

205 CD I rsquoI



209 D1 N ~N

210 D2 O lsquoO

211 D3 O rsquoO


217 D9 U lsquoU

218 DA U rsquoU

219 DB U Û220 DC U U


102



















103

















104


Name Date


105






References











106

Index




( (() 54

) ()) 53

) ()) 54

() 22 100- (-) 102 103 (a) 13 () 53

() 54

lt (⟨) 54

[ ([) 53

[ (⎡⎢⎢⎢⎢⎢⎣) 54

91] (]) 53

] (⎤⎥⎥⎥⎥⎥⎦) 54



) 82



) 79AAdaleth (D) 83


rvert






AchtBL ( ˇ ldquo==

) 79




Adobe Acrobat 99

adots ( ) 62 94







AltGr ( AltGr ) 69


AMS 7 8 21 25 30 36 37 3941 49ndash53 56 58 59 61ndash6366 87 104








text mode see AA





107














Arrowvert (ww) 53

Arrowvert (

XXXXXXX) 54

arrowvert () 53

arrowvert (




AsteriskBold (A) 74



AsteriskThin (C) 74





(EGGGGGGGGGGC) 60



(GGGGGBFGGGGG) 60



macr) 13


backslash () 54




Bart (


108





tion) 65BBm (

macr) 82

Bbm (macr

) 82bBm (

macr) 82


macr) 82

bbmb ( ˘) 82bbmx (



rdquoardquo) 15



e) 25



THORN) 26

bigboxbot (Ucirc

) 26bigboxcirc (

Otilde) 26


) 26bigboxdiv (

Oacute) 26

bigboxdot (Ocirc

) 26bigboxleft (

Oslash) 26

bigboxminus (Ntilde

) 26bigboxplus (

ETH) 26

bigboxright (Ugrave

) 26bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 26

bigcap (⋂



) 26


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 25


) 25


AElig) 26



Euml) 26

bigocirc (Aring


Ccedil) 26

bigodiv (Atilde

) 26bigodot (

⊙) 25


Egrave) 26

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


otimes) 25


Ecirc) 26


Iuml) 26


Igrave) 26

bigparallel (f) 25

bigparr (˙

) 30bigplus (

) 26

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 26


) 26

bigtimes (⨉) 29


`) 25





109


a) 25



⊎) 25



or) 25


and) 25


bigwith (˘






macr) 82

bm (package) 100 104 105bm 100bm (

macr) 82




bracevert () 53

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 54





Burns (

) 85




also hookleftarrow



Cc ( ) 82

110







checkmark (D) 77


Circle (5) 75










CircleShadow (d) 75






work 1 7 57 66 87 103104




∐) 20 25


111


Cross () 75








Ŕa) 15







Cutright (q) 71

DD (a

uml) 16




dashint (minusint

) 93


DavidStar (0) 74


ddashint (=int

) 93

ddddot (

) 56dddot (

) 56

dddtstile ( ) 34


ddots ( ) 61 94

ddots (⋱) 61

ddststile ( ) 34

ddtstile ( ) 34

ddttstile ( ) 34



DEL () 69Del ( Del ) 69






Dfourier ( c) 35

dfourier ( c ) 35

DFT ( ) 60

dft ( ) 60

112









LCD 67Mayan 62








divideontimes



dndtstile ( ) 34

dnststile ( ) 34

dntstile ( ) 34




dollar sign see $






macr) 28


dottedtilde (a) 15




113

downp ( ) 16

downparenthfill 95


downpropto () 32


downslice () 24

downspoon (⫰) 47

downt ( ) 16



downuparrows ( ) 42

downuparrows () 43



downVdash () 32

downvdash (⊤) 32

downY () 23

drsh ( ) 42

DS (SS) 79

Ds (ss) 79




dsbiological (B) 84

dschemical (C) 84

dscommercial (c) 84

dsdtstile ( ) 35


dsheraldical (H) 84

dsjuridical (J) 84

dsliterary (L) 84


dsmedical (m) 84

dsmilitary (X) 84

dsrailways (R) 84

dsststile ( ) 35

dstechnical (T) 84

dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35

dtimes () 23

dtimes (13) 23

dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35

DVI 18 69 97

dz ( ) 12

E


e (e) 51

ε-TEX 53

Earth ( ) 68

Earth (Ecirc) 68

earth () 68

Ecommerce () 17





EightStar ( ) 74









Enter ( Enter ) 69


eqslantgtr () 37

eqslantgtr (⪖) 39

eqslantless ( ) 38

eqslantless () 37


eqsmile () 48

equal (=) 32

equal (j) 82

equalclosed () 32

equalsfill 20 95

equidecomposable 91


equiv (equiv) 20 30

equiv (equiv) 32


equivclosed () 32

er ( ) 11

es-zet see ss

ESC () 69

Esc ( Esc ) 69


esh ( ) 11

esh ( ) 12


Estatically (J) 70



eta (η) 49

etaup (η) 50

ETB () 69

etc (P) 82

eth (eth) 63

eth ( ) 11

eth ( ) 12

ETX () 69

eufrak (package) 65

Euler Roman 50

EUR (e ) 17

EURcr (d) 17

EURdig (D) 17

EURhv (c) 17

euro 17

euro signs 17

blackboard bold 65


EURtm (e) 17



evil spirits 86

exclusive or 90

exists ( ) 51

exists (exist) 51

exists (exist) 51

exp (exp) 49





114




textquotesingle


Ferli (aa) 79

Fermi (aa







FF () 69fge (package) 47 52 56 62 64














40












(t) 75












fint (gt

) 27

fint (ffl) 28






FiveStar (8) 74




FiveStarOpen (9) 74


115





fixedddots ( ) 61

fixedvdots () 61






OT2 90T1 7 9 13 101 103T4 9 13 16T5 9 13TS1 103





FourAsterisk (1) 74



Fourier ( c) 35







gets see leftarrow






gtreqless (R) 37



116

gtreqqless (T) 37

gtreqqless (⪌) 39





h (ả) 13HA (A) 84











HandLeft () 72

HandLeftUp () 72


HandRight () 72



HB (B) 84

Hb (b) 84






HI (I) 84

Hi (i) 84Hibl (˝) 84

Hibp (ˆ) 84

Hibs (uml) 84


mathhill (a

) 15


radic) 93

HL (L) 84Hl (l) 84HM (M) 84

Hm (m) 84

Hman (ˇ) 84

Hmillion (7) 84



holter ( ) 60


Homer (


Hplus (+) 84HQ (Q) 84Hq (q) 84


Hs (s) 84

Hscribe (macr) 84


Hthousand (4) 84

Htongue (˘) 84

HU (U) 84


Hut () 81

HV (V) 84

117

Hv (v) 84hv () 12Hvbar (|) 84HW (W) 84

Hw (w) 84HX (X) 84

Hx (x) 84

HXthousand (5) 84

HY (Y) 84


HZ (Z) 84Hz (z) 84


iddots ( ) 62

iddots () 94


) 25

idotsint (

) 27


ifsym (package) 67 75 80 8188 90 104 105



) 25

iiiint (

) 27

iiiint (ˇ

) 28


micro) 26

iiint (intintint

) 25

iiint (

) 25 27

iiint (˝

) 28


acute) 26

iint (intint

) 25

iint (

) 25 27

iint (˜

) 28



and vdash


textquotedbl







int (sup3) 26

int (int

) 25

int (r

) 25

int (int) 29

intclockwise () 29






irony mark ( ) 90


Jj () 13

JackStar (2) 74







118

lambdaslash (n) 63

lambdaup (λ) 50


land see wedge

landdownint () 28


landupint () 28

landupint (⨙) 29

Langle (lt) 65

lAngle (〈〈) 55

langle (〈) 20 53

langle (⟨) 54

langlebar (n) 54

Laplace ( s c) 35

laplace ( c s) 35




largecircle () 74

largediamond () 74


largepencil (W) 72



largestar () 74






LArrow ( larr ) 69

larrowfill 60

Laserbeam (a) 70




latfric () 11

Latin 1 7 101 103 104

table 102

laundry symbols 80

Lbag (P) 52

lbag (N) 52


) 54

Lbrack ([) 65

lBrack ([[) 55

LCD digits 67

lCeil (dd) 55

lceil (d) 53

lceil (⎡⎢⎢⎢⎢⎢⎢) 54






leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55






leftwave (

ETH

ETH

ETH

ETH

) 55


119


lesseqgtr (Q) 37



lesseqqgtr (S) 37

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

LF () 69

lfilet (

7777) 54


lfloor (⎢⎢⎢⎢⎢⎢⎣) 54

lg (lg) 49

lgroup (

) 53

lgroup (⎧⎪⎪⎪⎪⎪⎩) 54







Lisa (

) 85lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 54


llcorner () 54



lmoustache (

) 53





and see wedge

not see neg and sim

or see vee





120

lrcorner () 54

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 54



lwave (

ETH

ETH

ETH

ETH

) 55

lWavy (_______

) 54

lwavy (^^^) 54

lz (1) 11

MM 9M (

macr) 82

m 9m (

macr) 82


Maggie ( ) 85


manpenkidney () 79





Marge (

















cient seeDH



121



micro (micro) 67


textperthousand





32 33 37 39 40 43ndash48 5051 54 56ndash58 61 63 64 74104 105










ncong () 30


nddtstile ( ) 35


122


ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 37 38


ngeqq () 37

ngeqq (iquest) 39

ngeqslant () 37





ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 12

NibLeft () 72


NibSolidLeft ( ) 72


123




nleq () 37 38


nleqq () 37

nleqq (frac34) 39

nleqslant () 37





nlessgtr () 38

nlessgtr (≸) 39



nnststile ( ) 35

nntstile ( ) 34


tion) 25




notni


npreceq () 30


124




nsststile ( ) 34

nststile ( ) 34



nsubseteq () 36


nsucceq () 30


nsupseteq (+) 36


ntdtstile ( ) 34


125






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35











˚) 15


ohm (Ω) 67

Ohne (a) 79


oiiint ()

) 27

oiiint (

) 29

oiiintclockwise (L

) 27


) 27

oiint (middot

) 26

oiint (

) 25 27

oiint (sbquo

) 28

oiint (

) 29

oiint (∯) 29

oiintclockwise (H

) 27

oiintctrclockwise (

) 27

oint (para) 26

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 29

ointctrclockwise (

) 27




126





oright (i) 24



overbrace (hkkikkj

) 58

overbrace (copy

) 58


) 58


) 57

overbracket ( ) 58


rdquoa) 15

overgroup (hkkkkj

) 58




overline ( ) 20 57






PP (para) 8 102p (

˙) 82

p 94package options



amsmath 7 49 56 91 99amssymb 7 20 30 36 4156 62 65 104 105 107









mathdots 56 61 62 94 104105



127





timing 67tipa 10 11 13 15 16 90104 105




wsuipa 11 15 16 88 90 94104 105

yfonts 65 104 105yhmath 57 59 62 94 104






















textperthousand


passedpawn (r) 82


Peace () 77

PencilLeft () 72


PencilLeftUp () 72

PencilRight () 72


PencilRightUp () 72

pencils 72

pentagon (D) 74

pentagram () 24

people see faces

percent sign see

permil (h) 19

Perp (y) 31

perp (perp) 30 93

perp (perp) 33


Pfund (pound) 17




Phaistos disk 83


PHarrow (J) 83

PHbee (h) 83

PHbeehive (X) 83

PHboomerang (R) 83

PHbow (K) 83

PHbullLeg (b) 83

PHcaptive (D) 83


PHcat (c) 83

PHchild (E) 83

PHclub (M) 83

PHcolumn (W) 83

PHcomb (U) 83

PHdolium (T) 83

PHdove (f) 83

PHeagle (e) 83

PHflute (o) 83

PHgaunlet (H) 83

PHgrater (p) 83

PHhelmet (G) 83

PHhide (a) 83

128


PHlid (Q) 83

PHlily (m) 83

PHmanacles (N) 83

PHmattock (O) 83



PHoxBack (n) 83

PHpapyrus (k) 83

PHpedestrian (A) 83

PHplaneTree (i) 83

PHplumedHead (B) 83

PHram (d) 83

PHrosette (l) 83

PHsaw (P) 83

PHshield (L) 83

PHship (Y) 83

PHsling (V) 83

PHsmallAxe (r) 83

PHstrainer (q) 83



PHvine (j) 83

PHwavyBand (s) 83



pipe see textpipe








macr) 82


polter ( ) 60



macr) 82

Ppp ( ˙˙) 82

ppp ( ˙˙

) 82Pppp ( ˙

˙) 82

pppp ( ˙˙

) 82Ppppp ( ˙

˙) 82

ppppp ( ˙˙




prod) 25




31 36 38 41 42 48 50 5162 63 65 87 101

Pxp ( ˙) 82pxp ( ˙ ) 82



129

RR ( sim

) 82r (a) 13r ( sim

) 82



Rain () 80



rangle (⟩) 54

ranglebar (s) 54

RArrow ( rarr ) 69



hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 54





recorder () 78

Rectangle (u) 75




rqm


textregistered



upharpoonright


Return ( larr ) 69


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

revD () 12

revddots ( ) 94


textbackslash


rfilet (

) 54


rfloor (⎥⎥⎥⎥⎥⎥⎦) 54

rgroup (

) 53

rgroup (⎫⎪⎪⎪⎪⎪⎭) 54



RightDiamond () 75

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55



130


rightwave (

ETH

ETH

ETH

ETH

) 55




rmoustache (

) 53




rrangle (⟫) 54


rsem (MQQQQQO) 54




rwave (

ETH

ETH

ETH

ETH

) 55

rWavy (_______

) 54

rwavy (^^^) 54








ScissorLeft () 71




() 71


scu (W) 12

scy (]) 12

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 79


) 79











union see cup

setminus () 20

131








([) 74

SixStar (G) 74







SmallCircle (E) 75












sndtstile ( ) 35

Snow () 80

SnowCloud () 80

Snowflake (`) 74



SNPP () 85

snststile ( ) 35

sntstile ( ) 35




Sparkle (]) 74


SpinDown () 75


sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

132

sqrt (radic


Square (0) 75



hooked see hksqrt


(k) 75




SquareShadowA () 75

SquareShadowB () 75


SquareShadowC () 75



SquareSolid (g) 75











squplus (]) 22

SS (SS) 9

ss (szlig) 9

ssdtstile ( ) 35

ssearrow () 42

sslash () 21

ssststile ( ) 35

sststile ( ) 35

ssttstile ( ) 35

sswarrow ($) 42

stackrel 20 91 95

standard state 91

star () 20 94

star (⋆) 24

Star of David 73 74

stars 63 73 74


staveI () 85

staveII () 85

staveIII () 85

staveIV () 85

staveIX () 85

staveL (1) 85 86

staveLI (2) 85

staveLII (3) 85

staveLIII (4) 85

staveLIV (5) 85

staveLIX () 85

staveLV (6) 85

staveLVI (7) 85

staveLVII (8) 85

staveLVIII (9) 85

staveLX () 85

staveLXI (lt) 85

staveLXII (=) 85

staveLXIII (gt) 86

staveLXIV () 86

staveLXV () 86

staveLXVI (A) 86

staveLXVII (B) 86

staveLXVIII (C) 86

staves 85


staveV () 85

staveVI () 85

staveVII () 85

staveVIII () 85

staveX () 85

staveXI () 85

staveXII () 85

staveXIII () 85

staveXIV (13) 85

staveXIX () 86

staveXL () 86

staveXLI (() 86

staveXLII ()) 86

staveXLIII () 86

staveXLIV (+) 86

staveXLIX (0) 85

staveXLV () 86

staveXLVI (-) 86

staveXLVII () 85

staveXLVIII () 85

staveXV () 85

staveXVI () 85

staveXVII () 86

staveXVIII () 86

staveXX () 86

staveXXI () 86

staveXXII () 86

staveXXIII () 86

staveXXIV () 85

staveXXIX () 85

staveXXV () 85

staveXXVI () 85

staveXXVII () 85

133

staveXXVIII () 85

staveXXX () 85

staveXXXI () 85

staveXXXII () 85

staveXXXIII ( ) 85

staveXXXIV () 85

staveXXXIX (amp) 85

staveXXXV () 85


stdtstile ( ) 34





StopWatchEnd () 81


strokedint (⨏) 29

StrokeFive () 81

StrokeFour () 81

StrokeOne () 81

StrokeThree () 81


stststile ( ) 34

sttstile ( ) 34

stttstile ( ) 34


^) 15



sublptr (aiexcl) 15






sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 81




SunCloud () 80





`) 62




134





) 82

t ( a) 13t ( otimes




Tape () 77


tddtstile ( ) 34

tdststile ( ) 34

tdtstile ( ) 34

tdttstile ( ) 35









8 13 17ndash19 41 56 64 6778 87 101 103ndash105


135


textdbend (




textlhdbend (~


136



mdasha) 14





) 76



rsaquo) 14




ˆ) 14

textsubdot (a˙) 14


lsaquo) 14


˚) 14


˜) 14



ˇ) 14



) 15



137





textperthousand




90 104 105tipx (package) 11 104 105

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35




alphabets math




TriangleDown (3) 75






TriangleUp (1) 75





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 70

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



31 36 38 41 42 48 50 5162 63 65 87 89 101 104105


UU (a

˘) 16




ulcorner () 54

ullcorner (6) 54

ulrcorner () 54



138


underbrace (reg) 58



underbracket ( ) 58


















urcorner () 54


˜) 15

utilde (˜) 59






139



varint (r




) 27


)

27varoiint (

) 28


) 27


) 27

varoint (u

) 25

varointclockwise (-

) 27



) 27



) 27







vdots () 61




Village () 81



˚) 12


macr) 82

vpppm (macr



17 19ndash21 25 30 36 38 4161ndash63 67 68 70 73 74 7888 104 105





Ţ) 15


140


widering (Ucirc) 58





90 94 104 105wupperhand (c) 82

Xx ( ˙˙) 82XBox (4) 73

Xdvi 90



Xi (Ξ) 49

xi (ξ) 49

xiup (ξ) 50










xlongequal (===) 60

xlongequal (===) 60









XML 103







Xs 73 76

XSolid () 73

XSolidBold ($) 73

XSolidBrush () 73







Ztransf ( s c) 35



ZwPa ( A ) 79

141



5




References 106

Index 107

6

1 Introduction





11 Document Usage








cent 17

e 17


permil 19 27

there4 30

B and F 31

and amp 37

62


L F etc 65

N Z R etc 65

minusint

92




7

2 Body-text symbols



















8



















9




10









11







˚vod


12





Alif Ayn





Aa =A=a Amacr

amacr










13











Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



Aˇ

aˇ




14


Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



15


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast









16















17







Ccopy ccsalowast





18








h permil

19





∐rdquo (coprod)















20









21




22










23


odplus






24



and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint



25


notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint



26


bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint

27


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28























intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)

29


˙bigparr

˘bigwith









A inplus B niplus



30








31






32






33







abc


defnntstileabcdef

abc

def

stdtstileabcdef

abc


defnnttstileabcdef

abc

def

stststileabcdef

abc


defnsdtstileabcdef

abc

def

sttstileabcdef

abc


defnsststileabcdef

abc

def

stttstileabcdef

abc


defnststileabcdef

abc

deftddtstileabcdef

abc


defnsttstileabcdef

abc

deftdststileabcdef

abc

defdntstileabcdef

abc

def

ntdtstileabcdefabc

deftdtstileabcdef


34


abc

defdnttstileabcdef

abc

def

ntststileabcdefabc

deftdttstileabcdef

abc

defdsdtstileabcdef

abc

def

nttstileabcdef abc

deftndtstileabcdef

abc

defdsststileabcdef

abc

def

ntttstileabcdef abc

deftnststileabcdef

abc

defdststileabcdef

abc


deftntstileabcdef

abc

defdsttstileabcdef

abc


deftnttstileabcdef

abc

def

dtdtstileabcdefabc


deftsdtstileabcdef

abc

def

dtststileabcdefabc


deftsststileabcdef

abc

def

dttstileabcdef abc


deftststileabcdef

abc

def

dtttstileabcdef abc


deftsttstileabcdef

abc


defsntstileabcdef

abc

def

ttdtstileabcdef

abc


defsnttstileabcdef

abc

defttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef






35











sqsubset A sqsupset



36



















37


apprge gt apprle

















38

























39









40

Table 95 Arrows






Table 96 Harpoons




Table 98 AMS Arrows






41









42






43









44




45












46


A chemarrow










47












48

















49















50














e e j im




51












niv vin

52



ww Downarrow [[

[ ]]

]

〈lang

langle 〉rang

rangle |∣∣∣ |

∥∥∥ |

dlceil

lceil erceil


~ww Uparrow

blfloor

lfloor crfloor


~w Updownarrow

((

( ))

)

∖

backslash




lgroup rgroup


bracevert



|∣∣∣ lvert |

∣∣∣ rvert

∥∥∥ lVert

∥∥∥ rVert



~

llbracket

rrbracket

53


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert


54


ETH

ETH

ETH

ETH

ETH

leftwave ETH

ETH

ETH

ETH

ETH

rightwave

Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

leftevaw Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

rightevaw



〈〈langlang


rAngle

[[[[

lBrack ]]]]

rBrack

ddlceillceil

lCeil eerceilrceil

rCeil

bblfloorlfloor


rFloor








triplegt

[[[[[[

triple[ ]]]]]]

triple]





55









a ddddota





a veca


A



56


a ringa

















˚abc wideringabc

57

















abc widearrowabc


58












abcrsaquo utildeabc














59


abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG




a dfta a DFTa












abcdef

holterabcdefabcdef

polterabcdef

60

Table 174 Dots





Table 175 AMS Dots











61


iddots


adots











`surd





62













63
















64















65


66















A AR



67




















68






















69





female male














70

5 Dingbats



















71

























72









baucross







73

























74





































75

















A skull


O rip



76









77

6 Other symbols














78








Aa

aa


Aa

aa


Alal KrAKra



a











79






bauforms bauhead












80





















81





times

amacr

bBm cc ˘ Mbb ˙˙

Pppp otimes

t

˘ Bmacr


˙pppp tsbm

˘ bmacr

Bbmmacr

m oo ˙˙

Ppppp tsmb

˘ Bb ˘ bbmbmacr

M˙

p ˙˙

ppppp tsmm


macrpm ps

macrvppm

˘ bbmacr


vpppm

˘ bBmacr


macrppm sim

R


ppp sim

r


˙Ppp otimes

T






82




















83


A HA I HI n Hn T HT

a Ha i Hi O HO t Ht









f Hf l Hl r Hr x Hx

F HF m Hm s Hs Y HY

G HG M HM S HS y Hy



H HH N HN ˚ Hsv







84


Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart



















85











86









72 Resizing symbols






87

Table

280

Sym

bol

Nam

eC

lash

es

Sym

bol

LAT E

X2 ε

AMS

stm

aryr

dw

asys

ymm

ath

abx

mar

vosy

mb

bd

ing

ifsy

md

ingb

atw

suip

a

baro

lt

bigtriangledown

5`

bigtriangleup

4a

checkmark

XD

Circle

5

Cross

dagger

ggg

≫Iuml

Letter

B

lightning

Lightning

E

lll

≪Icirc

Square

f

0Sun

Agrave

TriangleDown

o3

TriangleUp

n1

88



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


89

















90







endtabular












91

















92





one (ldquo=int






















93


makeatother








makeatother








e






94


makeatother













makeatother


95






ABCD












96










endcharend








97

1

2

3

4

5

6677

8






0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F




98



















99









Package Code Output










100
















101




192 C0 A lsquoA

193 C1 A rsquoA

194 C2 A Â195 C3 A ~A196 C4 A A


200 C8 E lsquoE

201 C9 E rsquoE

202 CA E Ê203 CB E E

204 CC I lsquoI

205 CD I rsquoI



209 D1 N ~N

210 D2 O lsquoO

211 D3 O rsquoO


217 D9 U lsquoU

218 DA U rsquoU

219 DB U Û220 DC U U


102



















103

















104


Name Date


105






References











106

Index




( (() 54

) ()) 53

) ()) 54

() 22 100- (-) 102 103 (a) 13 () 53

() 54

lt (⟨) 54

[ ([) 53

[ (⎡⎢⎢⎢⎢⎢⎣) 54

91] (]) 53

] (⎤⎥⎥⎥⎥⎥⎦) 54



) 82



) 79AAdaleth (D) 83


rvert






AchtBL ( ˇ ldquo==

) 79




Adobe Acrobat 99

adots ( ) 62 94







AltGr ( AltGr ) 69


AMS 7 8 21 25 30 36 37 3941 49ndash53 56 58 59 61ndash6366 87 104








text mode see AA





107














Arrowvert (ww) 53

Arrowvert (

XXXXXXX) 54

arrowvert () 53

arrowvert (




AsteriskBold (A) 74



AsteriskThin (C) 74





(EGGGGGGGGGGC) 60



(GGGGGBFGGGGG) 60



macr) 13


backslash () 54




Bart (


108





tion) 65BBm (

macr) 82

Bbm (macr

) 82bBm (

macr) 82


macr) 82

bbmb ( ˘) 82bbmx (



rdquoardquo) 15



e) 25



THORN) 26

bigboxbot (Ucirc

) 26bigboxcirc (

Otilde) 26


) 26bigboxdiv (

Oacute) 26

bigboxdot (Ocirc

) 26bigboxleft (

Oslash) 26

bigboxminus (Ntilde

) 26bigboxplus (

ETH) 26

bigboxright (Ugrave

) 26bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 26

bigcap (⋂



) 26


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 25


) 25


AElig) 26



Euml) 26

bigocirc (Aring


Ccedil) 26

bigodiv (Atilde

) 26bigodot (

⊙) 25


Egrave) 26

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


otimes) 25


Ecirc) 26


Iuml) 26


Igrave) 26

bigparallel (f) 25

bigparr (˙

) 30bigplus (

) 26

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 26


) 26

bigtimes (⨉) 29


`) 25





109


a) 25



⊎) 25



or) 25


and) 25


bigwith (˘






macr) 82

bm (package) 100 104 105bm 100bm (

macr) 82




bracevert () 53

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 54





Burns (

) 85




also hookleftarrow



Cc ( ) 82

110







checkmark (D) 77


Circle (5) 75










CircleShadow (d) 75






work 1 7 57 66 87 103104




∐) 20 25


111


Cross () 75








Ŕa) 15







Cutright (q) 71

DD (a

uml) 16




dashint (minusint

) 93


DavidStar (0) 74


ddashint (=int

) 93

ddddot (

) 56dddot (

) 56

dddtstile ( ) 34


ddots ( ) 61 94

ddots (⋱) 61

ddststile ( ) 34

ddtstile ( ) 34

ddttstile ( ) 34



DEL () 69Del ( Del ) 69






Dfourier ( c) 35

dfourier ( c ) 35

DFT ( ) 60

dft ( ) 60

112









LCD 67Mayan 62








divideontimes



dndtstile ( ) 34

dnststile ( ) 34

dntstile ( ) 34




dollar sign see $






macr) 28


dottedtilde (a) 15




113

downp ( ) 16

downparenthfill 95


downpropto () 32


downslice () 24

downspoon (⫰) 47

downt ( ) 16



downuparrows ( ) 42

downuparrows () 43



downVdash () 32

downvdash (⊤) 32

downY () 23

drsh ( ) 42

DS (SS) 79

Ds (ss) 79




dsbiological (B) 84

dschemical (C) 84

dscommercial (c) 84

dsdtstile ( ) 35


dsheraldical (H) 84

dsjuridical (J) 84

dsliterary (L) 84


dsmedical (m) 84

dsmilitary (X) 84

dsrailways (R) 84

dsststile ( ) 35

dstechnical (T) 84

dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35

dtimes () 23

dtimes (13) 23

dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35

DVI 18 69 97

dz ( ) 12

E


e (e) 51

ε-TEX 53

Earth ( ) 68

Earth (Ecirc) 68

earth () 68

Ecommerce () 17





EightStar ( ) 74









Enter ( Enter ) 69


eqslantgtr () 37

eqslantgtr (⪖) 39

eqslantless ( ) 38

eqslantless () 37


eqsmile () 48

equal (=) 32

equal (j) 82

equalclosed () 32

equalsfill 20 95

equidecomposable 91


equiv (equiv) 20 30

equiv (equiv) 32


equivclosed () 32

er ( ) 11

es-zet see ss

ESC () 69

Esc ( Esc ) 69


esh ( ) 11

esh ( ) 12


Estatically (J) 70



eta (η) 49

etaup (η) 50

ETB () 69

etc (P) 82

eth (eth) 63

eth ( ) 11

eth ( ) 12

ETX () 69

eufrak (package) 65

Euler Roman 50

EUR (e ) 17

EURcr (d) 17

EURdig (D) 17

EURhv (c) 17

euro 17

euro signs 17

blackboard bold 65


EURtm (e) 17



evil spirits 86

exclusive or 90

exists ( ) 51

exists (exist) 51

exists (exist) 51

exp (exp) 49





114




textquotesingle


Ferli (aa) 79

Fermi (aa







FF () 69fge (package) 47 52 56 62 64














40












(t) 75












fint (gt

) 27

fint (ffl) 28






FiveStar (8) 74




FiveStarOpen (9) 74


115





fixedddots ( ) 61

fixedvdots () 61






OT2 90T1 7 9 13 101 103T4 9 13 16T5 9 13TS1 103





FourAsterisk (1) 74



Fourier ( c) 35







gets see leftarrow






gtreqless (R) 37



116

gtreqqless (T) 37

gtreqqless (⪌) 39





h (ả) 13HA (A) 84











HandLeft () 72

HandLeftUp () 72


HandRight () 72



HB (B) 84

Hb (b) 84






HI (I) 84

Hi (i) 84Hibl (˝) 84

Hibp (ˆ) 84

Hibs (uml) 84


mathhill (a

) 15


radic) 93

HL (L) 84Hl (l) 84HM (M) 84

Hm (m) 84

Hman (ˇ) 84

Hmillion (7) 84



holter ( ) 60


Homer (


Hplus (+) 84HQ (Q) 84Hq (q) 84


Hs (s) 84

Hscribe (macr) 84


Hthousand (4) 84

Htongue (˘) 84

HU (U) 84


Hut () 81

HV (V) 84

117

Hv (v) 84hv () 12Hvbar (|) 84HW (W) 84

Hw (w) 84HX (X) 84

Hx (x) 84

HXthousand (5) 84

HY (Y) 84


HZ (Z) 84Hz (z) 84


iddots ( ) 62

iddots () 94


) 25

idotsint (

) 27


ifsym (package) 67 75 80 8188 90 104 105



) 25

iiiint (

) 27

iiiint (ˇ

) 28


micro) 26

iiint (intintint

) 25

iiint (

) 25 27

iiint (˝

) 28


acute) 26

iint (intint

) 25

iint (

) 25 27

iint (˜

) 28



and vdash


textquotedbl







int (sup3) 26

int (int

) 25

int (r

) 25

int (int) 29

intclockwise () 29






irony mark ( ) 90


Jj () 13

JackStar (2) 74







118

lambdaslash (n) 63

lambdaup (λ) 50


land see wedge

landdownint () 28


landupint () 28

landupint (⨙) 29

Langle (lt) 65

lAngle (〈〈) 55

langle (〈) 20 53

langle (⟨) 54

langlebar (n) 54

Laplace ( s c) 35

laplace ( c s) 35




largecircle () 74

largediamond () 74


largepencil (W) 72



largestar () 74






LArrow ( larr ) 69

larrowfill 60

Laserbeam (a) 70




latfric () 11

Latin 1 7 101 103 104

table 102

laundry symbols 80

Lbag (P) 52

lbag (N) 52


) 54

Lbrack ([) 65

lBrack ([[) 55

LCD digits 67

lCeil (dd) 55

lceil (d) 53

lceil (⎡⎢⎢⎢⎢⎢⎢) 54






leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55






leftwave (

ETH

ETH

ETH

ETH

) 55


119


lesseqgtr (Q) 37



lesseqqgtr (S) 37

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

LF () 69

lfilet (

7777) 54


lfloor (⎢⎢⎢⎢⎢⎢⎣) 54

lg (lg) 49

lgroup (

) 53

lgroup (⎧⎪⎪⎪⎪⎪⎩) 54







Lisa (

) 85lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 54


llcorner () 54



lmoustache (

) 53





and see wedge

not see neg and sim

or see vee





120

lrcorner () 54

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 54



lwave (

ETH

ETH

ETH

ETH

) 55

lWavy (_______

) 54

lwavy (^^^) 54

lz (1) 11

MM 9M (

macr) 82

m 9m (

macr) 82


Maggie ( ) 85


manpenkidney () 79





Marge (

















cient seeDH



121



micro (micro) 67


textperthousand





32 33 37 39 40 43ndash48 5051 54 56ndash58 61 63 64 74104 105










ncong () 30


nddtstile ( ) 35


122


ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 37 38


ngeqq () 37

ngeqq (iquest) 39

ngeqslant () 37





ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 12

NibLeft () 72


NibSolidLeft ( ) 72


123




nleq () 37 38


nleqq () 37

nleqq (frac34) 39

nleqslant () 37





nlessgtr () 38

nlessgtr (≸) 39



nnststile ( ) 35

nntstile ( ) 34


tion) 25




notni


npreceq () 30


124




nsststile ( ) 34

nststile ( ) 34



nsubseteq () 36


nsucceq () 30


nsupseteq (+) 36


ntdtstile ( ) 34


125






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35











˚) 15


ohm (Ω) 67

Ohne (a) 79


oiiint ()

) 27

oiiint (

) 29

oiiintclockwise (L

) 27


) 27

oiint (middot

) 26

oiint (

) 25 27

oiint (sbquo

) 28

oiint (

) 29

oiint (∯) 29

oiintclockwise (H

) 27

oiintctrclockwise (

) 27

oint (para) 26

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 29

ointctrclockwise (

) 27




126





oright (i) 24



overbrace (hkkikkj

) 58

overbrace (copy

) 58


) 58


) 57

overbracket ( ) 58


rdquoa) 15

overgroup (hkkkkj

) 58




overline ( ) 20 57






PP (para) 8 102p (

˙) 82

p 94package options



amsmath 7 49 56 91 99amssymb 7 20 30 36 4156 62 65 104 105 107









mathdots 56 61 62 94 104105



127





timing 67tipa 10 11 13 15 16 90104 105




wsuipa 11 15 16 88 90 94104 105

yfonts 65 104 105yhmath 57 59 62 94 104






















textperthousand


passedpawn (r) 82


Peace () 77

PencilLeft () 72


PencilLeftUp () 72

PencilRight () 72


PencilRightUp () 72

pencils 72

pentagon (D) 74

pentagram () 24

people see faces

percent sign see

permil (h) 19

Perp (y) 31

perp (perp) 30 93

perp (perp) 33


Pfund (pound) 17




Phaistos disk 83


PHarrow (J) 83

PHbee (h) 83

PHbeehive (X) 83

PHboomerang (R) 83

PHbow (K) 83

PHbullLeg (b) 83

PHcaptive (D) 83


PHcat (c) 83

PHchild (E) 83

PHclub (M) 83

PHcolumn (W) 83

PHcomb (U) 83

PHdolium (T) 83

PHdove (f) 83

PHeagle (e) 83

PHflute (o) 83

PHgaunlet (H) 83

PHgrater (p) 83

PHhelmet (G) 83

PHhide (a) 83

128


PHlid (Q) 83

PHlily (m) 83

PHmanacles (N) 83

PHmattock (O) 83



PHoxBack (n) 83

PHpapyrus (k) 83

PHpedestrian (A) 83

PHplaneTree (i) 83

PHplumedHead (B) 83

PHram (d) 83

PHrosette (l) 83

PHsaw (P) 83

PHshield (L) 83

PHship (Y) 83

PHsling (V) 83

PHsmallAxe (r) 83

PHstrainer (q) 83



PHvine (j) 83

PHwavyBand (s) 83



pipe see textpipe








macr) 82


polter ( ) 60



macr) 82

Ppp ( ˙˙) 82

ppp ( ˙˙

) 82Pppp ( ˙

˙) 82

pppp ( ˙˙

) 82Ppppp ( ˙

˙) 82

ppppp ( ˙˙




prod) 25




31 36 38 41 42 48 50 5162 63 65 87 101

Pxp ( ˙) 82pxp ( ˙ ) 82



129

RR ( sim

) 82r (a) 13r ( sim

) 82



Rain () 80



rangle (⟩) 54

ranglebar (s) 54

RArrow ( rarr ) 69



hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 54





recorder () 78

Rectangle (u) 75




rqm


textregistered



upharpoonright


Return ( larr ) 69


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

revD () 12

revddots ( ) 94


textbackslash


rfilet (

) 54


rfloor (⎥⎥⎥⎥⎥⎥⎦) 54

rgroup (

) 53

rgroup (⎫⎪⎪⎪⎪⎪⎭) 54



RightDiamond () 75

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55



130


rightwave (

ETH

ETH

ETH

ETH

) 55




rmoustache (

) 53




rrangle (⟫) 54


rsem (MQQQQQO) 54




rwave (

ETH

ETH

ETH

ETH

) 55

rWavy (_______

) 54

rwavy (^^^) 54








ScissorLeft () 71




() 71


scu (W) 12

scy (]) 12

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 79


) 79











union see cup

setminus () 20

131








([) 74

SixStar (G) 74







SmallCircle (E) 75












sndtstile ( ) 35

Snow () 80

SnowCloud () 80

Snowflake (`) 74



SNPP () 85

snststile ( ) 35

sntstile ( ) 35




Sparkle (]) 74


SpinDown () 75


sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

132

sqrt (radic


Square (0) 75



hooked see hksqrt


(k) 75




SquareShadowA () 75

SquareShadowB () 75


SquareShadowC () 75



SquareSolid (g) 75











squplus (]) 22

SS (SS) 9

ss (szlig) 9

ssdtstile ( ) 35

ssearrow () 42

sslash () 21

ssststile ( ) 35

sststile ( ) 35

ssttstile ( ) 35

sswarrow ($) 42

stackrel 20 91 95

standard state 91

star () 20 94

star (⋆) 24

Star of David 73 74

stars 63 73 74


staveI () 85

staveII () 85

staveIII () 85

staveIV () 85

staveIX () 85

staveL (1) 85 86

staveLI (2) 85

staveLII (3) 85

staveLIII (4) 85

staveLIV (5) 85

staveLIX () 85

staveLV (6) 85

staveLVI (7) 85

staveLVII (8) 85

staveLVIII (9) 85

staveLX () 85

staveLXI (lt) 85

staveLXII (=) 85

staveLXIII (gt) 86

staveLXIV () 86

staveLXV () 86

staveLXVI (A) 86

staveLXVII (B) 86

staveLXVIII (C) 86

staves 85


staveV () 85

staveVI () 85

staveVII () 85

staveVIII () 85

staveX () 85

staveXI () 85

staveXII () 85

staveXIII () 85

staveXIV (13) 85

staveXIX () 86

staveXL () 86

staveXLI (() 86

staveXLII ()) 86

staveXLIII () 86

staveXLIV (+) 86

staveXLIX (0) 85

staveXLV () 86

staveXLVI (-) 86

staveXLVII () 85

staveXLVIII () 85

staveXV () 85

staveXVI () 85

staveXVII () 86

staveXVIII () 86

staveXX () 86

staveXXI () 86

staveXXII () 86

staveXXIII () 86

staveXXIV () 85

staveXXIX () 85

staveXXV () 85

staveXXVI () 85

staveXXVII () 85

133

staveXXVIII () 85

staveXXX () 85

staveXXXI () 85

staveXXXII () 85

staveXXXIII ( ) 85

staveXXXIV () 85

staveXXXIX (amp) 85

staveXXXV () 85


stdtstile ( ) 34





StopWatchEnd () 81


strokedint (⨏) 29

StrokeFive () 81

StrokeFour () 81

StrokeOne () 81

StrokeThree () 81


stststile ( ) 34

sttstile ( ) 34

stttstile ( ) 34


^) 15



sublptr (aiexcl) 15






sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 81




SunCloud () 80





`) 62




134





) 82

t ( a) 13t ( otimes




Tape () 77


tddtstile ( ) 34

tdststile ( ) 34

tdtstile ( ) 34

tdttstile ( ) 35









8 13 17ndash19 41 56 64 6778 87 101 103ndash105


135


textdbend (




textlhdbend (~


136



mdasha) 14





) 76



rsaquo) 14




ˆ) 14

textsubdot (a˙) 14


lsaquo) 14


˚) 14


˜) 14



ˇ) 14



) 15



137





textperthousand




90 104 105tipx (package) 11 104 105

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35




alphabets math




TriangleDown (3) 75






TriangleUp (1) 75





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 70

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



31 36 38 41 42 48 50 5162 63 65 87 89 101 104105


UU (a

˘) 16




ulcorner () 54

ullcorner (6) 54

ulrcorner () 54



138


underbrace (reg) 58



underbracket ( ) 58


















urcorner () 54


˜) 15

utilde (˜) 59






139



varint (r




) 27


)

27varoiint (

) 28


) 27


) 27

varoint (u

) 25

varointclockwise (-

) 27



) 27



) 27







vdots () 61




Village () 81



˚) 12


macr) 82

vpppm (macr



17 19ndash21 25 30 36 38 4161ndash63 67 68 70 73 74 7888 104 105





Ţ) 15


140


widering (Ucirc) 58





90 94 104 105wupperhand (c) 82

Xx ( ˙˙) 82XBox (4) 73

Xdvi 90



Xi (Ξ) 49

xi (ξ) 49

xiup (ξ) 50










xlongequal (===) 60

xlongequal (===) 60









XML 103







Xs 73 76

XSolid () 73

XSolidBold ($) 73

XSolidBrush () 73







Ztransf ( s c) 35



ZwPa ( A ) 79

141




References 106

Index 107

6

1 Introduction





11 Document Usage








cent 17

e 17


permil 19 27

there4 30

B and F 31

and amp 37

62


L F etc 65

N Z R etc 65

minusint

92




7

2 Body-text symbols



















8



















9




10









11







˚vod


12





Alif Ayn





Aa =A=a Amacr

amacr










13











Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



Aˇ

aˇ




14


Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



15


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast









16















17







Ccopy ccsalowast





18








h permil

19





∐rdquo (coprod)















20









21




22










23


odplus






24



and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint



25


notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint



26


bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint

27


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28























intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)

29


˙bigparr

˘bigwith









A inplus B niplus



30








31






32






33







abc


defnntstileabcdef

abc

def

stdtstileabcdef

abc


defnnttstileabcdef

abc

def

stststileabcdef

abc


defnsdtstileabcdef

abc

def

sttstileabcdef

abc


defnsststileabcdef

abc

def

stttstileabcdef

abc


defnststileabcdef

abc

deftddtstileabcdef

abc


defnsttstileabcdef

abc

deftdststileabcdef

abc

defdntstileabcdef

abc

def

ntdtstileabcdefabc

deftdtstileabcdef


34


abc

defdnttstileabcdef

abc

def

ntststileabcdefabc

deftdttstileabcdef

abc

defdsdtstileabcdef

abc

def

nttstileabcdef abc

deftndtstileabcdef

abc

defdsststileabcdef

abc

def

ntttstileabcdef abc

deftnststileabcdef

abc

defdststileabcdef

abc


deftntstileabcdef

abc

defdsttstileabcdef

abc


deftnttstileabcdef

abc

def

dtdtstileabcdefabc


deftsdtstileabcdef

abc

def

dtststileabcdefabc


deftsststileabcdef

abc

def

dttstileabcdef abc


deftststileabcdef

abc

def

dtttstileabcdef abc


deftsttstileabcdef

abc


defsntstileabcdef

abc

def

ttdtstileabcdef

abc


defsnttstileabcdef

abc

defttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef






35











sqsubset A sqsupset



36



















37


apprge gt apprle

















38

























39









40

Table 95 Arrows






Table 96 Harpoons




Table 98 AMS Arrows






41









42






43









44




45












46


A chemarrow










47












48

















49















50














e e j im




51












niv vin

52



ww Downarrow [[

[ ]]

]

〈lang

langle 〉rang

rangle |∣∣∣ |

∥∥∥ |

dlceil

lceil erceil


~ww Uparrow

blfloor

lfloor crfloor


~w Updownarrow

((

( ))

)

∖

backslash




lgroup rgroup


bracevert



|∣∣∣ lvert |

∣∣∣ rvert

∥∥∥ lVert

∥∥∥ rVert



~

llbracket

rrbracket

53


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert


54


ETH

ETH

ETH

ETH

ETH

leftwave ETH

ETH

ETH

ETH

ETH

rightwave

Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

leftevaw Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

rightevaw



〈〈langlang


rAngle

[[[[

lBrack ]]]]

rBrack

ddlceillceil

lCeil eerceilrceil

rCeil

bblfloorlfloor


rFloor








triplegt

[[[[[[

triple[ ]]]]]]

triple]





55









a ddddota





a veca


A



56


a ringa

















˚abc wideringabc

57

















abc widearrowabc


58












abcrsaquo utildeabc














59


abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG




a dfta a DFTa












abcdef

holterabcdefabcdef

polterabcdef

60

Table 174 Dots





Table 175 AMS Dots











61


iddots


adots











`surd





62













63
















64















65


66















A AR



67




















68






















69





female male














70

5 Dingbats



















71

























72









baucross







73

























74





































75

















A skull


O rip



76









77

6 Other symbols














78








Aa

aa


Aa

aa


Alal KrAKra



a











79






bauforms bauhead












80





















81





times

amacr

bBm cc ˘ Mbb ˙˙

Pppp otimes

t

˘ Bmacr


˙pppp tsbm

˘ bmacr

Bbmmacr

m oo ˙˙

Ppppp tsmb

˘ Bb ˘ bbmbmacr

M˙

p ˙˙

ppppp tsmm


macrpm ps

macrvppm

˘ bbmacr


vpppm

˘ bBmacr


macrppm sim

R


ppp sim

r


˙Ppp otimes

T






82




















83


A HA I HI n Hn T HT

a Ha i Hi O HO t Ht









f Hf l Hl r Hr x Hx

F HF m Hm s Hs Y HY

G HG M HM S HS y Hy



H HH N HN ˚ Hsv







84


Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart



















85











86









72 Resizing symbols






87

Table

280

Sym

bol

Nam

eC

lash

es

Sym

bol

LAT E

X2 ε

AMS

stm

aryr

dw

asys

ymm

ath

abx

mar

vosy

mb

bd

ing

ifsy

md

ingb

atw

suip

a

baro

lt

bigtriangledown

5`

bigtriangleup

4a

checkmark

XD

Circle

5

Cross

dagger

ggg

≫Iuml

Letter

B

lightning

Lightning

E

lll

≪Icirc

Square

f

0Sun

Agrave

TriangleDown

o3

TriangleUp

n1

88



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


89

















90







endtabular












91

















92





one (ldquo=int






















93


makeatother








makeatother








e






94


makeatother













makeatother


95






ABCD












96










endcharend








97

1

2

3

4

5

6677

8






0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F




98



















99









Package Code Output










100
















101




192 C0 A lsquoA

193 C1 A rsquoA

194 C2 A Â195 C3 A ~A196 C4 A A


200 C8 E lsquoE

201 C9 E rsquoE

202 CA E Ê203 CB E E

204 CC I lsquoI

205 CD I rsquoI



209 D1 N ~N

210 D2 O lsquoO

211 D3 O rsquoO


217 D9 U lsquoU

218 DA U rsquoU

219 DB U Û220 DC U U


102



















103

















104


Name Date


105






References











106

Index




( (() 54

) ()) 53

) ()) 54

() 22 100- (-) 102 103 (a) 13 () 53

() 54

lt (⟨) 54

[ ([) 53

[ (⎡⎢⎢⎢⎢⎢⎣) 54

91] (]) 53

] (⎤⎥⎥⎥⎥⎥⎦) 54



) 82



) 79AAdaleth (D) 83


rvert






AchtBL ( ˇ ldquo==

) 79




Adobe Acrobat 99

adots ( ) 62 94







AltGr ( AltGr ) 69


AMS 7 8 21 25 30 36 37 3941 49ndash53 56 58 59 61ndash6366 87 104








text mode see AA





107














Arrowvert (ww) 53

Arrowvert (

XXXXXXX) 54

arrowvert () 53

arrowvert (




AsteriskBold (A) 74



AsteriskThin (C) 74





(EGGGGGGGGGGC) 60



(GGGGGBFGGGGG) 60



macr) 13


backslash () 54




Bart (


108





tion) 65BBm (

macr) 82

Bbm (macr

) 82bBm (

macr) 82


macr) 82

bbmb ( ˘) 82bbmx (



rdquoardquo) 15



e) 25



THORN) 26

bigboxbot (Ucirc

) 26bigboxcirc (

Otilde) 26


) 26bigboxdiv (

Oacute) 26

bigboxdot (Ocirc

) 26bigboxleft (

Oslash) 26

bigboxminus (Ntilde

) 26bigboxplus (

ETH) 26

bigboxright (Ugrave

) 26bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 26

bigcap (⋂



) 26


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 25


) 25


AElig) 26



Euml) 26

bigocirc (Aring


Ccedil) 26

bigodiv (Atilde

) 26bigodot (

⊙) 25


Egrave) 26

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


otimes) 25


Ecirc) 26


Iuml) 26


Igrave) 26

bigparallel (f) 25

bigparr (˙

) 30bigplus (

) 26

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 26


) 26

bigtimes (⨉) 29


`) 25





109


a) 25



⊎) 25



or) 25


and) 25


bigwith (˘






macr) 82

bm (package) 100 104 105bm 100bm (

macr) 82




bracevert () 53

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 54





Burns (

) 85




also hookleftarrow



Cc ( ) 82

110







checkmark (D) 77


Circle (5) 75










CircleShadow (d) 75






work 1 7 57 66 87 103104




∐) 20 25


111


Cross () 75








Ŕa) 15







Cutright (q) 71

DD (a

uml) 16




dashint (minusint

) 93


DavidStar (0) 74


ddashint (=int

) 93

ddddot (

) 56dddot (

) 56

dddtstile ( ) 34


ddots ( ) 61 94

ddots (⋱) 61

ddststile ( ) 34

ddtstile ( ) 34

ddttstile ( ) 34



DEL () 69Del ( Del ) 69






Dfourier ( c) 35

dfourier ( c ) 35

DFT ( ) 60

dft ( ) 60

112









LCD 67Mayan 62








divideontimes



dndtstile ( ) 34

dnststile ( ) 34

dntstile ( ) 34




dollar sign see $






macr) 28


dottedtilde (a) 15




113

downp ( ) 16

downparenthfill 95


downpropto () 32


downslice () 24

downspoon (⫰) 47

downt ( ) 16



downuparrows ( ) 42

downuparrows () 43



downVdash () 32

downvdash (⊤) 32

downY () 23

drsh ( ) 42

DS (SS) 79

Ds (ss) 79




dsbiological (B) 84

dschemical (C) 84

dscommercial (c) 84

dsdtstile ( ) 35


dsheraldical (H) 84

dsjuridical (J) 84

dsliterary (L) 84


dsmedical (m) 84

dsmilitary (X) 84

dsrailways (R) 84

dsststile ( ) 35

dstechnical (T) 84

dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35

dtimes () 23

dtimes (13) 23

dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35

DVI 18 69 97

dz ( ) 12

E


e (e) 51

ε-TEX 53

Earth ( ) 68

Earth (Ecirc) 68

earth () 68

Ecommerce () 17





EightStar ( ) 74









Enter ( Enter ) 69


eqslantgtr () 37

eqslantgtr (⪖) 39

eqslantless ( ) 38

eqslantless () 37


eqsmile () 48

equal (=) 32

equal (j) 82

equalclosed () 32

equalsfill 20 95

equidecomposable 91


equiv (equiv) 20 30

equiv (equiv) 32


equivclosed () 32

er ( ) 11

es-zet see ss

ESC () 69

Esc ( Esc ) 69


esh ( ) 11

esh ( ) 12


Estatically (J) 70



eta (η) 49

etaup (η) 50

ETB () 69

etc (P) 82

eth (eth) 63

eth ( ) 11

eth ( ) 12

ETX () 69

eufrak (package) 65

Euler Roman 50

EUR (e ) 17

EURcr (d) 17

EURdig (D) 17

EURhv (c) 17

euro 17

euro signs 17

blackboard bold 65


EURtm (e) 17



evil spirits 86

exclusive or 90

exists ( ) 51

exists (exist) 51

exists (exist) 51

exp (exp) 49





114




textquotesingle


Ferli (aa) 79

Fermi (aa







FF () 69fge (package) 47 52 56 62 64














40












(t) 75












fint (gt

) 27

fint (ffl) 28






FiveStar (8) 74




FiveStarOpen (9) 74


115





fixedddots ( ) 61

fixedvdots () 61






OT2 90T1 7 9 13 101 103T4 9 13 16T5 9 13TS1 103





FourAsterisk (1) 74



Fourier ( c) 35







gets see leftarrow






gtreqless (R) 37



116

gtreqqless (T) 37

gtreqqless (⪌) 39





h (ả) 13HA (A) 84











HandLeft () 72

HandLeftUp () 72


HandRight () 72



HB (B) 84

Hb (b) 84






HI (I) 84

Hi (i) 84Hibl (˝) 84

Hibp (ˆ) 84

Hibs (uml) 84


mathhill (a

) 15


radic) 93

HL (L) 84Hl (l) 84HM (M) 84

Hm (m) 84

Hman (ˇ) 84

Hmillion (7) 84



holter ( ) 60


Homer (


Hplus (+) 84HQ (Q) 84Hq (q) 84


Hs (s) 84

Hscribe (macr) 84


Hthousand (4) 84

Htongue (˘) 84

HU (U) 84


Hut () 81

HV (V) 84

117

Hv (v) 84hv () 12Hvbar (|) 84HW (W) 84

Hw (w) 84HX (X) 84

Hx (x) 84

HXthousand (5) 84

HY (Y) 84


HZ (Z) 84Hz (z) 84


iddots ( ) 62

iddots () 94


) 25

idotsint (

) 27


ifsym (package) 67 75 80 8188 90 104 105



) 25

iiiint (

) 27

iiiint (ˇ

) 28


micro) 26

iiint (intintint

) 25

iiint (

) 25 27

iiint (˝

) 28


acute) 26

iint (intint

) 25

iint (

) 25 27

iint (˜

) 28



and vdash


textquotedbl







int (sup3) 26

int (int

) 25

int (r

) 25

int (int) 29

intclockwise () 29






irony mark ( ) 90


Jj () 13

JackStar (2) 74







118

lambdaslash (n) 63

lambdaup (λ) 50


land see wedge

landdownint () 28


landupint () 28

landupint (⨙) 29

Langle (lt) 65

lAngle (〈〈) 55

langle (〈) 20 53

langle (⟨) 54

langlebar (n) 54

Laplace ( s c) 35

laplace ( c s) 35




largecircle () 74

largediamond () 74


largepencil (W) 72



largestar () 74






LArrow ( larr ) 69

larrowfill 60

Laserbeam (a) 70




latfric () 11

Latin 1 7 101 103 104

table 102

laundry symbols 80

Lbag (P) 52

lbag (N) 52


) 54

Lbrack ([) 65

lBrack ([[) 55

LCD digits 67

lCeil (dd) 55

lceil (d) 53

lceil (⎡⎢⎢⎢⎢⎢⎢) 54






leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55






leftwave (

ETH

ETH

ETH

ETH

) 55


119


lesseqgtr (Q) 37



lesseqqgtr (S) 37

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

LF () 69

lfilet (

7777) 54


lfloor (⎢⎢⎢⎢⎢⎢⎣) 54

lg (lg) 49

lgroup (

) 53

lgroup (⎧⎪⎪⎪⎪⎪⎩) 54







Lisa (

) 85lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 54


llcorner () 54



lmoustache (

) 53





and see wedge

not see neg and sim

or see vee





120

lrcorner () 54

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 54



lwave (

ETH

ETH

ETH

ETH

) 55

lWavy (_______

) 54

lwavy (^^^) 54

lz (1) 11

MM 9M (

macr) 82

m 9m (

macr) 82


Maggie ( ) 85


manpenkidney () 79





Marge (

















cient seeDH



121



micro (micro) 67


textperthousand





32 33 37 39 40 43ndash48 5051 54 56ndash58 61 63 64 74104 105










ncong () 30


nddtstile ( ) 35


122


ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 37 38


ngeqq () 37

ngeqq (iquest) 39

ngeqslant () 37





ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 12

NibLeft () 72


NibSolidLeft ( ) 72


123




nleq () 37 38


nleqq () 37

nleqq (frac34) 39

nleqslant () 37





nlessgtr () 38

nlessgtr (≸) 39



nnststile ( ) 35

nntstile ( ) 34


tion) 25




notni


npreceq () 30


124




nsststile ( ) 34

nststile ( ) 34



nsubseteq () 36


nsucceq () 30


nsupseteq (+) 36


ntdtstile ( ) 34


125






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35











˚) 15


ohm (Ω) 67

Ohne (a) 79


oiiint ()

) 27

oiiint (

) 29

oiiintclockwise (L

) 27


) 27

oiint (middot

) 26

oiint (

) 25 27

oiint (sbquo

) 28

oiint (

) 29

oiint (∯) 29

oiintclockwise (H

) 27

oiintctrclockwise (

) 27

oint (para) 26

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 29

ointctrclockwise (

) 27




126





oright (i) 24



overbrace (hkkikkj

) 58

overbrace (copy

) 58


) 58


) 57

overbracket ( ) 58


rdquoa) 15

overgroup (hkkkkj

) 58




overline ( ) 20 57






PP (para) 8 102p (

˙) 82

p 94package options



amsmath 7 49 56 91 99amssymb 7 20 30 36 4156 62 65 104 105 107









mathdots 56 61 62 94 104105



127





timing 67tipa 10 11 13 15 16 90104 105




wsuipa 11 15 16 88 90 94104 105

yfonts 65 104 105yhmath 57 59 62 94 104






















textperthousand


passedpawn (r) 82


Peace () 77

PencilLeft () 72


PencilLeftUp () 72

PencilRight () 72


PencilRightUp () 72

pencils 72

pentagon (D) 74

pentagram () 24

people see faces

percent sign see

permil (h) 19

Perp (y) 31

perp (perp) 30 93

perp (perp) 33


Pfund (pound) 17




Phaistos disk 83


PHarrow (J) 83

PHbee (h) 83

PHbeehive (X) 83

PHboomerang (R) 83

PHbow (K) 83

PHbullLeg (b) 83

PHcaptive (D) 83


PHcat (c) 83

PHchild (E) 83

PHclub (M) 83

PHcolumn (W) 83

PHcomb (U) 83

PHdolium (T) 83

PHdove (f) 83

PHeagle (e) 83

PHflute (o) 83

PHgaunlet (H) 83

PHgrater (p) 83

PHhelmet (G) 83

PHhide (a) 83

128


PHlid (Q) 83

PHlily (m) 83

PHmanacles (N) 83

PHmattock (O) 83



PHoxBack (n) 83

PHpapyrus (k) 83

PHpedestrian (A) 83

PHplaneTree (i) 83

PHplumedHead (B) 83

PHram (d) 83

PHrosette (l) 83

PHsaw (P) 83

PHshield (L) 83

PHship (Y) 83

PHsling (V) 83

PHsmallAxe (r) 83

PHstrainer (q) 83



PHvine (j) 83

PHwavyBand (s) 83



pipe see textpipe








macr) 82


polter ( ) 60



macr) 82

Ppp ( ˙˙) 82

ppp ( ˙˙

) 82Pppp ( ˙

˙) 82

pppp ( ˙˙

) 82Ppppp ( ˙

˙) 82

ppppp ( ˙˙




prod) 25




31 36 38 41 42 48 50 5162 63 65 87 101

Pxp ( ˙) 82pxp ( ˙ ) 82



129

RR ( sim

) 82r (a) 13r ( sim

) 82



Rain () 80



rangle (⟩) 54

ranglebar (s) 54

RArrow ( rarr ) 69



hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 54





recorder () 78

Rectangle (u) 75




rqm


textregistered



upharpoonright


Return ( larr ) 69


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

revD () 12

revddots ( ) 94


textbackslash


rfilet (

) 54


rfloor (⎥⎥⎥⎥⎥⎥⎦) 54

rgroup (

) 53

rgroup (⎫⎪⎪⎪⎪⎪⎭) 54



RightDiamond () 75

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55



130


rightwave (

ETH

ETH

ETH

ETH

) 55




rmoustache (

) 53




rrangle (⟫) 54


rsem (MQQQQQO) 54




rwave (

ETH

ETH

ETH

ETH

) 55

rWavy (_______

) 54

rwavy (^^^) 54








ScissorLeft () 71




() 71


scu (W) 12

scy (]) 12

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 79


) 79











union see cup

setminus () 20

131








([) 74

SixStar (G) 74







SmallCircle (E) 75












sndtstile ( ) 35

Snow () 80

SnowCloud () 80

Snowflake (`) 74



SNPP () 85

snststile ( ) 35

sntstile ( ) 35




Sparkle (]) 74


SpinDown () 75


sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

132

sqrt (radic


Square (0) 75



hooked see hksqrt


(k) 75




SquareShadowA () 75

SquareShadowB () 75


SquareShadowC () 75



SquareSolid (g) 75











squplus (]) 22

SS (SS) 9

ss (szlig) 9

ssdtstile ( ) 35

ssearrow () 42

sslash () 21

ssststile ( ) 35

sststile ( ) 35

ssttstile ( ) 35

sswarrow ($) 42

stackrel 20 91 95

standard state 91

star () 20 94

star (⋆) 24

Star of David 73 74

stars 63 73 74


staveI () 85

staveII () 85

staveIII () 85

staveIV () 85

staveIX () 85

staveL (1) 85 86

staveLI (2) 85

staveLII (3) 85

staveLIII (4) 85

staveLIV (5) 85

staveLIX () 85

staveLV (6) 85

staveLVI (7) 85

staveLVII (8) 85

staveLVIII (9) 85

staveLX () 85

staveLXI (lt) 85

staveLXII (=) 85

staveLXIII (gt) 86

staveLXIV () 86

staveLXV () 86

staveLXVI (A) 86

staveLXVII (B) 86

staveLXVIII (C) 86

staves 85


staveV () 85

staveVI () 85

staveVII () 85

staveVIII () 85

staveX () 85

staveXI () 85

staveXII () 85

staveXIII () 85

staveXIV (13) 85

staveXIX () 86

staveXL () 86

staveXLI (() 86

staveXLII ()) 86

staveXLIII () 86

staveXLIV (+) 86

staveXLIX (0) 85

staveXLV () 86

staveXLVI (-) 86

staveXLVII () 85

staveXLVIII () 85

staveXV () 85

staveXVI () 85

staveXVII () 86

staveXVIII () 86

staveXX () 86

staveXXI () 86

staveXXII () 86

staveXXIII () 86

staveXXIV () 85

staveXXIX () 85

staveXXV () 85

staveXXVI () 85

staveXXVII () 85

133

staveXXVIII () 85

staveXXX () 85

staveXXXI () 85

staveXXXII () 85

staveXXXIII ( ) 85

staveXXXIV () 85

staveXXXIX (amp) 85

staveXXXV () 85


stdtstile ( ) 34





StopWatchEnd () 81


strokedint (⨏) 29

StrokeFive () 81

StrokeFour () 81

StrokeOne () 81

StrokeThree () 81


stststile ( ) 34

sttstile ( ) 34

stttstile ( ) 34


^) 15



sublptr (aiexcl) 15






sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 81




SunCloud () 80





`) 62




134





) 82

t ( a) 13t ( otimes




Tape () 77


tddtstile ( ) 34

tdststile ( ) 34

tdtstile ( ) 34

tdttstile ( ) 35









8 13 17ndash19 41 56 64 6778 87 101 103ndash105


135


textdbend (




textlhdbend (~


136



mdasha) 14





) 76



rsaquo) 14




ˆ) 14

textsubdot (a˙) 14


lsaquo) 14


˚) 14


˜) 14



ˇ) 14



) 15



137





textperthousand




90 104 105tipx (package) 11 104 105

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35




alphabets math




TriangleDown (3) 75






TriangleUp (1) 75





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 70

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



31 36 38 41 42 48 50 5162 63 65 87 89 101 104105


UU (a

˘) 16




ulcorner () 54

ullcorner (6) 54

ulrcorner () 54



138


underbrace (reg) 58



underbracket ( ) 58


















urcorner () 54


˜) 15

utilde (˜) 59






139



varint (r




) 27


)

27varoiint (

) 28


) 27


) 27

varoint (u

) 25

varointclockwise (-

) 27



) 27



) 27







vdots () 61




Village () 81



˚) 12


macr) 82

vpppm (macr



17 19ndash21 25 30 36 38 4161ndash63 67 68 70 73 74 7888 104 105





Ţ) 15


140


widering (Ucirc) 58





90 94 104 105wupperhand (c) 82

Xx ( ˙˙) 82XBox (4) 73

Xdvi 90



Xi (Ξ) 49

xi (ξ) 49

xiup (ξ) 50










xlongequal (===) 60

xlongequal (===) 60









XML 103







Xs 73 76

XSolid () 73

XSolidBold ($) 73

XSolidBrush () 73







Ztransf ( s c) 35



ZwPa ( A ) 79

141

1 Introduction





11 Document Usage








cent 17

e 17


permil 19 27

there4 30

B and F 31

and amp 37

62


L F etc 65

N Z R etc 65

minusint

92




7

2 Body-text symbols



















8



















9




10









11







˚vod


12





Alif Ayn





Aa =A=a Amacr

amacr










13











Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



Aˇ

aˇ




14


Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



15


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast









16















17







Ccopy ccsalowast





18








h permil

19





∐rdquo (coprod)















20









21




22










23


odplus






24



and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint



25


notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint



26


bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint

27


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28























intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)

29


˙bigparr

˘bigwith









A inplus B niplus



30








31






32






33







abc


defnntstileabcdef

abc

def

stdtstileabcdef

abc


defnnttstileabcdef

abc

def

stststileabcdef

abc


defnsdtstileabcdef

abc

def

sttstileabcdef

abc


defnsststileabcdef

abc

def

stttstileabcdef

abc


defnststileabcdef

abc

deftddtstileabcdef

abc


defnsttstileabcdef

abc

deftdststileabcdef

abc

defdntstileabcdef

abc

def

ntdtstileabcdefabc

deftdtstileabcdef


34


abc

defdnttstileabcdef

abc

def

ntststileabcdefabc

deftdttstileabcdef

abc

defdsdtstileabcdef

abc

def

nttstileabcdef abc

deftndtstileabcdef

abc

defdsststileabcdef

abc

def

ntttstileabcdef abc

deftnststileabcdef

abc

defdststileabcdef

abc


deftntstileabcdef

abc

defdsttstileabcdef

abc


deftnttstileabcdef

abc

def

dtdtstileabcdefabc


deftsdtstileabcdef

abc

def

dtststileabcdefabc


deftsststileabcdef

abc

def

dttstileabcdef abc


deftststileabcdef

abc

def

dtttstileabcdef abc


deftsttstileabcdef

abc


defsntstileabcdef

abc

def

ttdtstileabcdef

abc


defsnttstileabcdef

abc

defttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef






35











sqsubset A sqsupset



36



















37


apprge gt apprle

















38

























39









40

Table 95 Arrows






Table 96 Harpoons




Table 98 AMS Arrows






41









42






43









44




45












46


A chemarrow










47












48

















49















50














e e j im




51












niv vin

52



ww Downarrow [[

[ ]]

]

〈lang

langle 〉rang

rangle |∣∣∣ |

∥∥∥ |

dlceil

lceil erceil


~ww Uparrow

blfloor

lfloor crfloor


~w Updownarrow

((

( ))

)

∖

backslash




lgroup rgroup


bracevert



|∣∣∣ lvert |

∣∣∣ rvert

∥∥∥ lVert

∥∥∥ rVert



~

llbracket

rrbracket

53


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert


54


ETH

ETH

ETH

ETH

ETH

leftwave ETH

ETH

ETH

ETH

ETH

rightwave

Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

leftevaw Ntilde

Ntilde

Ntilde

Ntilde

Ntilde

rightevaw



〈〈langlang


rAngle

[[[[

lBrack ]]]]

rBrack

ddlceillceil

lCeil eerceilrceil

rCeil

bblfloorlfloor


rFloor








triplegt

[[[[[[

triple[ ]]]]]]

triple]





55









a ddddota





a veca


A



56


a ringa

















˚abc wideringabc

57

















abc widearrowabc


58












abcrsaquo utildeabc














59


abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG




a dfta a DFTa












abcdef

holterabcdefabcdef

polterabcdef

60

Table 174 Dots





Table 175 AMS Dots











61


iddots


adots











`surd





62













63
















64















65


66















A AR



67




















68






















69





female male














70

5 Dingbats



















71

























72









baucross







73

























74





































75

















A skull


O rip



76









77

6 Other symbols














78








Aa

aa


Aa

aa


Alal KrAKra



a











79






bauforms bauhead












80





















81





times

amacr

bBm cc ˘ Mbb ˙˙

Pppp otimes

t

˘ Bmacr


˙pppp tsbm

˘ bmacr

Bbmmacr

m oo ˙˙

Ppppp tsmb

˘ Bb ˘ bbmbmacr

M˙

p ˙˙

ppppp tsmm


macrpm ps

macrvppm

˘ bbmacr


vpppm

˘ bBmacr


macrppm sim

R


ppp sim

r


˙Ppp otimes

T






82




















83


A HA I HI n Hn T HT

a Ha i Hi O HO t Ht









f Hf l Hl r Hr x Hx

F HF m Hm s Hs Y HY

G HG M HM S HS y Hy



H HH N HN ˚ Hsv







84


Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart



















85











86









72 Resizing symbols






87

Table

280

Sym

bol

Nam

eC

lash

es

Sym

bol

LAT E

X2 ε

AMS

stm

aryr

dw

asys

ymm

ath

abx

mar

vosy

mb

bd

ing

ifsy

md

ingb

atw

suip

a

baro

lt

bigtriangledown

5`

bigtriangleup

4a

checkmark

XD

Circle

5

Cross

dagger

ggg

≫Iuml

Letter

B

lightning

Lightning

E

lll

≪Icirc

Square

f

0Sun

Agrave

TriangleDown

o3

TriangleUp

n1

88



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


89

















90







endtabular












91

















92





one (ldquo=int






















93


makeatother








makeatother








e






94


makeatother













makeatother


95






ABCD












96










endcharend








97

1

2

3

4

5

6677

8






0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F




98



















99









Package Code Output










100
















101




192 C0 A lsquoA

193 C1 A rsquoA

194 C2 A Â195 C3 A ~A196 C4 A A


200 C8 E lsquoE

201 C9 E rsquoE

202 CA E Ê203 CB E E

204 CC I lsquoI

205 CD I rsquoI



209 D1 N ~N

210 D2 O lsquoO

211 D3 O rsquoO


217 D9 U lsquoU

218 DA U rsquoU

219 DB U Û220 DC U U


102



















103

















104


Name Date


105






References











106

Index




( (() 54

) ()) 53

) ()) 54

() 22 100- (-) 102 103 (a) 13 () 53

() 54

lt (⟨) 54

[ ([) 53

[ (⎡⎢⎢⎢⎢⎢⎣) 54

91] (]) 53

] (⎤⎥⎥⎥⎥⎥⎦) 54



) 82



) 79AAdaleth (D) 83


rvert






AchtBL ( ˇ ldquo==

) 79




Adobe Acrobat 99

adots ( ) 62 94







AltGr ( AltGr ) 69


AMS 7 8 21 25 30 36 37 3941 49ndash53 56 58 59 61ndash6366 87 104








text mode see AA





107














Arrowvert (ww) 53

Arrowvert (

XXXXXXX) 54

arrowvert () 53

arrowvert (




AsteriskBold (A) 74



AsteriskThin (C) 74





(EGGGGGGGGGGC) 60



(GGGGGBFGGGGG) 60



macr) 13


backslash () 54




Bart (


108





tion) 65BBm (

macr) 82

Bbm (macr

) 82bBm (

macr) 82


macr) 82

bbmb ( ˘) 82bbmx (



rdquoardquo) 15



e) 25



THORN) 26

bigboxbot (Ucirc

) 26bigboxcirc (

Otilde) 26


) 26bigboxdiv (

Oacute) 26

bigboxdot (Ocirc

) 26bigboxleft (

Oslash) 26

bigboxminus (Ntilde

) 26bigboxplus (

ETH) 26

bigboxright (Ugrave

) 26bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 26

bigcap (⋂



) 26


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 25


) 25


AElig) 26



Euml) 26

bigocirc (Aring


Ccedil) 26

bigodiv (Atilde

) 26bigodot (

⊙) 25


Egrave) 26

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


otimes) 25


Ecirc) 26


Iuml) 26


Igrave) 26

bigparallel (f) 25

bigparr (˙

) 30bigplus (

) 26

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 26


) 26

bigtimes (⨉) 29


`) 25





109


a) 25



⊎) 25



or) 25


and) 25


bigwith (˘






macr) 82

bm (package) 100 104 105bm 100bm (

macr) 82




bracevert () 53

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 54





Burns (

) 85




also hookleftarrow



Cc ( ) 82

110







checkmark (D) 77


Circle (5) 75










CircleShadow (d) 75






work 1 7 57 66 87 103104




∐) 20 25


111


Cross () 75








Ŕa) 15







Cutright (q) 71

DD (a

uml) 16




dashint (minusint

) 93


DavidStar (0) 74


ddashint (=int

) 93

ddddot (

) 56dddot (

) 56

dddtstile ( ) 34


ddots ( ) 61 94

ddots (⋱) 61

ddststile ( ) 34

ddtstile ( ) 34

ddttstile ( ) 34



DEL () 69Del ( Del ) 69






Dfourier ( c) 35

dfourier ( c ) 35

DFT ( ) 60

dft ( ) 60

112









LCD 67Mayan 62








divideontimes



dndtstile ( ) 34

dnststile ( ) 34

dntstile ( ) 34




dollar sign see $






macr) 28


dottedtilde (a) 15




113

downp ( ) 16

downparenthfill 95


downpropto () 32


downslice () 24

downspoon (⫰) 47

downt ( ) 16



downuparrows ( ) 42

downuparrows () 43



downVdash () 32

downvdash (⊤) 32

downY () 23

drsh ( ) 42

DS (SS) 79

Ds (ss) 79




dsbiological (B) 84

dschemical (C) 84

dscommercial (c) 84

dsdtstile ( ) 35


dsheraldical (H) 84

dsjuridical (J) 84

dsliterary (L) 84


dsmedical (m) 84

dsmilitary (X) 84

dsrailways (R) 84

dsststile ( ) 35

dstechnical (T) 84

dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35

dtimes () 23

dtimes (13) 23

dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35

DVI 18 69 97

dz ( ) 12

E


e (e) 51

ε-TEX 53

Earth ( ) 68

Earth (Ecirc) 68

earth () 68

Ecommerce () 17





EightStar ( ) 74









Enter ( Enter ) 69


eqslantgtr () 37

eqslantgtr (⪖) 39

eqslantless ( ) 38

eqslantless () 37


eqsmile () 48

equal (=) 32

equal (j) 82

equalclosed () 32

equalsfill 20 95

equidecomposable 91


equiv (equiv) 20 30

equiv (equiv) 32


equivclosed () 32

er ( ) 11

es-zet see ss

ESC () 69

Esc ( Esc ) 69


esh ( ) 11

esh ( ) 12


Estatically (J) 70



eta (η) 49

etaup (η) 50

ETB () 69

etc (P) 82

eth (eth) 63

eth ( ) 11

eth ( ) 12

ETX () 69

eufrak (package) 65

Euler Roman 50

EUR (e ) 17

EURcr (d) 17

EURdig (D) 17

EURhv (c) 17

euro 17

euro signs 17

blackboard bold 65


EURtm (e) 17



evil spirits 86

exclusive or 90

exists ( ) 51

exists (exist) 51

exists (exist) 51

exp (exp) 49





114




textquotesingle


Ferli (aa) 79

Fermi (aa







FF () 69fge (package) 47 52 56 62 64














40












(t) 75












fint (gt

) 27

fint (ffl) 28






FiveStar (8) 74




FiveStarOpen (9) 74


115





fixedddots ( ) 61

fixedvdots () 61






OT2 90T1 7 9 13 101 103T4 9 13 16T5 9 13TS1 103





FourAsterisk (1) 74



Fourier ( c) 35







gets see leftarrow






gtreqless (R) 37



116

gtreqqless (T) 37

gtreqqless (⪌) 39





h (ả) 13HA (A) 84











HandLeft () 72

HandLeftUp () 72


HandRight () 72



HB (B) 84

Hb (b) 84






HI (I) 84

Hi (i) 84Hibl (˝) 84

Hibp (ˆ) 84

Hibs (uml) 84


mathhill (a

) 15


radic) 93

HL (L) 84Hl (l) 84HM (M) 84

Hm (m) 84

Hman (ˇ) 84

Hmillion (7) 84



holter ( ) 60


Homer (


Hplus (+) 84HQ (Q) 84Hq (q) 84


Hs (s) 84

Hscribe (macr) 84


Hthousand (4) 84

Htongue (˘) 84

HU (U) 84


Hut () 81

HV (V) 84

117

Hv (v) 84hv () 12Hvbar (|) 84HW (W) 84

Hw (w) 84HX (X) 84

Hx (x) 84

HXthousand (5) 84

HY (Y) 84


HZ (Z) 84Hz (z) 84


iddots ( ) 62

iddots () 94


) 25

idotsint (

) 27


ifsym (package) 67 75 80 8188 90 104 105



) 25

iiiint (

) 27

iiiint (ˇ

) 28


micro) 26

iiint (intintint

) 25

iiint (

) 25 27

iiint (˝

) 28


acute) 26

iint (intint

) 25

iint (

) 25 27

iint (˜

) 28



and vdash


textquotedbl







int (sup3) 26

int (int

) 25

int (r

) 25

int (int) 29

intclockwise () 29






irony mark ( ) 90


Jj () 13

JackStar (2) 74







118

lambdaslash (n) 63

lambdaup (λ) 50


land see wedge

landdownint () 28


landupint () 28

landupint (⨙) 29

Langle (lt) 65

lAngle (〈〈) 55

langle (〈) 20 53

langle (⟨) 54

langlebar (n) 54

Laplace ( s c) 35

laplace ( c s) 35




largecircle () 74

largediamond () 74


largepencil (W) 72



largestar () 74






LArrow ( larr ) 69

larrowfill 60

Laserbeam (a) 70




latfric () 11

Latin 1 7 101 103 104

table 102

laundry symbols 80

Lbag (P) 52

lbag (N) 52


) 54

Lbrack ([) 65

lBrack ([[) 55

LCD digits 67

lCeil (dd) 55

lceil (d) 53

lceil (⎡⎢⎢⎢⎢⎢⎢) 54






leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55






leftwave (

ETH

ETH

ETH

ETH

) 55


119


lesseqgtr (Q) 37



lesseqqgtr (S) 37

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

LF () 69

lfilet (

7777) 54


lfloor (⎢⎢⎢⎢⎢⎢⎣) 54

lg (lg) 49

lgroup (

) 53

lgroup (⎧⎪⎪⎪⎪⎪⎩) 54







Lisa (

) 85lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 54


llcorner () 54



lmoustache (

) 53





and see wedge

not see neg and sim

or see vee





120

lrcorner () 54

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 54



lwave (

ETH

ETH

ETH

ETH

) 55

lWavy (_______

) 54

lwavy (^^^) 54

lz (1) 11

MM 9M (

macr) 82

m 9m (

macr) 82


Maggie ( ) 85


manpenkidney () 79





Marge (

















cient seeDH



121



micro (micro) 67


textperthousand





32 33 37 39 40 43ndash48 5051 54 56ndash58 61 63 64 74104 105










ncong () 30


nddtstile ( ) 35


122


ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 37 38


ngeqq () 37

ngeqq (iquest) 39

ngeqslant () 37





ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 12

NibLeft () 72


NibSolidLeft ( ) 72


123




nleq () 37 38


nleqq () 37

nleqq (frac34) 39

nleqslant () 37





nlessgtr () 38

nlessgtr (≸) 39



nnststile ( ) 35

nntstile ( ) 34


tion) 25




notni


npreceq () 30


124




nsststile ( ) 34

nststile ( ) 34



nsubseteq () 36


nsucceq () 30


nsupseteq (+) 36


ntdtstile ( ) 34


125






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35











˚) 15


ohm (Ω) 67

Ohne (a) 79


oiiint ()

) 27

oiiint (

) 29

oiiintclockwise (L

) 27


) 27

oiint (middot

) 26

oiint (

) 25 27

oiint (sbquo

) 28

oiint (

) 29

oiint (∯) 29

oiintclockwise (H

) 27

oiintctrclockwise (

) 27

oint (para) 26

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 29

ointctrclockwise (

) 27




126





oright (i) 24



overbrace (hkkikkj

) 58

overbrace (copy

) 58


) 58


) 57

overbracket ( ) 58


rdquoa) 15

overgroup (hkkkkj

) 58




overline ( ) 20 57






PP (para) 8 102p (

˙) 82

p 94package options



amsmath 7 49 56 91 99amssymb 7 20 30 36 4156 62 65 104 105 107









mathdots 56 61 62 94 104105



127





timing 67tipa 10 11 13 15 16 90104 105




wsuipa 11 15 16 88 90 94104 105

yfonts 65 104 105yhmath 57 59 62 94 104






















textperthousand


passedpawn (r) 82


Peace () 77

PencilLeft () 72


PencilLeftUp () 72

PencilRight () 72


PencilRightUp () 72

pencils 72

pentagon (D) 74

pentagram () 24

people see faces

percent sign see

permil (h) 19

Perp (y) 31

perp (perp) 30 93

perp (perp) 33


Pfund (pound) 17




Phaistos disk 83


PHarrow (J) 83

PHbee (h) 83

PHbeehive (X) 83

PHboomerang (R) 83

PHbow (K) 83

PHbullLeg (b) 83

PHcaptive (D) 83


PHcat (c) 83

PHchild (E) 83

PHclub (M) 83

PHcolumn (W) 83

PHcomb (U) 83

PHdolium (T) 83

PHdove (f) 83

PHeagle (e) 83

PHflute (o) 83

PHgaunlet (H) 83

PHgrater (p) 83

PHhelmet (G) 83

PHhide (a) 83

128


PHlid (Q) 83

PHlily (m) 83

PHmanacles (N) 83

PHmattock (O) 83



PHoxBack (n) 83

PHpapyrus (k) 83

PHpedestrian (A) 83

PHplaneTree (i) 83

PHplumedHead (B) 83

PHram (d) 83

PHrosette (l) 83

PHsaw (P) 83

PHshield (L) 83

PHship (Y) 83

PHsling (V) 83

PHsmallAxe (r) 83

PHstrainer (q) 83



PHvine (j) 83

PHwavyBand (s) 83



pipe see textpipe








macr) 82


polter ( ) 60



macr) 82

Ppp ( ˙˙) 82

ppp ( ˙˙

) 82Pppp ( ˙

˙) 82

pppp ( ˙˙

) 82Ppppp ( ˙

˙) 82

ppppp ( ˙˙




prod) 25




31 36 38 41 42 48 50 5162 63 65 87 101

Pxp ( ˙) 82pxp ( ˙ ) 82



129

RR ( sim

) 82r (a) 13r ( sim

) 82



Rain () 80



rangle (⟩) 54

ranglebar (s) 54

RArrow ( rarr ) 69



hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 54





recorder () 78

Rectangle (u) 75




rqm


textregistered



upharpoonright


Return ( larr ) 69


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55

revD () 12

revddots ( ) 94


textbackslash


rfilet (

) 54


rfloor (⎥⎥⎥⎥⎥⎥⎦) 54

rgroup (

) 53

rgroup (⎫⎪⎪⎪⎪⎪⎭) 54



RightDiamond () 75

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 55



130


rightwave (

ETH

ETH

ETH

ETH

) 55




rmoustache (

) 53




rrangle (⟫) 54


rsem (MQQQQQO) 54




rwave (

ETH

ETH

ETH

ETH

) 55

rWavy (_______

) 54

rwavy (^^^) 54








ScissorLeft () 71




() 71


scu (W) 12

scy (]) 12

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 79


) 79











union see cup

setminus () 20

131








([) 74

SixStar (G) 74







SmallCircle (E) 75












sndtstile ( ) 35

Snow () 80

SnowCloud () 80

Snowflake (`) 74



SNPP () 85

snststile ( ) 35

sntstile ( ) 35




Sparkle (]) 74


SpinDown () 75


sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

132

sqrt (radic


Square (0) 75



hooked see hksqrt


(k) 75




SquareShadowA () 75

SquareShadowB () 75


SquareShadowC () 75



SquareSolid (g) 75











squplus (]) 22

SS (SS) 9

ss (szlig) 9

ssdtstile ( ) 35

ssearrow () 42

sslash () 21

ssststile ( ) 35

sststile ( ) 35

ssttstile ( ) 35

sswarrow ($) 42

stackrel 20 91 95

standard state 91

star () 20 94

star (⋆) 24

Star of David 73 74

stars 63 73 74


staveI () 85

staveII () 85

staveIII () 85

staveIV () 85

staveIX () 85

staveL (1) 85 86

staveLI (2) 85

staveLII (3) 85

staveLIII (4) 85

staveLIV (5) 85

staveLIX () 85

staveLV (6) 85

staveLVI (7) 85

staveLVII (8) 85

staveLVIII (9) 85

staveLX () 85

staveLXI (lt) 85

staveLXII (=) 85

staveLXIII (gt) 86

staveLXIV () 86

staveLXV () 86

staveLXVI (A) 86

staveLXVII (B) 86

staveLXVIII (C) 86

staves 85


staveV () 85

staveVI () 85

staveVII () 85

staveVIII () 85

staveX () 85

staveXI () 85

staveXII () 85

staveXIII () 85

staveXIV (13) 85

staveXIX () 86

staveXL () 86

staveXLI (() 86

staveXLII ()) 86

staveXLIII () 86

staveXLIV (+) 86

staveXLIX (0) 85

staveXLV () 86

staveXLVI (-) 86

staveXLVII () 85

staveXLVIII () 85

staveXV () 85

staveXVI () 85

staveXVII () 86

staveXVIII () 86

staveXX () 86

staveXXI () 86

staveXXII () 86

staveXXIII () 86

staveXXIV () 85

staveXXIX () 85

staveXXV () 85

staveXXVI () 85

staveXXVII () 85

133

staveXXVIII () 85

staveXXX () 85

staveXXXI () 85

staveXXXII () 85

staveXXXIII ( ) 85

staveXXXIV () 85

staveXXXIX (amp) 85

staveXXXV () 85


stdtstile ( ) 34





StopWatchEnd () 81


strokedint (⨏) 29

StrokeFive () 81

StrokeFour () 81

StrokeOne () 81

StrokeThree () 81


stststile ( ) 34

sttstile ( ) 34

stttstile ( ) 34


^) 15



sublptr (aiexcl) 15






sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 81




SunCloud () 80





`) 62




134





) 82

t ( a) 13t ( otimes




Tape () 77


tddtstile ( ) 34

tdststile ( ) 34

tdtstile ( ) 34

tdttstile ( ) 35









8 13 17ndash19 41 56 64 6778 87 101 103ndash105


135


textdbend (




textlhdbend (~


136



mdasha) 14





) 76



rsaquo) 14




ˆ) 14

textsubdot (a˙) 14


lsaquo) 14


˚) 14


˜) 14



ˇ) 14



) 15



137





textperthousand




90 104 105tipx (package) 11 104 105

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35




alphabets math




TriangleDown (3) 75






TriangleUp (1) 75





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 70

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



31 36 38 41 42 48 50 5162 63 65 87 89 101 104105


UU (a

˘) 16




ulcorner () 54

ullcorner (6) 54

ulrcorner () 54



138


underbrace (reg) 58



underbracket ( ) 58


















urcorner () 54


˜) 15

utilde (˜) 59






139



varint (r




) 27


)

27varoiint (

) 28


) 27


) 27

varoint (u

) 25

varointclockwise (-

) 27



) 27



) 27







vdots () 61




Village () 81



˚) 12


macr) 82

vpppm (macr



17 19ndash21 25 30 36 38 4161ndash63 67 68 70 73 74 7888 104 105





Ţ) 15


140


widering (Ucirc) 58





90 94 104 105wupperhand (c) 82

Xx ( ˙˙) 82XBox (4) 73

Xdvi 90



Xi (Ξ) 49

xi (ξ) 49

xiup (ξ) 50










xlongequal (===) 60

xlongequal (===) 60









XML 103







Xs 73 76

XSolid () 73

XSolidBold ($) 73

XSolidBrush () 73







Ztransf ( s c) 35



ZwPa ( A ) 79

141

the comprehensive latex symbol list - uspthe comprehensive latex symbol list - usp ... atex 7

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