The Comprehensive LaTeX Symbol List - The UK TeX Archive Web pages

The Comprehensive LATEX Symbol List

Scott Pakin ltscott+clslpakinorggtlowast

9 November 2009

Abstract

This document lists 5913 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

Contents 1

1 Introduction 811 Document Usage 812 Frequently Requested Symbols 8

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

Holt See Section 88 on page 118 for more information about who did what

1

Table 28 wsuipa Diacritics 18Table 29 textcomp Diacritics 18Table 30 textcomp Currency Symbols 18Table 31 marvosym Currency Symbols 18Table 32 wasysym Currency Symbols 18Table 33 ChinA2e Currency Symbols 19Table 34 teubner Currency Symbols 19Table 35 eurosym Euro Signs 19Table 36 fourier Euro Signs 19Table 37 textcomp Legal Symbols 19Table 38 cclicenses Creative Commons License Icons 19Table 39 textcomp Old-style Numerals 20Table 40 Miscellaneous textcomp Symbols 20Table 41 Miscellaneous wasysym Text-mode Symbols 20

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

2

Table 84 fourier Binary Relations 36Table 85 Subset and Superset Relations 36Table 86 AMS Subset and Superset Relations 36Table 87 stmaryrd Subset and Superset Relations 37Table 88 wasysym Subset and Superset Relations 37Table 89 txfontspxfonts Subset and Superset Relations 37Table 90 mathabx Subset and Superset Relations 37Table 91 MnSymbol Subset and Superset Relations 37Table 92 Inequalities 37Table 93 AMS Inequalities 38Table 94 wasysym Inequalities 38Table 95 txfontspxfonts Inequalities 38Table 96 mathabx Inequalities 38Table 97 MnSymbol Inequalities 39Table 98 AMS Triangle Relations 39Table 99 stmaryrd Triangle Relations 40Table 100 mathabx Triangle Relations 40Table 101 MnSymbol Triangle Relations 40Table 102 Arrows 41Table 103 Harpoons 41Table 104 textcomp Text-mode Arrows 41Table 105 AMS Arrows 41Table 106 AMS Negated Arrows 41Table 107 AMS Harpoons 41Table 108 stmaryrd Arrows 42Table 109 txfontspxfonts Arrows 42Table 110 mathabx Arrows 42Table 111 mathabx Negated Arrows 42Table 112 mathabx Harpoons 43Table 113 MnSymbol Arrows 43Table 114 MnSymbol Negated Arrows 44Table 115 MnSymbol Harpoons 46Table 116 MnSymbol Negated Harpoons 46Table 117 harpoon Extensible Harpoons 47Table 118 chemarrow Arrows 47Table 119 fge Arrows 47Table 120 MnSymbol Spoons 47Table 121 MnSymbol Pitchforks 47Table 122 MnSymbol Smiles and Frowns 48Table 123 ulsy Contradiction Symbols 48Table 124 Extension Characters 48Table 125 stmaryrd Extension Characters 48Table 126 txfontspxfonts Extension Characters 48Table 127 mathabx Extension Characters 49Table 128 Log-like Symbols 49Table 129 AMS Log-like Symbols 49Table 130 ChinA2e Number Sets 49Table 131 Greek Letters 50Table 132 AMS Greek Letters 50Table 133 txfontspxfonts Upright Greek Letters 50Table 134 upgreek Upright Greek Letters 51Table 135 fourier Variant Greek Letters 51Table 136 txfontspxfonts Variant Latin Letters 51Table 137 AMS Hebrew Letters 51Table 138 MnSymbol Hebrew Letters 51Table 139 Letter-like Symbols 51Table 140 AMS Letter-like Symbols 52

3

Table 141 txfontspxfonts Letter-like Symbols 52Table 142 mathabx Letter-like Symbols 52Table 143 MnSymbol Letter-like Symbols 52Table 144 trfsigns Letter-like Symbols 52Table 145 mathdesign Letter-like Symbols 52Table 146 fge Letter-like Symbols 53Table 147 fourier Letter-like Symbols 53Table 148 AMS Delimiters 53Table 149 stmaryrd Delimiters 53Table 150 mathabx Delimiters 53Table 151 nath Delimiters 53Table 152 Variable-sized Delimiters 54Table 153 Large Variable-sized Delimiters 54Table 154 AMS Variable-sized Delimiters 54Table 155 stmaryrd Variable-sized Delimiters 54Table 156 mathabx Variable-sized Delimiters 55Table 157 MnSymbol Variable-sized Delimiters 55Table 158 mathdesign Variable-sized Delimiters 56Table 159 nath Variable-sized Delimiters (Double) 56Table 160 nath Variable-sized Delimiters (Triple) 57Table 161 fourier Variable-sized Delimiters 57Table 162 textcomp Text-mode Delimiters 57Table 163 metre Text-mode Delimiters 57Table 164 Math-mode Accents 57Table 165 AMS Math-mode Accents 58Table 166 MnSymbol Math-mode Accents 58Table 167 fge Math-mode Accents 58Table 168 yhmath Math-mode Accents 58Table 169 Extensible Accents 59Table 170 overrightarrow Extensible Accents 59Table 171 yhmath Extensible Accents 59Table 172 AMS Extensible Accents 59Table 173 MnSymbol Extensible Accents 60Table 174 mathtools Extensible Accents 60Table 175 mathabx Extensible Accents 60Table 176 fourier Extensible Accents 60Table 177 esvect Extensible Accents 61Table 178 undertilde Extensible Accents 61Table 179 ushort Extensible Accents 61Table 180 AMS Extensible Arrows 61Table 181 mathtools Extensible Arrows 62Table 182 chemarr Extensible Arrows 62Table 183 chemarrow Extensible Arrows 62Table 184 extarrows Extensible Arrows 62Table 185 extpfeil Extensible Arrows 63Table 186 DotArrow Extensible Arrows 63Table 187 trfsigns Extensible Transform Symbols 63Table 188 holtpolt Non-commutative Division Symbols 63Table 189 Dots 63Table 190 AMS Dots 64Table 191 wasysym Dots 64Table 192 MnSymbol Dots 64Table 193 mathdots Dots 64Table 194 yhmath Dots 64Table 195 teubner Dots 64Table 196 mathcomp Math Symbols 65Table 197 marvosym Digits 65

4

Table 198 fge Digits 65Table 199 dozenal Base-12 Digits 65Table 200 mathabx Mayan Digits 65Table 201 Miscellaneous LATEX 2ε Math Symbols 65Table 202 Miscellaneous AMS Math Symbols 66Table 203 Miscellaneous wasysym Math Symbols 66Table 204 Miscellaneous txfontspxfonts Math Symbols 66Table 205 Miscellaneous mathabx Math Symbols 66Table 206 Miscellaneous MnSymbol Math Symbols 66Table 207 Miscellaneous Internal MnSymbol Math Symbols 67Table 208 Miscellaneous textcomp Text-mode Math Symbols 67Table 209 Miscellaneous marvosym Math Symbols 67Table 210 Miscellaneous fge Math Symbols 67Table 211 Miscellaneous mathdesign Math Symbols 67Table 212 Miscellaneous arev Math Symbols 67Table 213 Math Alphabets 68

4 Science and technology symbols 70Table 214 gensymb Symbols Defined to Work in Both Math and Text Mode 70Table 215 wasysym Electrical and Physical Symbols 70Table 216 ifsym Pulse Diagram Symbols 70Table 217 ar Aspect Ratio Symbol 70Table 218 textcomp Text-mode Science and Engineering Symbols 70Table 219 steinmetz Extensible Phasor Symbol 70Table 220 wasysym Astronomical Symbols 71Table 221 marvosym Astronomical Symbols 71Table 222 mathabx Astronomical Symbols 71Table 223 wasysym APL Symbols 71Table 224 wasysym APL Modifiers 71Table 225 marvosym Computer Hardware Symbols 72Table 226 keystroke Computer Keys 72Table 227 ascii Control Characters (CP437) 72Table 228 milstd Logic Gates 73Table 229 marvosym Communication Symbols 73Table 230 marvosym Engineering Symbols 73Table 231 wasysym Biological Symbols 73Table 232 marvosym Biological Symbols 74Table 233 marvosym Safety-related Symbols 74Table 234 feyn Feynman Diagram Symbols 74

5 Dingbats 75Table 235 bbding Arrows 75Table 236 pifont Arrows 75Table 237 universal Arrows 75Table 238 marvosym Scissors 75Table 239 bbding Scissors 75Table 240 pifont Scissors 75Table 241 dingbat Pencils 76Table 242 bbding Pencils and Nibs 76Table 243 pifont Pencils and Nibs 76Table 244 dingbat Fists 76Table 245 bbding Fists 76Table 246 pifont Fists 76Table 247 fourier Fists 76Table 248 bbding Crosses and Plusses 76Table 249 pifont Crosses and Plusses 77Table 250 bbding Xs and Check Marks 77Table 251 pifont Xs and Check Marks 77

5

Table 252 wasysym Xs and Check Marks 77Table 253 universal Xs 77Table 254 pifont Circled Numbers 77Table 255 wasysym Stars 77Table 256 bbding Stars Flowers and Similar Shapes 78Table 257 pifont Stars Flowers and Similar Shapes 78Table 258 fourier Ornaments 78Table 259 wasysym Geometric Shapes 78Table 260 MnSymbol Geometric Shapes 79Table 261 ifsym Geometric Shapes 79Table 262 bbding Geometric Shapes 80Table 263 pifont Geometric Shapes 80Table 264 universa Geometric Shapes 80Table 265 universal Geometric Shapes 80Table 266 Miscellaneous dingbat Dingbats 80Table 267 Miscellaneous bbding Dingbats 80Table 268 Miscellaneous pifont Dingbats 80

6 Ancient languages 81Table 269 phaistos Symbols from the Phaistos Disk 81Table 270 protosem Proto-Semitic Characters 81Table 271 hieroglf Hieroglyphics 82Table 272 linearA Linear A Script 82Table 273 linearb Linear B Basic and Optional Letters 85Table 274 linearb Linear B Numerals 85Table 275 linearb Linear B Weights and Measures 85Table 276 linearb Linear B Ideograms 86Table 277 linearb Unidentified Linear B Symbols 86Table 278 cypriot Cypriot Letters 86Table 279 sarabian South Arabian Letters 87Table 280 teubner Archaic Greek Letters and Greek Numerals 87

7 Other symbols 88Table 281 textcomp Genealogical Symbols 88Table 282 wasysym General Symbols 88Table 283 wasysym Circles 88Table 284 wasysym Musical Symbols 88Table 285 arev Musical Symbols 88Table 286 harmony Musical Symbols 89Table 287 harmony Musical Accents 89Table 288 manfnt Dangerous Bend Symbols 89Table 289 Miscellaneous manfnt Symbols 89Table 290 marvosym Navigation Symbols 90Table 291 marvosym Laundry Symbols 90Table 292 marvosym Information Symbols 90Table 293 Other marvosym Symbols 90Table 294 Miscellaneous universa Symbols 90Table 295 Miscellaneous universal Symbols 90Table 296 Miscellaneous fourier Symbols 91Table 297 ifsym Weather Symbols 91Table 298 ifsym Alpine Symbols 91Table 299 ifsym Clocks 91Table 300 Other ifsym Symbols 92Table 301 clock Clocks 92Table 302 epsdice Dice 92Table 303 hhcount Dice 92Table 304 hhcount Tally Markers 92Table 305 skull Symbols 93

6

Table 306 Non-Mathematical mathabx Symbols 93Table 307 skak Chess Informator Symbols 93Table 308 skak Chess Pieces and Chessboard Squares 94Table 309 igo Go Stones 94Table 310 metre Metrical Symbols 95Table 311 metre Small and Large Metrical Symbols 95Table 312 teubner Metrical Symbols 95Table 313 dictsym Dictionary Symbols 96Table 314 simpsons Characters from The Simpsons 96Table 315 pmboxdraw Box-Drawing Symbols 97Table 316 staves Magical Staves 97Table 317 pigpen Cipher Symbols 98Table 318 ChinA2e Phases of the Moon 98Table 319 Other ChinA2e Symbols 98Table 320 recycle Recycling Symbols 99

8 Additional Information 10081 Symbol Name Clashes 10082 Resizing symbols 10083 Where can I find the symbol for 10084 Math-mode spacing 11285 Bold mathematical symbols 11386 ASCII and Latin 1 quick reference 11487 Unicode characters 11788 About this document 11889 Copyright and license 121

References 122

Index 123

7

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 5913symbolsmdashquite 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 39 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 8 contains some additional information about the symbols in this document It discusses howcertain mathematical symbols can vary in height shows which symbol names are not unique across packagesgives examples of how to create new symbols out of existing symbols explains how symbols are spaced inmath mode compares various schemes for boldfacing symbols presents LATEX ASCII and Latin 1 tablesshows how to input and output Unicode characters and provides some information about this document itselfThe Comprehensive LATEX Symbol List ends with an index of all the symbols in the document and variousadditional 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 9

ı ı ı ı etc (versus ı ı i and ı) 14

cent 18

e 18

copy reg and trade 19

permil 20 27

there4 30

B and F 31

and amp 38

64

deg as in ldquo180degrdquo or ldquo15rdquo 67

L F etc 68

N Z R etc 68

r 68

minusint

105

acutea è etc (ie several accents per character) 107

lt gt and | (instead of iexcl iquest and mdash) 114

ˆ and ˜ (or sim) 115

8

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 textasciicircumlowast lt textless˜ textasciitildelowast a ordf textordfemininelowast textasteriskcentered o ordm textordmasculine textbackslash para textparagraphdagger

| textbar middot textperiodcentered textbraceleftdagger iquest textquestiondown textbracerightdagger ldquo textquotedblleftbull textbullet rdquo textquotedblright

ccopy copy textcopyrightdagger lsquo textquoteleftdagger textdaggerdagger rsquo textquoterightDagger textdaggerdbldagger rcopy reg textregistered$ textdollardagger sect textsectiondagger

textellipsisdagger pound textsterlingdagger

mdash textemdash TM trade texttrademarkndash textendash textunderscoredagger

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 ^ and ~ can be used instead of textasciicircum and textasciitildeSee the discussion of ldquo˜rdquo on page 115

dagger 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


9

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

X checkmark r circledR z maltese

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

10

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 textscn

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 textupstep

(continued on next page)

11

(continued from previous page)

S textesh Ccedil textrhookrevepsilon Š textvertlineR 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

12

Table 12 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 scriptalt 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 13 wasysym Phonetic Symbols

D DH k dh l openoTHORN Thorn U inve thorn thorn

Table 14 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

13

Table 15 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 10) but usingthe same names as the tipa characters presented in Table 10 on page 11

Table 16 semtrans Transliteration Symbols

Alif Ayn

Table 17 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 in encodings that need to composite (ie combine) letters and accents Forexample ldquonaiverdquo always produces a correct ldquonaıverdquo while ldquonaiverdquoyields the rather odd-looking ldquonaiverdquo when using the OT1 font encoding and olderversions of LATEX Font encodings other than OT1 and newer versions of LATEXproperly typeset ldquonaiverdquo as ldquonaıverdquo

14

Table 18 tipa Text-mode Accents

acuteAacutea textacutemacronAtextacutemacronaacuteAacutea textacutewedgeAtextacutewedgea

Affi affi textadvancingAtextadvancinga

Altalt textbottomtiebarAtextbottomtiebara˘A˘a textbrevemacronAtextbrevemacronaŻAŻa textcircumacuteAtextcircumacuteaÂâ textcircumdotAtextcircumdotasectAsecta textdotacuteAtextdotacutea˙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


15


Amdashamdash textsubwAtextsubwa

Aˇ

aˇ

textsubwedgeAtextsubwedgea

Aampaamp textsuperimposetildeAtextsuperimposetildea

Aa

textsyllabicAtextsyllabicaÃã texttildedotAtexttildedotagtAgta texttoptiebarAtexttoptiebaraĲAĲa textvbaraccentAtextvbaraccenta

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

Table 19 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 20 wsuipa Text-mode Accents

Ag ag dentalAdentala

Aa underarchAunderarcha

Table 21 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

16

Table 22 metre Text-mode Accents

Aa acutusAacutusa

Aa breveAbreveaAa circumflexusAcircumflexusaAa diaeresisAdiaeresisa

Aa gravisAgravisaAa macronAmacrona

Table 23 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 17on page 14) but using the same names as the tipa accents presented in Table 18 onpage 15

Table 24 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 25 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 26 ogonek Accents

A a kAka

Table 27 combelow Accents

A a cbAcba

cb places a comma above letters with descenders Hence while ldquocbsrdquo producesldquosrdquo ldquocbgrdquo produces ldquoglsquordquo

17

Table 28 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

Table 29 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 30 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 9because the symbols in that table work properly in both text mode and math mode

Table 31 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 197 (EURdig) The mathdesign package redefines texteuroto be visually compatible with one of three additional fonts Utopia (euro) Char-ter (euro) or Garamond (euro)

Table 32 wasysym Currency Symbols

cent cent curren currency

18

Table 33 ChinA2e Currency Symbols

yuml Euro thorn Pound

Table 34 teubner Currency Symbols

Ε denarius Α hemiobelion Β tetartemorionΔ dracma ῝ stater

Table 35 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

Table 36 fourier Euro Signs

( eurologo euro texteuro

Table 37 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 38 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 someDVI viewers

19

Table 39 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

Table 40 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 41 Miscellaneous wasysym Text-mode Symbols

h permil

20

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 213 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 (various1) and ldquodef=rdquo (stackreltexttiny def=) See also the example ofequalsfill on page 108 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 symbols2 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 42 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 9because the symbols in that table work properly in both text mode and math mode

Table 43 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

1In txfonts pxfonts and mathtools the symbol is called coloneqq In mathabx and MnSymbol itrsquos called coloneq Incolonequals itrsquos called colonequals

2Bob Tennent listed these and other disjoint-union symbol possibilities in a November 2007 post to comptexttex

21

Table 44 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

Table 45 AMS Binary Operators

Z barwedge circledcirc ᵀ intercallowast

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

lowast Some people use a superscripted intercal for matrix transposeldquoAîntercalrdquo 7rarr ldquoAᵀrdquo (See the May 2009 comptexttex thread ldquorais-ing math symbolsrdquo for suggestions about altering the height of the superscript)top (Table 139 on page 51) T and mathsfT are other popular choices ldquoAgtrdquoldquoAT rdquo ldquoATrdquo

Table 46 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

22

Table 47 wasysym Binary Operators

C lhd ocircle RHD D unrhd LHD B rhd E unlhd

Table 48 txfontspxfonts Binary Operators

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

Table 49 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

Table 50 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 ⊔ sqcup


23


frac34 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 51 mathdesign Binary Operators

_ dtimes ] udtimes ^ utimes

The mathdesign package additionally provides versions of each of the binary oper-ators shown in Table 45 on page 22

Table 52 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

Table 53 shuffle Binary Operators

cshuffle shuffle

Table 54 ulsy Geometric Binary Operators

odplus

24

Table 55 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 56 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

Table 57 Variable-sized Math Operators⋂ ⋂bigcap

otimesotimesbigotimes

and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus

int intintoplusoplus

bigoplusor or

bigvee∮ ∮

oint

25

Table 58 AMS Variable-sized Math Operators

intint intintiint

intintint intintintiiint

intintintint intintintintiiiint

intmiddotmiddot middotint int

middot middot middotint

idotsint

Table 59 stmaryrd Variable-sized Math Operators

embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup

Table 60 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 57) is used

Table 61 mathabx Variable-sized Math Operators

notbigcurlyvee

Yacuteyacutebigboxslash

Eacuteeacutebigoright

brvbarbigsqcap

Ograveogravebigboxtimes

Iacuteiacutebigoslash

laquobigcurlywedge

Uacuteuacutebigboxtop

Ecircecircbigotop

Oumloumlbigboxasterisk

szligyumlbigboxtriangleup

Iumliumlbigotriangleup


26


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

Table 62 txfontspxfonts Variable-sized Math Operators

bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint

F Gvaroiiintclockwise


27


iint

N Ovaroiiintctrclockwise

L Moiiintclockwise

B Cvaroiintclockwise

D Eoiiintctrclockwise

J Kvaroiintctrclockwise

) oiiint

- varointclockwise

H Ioiintclockwise

+ varointctrclockwise

Aoiintctrclockwise

varprod

oiint

Table 63 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 64 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

29

Table 65 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

)

Table 66 cmll Large Math Operators

˙bigparr

˘bigwith

Table 67 Binary Relations

asymp approx equiv equiv perp perp ^ smile asymp _ frown ≺ prec succ bowtie Z Joinlowast preceq succeq cong | middagger 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

dagger The difference between mid and | is that the former is a binary relation whilethe latter is a math ordinal Consequently LATEX typesets the two with differentsurrounding spacing Contrast ldquoP(A | B)rdquo 7rarr ldquoP (A|B)rdquo with ldquoP(A mid B)rdquo 7rarrldquoP (A | B)rdquo

Table 68 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

30

Table 69 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 70 stmaryrd Binary Relations

A inplus B niplus

Table 71 wasysym Binary Relations

invneg leadsto wasyproptoZ Join logof

Table 72 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 73 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

31

Table 74 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

Table 75 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 76 MnSymbol Binary Relations

asymp approx eqbump nwfootline iuml seVdash≊ approxeq ≖ eqcirc nwfree ∥ shortparallel backapprox ⩦ eqdot aring nwmodels sim sim backapproxeq ≂ eqsim otilde nwModels ≃ simeq≌ backcong = equal nwsecrossing ≻ succ backeqsim Yacute equalclosed Oacute nwseline ⪸ succapprox∽ backsim equiv equiv times Nwseline ≽ succcurlyeq⋍ backsimeq THORN equivclosed Yacute nwvdash ⪰ succeq backtriplesim ≒ fallingdotseq iacute nwVdash ≿ succsim between ≙ hateq ≺ prec ~ swfootline


32


≏ bumpeq hcrossing ⪷ precapprox swfree≎ Bumpeq z leftfootline ≼ preccurlyeq aelig swmodels≗ circeq leftfree ⪯ preceq ouml swModelsUuml closedequal acirc leftmodels ≾ precsim THORN swvdashfrac12 closedprec ograve leftModels x rightfootline icirc swVdashraquo closedsucc prop leftpropto rightfree ≋ triplesim∶= coloneq 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

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 77 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


33


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


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 78 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

34

Table 79 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

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

def

ttststileabcdef

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

35

Table 80 trsym Binary Relations

InversTransformHoriz TransformHoriz

InversTransformVert TransformVert

Table 81 trfsigns Binary Relations

dfourier Dfourier

fourier Fourier

laplace Laplace ztransf Ztransf

Table 82 cmll Binary Relations

uml coh ˝ scoh˚ incoh ˇ sincoh

Table 83 colonequals Binary Relations

asymp approxcolon minus coloncolonminus = equalscoloncolonasymp approxcoloncolon sim coloncolonsim minus minuscolonasymp colonapprox = colonequals minus minuscoloncolon coloncolon minus colonminus ratioasymp coloncolonapprox sim colonsim sim simcolon= coloncolonequals = equalscolon sim simcoloncolon

Table 84 fourier Binary Relations

Ocirc nparallelslant Euml parallelslant

Table 85 Subset and Superset Relations

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


Table 86 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

36

Table 87 stmaryrd Subset and Superset Relations

D subsetplus E supsetplusF subsetpluseq G supsetpluseq

Table 88 wasysym Subset and Superset Relations

sqsubset A sqsupset

Table 89 txfontspxfonts Subset and Superset Relations

a nsqsubset A nsqsupseteq nSupset nsqsubseteq gt nSubsetb nsqsupset nsubseteqq

Table 90 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 91 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 92 Inequalities

ge geq gg le leq ll neq

37

Table 93 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

Table 94 wasysym Inequalities

apprge gt apprle

Table 95 txfontspxfonts Inequalities

4 ngg ngtrsim nlesssim ngtrapprox nlessapprox 3 nllamp ngtrless nlessgtr

Table 96 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 97 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 98 AMS Triangle Relations

J blacktriangleleft 7 ntriangleright D trianglerighteqI blacktriangleright 4 ntrianglerighteq C vartriangleleft6 ntriangleleft E trianglelefteq B vartriangleright5 ntrianglelefteq triangleq

39

Table 99 stmaryrd Triangle Relations

P trianglelefteqslant Q trianglerighteqslantR ntrianglelefteqslant S ntrianglerighteqslant

Table 100 mathabx Triangle Relations

ntriangleleft ntrianglerighteq triangleright vartriangleright ntrianglelefteq triangleleft trianglerighteq ntriangleright trianglelefteq vartriangleleft

Table 101 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 102 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 169 for information about how to put a diagonal arrow

across a mathematical expression (as in ldquo0

nabla middot ~B rdquo)

Table 103 Harpoons

leftharpoondown rightharpoondown rightleftharpoons leftharpoonup rightharpoonup

Table 104 textcomp Text-mode Arrows

darr textdownarrow rarr textrightarrowlarr textleftarrow uarr textuparrow

Table 105 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 106 AMS Negated Arrows

nLeftarrow lt nLeftrightarrow nRightarrow8 nleftarrow = nleftrightarrow 9 nrightarrow

Table 107 AMS Harpoons

downharpoonleft leftrightharpoons upharpoonleft downharpoonright rightleftharpoons upharpoonright

41

Table 108 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 109 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 110 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 111 mathabx Negated Arrows

ouml nLeftarrow Uuml nleftrightarrow Ucirc nrightarrowUacute nleftarrow oslash nLeftrightarrow divide nRightarrow

42

Table 112 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 113 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 twoheaddownarrow


43


larr leftarrow ∳ partialvartrcirclerightintlowast twoheadleftarrow 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 114 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 nsearrow


44


c ndasheddownarrow $ nnearrowtail nsearrowtailb ndashedleftarrow curren nnelsquigarrow sect nselsquigarrowd 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 115 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 116 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 117 harpoon Extensible Harpoons

abc overleftharpabcabc overrightharpdownabc abc underrightharpabc

abc overleftharpdownabc abc underleftharpabc abc underrightharpdownabcabc overrightharpabc abc underleftharpdownabc

All of the harpoon symbols are implemented using the graphics package (specificallygraphicsrsquos resizebox command) Consequently only TEX backends that supportgraphical transformations (eg not Xdvi) can properly display these symbols

Table 118 chemarrow Arrows

A chemarrow

Table 119 fge Arrows

fgerightarrow fgeuparrow

Table 120 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 121 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 122 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 123 ulsy Contradiction Symbols

blitza blitzb blitzc blitzd 13 blitze

Table 124 Extension Characters

minus relbar = Relbar

Table 125 stmaryrd Extension Characters

Y Arrownot Mapsfromchar MapstocharX arrownot [ mapsfromchar

Table 126 txfontspxfonts Extension Characters

Mappedfromchar Mmappedfromchar Mmapstochar mappedfromchar mmappedfromchar mmapstochar

48

Table 127 mathabx Extension Characters

szlig mapsfromchar THORN mapstocharucirc Mapsfromchar uacute Mapstochar

Table 128 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 misleading3 Each log-like symbol merelyproduces the eponymous textual equivalent but with proper surrounding spac-ing See Section 84 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 129 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 84 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 130 ChinA2e Number Sets

Atilde Complex Uacute Integer Icirc Natural Ntilde Rational Ograve Realraquo COMPLEX iquest INTEGER frac14 NATURAL frac12 RATIONAL frac34 REAL

3Michael J Downes prefers the more general term ldquoatomic math objectsrdquo

49

Table 131 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 ldquomicrordquo

See Section 85 for examples of how to produce bold Greek letters

The symbols in this table are intended to be used in mathematical typesettingGreek body text can be typeset using the babel packagersquos greek (or polutonikogreek)optionmdashand of course a font that provides the glyphs for the Greek alphabet

Table 132 AMS Greek Letters

z digamma κ varkappa

Table 133 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

50

Table 134 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 135 fourier Variant Greek Letters

π pi ρ rho$ varpi varrhoEgrave varvarpi AElig varvarrho

Table 136 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 137 AMS Hebrew Letters

i beth ג gimel k daleth

aleph (alefsym) appears in Table 201 on page 65

Table 138 MnSymbol Hebrew Letters

alefsym aleph ℶ beth ℷ gimel ℸ daleth

Table 139 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

51

Table 140 AMS Letter-like Symbols

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

Table 141 txfontspxfonts Letter-like Symbols

cent mathcent pound mathsterlinglowast lt notin = notni


Table 142 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 143 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 144 trfsigns Letter-like Symbols

e e j im

Table 145 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 140

52

Table 146 fge Letter-like Symbols

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

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

Table 147 fourier Letter-like Symbols

part partialCcedil varpartialdiff

Table 148 AMS Delimiters

p ulcorner q urcornerx llcorner y lrcorner

Table 149 stmaryrd Delimiters

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

Table 150 mathabx Delimiters

v lcorners w rcorners

x ulcorner y urcornerz llcorner lrcorner

Table 151 nath Delimiters

niv vin

53

Table 152 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 153 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 154 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 152) are intended to be used as operators (eg as in ldquop|qrdquo)

Table 155 stmaryrd Variable-sized Delimiters

~

llbracket

rrbracket

54

Table 156 mathabx Variable-sized Delimiters

v1

ldbrack w9

rdbrack

7 7777 lfilet rfilet

~ thickvert ~

vvvert

Table 157 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

55

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

Table 158 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 159 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 159 can also be expressed using the double macroSee the nath documentation for examples and additional information

56

Table 160 nath Variable-sized Delimiters (Triple)

〈〈〈langlanglang

triplelt 〉〉〉rangrangrang

triplegt

[[[[[[

triple[ ]]]]]]

triple]

|||∣∣∣∣∣∣∣∣∣ ltriple|lowast |||

∣∣∣∣∣∣∣∣∣ rtriple|lowast

lowast Similar to lVert and rVert in Table 159 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

Table 161 fourier Variable-sized Delimiters

llbracket

rrbracket

VERT

Table 162 textcomp Text-mode Delimiters

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

Table 163 metre Text-mode Delimiters

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

Table 164 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 201 on page 65) 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

57

Table 165 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 166 MnSymbol Math-mode Accents

a veca

Table 167 fge Math-mode Accents

Andash

andash spirituslenisAspirituslenisalowast

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

Table 168 yhmath Math-mode Accents

a ringa

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

58

Table 169 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 considerusing 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 170 overrightarrow Extensible Accents=rArrabc Overrightarrowabc

Table 171 yhmath Extensible Accents

abc wideparenabc Egraveabc widetriangleabc

˚abc wideringabc

Table 172 AMS Extensible Accents

larrrarrabc overleftrightarrowabc abclarrrarr underleftrightarrowabc

abclarrminus underleftarrowabc abcminusrarr underrightarrowabc

59

Table 173 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 174 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 175 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

Table 176 fourier Extensible Accents

Ugraveabc widearcabc abc wideparenabc

aringabc wideOarcabc abc wideringabc

60

Table 177 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 178 undertilde Extensible Accents

abcrsaquo utildeabc

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

Table 179 ushort Extensible Accents

abc ushortdwabc abc ushortwabc

ushortw and ushortdw are intended to be used with multi-character argu-ments (ldquowordsrdquo) while ushortand ushortd are intended to be used with single-character arguments

The underlines produced by the ushort commands are shorter than those pro-duced by the underline command Consider the output from the expres-sion ldquoushortxushortyunderlinexunderlineyrdquo which looks likeldquoxyxyrdquo

Table 180 AMS Extensible Arrows

abclarrminusminus xleftarrowabcabcminusminusrarr xrightarrowabc

61

Table 181 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 182 chemarr Extensible Arrowsabcminusminusminusminus xrightleftharpoonsabc

Table 183 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 184 extarrows Extensible ArrowsabclArr=rArr xLeftrightarrowabc

abclArr==rArr xLongleftrightarrowabcabclarrminusrarr xleftrightarrowabc

abclarrminusminusrarr xlongleftrightarrowabcabc==== xlongequalabc

abc==rArr xLongrightarrowabcabclArr== xLongleftarrowabc

abcminusminusrarr xlongrightarrowabcabclarrminusminus xlongleftarrowabc

62

Table 185 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 186 DotArrow Extensible Arrowsa dotarrowa

The DotArrow package provides mechanisms for lengthening the arrow adjustingthe distance between the arrow and its symbol and altering the arrowhead Seethe DotArrow documentation for more information

Table 187 trfsigns Extensible Transform Symbols

a dfta a DFTa

Table 188 holtpolt Non-commutative Division Symbols

abcdef

holterabcdefabcdef

polterabcdef

Table 189 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 84 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

63

Table 190 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 68 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 191 wasysym Dots

there4 wasytherefore

Table 192 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 50 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

Table 193 mathdots Dots

iddots

Table 194 yhmath Dots

adots

Table 195 teubner Dots

antilabe

64

Table 196 mathcomp Math Symbols

tccentigrade Ω tcohm permil tcperthousandmicro tcmu tcpertenthousand

Table 197 marvosym Digits

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

Table 198 fge Digits

0 fgestruckzero 1 fgestruckone

Table 199 dozenal Base-12 Digits

X x E e

Table 200 mathabx Mayan Digits

0 maya0 2 maya2 4 maya41 maya1 3 maya3 5 maya5

Table 201 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 202) to that ofLATEXrsquos emptyset

65

Table 202 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 203 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 204 Miscellaneous txfontspxfonts Math Symbols

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

Table 205 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 206 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

66

Table 207 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 64 on page 29 but can nevertheless be used in isolation

Table 208 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) or the newer xfrac package can be used toconstruct vulgar fractions like ldquo12rdquo ldquo14rdquo ldquo34rdquo and even ldquocordquo

Table 209 Miscellaneous marvosym Math Symbols

W Anglesign divide Squaredot P Vectorarrowhigh= Corresponds p Vectorarrow

Table 210 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 211 Miscellaneous mathdesign Math Symbols∟ rightangle

Table 212 Miscellaneous arev Math Symbols

steaming diams vardiamond varspade varclub hearts varheart

67

Table 213 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 optionAacuteAcircAtilde symAsymBsymC china2eDagger

ABCdef123 mathfrakABCdef123 eufrakABCdef123 textfrakABCdef123 yfontspara

ABCdef123 textswabABCdef123 yfontspara

ABCˇf123 textgothABCdef123 yfontspara

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 ldquor 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 mathbbolmdashGreek 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 The sym commands provided by the ChinA2e package are actually text-modecommands They are included in Table 213 because they resemble the blackboard-bold symbols that appear in the rest of the table In addition to the 26 lettersof the English alphabet ChinA2e provides three umlauted blackboard-bold letterssymAE (ldquoUcircrdquo) symOE (ldquoUumlrdquo) and symUE (ldquoYacuterdquo) Note that ChinA2e does providemath-mode commands for the most common number-set symbols These are pre-sented in Table 130 on page 49

68

para As their text names imply the fonts provided by the yfonts package areactually text fonts They are included in Table 213 because they are frequentlyused in a mathematical context

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

69

4 Science and technology symbols

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

Table 214 gensymb Symbols Defined to Work in Both Math and Text Mode

celsius micro micro permil perthousanddeg degree Ω ohm

Table 215 wasysym Electrical and Physical Symbols

AC VHF photon F HF QPPPPPPR gluon

Table 216 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 217 ar Aspect Ratio Symbol

A AR

Table 218 textcomp Text-mode Science and Engineering Symbols

textcelsius textmho micro textmu Ω textohm

Table 219 steinmetz Extensible Phasor Symbol

abc phaseabc

The phase command uses the pict2e package to draw a horizontally and verti-cally scalable Steinmetz phasor symbol Consequently phase works only withthose TEX backends supported by pict2e See the pict2e documentation for moreinformation

70

Table 220 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 221 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 222 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 223 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 224 wasysym APL Modifiers

APLcirc sim APLnot | APLvert

71

Table 225 marvosym Computer Hardware Symbols

Iacute ComputerMouse Ntilde ParallelPort Icirc SerialInterfaceIuml Keyboard Ograve Printer ETH SerialPort

Table 226 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 227 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

72

Table 228 milstd Logic Gates

ANDd BUFu NANDl ORd

ANDl BusWidth NANDr ORl

ANDr INVd NANDu ORr

ANDu INVl NORd ORu

BUFd INVr NORl

BUFl INVu 13 NORr

BUFr NANDd NORu

The milstd package which provides the digital logic-gate symbols specified by theUS Department of Defensersquos MIL-STD-806 standard was written as a LATEX 209tex file not as a LATEX 2ε package Consequently it must be loaded into adocument with input milstd not with the more modern usepackagemilstd

Table 229 marvosym Communication Symbols

k Email t fax v Faxmachine E Lightning A Pickup

z Emailct u FAX B Letter H Mobilefone T Telefon

Table 230 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 231 wasysym Biological Symbols

female male

73

Table 232 marvosym Biological Symbols

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

Table 233 marvosym Safety-related Symbols

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

Table 234 feyn Feynman Diagram Symbols

bigbosonloop k hfermion smallbosonloopV

[ bigbosonloopA l shfermion d wfermion

bigbosonloopV | smallbosonloop m whfermion

gvcropped smallbosonloopA

a feyna e feynfu | feynglS K feynhs

c feync b feynfv z feynglu i feynhu

f feynf g feyng u feyngu m feynm

d feynfd q feyng1 feyngv feynms

l feynfl v feyngd s feyngvs p feynp

o feynflS y feyngl h feynh P feynP

k feynfs feynglB j feynhd x feynx

All other arguments to the feyn command produce a ldquo rdquo symbol

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

74

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 235 bbding Arrows

y ArrowBoldDownRight z ArrowBoldRightShort x ArrowBoldUpRight

ArrowBoldRightCircled w ArrowBoldRightStrobe

Table 236 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 237 universal Arrows

bauarrow bauwhitearrow

Table 238 marvosym Scissors

s Cutleft q Cutright S Leftscissorsr Cutline R Kutline Q Rightscissors

Table 239 bbding Scissors

ScissorHollowLeft ScissorLeftBrokenTop

ScissorHollowRight ScissorRight

ScissorLeft ScissorRightBrokenBottom

ScissorLeftBrokenBottom ScissorRightBrokenTop

Table 240 pifont Scissors

ding33 ding34 ding35 $ ding36

75

Table 241 dingbat Pencils

W largepencil P smallpencil

Table 242 bbding Pencils and Nibs

NibLeft PencilLeft PencilRightDown

NibRight PencilLeftDown PencilRightUp

NibSolidLeft PencilLeftUp

NibSolidRight PencilRight

Table 243 pifont Pencils and Nibs

ding46 ding47 0 ding48 1 ding49 2 ding50

Table 244 dingbat Fists

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

Table 245 bbding Fists

HandCuffLeft HandCuffRightUp HandPencilLeft

HandCuffLeftUp HandLeft HandRight

13 HandCuffRight HandLeftUp HandRightUp

Table 246 pifont Fists

ding42 + ding43 ding44 - ding45

Table 247 fourier Fists

t lefthand u righthand

Table 248 bbding Crosses and Plusses

Cross + CrossOpenShadow amp PlusOutline

- CrossBoldOutline CrossOutline ) PlusThinCenterOpen

4 CrossClowerTips Plus

CrossMaltese ( PlusCenterOpen

76

Table 249 pifont Crosses and Plusses

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

Table 250 bbding Xs and Check Marks

Checkmark XSolid XSolidBrush

CheckmarkBold $ XSolidBold

Table 251 pifont Xs and Check Marks

3 ding51 5 ding53 7 ding554 ding52 6 ding54 8 ding56

Table 252 wasysym Xs and Check Marks

2 CheckedBox Square 4 XBox

Table 253 universal Xs

baucross

Table 254 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 bullets4 See the psnfss docu-mentation for more information

Table 255 wasysym Stars

C davidsstar A hexstar B varhexstar

4In fact dingautolist can use any set of consecutive Zapf Dingbats symbols

77

Table 256 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 257 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 258 fourier Ornaments

o aldine X decoone c floweronerightm aldineleft ] decosix g leafleftn aldineright Y decothreeleft f leafNEj aldinesmall Z decothreeright h leafright[ decofourleft a decotwo d starredbullet decofourright b floweroneleft

Table 259 wasysym Geometric Shapes

7 hexagon 8 octagon D pentagon 9 varhexagon

78

Table 260 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

Table 261 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 83 for more information about constructing newsymbols out of existing symbols

79

Table 262 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 263 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

Table 264 universa Geometric Shapes

baucircle bausquare bautriangle

Table 265 universal Geometric Shapes

baucircle bauhole bausquare baueclipse baupunct bautriangle

Table 266 Miscellaneous dingbat Dingbats

O anchor E eye S SborderC carriagereturn C filledsquarewithdots B squarewithdots

D checkmark I satellitedish Z Zborder

Table 267 Miscellaneous bbding Dingbats

Envelope Peace PhoneHandset T SunshineOpenCircled

q OrnamentDiamondSolid Phone Plane Tape

Table 268 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

80

6 Ancient languages

This section presents letters and ideograms from various ancient scripts Some of these symbols may also beuseful in other typesetting contexts

Table 269 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 270 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

81

Table 271 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 272 linearA Linear A Script

LinearAI b LinearAXCIX LinearACXCVII t LinearACCXCV LinearAII c LinearAC LinearACXCVIII u LinearACCXCVI LinearAIII d LinearACI LinearACXCIX v LinearACCXCVII LinearAIV e LinearACII LinearACC w LinearACCXCVIII LinearAV f LinearACIII LinearACCI x LinearACCXCIX LinearAVI g LinearACIV LinearACCII y LinearACCC LinearAVII h LinearACV LinearACCIII z LinearACCCI LinearAVIII i LinearACVI LinearACCIV LinearACCCII LinearAIX j LinearACVII LinearACCV | LinearACCCIII LinearAX k LinearACVIII LinearACCVI LinearACCCIV LinearAXI l LinearACIX LinearACCVII ~ LinearACCCV LinearAXII m LinearACX LinearACCVIII LinearACCCVI LinearAXIII n LinearACXI LinearACCIX LinearACCCVII


82


13 LinearAXIV o LinearACXII LinearACCX LinearACCCVIII LinearAXV p LinearACXIII LinearACCXI LinearACCCIX LinearAXVI q LinearACXIV LinearACCXII LinearACCCX LinearAXVII r LinearACXV LinearACCXIII LinearACCCXI LinearAXVIII s LinearACXVI LinearACCXIV LinearACCCXII LinearAXIX t LinearACXVII $ LinearACCXV LinearACCCXIII

LinearAXX u LinearACXVIII LinearACCXVI LinearACCCXIV LinearAXXI v LinearACXIX amp LinearACCXVII LinearACCCXV LinearAXXII w LinearACXX LinearACCXVIII LinearACCCXVI LinearAXXIII x LinearACXXI ( LinearACCXIX LinearACCCXVII

LinearAXXIV y LinearACXXII ) LinearACCXX LinearACCCXVIII LinearAXXV z LinearACXXIII LinearACCXXI LinearACCCXIX LinearAXXVI LinearACXXIV + LinearACCXXII LinearACCCXX LinearAXXVII | LinearACXXV LinearACCXXIII LinearACCCXXI LinearAXXVIII LinearACXXVI - LinearACCXXIV LinearACCCXXII LinearAXXIX ~ LinearACXXVII LinearACCXXV LinearACCCXXIII LinearAXXX LinearACXXVIII LinearACCXXVI LinearACCCXXIV

LinearAXXXI LinearACXXIX 0 LinearACCXXVII LinearACCCXXV LinearAXXXII LinearACXXX 1 LinearACCXXVIII LinearACCCXXVI

LinearAXXXIII LinearACXXXI 2 LinearACCXXIX LinearACCCXXVII LinearAXXXIV LinearACXXXII 3 LinearACCXXX LinearACCCXXVIII LinearAXXXV LinearACXXXIII 4 LinearACCXXXI LinearACCCXXIX LinearAXXXVI LinearACXXXIV 5 LinearACCXXXII LinearACCCXXX$ LinearAXXXVII LinearACXXXV 6 LinearACCXXXIII LinearACCCXXXI LinearAXXXVIII LinearACXXXVI 7 LinearACCXXXIV LinearACCCXXXIIamp LinearAXXXIX LinearACXXXVII 8 LinearACCXXXV LinearACCCXXXIII LinearAXL LinearACXXXVIII 9 LinearACCXXXVI LinearACCCXXXIV( LinearAXLI LinearACXXXIX LinearACCXXXVII LinearACCCXXXV) LinearAXLII LinearACXL LinearACCXXXVIII LinearACCCXXXVI LinearAXLIII LinearACXLI lt LinearACCXXXIX LinearACCCXXXVII+ LinearAXLIV LinearACXLII = LinearACCXL LinearACCCXXXVIII LinearAXLV LinearACXLIII gt LinearACCXLI LinearACCCXXXIX- LinearAXLVI LinearACXLIV LinearACCXLII iexcl LinearACCCXL LinearAXLVII LinearACXLV LinearACCXLIII cent LinearACCCXLI LinearAXLVIII LinearACXLVI A LinearACCXLIV pound LinearACCCXLII0 LinearAXLIX LinearACXLVII B LinearACCXLV curren LinearACCCXLIII1 LinearAL LinearACXLVIII C LinearACCXLVI yen LinearACCCXLIV2 LinearALI LinearACXLIX D LinearACCXLVII brvbar LinearACCCXLV3 LinearALII LinearACL E LinearACCXLVIII sect LinearACCCXLVI4 LinearALIII LinearACLI F LinearACCXLIX uml LinearACCCXLVII5 LinearALIV LinearACLII G LinearACCL copy LinearACCCXLVIII6 LinearALV LinearACLIII H LinearACCLI ordf LinearACCCXLIX7 LinearALVI LinearACLIV I LinearACCLII laquo LinearACCCL8 LinearALVII LinearACLV J LinearACCLIII not LinearACCCLI9 LinearALVIII LinearACLVI K LinearACCLIV shy LinearACCCLII LinearALIX LinearACLVII L LinearACCLV reg LinearACCCLIII LinearALX LinearACLVIII M LinearACCLVI macr LinearACCCLIVlt LinearALXI LinearACLIX N LinearACCLVII deg LinearACCCLV= LinearALXII LinearACLX O LinearACCLVIII plusmn LinearACCCLVIgt LinearALXIII LinearACLXI P LinearACCLIX sup2 LinearACCCLVII LinearALXIV iexcl LinearACLXII Q LinearACCLX sup3 LinearACCCLVIII LinearALXV cent LinearACLXIII R LinearACCLXI acute LinearACCCLIX


83


A LinearALXVI pound LinearACLXIV S LinearACCLXII micro LinearACCCLXB LinearALXVII curren LinearACLXV T LinearACCLXIII para LinearACCCLXIC LinearALXVIII yen LinearACLXVI U LinearACCLXIV middot LinearACCCLXIID LinearALXIX brvbar LinearACLXVII V LinearACCLXV cedil LinearACCCLXIIIE LinearALXX sect LinearACLXVIII W LinearACCLXVI sup1 LinearACCCLXIVF LinearALXXI uml LinearACLXIX X LinearACCLXVII ordm LinearACCCLXVG LinearALXXII copy LinearACLXX Y LinearACCLXVIII raquo LinearACCCLXVIH LinearALXXIII ordf LinearACLXXI Z LinearACCLXIX frac14 LinearACCCLXVIII LinearALXXIV laquo LinearACLXXII [ LinearACCLXX frac12 LinearACCCLXVIIIJ LinearALXXV not LinearACLXXIII LinearACCLXXI frac34 LinearACCCLXIXK LinearALXXVI shy LinearACLXXIV ] LinearACCLXXII iquest LinearACCCLXXL LinearALXXVII reg LinearACLXXV ^ LinearACCLXXIII Agrave LinearACCCLXXIM LinearALXXVIII macr LinearACLXXVI _ LinearACCLXXIV Aacute LinearACCCLXXII

N LinearALXXIX deg LinearACLXXVII ` LinearACCLXXV Acirc LinearACCCLXXIIIO LinearALXXX plusmn LinearACLXXVIII a LinearACCLXXVI Atilde LinearACCCLXXIVP LinearALXXXI LinearACLXXIX b LinearACCLXXVII Auml LinearACCCLXXVQ LinearALXXXII LinearACLXXX c LinearACCLXXVIII Aring LinearACCCLXXVIR LinearALXXXIII LinearACLXXXI d LinearACCLXXIX AElig LinearACCCLXXVIIS LinearALXXXIV LinearACLXXXII e LinearACCLXXX Ccedil LinearACCCLXXVIIIT LinearALXXXV LinearACLXXXIII f LinearACCLXXXI Egrave LinearACCCLXXIXU LinearALXXXVI LinearACLXXXIV g LinearACCLXXXII Eacute LinearACCCLXXXV LinearALXXXVII LinearACLXXXV h LinearACCLXXXIII Ecirc LinearACCCLXXXIW LinearALXXXVIII LinearACLXXXVI i LinearACCLXXXIV Euml LinearACCCLXXXIIX LinearALXXXIX LinearACLXXXVII j LinearACCLXXXV Igrave LinearACCCLXXXIIIY LinearALXXXX LinearACLXXXVIII k LinearACCLXXXVI Iacute LinearACCCLXXXIVZ LinearAXCI LinearACLXXXIX l LinearACCLXXXVII Icirc LinearACCCLXXXV[ LinearAXCII LinearACLXXXX m LinearACCLXXXVIII Iuml LinearACCCLXXXVI LinearAXCIII LinearACXCI n LinearACCLXXXIX ETH LinearACCCLXXXVII] LinearAXCIV 13 LinearACXCII o LinearACCLXXXX Ntilde LinearACCCLXXXVIII^ LinearAXCV LinearACXCIII p LinearACCXCI Ograve LinearACCCLXXXIX_ LinearAXCVI LinearACXCIV q LinearACCXCII` LinearAXCVII LinearACXCV r LinearACCXCIIIa LinearAXCVIII LinearACXCVI s LinearACCXCIV

84

Table 273 linearb Linear B Basic and Optional Letters

a Ba j Bja B Bmu ] Bpte lsquo Broii 4 Bto

Baii J Bje n Bna I Bpu V Bru 5 Btu

lt Baiii b Bjo N Bne Bpuii s Bsa ~ Btwo

= Bau L Bju C Bni q Bqa S Bse u Bu

d Bda k Bka E Bno Q Bqe Y Bsi w Bwa

D Bde K Bke F Bnu X Bqi 1 Bso W Bwe

f Bdi c Bki Bnwa 8 Bqo 2 Bsu 6 Bwi

g Bdo h Bko o Bo r Bra Bswa 7 Bwo

x Bdu v Bku p Bpa ^ Braii | Bswi z Bza

gt Bdwe m Bma [ Bpaiii _ Braiii t Bta Z Bze

Bdwo M Bme P Bpe R Bre Btaii 9 Bzo

e Be y Bmi G Bpi O Bri T Bte

i Bi A Bmo H Bpo U Bro 3 Bti

These symbols must appear either within the argument to textlinb orfollowing the linbfamily font-selection command within a scope Single-character shortcuts are also supported Both ldquotextlinbBpaBkiBnardquo andldquotextlinbpcnrdquo produce ldquopcnrdquo for example See the linearb documentationfor more information

Table 274 linearb Linear B Numerals

acute BNi ˇ BNvii sbquo BNxl laquo BNc ı BNdcc

ˆ BNii ˘ BNviii lsaquo BNl raquo BNcc ȷ BNdccc

˜ BNiii macr BNix rsaquo BNlx ndash BNccc ff BNcm

uml BNiv ˙ BNx ldquo BNlxx mdash BNcd fi BNm

˝ BNv cedil BNxx rdquo BNlxxx zwnj BNd

˚ BNvi ˛ BNxxx bdquo BNxc permil BNdc

These symbols must appear either within the argument to textlinb or followingthe linbfamily font-selection command within a scope

Table 275 linearb Linear B Weights and Measures

Ď BPtalent Ľ BPvolb Ń BPvolcf Ą BPwtb Č BPwtd

Ĺ BPvola Ł BPvolcd Ă BPwta Ć BPwtc


85

Table 276 linearb Linear B Ideograms

Ž BPamphora ź BPchassis ă BPman Š BPwheat

ĳ BParrow Ř BPcloth ț BPnanny ž BPwheel

Ş BPbarley ŋ BPcow Ț BPolive Ť BPwine

ť BPbilly Ÿ BPcup ń BPox Ż BPwineiih

ľ BPboar š BPewe ĺ BPpig Ĳ BPwineiiih

Ű BPbronze ě BPfoal ś BPram İ BPwineivh

ň BPbull ş BPgoat ř BPsheep ą BPwoman

đ BPcauldroni Ź BPgoblet ł BPsow Ś BPwool

sect BPcauldronii Ů BPgold iexcl BPspear

yuml BPchariot ď BPhorse ż BPsword


Table 277 linearb Unidentified Linear B Symbols

fl BUi BUiv BUvii amp BUx shy Btwe

ffi BUii BUv $ BUviii rsquo BUxi

ffl BUiii BUvi BUix shy BUxii


Table 278 cypriot Cypriot Letters

a Ca v Cku B Cmu H Cpo 1 Cso 6 Cwi

e Ce l Cla n Cna I Cpu 2 Csu 7 Cwo

g Cga L Cle N Cne r Cra t Cta x Cxa

i Ci d Cli C Cni R Cre T Cte X Cxe

j Cja f Clo E Cno O Cri 3 Cti j Cya

b Cjo q Clu F Cnu U Cro 4 Cto b Cyo

k Cka m Cma o Co V Cru 5 Ctu g Cza

K Cke M Cme p Cpa s Csa u Cu 9 Czo

c Cki y Cmi P Cpe S Cse w Cwa

h Cko A Cmo G Cpi Y Csi W Cwe

These symbols must appear either within the argument to textcypr orfollowing the cyprfamily font-selection command within a scope Single-character shortcuts are also supported Both ldquotextcyprCpaCkiCnardquo andldquotextcyprpcnrdquo produce ldquopcnrdquo for example See the cypriot documentationfor more information

86

Table 279 sarabian South Arabian Letters

a SAa z SAz m SAm x SAsd D SAdbb SAb H SAhd n SAn q SAq J SAtbg SAg T SAtd s SAs r SAr G SAgad SAd y SAy f SAf S SAsv Z SAzdh SAh k SAk lsquo SAlq t SAt X SAsaw SAw l SAl o SAo I SAhu B SAdd

These symbols must appear either within the argument to textsarab orfollowing the sarabfamily font-selection command within a scope Single-character shortcuts are also supported Both ldquotextsarabSAbSAkSAnrdquo andldquotextsarabbknrdquo produce ldquobknrdquo for example See the sarabian documentationfor more information

Table 280 teubner Archaic Greek Letters and Greek Numerals

Ϙ Coppadagger Ϝ Digammalowast ϡ sampilowast ϛ varstigmaϙ coppadagger ϟ koppalowast Ϛ Stigmaϝ digammalowastDagger Ϡ Sampi ϛ stigmalowast

lowast Technically these symbols do not require teubner it is sufficient to load the babelpackage with the greek option (upon which teubner depends)mdashbut use qoppa forkoppa and ddigamma for digammadagger For compatibility with other naming conventions teubner defines Koppa as a syn-

onym for Coppa and varcoppa as a synonym for coppaDagger If both teubner and amssymb are loaded teubnerrsquos digamma replaces amssymbrsquosdigamma regardless of package-loading order

87

7 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 281 textcomp Genealogical Symbols

b textborn c textdivorced m textmarriedd textdied l textleaf

Table 282 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 283 wasysym Circles

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

Table 284 wasysym Musical Symbols

eighthnote 13 halfnote twonotes fullnote quarternote

See also flat sharp and natural (Table 201 on page 65)

Table 285 arev Musical Symbols

quarternote eighthnote sixteenthnote


88

Table 286 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 287 harmony Musical Accents

Aa

aa

FerliAFerlialowast A a 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 288 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 289 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

89

Table 290 marvosym Navigation Symbols

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

Table 291 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 292 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

Table 293 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 294 Miscellaneous universa Symbols

bauforms bauhead

Table 295 Miscellaneous universal Symbols

baudash bauforms bauquarter varQ bauequal bauhead bauquestion13 bauface bauplus bauwindow

90

Table 296 Miscellaneous fourier Symbols

L bomb M grimace N textthinglowast T textxswuplowast

B danger A noway U textxswdownlowast

lowast fourier defines math-mode aliases for a few of the preceding symbolsthething (ldquoNrdquo) xswordsup (ldquoTrdquo) and xswordsdown (ldquoUrdquo)

Table 297 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

Table 298 ifsym Alpine Symbols

SummitSign Summit SurveySign HalfFilledHut

StoneMan Mountain Joch VarSummit

Hut IceMountain Flag

FilledHut VarMountain VarFlag

Village VarIceMountain Tent

Table 299 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 ldquoDrdquo 〈hours〉 must be an integer from 0 to 11 and 〈minutes〉 must be aninteger multiple of 5 from 0 to 55

91

Table 300 Other ifsym Symbols

FilledSectioningDiamond Letter Radiation

Fire PaperLandscape SectioningDiamond

Irritant PaperPortrait ( Telephone

Cube1 Cube3 Cube5

Cube2 Cube4 Cube6

StrokeOne StrokeThree StrokeFive

StrokeTwo StrokeFour

Table 301 clock Clocks

ClockStyle ClockFramefalse ClockFrametrue

0 i i01 i1 i102 i2 i203 i3 i30

The clock package provides a clock command to typeset an arbitrary time onan analog clock (and clocktime to typeset the documentrsquos build time) Forexample the clocks in the above table were produced with clock1541 Clocksymbols are composed from a font of clock-face fragments using one of four valuesfor ClockStyle and either ClockFrametrue or ClockFrametrue as illustratedabove See the clock documentation for more information

Table 302 epsdice Dice

epsdice1 epsdice3 epsdice5epsdice2 epsdice4 epsdice6

Table 303 hhcount Dice

fcdice1 fcdice3 fcdice5fcdice2 fcdice4 fcdice6

The fcdice command accepts values larger than 6 For example ldquofcdice47rdquoproduces ldquo rdquo

Table 304 hhcount Tally Markers

fcscore1 fcscore3 fcscore5fcscore2 fcscore4

The fcscore command accepts values larger than 5 For exampleldquofcscore47rdquo produces ldquo rdquo

92

Table 305 skull Symbols

A skull

Table 306 Non-Mathematical mathabx Symbols

O rip

Table 307 skak Chess Informator Symbols

g bbetter d doublepawns q seppawnsi bdecisive L ending O-O shortcastlingb betteris j equal T timelimita bishoppair H file k uncleare bupperhand O kside u unitedpawnsX capturesymbol O-O-O longcastling R variousO castlingchar x markera f wbetter- castlinghyphen y markerb h wdecisiveI centre m mate J weakpt+ checksymbol S morepawns v withRR chesscomment U moreroom A withattackP chessetc N novelty E withideal chesssee F onlymove C withinitn compensation o opposbishops w withoutV counterplay r passedpawn c wupperhandt devadvantage M qside D zugzwangG diagonal s samebishops

93

Table 308 skak Chess Pieces and Chessboard Squares

a BlackBishopOnBlack s BlackRookOnBlack J WhiteKingOnBlack

b BlackBishopOnWhite r BlackRookOnWhite K WhiteKingOnWhite

Z BlackEmptySquare B symbishop M WhiteKnightOnBlack

j BlackKingOnBlack K symking N WhiteKnightOnWhite

k BlackKingOnWhite N symknight O WhitePawnOnBlack

m BlackKnightOnBlack p sympawn P WhitePawnOnWhite

n BlackKnightOnWhite Q symqueen L WhiteQueenOnBlack

o BlackPawnOnBlack R symrook Q WhiteQueenOnWhite

p BlackPawnOnWhite A WhiteBishopOnBlack S WhiteRookOnBlack

l BlackQueenOnBlack B WhiteBishopOnWhite R WhiteRookOnWhite

q BlackQueenOnWhite 0 WhiteEmptySquare

The skak package also provides commands for drawing complete chessboards Seethe skak documentation for more information

Table 309 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

94

Table 310 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 311 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

Table 312 teubner Metrical Symbols

Ι aeolicbii ι barbrevis η ipercatalΘ aeolicbiii ς bbrevis λ longaΚ aeolicbiv β brevis ε ubarbbrevisΞ anceps γ catal δ ubarbrevisΖ ancepsdbrevis corona φ ubarsbrevisΨ banceps Ϙ coronainv κ ubrevislongaθ barbbrevis H hiatus

The teubner package provides a newmetrics command that helps users combinethe preceding symbols as well as other teubner symbols For example the predefinedpentam symbol uses newmetrics to juxtapose six longas two barbbrevisesfour brevises and a dBar into ldquoλθλθλ||λββλββλrdquo See the teubner docu-mentation for more information

95

Table 313 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

Table 314 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

96

Table 315 pmboxdraw Box-Drawing Symbols

textblock textSFli textSFxli textSFxxiii

textdkshade textSFlii textSFxlii textSFxxiv

textdnblock textSFliii textSFxliii textSFxxv

textlfblock textSFliv textSFxliv textSFxxvi

textltshade textSFv textSFxlix textSFxxvii

textrtblock textSFvi textSFxlv textSFxxviii

textSFi textSFvii textSFxlvi textSFxxxix

textSFii textSFviii textSFxlvii textSFxxxvi

textSFiii textSFx textSFxlviii textSFxxxvii

textSFiv textSFxi textSFxx textSFxxxviii

textSFix textSFxix textSFxxi textshade

textSFl textSFxl textSFxxii textupblock

Code Page 437 (CP437) which was first utilized by the original IBM PC containsthe set of box-drawing symbols (sides corners and intersections of single- anddouble-ruled boxes) shown above in character positions 176ndash223 These symbolsalso appear in the Unicode Box Drawing and Block Element tables

The pmboxdraw package draws the CP437 box-drawing symbols using TEX rules(specifically vrule) instead of with a font and thereby provides the ability toalter both rule width and the separation between rules See the pmboxdraw docu-mentation for more information

Table 316 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


97


staveXII staveXXXV 9 staveLVIII

staveXIII staveXXXVI staveLIX

13 staveXIV $ staveXXXVII staveLX

staveXV staveXXXVIII lt staveLXI

staveXVI amp staveXXXIX = staveLXII

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

Table 317 pigpen Cipher Symbols

A pigpenfont A J pigpenfont J S pigpenfont S

B pigpenfont B K pigpenfont K T pigpenfont T

C pigpenfont C L pigpenfont L U pigpenfont U

D pigpenfont D M pigpenfont M V pigpenfont V

E pigpenfont E N pigpenfont N W pigpenfont W

F pigpenfont F O pigpenfont O X pigpenfont X

G pigpenfont G P pigpenfont P Y pigpenfont Y

H pigpenfont H Q pigpenfont Q Z pigpenfont Z

I pigpenfont I R pigpenfont R

Table 318 ChinA2e Phases of the Moon

MoonPha1 | MoonPha2 MoonPha3 ~ MoonPha4

Table 319 Other ChinA2e Symbols

Greenpoint Postbox Telephonelt Info gt Request

98

Table 320 recycle Recycling Symbols

A recycleA Recycle

A RECYCLE

The METAFONT code that implements the recycling symbols shown above isin the words of its author ldquoawful code [that] doesnrsquot even put the logoin a box (properly)rdquo Expect to receive ldquoInconsistent equation (off by〈number〉)rdquo errors from METAFONT Fortunately if you tell METAFONT to pro-ceed past those errors (eg by pressing Enter after each one or by specifyingldquo-interaction=nonstopmoderdquo on the METAFONT command line) it should pro-duce a valid font

The commands listed above should be used within a group (eg ldquorecyclerdquo)because they exhibit the side effect of changing the font to the recycle font

99

8 Additional Information

Unlike the previous sections of this document Section 8 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

81 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 321 on the following page presents a selection ofname clashes that appear in 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 321 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 321 because they are designed to be compatible with the symbols they replace Table 322 on page 102illustrates 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

82 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 323 on page 102 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 102 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

83 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

100

Table

321

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

101

Table 322 Example of a Benign Name Clash

Default txfontsSymbol (Computer Modern) (Times Roman)

R R Rtextrecipe

Table 323 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

102

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 font5 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 transformations6 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 rotatebox7

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 67 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

5pifont defines a convenient Pisymbol command for accessing symbols in PostScript fonts by number For exampleldquoPisymbolpsy191rdquo produces ldquocrarrrdquo

6As an example Xdvi ignores both reflectbox and rotatebox7More common symbols for representing ldquosuch thatrdquo include ldquo|rdquo ldquordquo and ldquostrdquo

103

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 oversetGsim8 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)9 is due to an October 2007 comptexttex post by Donald Arseneau

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

8LATEXrsquos stackrel command is similar but is limited to placing a symbol above a binary relation9While barcirc illustrates how to combine symbols using ooalign the stmaryrd packagersquos minuso command (Table 46 on

page 22) provides a similar glyph (ldquordquo) as a single indivisible symbol

104

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 103

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 84) 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 centernot might be used for exampleto create a ldquodoes not implyrdquo symbol

6=rArr notLongrightarrow

vs6=rArr 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

defXint1mathchoiceXXintdisplaystyletextstyle1XXinttextstylescriptstyle1XXintscriptstylescriptscriptstyle1XXintscriptscriptstylescriptscriptstyle1

105

intdefXXint123setbox0=hbox$123int$

vcenterhbox$23$kern-5wd0defddashintXint=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)10

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

10Note that if your goal is to typeset commutative diagrams or pushoutpullback diagrams then you should probably be usingXY-pic

106

makeatletterdefmoverlaymathpalettemovrlaydefmovrlay12leavevmodevtop

baselineskipzskip 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 105 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 189 on page 63) 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

107

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 and subsequent modifications by BillyYu and Scott Pakin) for typesetting annuity and life-insurance symbols

DeclareRobustCommandactuarial[2][]defarraystretch0setlengtharraycolsep05ptsetlengtharrayrulewidth05ptsetbox0=hbox$scriptstyle12$beginarray[b]2gtscriptstylec|cline2-2rule[125pt]0ptht01 amp 2

endarray

Using the preceding definition one can type eg ldquo$a_actuarialn$rdquo to produce ldquoan rdquo andldquo$a_actuarial[x]n$rdquo to produce ldquoaxn rdquo

A more complex example of composing accents is the following definition of extensible overbracketunderbracket 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

108

Table 324 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 underparenthesismerely create a table whose width is determined by the given text thereby constraining the width of thehorizontal rules

Table 324 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 You may alsowant to read the freely available METAFONT primer located at httpmetafonttutorialfreefr 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)11 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

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

The code in Figures Figure 2 and Figure 3 is heavily commented and should demonstrate some of thebasic concepts behind METAFONT usage declaring variables defining points drawing lines and curves andpreparing to debug or fine-tune the output Again The METAFONTbook [Knu86b] is the definitive referenceon METAFONT programming

11Irsquom not a very good artist yoursquoll have to pretend that ldquoArdquo looks like a light bulb

109

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)

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)

110

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

1

2

3

4

5

6677

8

Figure 4 Proof diagram of lightbulb10mf

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 = lightbulb10Now 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)

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 font

111

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

DeclareFontFamilyUbulbDeclareFontShapeUbulbmnlt-gt lightbulb10

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

series (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 fontsuch 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

84 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 Table 128 and Table 129 is to provide the correct amount ofspacing around and within multiletter function names Table 325 on the following page contrasts the output ofthe log-like symbols with various naıve alternatives In addition to spacing the log-like symbols also handlesubscripts properly For example ldquomax_p in Prdquo produces ldquomaxpisinP rdquo in text but ldquomax

pisinPrdquo as part of a

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

DeclareMathOperatoratanatanDeclareMathOperatorlcmlcm

112

Table 325 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 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 326 contrasts symbols declared with DeclareMathOperator and DeclareMathOperator in both textstyle ($ $) and display style ([ ])12

Table 326 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 129 utilize this spacing convention

85 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 327contrasts 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 327 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

12Note that displaystyle can be used to force display style within $ $ and textstyle can be used to force text stylewithin [ ]

113

86 ASCII and Latin 1 quick reference

Table 328 amalgamates data from various other tables in this document into a convenient reference forLATEX 2ε typesetting of ASCII characters ie the characters available on a typical US computer keyboardThe first two columns list the characterrsquos ASCII code in decimal and hexadecimal The third column showswhat the character looks like The fourth column lists the LATEX 2ε command to typeset the character as a textcharacter And the fourth column lists the LATEX 2ε command to typeset the character within a texttt command (or more generally when ttfamily is in effect)

Table 328 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 ˜ ~ ~

The following are some additional notes about the contents of Table 328

bull ldquordquo is not available in the OT1 font encoding

bull Table 328 shows a close quote for character 39 for consistency with the open quote shown for character 96A straight quote can be typeset using textquotesingle (cf Table 40)

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 encoding13 The following are some alternativesfor typesetting ldquoltrdquo ldquogtrdquo and ldquo|rdquo

ndash Specify a document font encoding other than OT1 (as described on page 8)

ndash Use the appropriate symbol commands from Table 2 on page 9 viz textless textgreaterand textbar

ndash Enter the symbols in math mode instead of text mode ie $lt$ $gt$ and $|$

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

13Donald Knuth didnrsquot think such symbols were important outside of mathematics so he omitted them from his text fonts

114

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 67 on page 30)which produces a somewhat wide ldquosimrdquo or the textcomp packagersquos texttildelow (shown in Table 40on page 20) 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 227 on page 72

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 328 Table 329 on the next page is an amalgamation of data from other tables in thisdocument While Table 328 shows how to typeset the 7-bit ASCII character set Table 329 shows the Latin 1(Western European) character set also known as ISO-8859-1


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 17 onpage 14 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 8) 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 330 presents thecharacters with which CP1252 augments the standard Latin 1 table


bull As in Table 329 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

115

Table 329 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

116

Table 330 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

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 environment14

87 Unicode characters

Unicode is a ldquouniversal character setrdquomdasha standard for encoding (ie assigning unique numbers to) the symbolsappearing in many of the worldrsquos languages While ASCII can represent 128 symbols and Latin 1 can represent256 symbols Unicode can represent an astonishing 1114112 symbols

Because TEX and LATEX predate the Unicode standard and Unicode fonts by almost a decade support forUnicode has had to be added to the base TEX and LATEX systems Note first that LATEX distinguishes betweeninput encodingmdashthe characters used in the tex filemdashand output encodingmdashthe characters that appear in thegenerated dvi pdf etc file

Inputting Unicode characters

To include Unicode characters in a tex file load the ucs package and load the inputenc package with the utf8x(ldquoUTF-8 extendedrdquo) option15 These packages enable LATEX to translate UTF-8 sequences to LATEX commandswhich are subsequently processed as normal For example the UTF-8 text ldquoCopyright copy 2009rdquomdashldquocopyrdquo is notan ASCII character and therefore cannot be input directly without packages such as ucsinputencmdashis convertedinternally by inputenc to ldquoCopyright textcopyright 2009rdquo and therefore typeset as ldquoCopyright copy 2009rdquo

The ucsinputenc combination supports only a tiny subset of Unicodersquos million-plus sym-bols Additional symbols can be added manually using the DeclareUnicodeCharacter commandDeclareUnicodeCharacter takes two arguments a Unicode number and a LATEX command to executewhen the corresponding Unicode character is encountered in the input For example the Unicode characterldquodegree celsiusrdquo (ldquo rdquo) appears at character position U+210316 However ldquo rdquo is not one of the charactersthat ucs and inputenc recognize The following document shows how to use DeclareUnicodeCharacter totell LATEX that the ldquo rdquo character should be treated as a synonym for textcelsius

documentclassarticleusepackageucsusepackage[utf8x]inputenc

14isoent 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

15UTF-8 is the 8-bit Unicode Transformation Format a popular mechanism for representing Unicode symbol numbers assequences of one to four bytes

16The Unicode convention is to express character positions as ldquoU+〈hexadecimal number〉rdquo

117

usepackagetextcomp

DeclareUnicodeCharacter2103textcelsius Enable direct input of U+2103

begindocumentIt was a balmy 21enddocument

which produces

It was a balmy 21

See the ucs documentation for more information and for descriptions of the various options that controlucsrsquos behavior

Outputting Unicode characters

Orthogonal to the ability to include Unicode characters in a LATEX input file is the ability to include a givenUnicode character in the corresponding output file By far the easiest approach is to use X ELATEX instead ofpdfLATEX or ordinary LATEX X ELATEX handles Unicode input and output natively and can utilize system fontsdirectly without having to expose them via tfm fd and other such files To output a Unicode charactera X ELATEX document can either include that character directly as UTF-8 text or use TEXrsquos char primitivewhich X ELATEX extends to accept numbers larger than 255

Suppose we want to output the symbols for versicle (ldquo rdquo) and response (ldquo rdquo) in a document The Unicodecharts list ldquoversiclerdquo at position U+2123 and ldquoresponserdquo at position U+211F We therefore need to install afont that contains those characters at their proper positions One such font that is freely available from CTANis Junicode Regular (Junicode-Regularttf) from the junicode package The fontspec package makes it easyfor a X ELATEX document to utilize a system font The following example defines a textjuni command thatuses fontspec to typeset its argument in Junicode Regular

documentclassarticleusepackagefontspec

newcommandtextjuni[1]fontspecJunicode-Regular1

begindocumentWe use lsquolsquotextjunichar2123rsquorsquo for a versicleand lsquolsquotextjunichar211Frsquorsquo for a responseenddocument

which produces

We use ldquo rdquo for a versicle and ldquo rdquo for a response

(Typesetting the entire document in Junicode Regular would be even easier See the fontspec documentationfor more information regarding font selection) Note how the preceding example uses char to specify aUnicode character by number The double quotes before the number indicate that the number is representedin hexadecimal instead of decimal

88 About this document

History David Carlisle wrote the first version of this document in October 1994 It originally containedall of the native LATEX symbols (Table 44 Table 57 Table 67 Table 102 Table 128 Table 131 Table 152Table 153 Table 164 Table 169 Table 201 and a few tables that have since been reorganized) and was designedto be nearly identical to the tables in Chapter 3 of Leslie Lamportrsquos book [Lam86] Even the table captionsand the order of the symbols within each table matched The AMS symbols (Table 45 Table 68 Table 69Table 105 Table 106 Table 132 Table 137 Table 148 and Table 202) and an initial Math Alphabets table(Table 213) were added thereafter Later Alexander Holt provided the stmaryrd tables (Table 46 Table 59Table 70 Table 108 Table 125 and Table 149)

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

118

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 ancient languages and other symbols to provide a more user-friendlydocument structure

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

bull symbol tables rewritten to list the symbols in alphabetical order

bull appendices providing 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 David Carlislersquos originalversion Most of the changes are geared towards making the document easier to extend modify and reformat

Build characteristics Table 331 lists some of this documentrsquos build characteristics Most important is the listof packages that LATEX couldnrsquot find but that symbolstex otherwise would have been able to take advantageof Complete prebuilt versions of this document are available from CTAN (httpwwwctanorg or oneof its many mirror sites) in the directory tex-archiveinfosymbolscomprehensive Table 332 shows thepackage date (specified in the sty file with ProvidesPackage) for each package that was used to build thisdocument and that specifies a package date Packages are not listed in any particular order in either Table 331or Table 332

Table 331 Document Characteristics

Characteristic Value

Source file symbolstexBuild date November 9 2009Symbols documented 5913Packages 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 colonequals shuffle fourierdozenal pmboxdraw pigpen clock teubner linearA linearbcypriot sarabian china2e harpoon steinmetz milstd recycleDotArrow ushort hhcount ogonek combelow accentsnicefrac bm mathrsfs chancery calligra bbold mbboarddsfont bbm

Packages omitted none

Table 332 Package versions used in the preparation of this document

Name Date

textcomp 20050927latexsym 19980817


119


Name Date

amssymb 20020122stmaryrd 19940303euscript 20011001wasysym 20031030pifont 20050412manfnt 19990701bbding 19990415undertilde 20000808ifsym 20000418tipa 20020808tipx 20030101wsuipa 19940716metre 20011205txfonts 20080122mathabx 20030729skak 20081009ascii 20060530dingbat 20010427skull 20020123eurosym 19980806yfonts 20030108mathdots 20060316trsym 20000625universa 980801upgreek 20030212chemarr 20060220mathtools 20080801phaistos 20040423arcs 20040509t4phonet 20040601semtrans 19980210dictsym 20040726extarrows 20080515protosem 20050318harmony 20070503hieroglf 20000923cclicenses 20050520arev 20050614MnSymbol 20070121extpfeil 20060727keystroke 20030815fge 20070603turnstile 20070623epsdice 20070215feyn 20080229universal 971224colonequals 20060801shuffle 20081027pmboxdraw 20060503pigpen 20081207clock 20010410teubner 20080210


120


Name Date

linearA 20060313linearb 20050622cypriot 19990620sarabian 20051112china2e 19970601harpoon 19941102steinmetz 20090614DotArrow 20070212ushort 20010613hhcount 19950331ogonek 950717combelow 20090823accents 20060512nicefrac 19980804bm 20040226calligra 19960718

89 Copyright and license

The Comprehensive LATEX Symbol ListCopyright copy 2009 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 later

This work has the LPPL maintenance status ldquomaintainedrdquo

The current maintainer of this work is Scott Pakin

121

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)

122

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 name17

Symbols (a) 14 () 9 114$ ($) 9 114 () 9 114amp (amp) 9 114rsquo (a) 14( (() 54

( (() 55

) ()) 54

) ()) 55

() 23 113- (-) 115 116 (a) 14 () 54

() 55

( ) 64

() 64

lt (⟨) 55

() 64

[ ([) 54

[ (⎡⎢⎢⎢⎢⎢⎣) 55

104] (]) 54

] (⎤⎥⎥⎥⎥⎥⎦) 55

^ (a) 14^ (ˆ) 9 115| () 54| () 54 56| (iquesta) 14= (a) 14= (macr) 115

| (

RRRRRRR) 55| (|) 30 54 56 57_ ( ) 9 115 () 9 54 115 () 9 54 115lsquo (a) 14~ (a) 14~ (˜) 9 115

Aa (esvect package option) 61a (times

) 95

AA (A) 10aa (a) 10

AAaleph (A) 81

AAayin (O) 81

AAbeth (B) 81

AAcht ( ˇ ldquo ˇ ldquo==

) 89

AAdaleth (D) 81

AAhe (E) 81

AAhelmet (V) 81

AAheth (h) 81

AAkaph (K) 81

AAlamed (L) 81

Aaleph (a) 81

AApe (P) 81

AAqoph (Q) 81

AAresh (R) 81

AAsade (X) 81

Aayin (o) 81

AAyod (Y) 81

Abeth (b) 81

absolute value see lvert andrvert

abzuglich see textdiscount

AC () 70

acarc 16

acbar 16

accents 14ndash18 57ndash61 71 89107ndash109

acute (a) 14ndash18 57

any character as 107

arc (a) 14ndash17 59 60

breve (a) 14ndash18 57

caron (a) 14 18 57 60

cedilla (cedil) 14

circumflex (a) 14ndash16 57 5960

comma-below (a) 17

diaeligresis (a) 14 17 18 5768

dot (a or ) 14ndash16 57

double acute (a) 14 18

extensible 59ndash61 63108ndash109

grave (a) 14ndash18 57

hacek see accents caron

hook (ả) 14

Hungarian umlaut seeaccents double acute

krouzek see accents ring

macron (a) 14 17 18 5759 60

multiple per character 15ndash16107

ogonek ( ˛) 14ndash17

ring (a) 14ndash16 18 57 58

Romanian comma-belo ac-cent see accentscomma-below

trema see accents diaeligresisumlaut see accents diaeligresis

accents (package) 58 107 119121

accentset 107

Acht ( ˇ ldquo( ) 89

AchtBL ( ˇ ldquo==

) 89

AchtBR ( ˇ ldquo==) 89

ACK () 72acontraction 109

AcPa ( ) 89actuarial ( ) 108actuarial symbols 108acute (acute) 57acute (a) see accentsacutus (a) 17Adaleth (d) 81adeles (A) see alphabets mathadjoint (dagger) see dag

Adobe Acrobat 112

adots ( ) 64 107

advancing see textadvancing

AE (AElig) 10ae (aelig) 10aeolicbii (Ι) 95aeolicbiii (Θ) 95aeolicbiv (Κ) 95agemO (0) 66Agimel (g) 81Ahe (e) 81Ahelmet (v) 81Aheth (H) 81ain (s) 18Akaph (k) 81

Alad () 57alad () 57Alamed (l) 81

Alas () 57alas () 57aldine (o) 78aldineleft (m) 78aldineright (n) 78aldinesmall (j) 78aleph (alefsym) 51 65aleph (alefsym) 51Alif () 14alpha (α) 50alphabets

African 10

17This occurs frequently between amssymb and mathabx for example

123

Cypriot 86Cyrillic 103Greek 50 51 68 87Hebrew 51 68hieroglyphic 82Linear A 82Linear B 85math 68phonetic 11ndash14proto-Semitic 81South Arabian 87Vietnamese 10

alphaup (α) 50alpine symbols 91Alt ( Alt ) 72

alternative denial see uparrow

and |

AltGr ( AltGr ) 72

amalg (q) 22amalg (∐) 23Amem (m) 81ampersand see amp

AMS 8 10 22 26 30 31 3638 39 41 49ndash54 58 59 6164ndash66 69 100 118

amsbsy (package) 113amsfonts (package) 22 30 36 41

65 68amsmath (package) 8 49 58

104 112amssymb (package) 8 22 30 36

41 58 65 68 87 119 120123

amstext (package) 105 106Anaclasis (divide) 95anaclasis (divide) 95anceps (Ξ) 95ancepsdbrevis (Ζ) 95

anchor (O) 80ancient-language symbols 81ndash87and see wedge

AND gates 73

ANDd () 73

ANDl () 73

ANDr () 73

ANDu () 73angle (ang) 66angle ( 6 ) 65angle (ang) 66angle notation 70angles 65ndash67Anglesign (W) 67

Angstrom unitmath mode see mathring

text mode see AA

Angud (〉) 57angud (〉) 57angular minutes see prime

angular seconds see second

Angus (〈) 57angus (〈) 57animals 81 82 86Ankh (ˆ) 90annuity symbols 108Antidiple (lt) 95antidiple (lt) 95Antidiple (ltmiddotmiddot ) 95antidiple (ltmiddotmiddot ) 95antilabe ( ) 64Antisigma (sup) 95antisigma (sup) 95Anun (n) 81Ape (p) 81APL

modifiers 71symbols 71

APLbox (~) 71APLcirc () 71APLcomment () 71APLdown (F) 71APLdownarrowbox (o) 71APLinput () 71APLinv (divide~) 71APLleftarrowbox (p) 71APLlog () 71

APLminus (minus) 71APLnot (sim) 71APLrightarrowbox (q) 71APLstar (E) 71APLup () 71APLuparrowbox (n) 71APLvert ( | ) 71apprge () 38apprle (gt) 38approx (asymp) 30approx (asymp) 32approxcolon (asymp) 36approxcoloncolon (asymp) 36approxeq (u) 30approxeq (≊) 32Aqoph (q) 81Aquarius (ecirc) 71aquarius (e) 71AR (A) 70ar (package) 70 119arc (a) see accentsarccos (arccos) 49arcminutes see prime

arcs (package) 17 119 120arcseconds see second

arcsin (arcsin) 49arctan (arctan) 49Aresh (r) 81arev (package) 67 88 119 120arg (arg) 49Aries (P) 71Aries (agrave) 71aries () 71

ArrowBoldDownRight (y) 75

ArrowBoldRightCircled () 75

ArrowBoldRightShort (z) 75

ArrowBoldRightStrobe (w) 75

ArrowBoldUpRight (x) 75Arrownot ( Y) 48arrownot ( X) 48arrows 41ndash43 47 61ndash63 72 75

81 86 90 103diagonal for reducing subex-pressions 59

dotted 63double-headed diagonal 106extensible 59ndash63fletched 47 75negated 41 42 44

Arrowvert (ww) 54

Arrowvert (

XXXXXXX) 55

arrowvert () 54

arrowvert (

RRRRRRR) 55Arseneau Donald 104 106ndash108Asade (x) 81Asamekh (s) 81ASCII 8 10 72 100 114ndash115

117 119table 114

ascii (package) 72 115 119 120ascnode () 71Ashin (S) 81aspect ratio 70ast () 23ast (lowast) 22ast (lowast) 23Asteriscus (timesmiddotmiddotmiddotmiddot ) 95asteriscus (timesmiddotmiddotmiddotmiddot ) 95Asterisk () 23

Asterisk (N) 78asterisk () 23

AsteriskBold (A) 78

AsteriskCenterOpen (B) 78

AsteriskRoundedEnds (X) 78asterisks 23 78

AsteriskThin (C) 78

AsteriskThinCenterOpen (D) 78

asterism ( ) 104astrological symbols 71astronomical symbols 71 98astrosun () 71asymp () 30asymp (≍) 48atan (atan) 113ataribox (m) 88Atav (t) 81Ateth (T) 81AtForty (Oslash) 90AtNinetyFive (Oacute) 90atomic math objects 49 113AtSixty (Otilde) 90

124

autoleftarrow (DGGGGG) 62

autoleftrightharpoons

(EGGGGGGGGGGC) 62

autorightarrow (GGGGGA) 62

autorightleftharpoons

(GGGGGBFGGGGG) 62

Avav (w) 81average 21Ayn () 14Ayod (y) 81Azayin (z) 81

BB 10B (˘) 95b (esvect package option) 61b (a

macr) 14

b (˘) 95

Ba (a) 85babel (package) 50 87babygamma () 13backapprox () 32backapproxeq () 32backcong (≌) 32backepsilon () 30backeqsim () 32backneg () 66backprime (8) 66backprime () 66backsim (v) 30backsim (∽) 32backsimeq (w) 30backsimeq (⋍) 32backslash () 54 65

backslash () 55

backslashdiv () 23backtriplesim () 32

Baii () 85

Baiii (lt) 85banana brackets

see llparenthesis andrrparenthesis

banceps (Ψ) 95bar (macr) 57barb () 13barbbrevis (θ) 95barbrevis (ι) 95barcirc (minus ) 104bard () 13bari () 13barin (V) 52barj (j) 13barl () 13barlambda () 13barleftharpoon (THORN) 43baro () 22baro ( vs lt) 101

baro (lt) 13barp (A) 13barred letters 104barrightharpoon (szlig) 43barsci (+) 13barscu (X) 13

Bart (

) 96baru (T) 13barwedge (X) 23barwedge (Z) 22base-twelve digits 65Bat (yacute) 90

Bau (=) 85bauarrow () 75baucircle () 80baucircle () 80baucross () 77baudash () 90baueclipse () 80bauequal () 90bauface (13) 90bauforms () 90

bauforms () 90bauhead () 90

bauhead () 90bauhole () 80bauplus () 90baupunct () 80bauquarter () 90bauquestion () 90bausquare () 80bausquare () 80bautriangle () 80bautriangle () 80bauwhitearrow () 75bauwindow () 90BB (˘ ) 95Bb (˘ ) 95bB (˘ ) 95bb (˘ ) 95bba ( times) 95bbalpha () 68bbar (b) 104bbb (˘) 95bbbeta () 68Bbbk (k) 52bbding (package) 75ndash78 80 101

119 120bbdollar ($) 68bbetter (g) 93bbeuro (ucirc) 68bbfinalnun (Iuml) 68bbgamma (13) 68bbgreekl (mathbbol package op-

tion) 68BBm (

macr) 95

Bbm (macr

) 95bBm (

macr) 95

bbm (package) 68 119

bbm (macr

) 95bbmb ( ˘) 95bbmx (

macr ˘) 95bbnabla () 68bbold (package) 68 119bbpe (Ocirc) 68bbqof (times) 68bbrevis (ς) 95bbslash (13) 22bbyod (Eacute) 68bcontraction 109

Bda (d) 85

Bde (D) 85bdecisive (i) 93

Bdi (f) 85

Bdo (g) 85

Bdu (x) 85

Bdwe (gt) 85

Bdwo () 85

Be (e) 85Beam () 73Bearing () 73because (∵) 30 64because (∵) 64BEL () 72bell () 88Berry Karl 122beta (β) 50betaup (β) 50beth (i) 51beth (ℶ) 51betteris (b) 93between ( ) 32between (G) 30between () 32

Bi (i) 85bibridge (

rdquoardquo) 16

biconditional see leftrightarrow andequiv

Bicycle (reg) 90Big 100 102big 100 102big O (O) see alphabets mathbigast () 23

bigbosonloop ( ) 74

bigbosonloopA ([) 74

bigbosonloopV () 74bigbox (

e) 26

bigboxasterisk (Ouml

) 26bigboxbackslash (

THORN) 27

bigboxbot (Ucirc

) 27bigboxcirc (

Otilde) 27

bigboxcoasterisk (times

) 27bigboxdiv (

Oacute) 27

bigboxdot (Ocirc

) 27bigboxleft (

Oslash) 27

bigboxminus (Ntilde

) 27bigboxplus (

ETH) 27

125

bigboxright (Ugrave

) 27bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26

bigboxtriangleup (szlig

) 26bigboxvoid (

Uuml) 27

bigcap (⋂

) 25bigcap (⋂) 29bigcapdot (⩀) 29bigcapplus ($) 29bigcirc (copy) 22bigcirc () 79

BigCircle () 79bigcircle () 29bigcoast () 23bigcomplementop (

) 27

BigCross (13) 79bigcup (

⋃) 25

bigcup (⋃) 29bigcupdot (⊍) 29

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

) 26

bigcurlyvee (b

) 26bigcurlyvee (⋎) 29bigcurlyveedot () 29bigcurlywedge (

) 26

bigcurlywedge (c

) 26bigcurlywedge (⋏) 29bigcurlywedgedot () 29

BigDiamondshape (amp) 79bigdoublecurlyvee () 29bigdoublecurlywedge () 29bigdoublevee (⩔) 29bigdoublewedge (⩕) 29Bigg 100 102bigg 100 102

BigHBar () 79biginterleave (

g) 26

BigLowerDiamond (_) 79bignplus (

) 26

bigoast (⊛) 29bigoasterisk (

AElig) 27

bigobackslash (Icirc

) 27bigobackslash (⦸) 29bigobot (

Euml) 27

bigocirc (Aring

) 27bigocirc (⊚) 29bigocoasterisk (

Ccedil) 27

bigodiv (Atilde

) 27bigodot (

⊙) 25

bigodot (⊙) 29bigoleft (

Egrave) 27

bigominus (Aacute

) 27bigominus (⊖) 29bigoplus (

oplus) 25

bigoplus (oplus) 29bigoright (

Eacute) 26

bigoslash (Iacute

) 26bigoslash (⊘) 29bigostar () 29

bigotimes (otimes

) 25bigotimes (otimes) 29bigotop (

Ecirc) 26

bigotriangle (F) 29bigotriangleup (

Iuml) 26

bigovert (⦶) 29bigovoid (

Igrave) 27

bigparallel (f) 26

bigparr (˙

) 30bigplus (

) 27

bigplus (+) 29

BigRightDiamond () 79bigsqcap (

) 26

bigsqcap (

) 26bigsqcap (⊓) 29bigsqcapdot () 29bigsqcapplus (

) 27

bigsqcapplus (0) 29bigsqcup (

⊔) 25

bigsqcup (⊔) 29bigsqcupdot () 29bigsqcupplus (

) 27

bigsqcupplus (2) 29

BigSquare ( ) 79bigsquplus (

) 27

bigstar () 23bigstar (F) 66bigstar () 79bigtimes (

) 27

bigtimes (⨉) 29

BigTriangleDown () 79bigtriangledown (

`) 26

bigtriangledown (5 vs`

) 101bigtriangledown (5) 22bigtriangledown () 40

BigTriangleLeft () 79

BigTriangleRight ($) 79

BigTriangleUp () 79bigtriangleup (

a) 26

bigtriangleup (4 vsa

) 101bigtriangleup (4) 22bigtriangleup () 40biguplus (

⊎) 25

biguplus (⊎) 29bigvarstar () 23

BigVBar () 79bigvee (

or) 25

bigvee (⋁) 29bigveedot () 29bigwedge (

and) 25

bigwedge (⋀) 29bigwedgedot () 29

bigwith (˘

) 30binampersand (N) 22binary operators 22ndash25binary relations 30ndash32 34ndash39

47 48negated 31ndash33

bindnasrepma (O) 22Biohazard (h) 74biological symbols 74

birds 82bishop 94bishoppair (a) 93

Bja (j) 85

Bje (J) 85

Bjo (b) 85

Bju (L) 85

Bka (k) 85

Bke (K) 85

Bki (c) 85

Bko (h) 85

Bku (v) 85

BlackBishopOnBlack (a) 94

BlackBishopOnWhite (b) 94blackboard bold see alphabets

mathblackdiamond () 23

BlackEmptySquare (Z) 94

BlackKingOnBlack (j) 94

BlackKingOnWhite (k) 94

BlackKnightOnBlack (m) 94

BlackKnightOnWhite (n) 94blacklozenge () 66blacklozenge (⧫) 79

BlackPawnOnBlack (o) 94

BlackPawnOnWhite (p) 94

BlackQueenOnBlack (l) 94

BlackQueenOnWhite (q) 94

BlackRookOnBlack (s) 94

BlackRookOnWhite (r) 94blacksmiley (-) 88blacksquare () 66blacksquare (∎) 25blackstone 94blacktriangle (N) 66blacktriangle () 40blacktriangledown () 25blacktriangledown (H) 66blacktriangledown () 40blacktriangleleft () 25blacktriangleleft (J) 39blacktriangleleft () 40blacktriangleright () 25blacktriangleright (I) 39blacktriangleright () 40blacktriangleup () 25

126

blank see textblank

Bleech (Euml) 90blitza () 21 48blitzb () 48blitzc () 48blitzd () 48blitze (13) 48block-element symbols 97Bm (

macr) 95

bm (package) 113 119 121bm 113bm (

macr) 95

Bma (m) 85

Bme (M) 85

Bmi (y) 85

Bmo (A) 85bmod 49

Bmu (B) 85

Bna (n) 85

BNc (laquo) 85

BNcc (raquo) 85

BNccc (ndash) 85

BNcd (mdash) 85

BNcm (ff) 85

BNd (zwnj) 85

BNdc (permil) 85

BNdcc (ı) 85

BNdccc (ȷ) 85

Bne (N) 85

BNi (acute) 85

Bni (C) 85

BNii (ˆ) 85

BNiii (˜) 85

BNiv (uml) 85

BNix (macr) 85

BNl (lsaquo) 85

BNlx (rsaquo) 85

BNlxx (ldquo) 85

BNlxxx (rdquo) 85

BNm (fi) 85

Bno (E) 85

Bnu (F) 85

BNv (˝) 85

BNvi (˚) 85

BNvii (ˇ) 85

BNviii (˘) 85

Bnwa () 85

BNx (˙) 85

BNxc (bdquo) 85

BNxl (sbquo) 85

BNxx (cedil) 85

BNxxx (˛) 85

Bo (o) 85body-text symbols 9ndash20

bold symbols 113boldmath 113boldsymbol 113bomb (L) 91Boolean domain (B) see

alphabets mathBoolean logic gates 73born see textborn

bosons 74bot (perp) 21 51 105bot () 52botdoteq () 32Bouquet (yen) 90Bowtie (1) 88bowtie () 30bowtie (amp) 23 24Box () 65Box (2) 66Box (◻) 25box-drawing symbols 97boxast (i) 22boxasterisk (f) 25boxbackslash (n) 25boxbackslash (⧅) 25boxbar (k) 22boxbot (k) 25boxbox () 22boxbox (⧈) 25boxbslash (j) 22boxcirc (e) 25boxcircle () 22boxcoasterisk (g) 25boxdiv (c) 25boxdot (d) 25boxdot () 22boxdot (⊡) 25boxdotLeft () 42boxdotleft () 42boxdotRight () 42boxdotright () 42boxempty () 22boxLeft () 42boxleft (h) 25boxleft () 42boxminus (a) 25boxminus () 22boxminus (⊟) 25boxplus (`) 25boxplus () 22boxplus (⊞) 25boxRight () 42boxright (i) 25boxright () 42boxslash (m) 25boxslash (l) 22boxslash (⧄) 25boxtimes (b) 25boxtimes () 22boxtimes (⊠) 25boxtop (j) 25boxtriangleup (o) 25boxvert (q) 25boxvoid (l) 25

boy (D) 71

Bpa (p) 85

Bpaiii ([) 85

BPamphora (Ž) 86

BParrow (ĳ) 86

BPbarley (Ş) 86

BPbilly (ť) 86

BPboar (ľ) 86

BPbronze (Ű) 86

BPbull (ň) 86

BPcauldroni (đ) 86

BPcauldronii (sect) 86

BPchariot (yuml) 86

BPchassis (ź) 86

BPcloth (Ř) 86

BPcow (ŋ) 86

BPcup (Ÿ) 86

Bpe (P) 85

BPewe (š) 86

BPfoal (ě) 86

BPgoat (ş) 86

BPgoblet (Ź) 86

BPgold (Ů) 86

BPhorse (ď) 86

Bpi (G) 85

BPman (ă) 86

BPnanny (ț) 86

Bpo (H) 85

BPolive (Ț) 86

BPox (ń) 86

BPpig (ĺ) 86

BPram (ś) 86

BPsheep (ř) 86

BPsow (ł) 86

BPspear (iexcl) 86

BPsword (ż) 86

BPtalent (Ď) 85

Bpte (]) 85

Bpu (I) 85

Bpuii () 85

BPvola (Ĺ) 85

BPvolb (Ľ) 85

BPvolcd (Ł) 85

BPvolcf (Ń) 85

BPwheat (Š) 86

BPwheel (ž) 86

BPwine (Ť) 86

BPwineiih (Ż) 86

BPwineiiih (Ĳ) 86

BPwineivh (İ) 86

BPwoman (ą) 86

BPwool (Ś) 86

127

BPwta (Ă) 85

BPwtb (Ą) 85

BPwtc (Ć) 85

BPwtd (Č) 85

Bqa (q) 85

Bqe (Q) 85

Bqi (X) 85

Bqo (8) 85

Bra (r) 85

bra 54

braceld (︷) 109

bracerd (︷) 109

bracevert () 54

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 55

brackets see delimiters

Braii (^) 85

Braiii (_) 85

braket (package) 54

Bre (R) 85

Break ( Break ) 72

breve (˘) 57

breve (a) 17

breve (a) see accents

brevis (β) 95

Bri (O) 85

Bro (U) 85

Broii (lsquo) 85

brokenvert (|) 88

Bronger Torsten 105

Bru (V) 85

BS () 72

Bsa (s) 85

Bse (S) 85

BSEfree (n) 74

Bsi (Y) 85

Bso (1) 85

BSpace ( 7minusrarr ) 72

Bsu (2) 85

Bswa () 85

Bswi (|) 85

Bta (t) 85

Btaii () 85

Bte (T) 85

Bti (3) 85

Bto (4) 85

Btu (5) 85

Btwe (shy) 86

Btwo (~) 85

Bu (u) 85

BUFd () 73

buffers 73

BUFl () 73

BUFr () 73

BUFu () 73

BUi (fl) 86

BUii (ffi) 86

BUiii (ffl) 86

BUiv () 86

BUix () 86bullet (bull) 22bullet () 23bullseye see textbullseye

Bumpedeq () 32bumpedeq () 32Bumpeq (m) 30Bumpeq (≎) 33bumpeq (l) 30bumpeq (≏) 33bupperhand (e) 93

Burns (

) 96BusWidth () 73

BUv () 86

BUvi () 86

BUvii () 86

BUviii ($) 86

BUx (amp) 86

BUxi (rsquo) 86

BUxii (shy) 86

Bwa (w) 85

Bwe (W) 85

Bwi (6) 85

Bwo (7) 85

Bza (z) 85

Bze (Z) 85

Bzo (9) 85

CC ( ) 95c (esvect package option) 61c (a) 14 116c ( ) 95

Ca (a) 86calligra (package) 68 119 121Calligra (font) 68calrsfs (package) 68CAN () 72cancel (package) 59Cancer (atilde) 71cancer (_) 71Cap (e) 22Cap (⋒) 24cap (X) 23cap (cap) 22cap (cap) 23capdot (⩀) 23capplus () 23Capricorn (eacute) 71

capricornus (d) 71capturesymbol (X) 93card suits 65ndash67 80cardinality see aleph

care of (co) 67caret see ^

Carlisle David 1 118 119caron (a) see accentscarriage return 72 80 103carriagereturn (C) 80Cartesian product see times

castle 94castlingchar (O) 93castlinghyphen (-) 93catal (γ) 95Catalexis (and) 95catalexis (and) 95catamorphism


cb (a) 17Cc ( ) 95cc ( CCcopy ) 19cc ( ) 95ccby ( BYcopy ) 19Ccc ( ) 95cclicenses (package) 19 119 120ccnc ( $copy ) 19ccnd ( =copy ) 19ccsa (

Ccopy ) 19cdot (middot) 22 104cdot (sdot) 23 64cdotp (middot) 63cdotp (sdot) 64cdots (middot middot middot ) 63

Ce (e) 86Cedi see textcolonmonetary

cedilla (cedil) see accentscelestial bodies 71 98celsius () 70Celtcross (Dagger) 90cent (cent) 18centerdot (13) 23centerdot () 22centernot (package) 105centernot 105centigrade see textcelsius

centre (I) 93cents see textcent

CEsign (C) 74

Cga (g) 86chancery (package) 119changenotsign 32char 8 103 112 115 118Charter (font) 18 30check (ˇ) 57check marks 10 66 77 80 88

90 101checked () 88CheckedBox (2) 77Checkedbox (V) 90

Checkmark () 77

128

checkmark (X) 10checkmark () 66

checkmark (X vs D) 101

checkmark (D) 80

CheckmarkBold () 77checksymbol (+) 93chemarr (package) 62 119 120chemarrow (package) 47 62 119chemarrow (A) 47Chen Raymond 122chess symbols 93 94chesscomment (RR) 93chessetc (P) 93chesssee (l) 93chi (χ) 50china2e (package) 19 49 68 98

119 121chiup (χ) 50

Ci (i) 86cipher symbols 98circ () 22 67 105circ () 23circeq () 32circeq ($) 30circeq (≗) 33CIRCLE ( ) 88

Circle (5) 79

Circle ( vs 5) 101Circle () 88circlearrowleft (ouml) 42circlearrowleft () 41circlearrowleft () 44circlearrowright (divide) 42circlearrowright () 41circlearrowright () 44circled numbers 77 94CircledA (ordf) 90circledast (~) 22circledast (⊛) 25circledbar (V) 23circledbslash (W) 23circledcirc () 22circledcirc (⊚) 25circleddash () 22circleddash (⊖) 25circleddot see odot

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

circledotleft seecircleddotleft

circledotright seecircleddotright

circledplus see oplus

circledR (r) 10 52circledS (s) 52circledslash see oslash

circledtimes see otimes

circledvee (U) 23

circledwedge (T) 23circleleft () 42circleright () 42circles 79ndash80 88 94

CircleShadow (d) 80

CircleSolid (a) 80Circpipe (rsaquo) 73circplus () 23Circsteel (bull) 73circumflex (a) see accentscircumflexus (a) 17

Cja (j) 86

Cjo (b) 86

Cka (k) 86

Cke (K) 86

Cki (c) 86

Cko (h) 86

Cku (v) 86

Cla (l) 86

Cle (L) 86CleaningA (laquo) 90CleaningF (frac34) 90CleaningFF (iquest) 90CleaningP (not) 90CleaningPP (shy) 90

Cli (d) 86clickb () 13clickc () 13clickt (R) 13

Clo (f) 86clock (package) 92 119 120

clock (i1) 92

clock () 88clock symbols 88 90ndash92ClockFramefalse 92ClockFrametrue 92Clocklogo (U) 90ClockStyle 92clocktime 92closedcurlyvee (frac34) 24closedcurlywedge (frac14) 24closedequal (Uuml) 33closedniomega () 13closedprec (frac12) 33closedrevepsilon () 13closedsucc (raquo) 33Cloud () 91clovers 78

Clu (q) 86clubs (suit) 65ndash67 80clubsuit (clubs) 65clubsuit (clubs) 66

Cma (m) 86

Cme (M) 86

Cmi (y) 86cmll (package) 21 24 30 36 119

Cmo (A) 86

Cmu (B) 86

Cna (n) 86

Cne (N) 86

Cni (C) 86

Cno (E) 86

Cnu (F) 86

Co (o) 86coAsterisk () 23coasterisk () 23code page 1252 115

table 117code page 437 72 97 115Coffeecup (K) 90coh (uml) 36coins ancient 19colon 63colon ( ) 63colon (∶) 64Colonapprox () 31Colonapprox (asymp) 34colonapprox (asymp) 36colonapprox (asymp) 34colonapprox (13) 31coloncolon () 36coloncolonapprox (asymp) 36coloncolonequals (=) 36coloncolonminus (minus) 36coloncolonsim (sim) 36Coloneq (H) 31Coloneq (minus) 34coloneq () 21 32coloneq (minus) 34coloneq (D) 31coloneq (∶=) 33Coloneqq (F) 31Coloneqq (=) 34coloneqq (=) 34coloneqq (B) 21 31colonequals (package) 21 36 119

120colonequals (=) 21 36colonminus (minus) 36Colonsim () 31Colonsim (sim) 34colonsim (sim) 36colonsim (sim) 34colonsim () 31combelow (package) 17 119 121combinatorial logic gates 73comma-below accent (a) see

accentscommunication symbols 73commutative diagrams 106comptexttex (newsgroup) 8

21 22 103ndash108compensation (n) 93complement (A) 52complement () 52complement (∁) 29complete shuffle product () 24

COMPLEX (raquo) 49

Complex (Atilde) 49

129

complex numbers (C) seealphabets math

composited accents 14Comprehensive TEX Archive Net-

work 1 8 59 69 100117ndash119

computer hardware symbols 72computer keys 72Computer Modern (font) 100

102 115ComputerMouse (Iacute) 72cong () 30cong (cong) 33congruent see equiv

conjunction (V) 71conjunction logical see wedge

and amp

consequence relations 35contradiction symbols 21 48control characters 72converse implication see

leftarrow and subset

converse nonimplication seenleftarrow and nsubset

convolution () 23Coppa (Ϙ) 87coppa (ϙ) 87coprod (

∐) 21 25

coprod (∐) 29copyright 9 19 116copyright (copy) 9corner (k) 18corners box 97corona () 95coronainv (Ϙ) 95Corresponds (=) 67corresponds () 32cos (cos) 49 113cosh (cosh) 49cot (cot) 49coth (coth) 49counterplay (V) 93Courier (font) 18CP1252 see code page 1252CP437 see code page 437

Cpa (p) 86

Cpe (P) 86

Cpi (G) 86

Cpo (H) 86

Cpu (I) 86CR () 72cr 104

Cra (r) 86

Cre (R) 86Creative Commons licenses 19crescent (fge package option) 58

Cri (O) 86

Cro (U) 86

Cross () 79

Cross (dagger vs vs ) 101

Cross () 76Cross (dagger) 90cross ratio see textrecipe

crossb () 13

CrossBoldOutline (-) 76

CrossClowerTips (4) 76crossd (13) 13Crossedbox (X) 90crosses 76 77 90 94crossh () 13

CrossMaltese () 76crossnilambda (3) 13

CrossOpenShadow (+) 76

CrossOutline () 76crotchet see musical symbolscrtilde (

Ŕa) 16

Cru (V) 86crucifixes 76 77 90Crux (dagger) 57crux (dagger) 57

Csa (s) 86csc (csc) 49

Cse (S) 86cshuffle () 24

Csi (Y) 86

Cso (1) 86

Csu (2) 86

Cta (t) 86CTAN see Comprehensive TEX

Archive NetworkCte (T) 86

Cti (3) 86

Cto (4) 86Ctrl ( Ctrl ) 72

Ctu (5) 86

Cu (u) 86

Cube ( ) 92 103cube root see sqrt

Cup (d) 22Cup (⋓) 24cup (Y) 23cup (cup) 22 104 112cup (cup) 24cupdot (⊍) 24cupplus (⊎) 24curlyc () 13curlyeqprec (para) 32curlyeqprec (2) 30curlyeqprec (⋞) 33curlyeqsucc (middot) 32curlyeqsucc (3) 30curlyeqsucc (⋟) 33curlyesh (N) 13curlyvee (O) 23curlyvee (g) 22curlyvee (⋎) 24curlyveedot (5) 24curlyveedownarrow () 22curlyveeuparrow () 22

curlywedge (N) 23curlywedge (f) 22curlywedge (⋏) 24curlywedgedot (4) 24curlywedgedownarrow () 22curlywedgeuparrow (amp) 22curlyyogh (a) 13curlyz (^) 13currency (curren) 18currency symbols 18 19 68curvearrowbotleft (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) 75Cutline (r) 75cutoff subtraction see dotdiv

Cutright (q) 75

Cwa (w) 86

Cwe (W) 86

Cwi (6) 86

Cwo (7) 86

Cxa (x) 86

Cxe (X) 86

Cya (j) 86

Cyo (b) 86cyprfamily 86Cypriot 86cypriot (package) 86 119 121

Cza (g) 86

Czo (9) 86

DD (a

uml) 17

d (esvect package option) 61d (a) 14dag (dagger) 9 117dagger (dagger) 22daleth (k) 51daleth (ℸ) 51danger (B) 91dangerous bend symbols 89DArrow ( darr ) 72

dasharrow seedashrightarrow

dasheddownarrow () 43

130

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

dashint (minusint

) 106

dashleftarrow (c) 41dashleftarrow () 44dashleftrightarrow (e) 42dashrightarrow (d) 41dashrightarrow () 44DashV ()) 32Dashv ()) 32dashv (a) 30dashv (⊣) 33dashVv (-) 32davidsstar (C) 77

DavidStar (0) 78

DavidStarSolid () 78dBar (||) 95dbar (d) 104dbend () 89dblaccnt (package) 107dblcolon () 34DCa () 72DCb () 72DCc () 72DCd () 72DD (DD) 89ddag (Dagger) 9 117ddagger (Dagger) 22

ddashint (=int

) 106

ddddot (

) 58dddot (

) 58

dddtstile ( ) 35

ddigamma (ϝ) 87

DDohne (DD ) 89ddot (uml) 57ddotdot () 24 64

ddots ( ) 63 107

ddots (⋱) 64

ddststile ( ) 35

ddtstile ( ) 35

ddttstile ( ) 35

DeclareFontFamily 111DeclareFontShape 111DeclareMathOperator 113DeclareMathOperator 113declareslashed 105DeclareUnicodeCharacter 117decofourleft ([) 78decofourright () 78decoone (X) 78decosix (]) 78decothreeleft (Y) 78decothreeright (Z) 78decotwo (a) 78

definite-description operator ( ι) 103

definition symbols 21 108deg (deg) 49degree (0) 66degree (deg) 70degrees see textdegree

DEL () 72Del ( Del ) 72

Deleatur see Denarius

delimiters 53ndash57text-mode 57variable-sized 54ndash57wavy-line 55 56

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

symbolsDenarius (cent) 18denarius (Ε) 19dental (ag) 16derivitive partial see partial

descnode () 71det (det) 49devadvantage (t) 93

Dfourier ( ) 36

dfourier ( ) 36

DFT ( ) 63

dft ( ) 63DH ( D) 13DH (ETH) 10 116dh (k) 13dh (eth) 10 116diacritics see accentsdiaeresis (a) 17diaeligresis (a) see accentsdiagdown (aring) 66diagdown () 66diagdown (Oacute) 33diagonal (G) 93diagup (auml) 66diagup () 66diagup (Ograve) 33diameter (I) 66diameter () 21diameter (empty) 66diameter () 88Diamond (^) 65Diamond (3) 66Diamond () 25diamond () 22diamond () 25diamondbackslash () 25Diamondblack (_) 66diamonddiamond () 25Diamonddot () 66diamonddot (⟐) 25DiamonddotLeft () 42Diamonddotleft () 42DiamonddotRight () 42Diamonddotright () 42

diamonddots (13) 24 64DiamondLeft () 42Diamondleft () 42diamondminus (x) 25diamondplus (|) 25DiamondRight () 42Diamondright () 42diamonds 79ndash80diamonds (suit) 65ndash67 80

DiamondShadowA () 79

DiamondShadowB () 79

DiamondShadowC () 79

Diamondshape (6) 79diamondslash (z) 25

DiamondSolid (p) 80diamondsuit (diams) 65diamondsuit () 66diamondtimes () 25diamondvert (y) 25diatop 18 107diaunder 18 107dice 92 103dictionary symbols 11ndash14 96dictsym (package) 96 119 120died see textdied

differential inexact see dbar

Digamma (Ϝ) 87digamma (z) 50 87digamma (ϝ) 87digital logic gates 73digits 65

LCD 70Mayan 65old-style 20segmented 70

dim (dim) 49ding 10 75ndash78 80dingautolist 77dingbat (package) 76 80 101

119 120dingbat symbols 75ndash80Diple (gt) 95diple (gt) 95Diple (gtmiddotmiddot ) 95diple (gtmiddotmiddot ) 95Dirac notation 54discount see textdiscount

discretionary hyphen 115disjoint union 21disjunction see vee

displaystyle 105 106 108113

ditto marks see textquotedbl

div (divide) 22div (divide) 24divdot () 23divideontimes () 23divideontimes (gt) 22divides () 32divides (Ograve) 33division 22 59

non-commutative 63

131

division times seedivideontimes

divorced see textdivorced

DJ (ETH) 10dj (đ) 10dlbari (() 13DLE () 72dlsh (ecirc) 42

dndtstile ( ) 35

dnststile ( ) 35

dntstile ( ) 35

dnttstile ( ) 35do not enter see noway

does not divide see nmid

does not exist see nexists

does not imply 105

Dohne (D ) 89dollar see textdollar

dollar sign see $

Dontwash (Yacute) 90dot ( ˙ ) 57dot accent (a or ) see accentsdot symbols 9 63 64 107DotArrow (package) 63 119 121

dotarrow ( ) 63dotcup ( middotcup) 21 104dotdiv () 23Doteq see doteqdot

Doteq (≑) 33doteq () 30doteq (≐) 33doteqdot (+) 30doteqdot (≑) 33dotless j ()

text mode 14dotless i (ı)

math mode 57 65text mode 14

dotless j ()math mode 57 65

dotmedvert () 24dotminus () 24dotplus () 23dotplus (u) 22dots ( ) 9 117dots (ellipses) 9 63ndash65 107dotsb (middot middot middot ) 64dotsc ( ) 64dotseq () 32dotsi (middot middot middot ) 64dotsint (

macr) 28

dotsm (middot middot middot ) 64dotso ( ) 64dotted arrows 63dotted union (cup) 112

dottedtilde (a) 16

dottimes () 23double 56 57double acute (a) see accentsdoublebarwedge (Z) 23doublebarwedge ([) 22

doublecap see Cap

doublecap () 23doublecap (⋒) 24doublecup see Cup

doublecup (]) 23doublecup (⋓) 24doublecurlyvee (7) 24doublecurlywedge (6) 24doublefrown () 48doublefrowneq () 48doublepawns (d) 93doublesmile () 48doublesmileeq ($) 48doublesqcap (⩎) 24doublesqcup (⩏) 23doubletilde (ã) 16doublevee (⩔) 23doublewedge (⩕) 23DOWNarrow (L) 88Downarrow (dArr) 41 54Downarrow (dArr) 43downarrow 112downarrow (darr) 41 54downarrow (darr) 43downarrowtail () 43downbracketfill 109downdownarrows (Oacute) 42downdownarrows () 41downdownarrows () 43downdownharpoons (Ucirc) 43Downes Michael J 49 122downfilledspoon (s) 47downfootline () 33downfree (⫝) 33downharpoonccw () 46downharpooncw () 46downharpoonleft (aring) 43downharpoonleft () 41downharpoonright (ccedil) 43downharpoonright () 41downlsquigarrow (pound) 43downmapsto () 43downModels (oacute) 33downmodels (atilde) 33downp (u) 18downparenthfill 109downpitchfork (⫛) 47downpropto () 33downrsquigarrow (laquo) 43downslice (Acirc) 25downspoon (⫰) 47downt (m) 18downtherefore (∵) 23 64downtouparrow (yuml) 42downuparrows (times) 42downuparrows () 43downupharpoons (euml) 43downupharpoons (⥯) 46downVdash () 33downvdash (⊤) 33downY (+) 23dozenal (package) 65 119dozenal digits 65

dracma (Δ) 19drsh (euml) 42DS (SS) 89Ds (ss) 89dsaeronautical (a) 96dsagricultural (G) 96dsarchitectural (A) 96dsbiological (B) 96dschemical (C) 96dscommercial (c) 96

dsdtstile ( ) 35dsfont (package) 68 119dsheraldical (H) 96dsjuridical (J) 96dsliterary (L) 96dsmathematical (M) 96dsmedical (m) 96dsmilitary (X) 96dsrailways (R) 96

dsststile ( ) 35dstechnical (T) 96

dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35

dtimes (_) 24dtimes () 23

dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35

duodecimal (base-12) digits 65DVI 19 72 111dz () 13

Ee (esvect package option) 61e (e) 52e (E) 65ε-TEX 54Earth (C) 71Earth (Ecirc) 71earth () 71Ecommerce () 18

EightAsterisk (Z) 78

EightFlowerPetal (S) 78

EightFlowerPetalRemoved (Y) 78

eighth note see musical symbolseighthnote () 88eighthnote () 88

EightStar (H) 78

EightStarBold (I) 78

EightStarConvex (F) 78

EightStarTaper (E) 78ejective (e) 13electrical symbols 70electromotive force (E) see

alphabets mathelement of see in

132

ell (`) 51

Ellipse (b) 80ellipses (dots) 9 63ndash65 107ellipses (ovals) 80

EllipseShadow (e) 80

EllipseSolid (c) 80EM () 72Email (k) 73Emailct (z) 73emgma (M) 13emptyset (empty) 65emptyset (empty) 66End ( End ) 72

end of proof 65ending (L) 93eng (8) 13engineering symbols 70 73engma (n) 13ENQ () 72entails see models

Enter ( Enter ) 72

Envelope () 80envelopes 80 98enya (N) 13EOT () 72epsdice (package) 92 119 120epsdice ( ) 92epsi () 13epsilon (ε) 50epsilonup (ε) 50eqbump () 32eqbumped () 32eqcirc () 32eqcirc (P) 30eqcirc (≖) 32Eqcolon (I) 31Eqcolon (minus) 34eqcolon () 32eqcolon (minus) 34eqcolon (E) 31eqdot (⩦) 32eqfrown () 48Eqqcolon (G) 31Eqqcolon (=) 34eqqcolon (=) 34eqqcolon (C) 31eqsim (h) 31eqsim (≂) 32eqslantgtr (middot) 38eqslantgtr (1) 38eqslantgtr (⪖) 39eqslantless (para) 38eqslantless (0) 38eqslantless (⪕) 39eqsmile () 48equal (=) 32equal (j) 93equalclosed (Yacute) 32equalscolon (=) 36equalscoloncolon (=) 36equalsfill 21 108equidecomposable 104

equilibrium seerightleftharpoons

equiv (equiv) 21 30equiv (equiv) 32equivalence see

equiv leftrightarrowand threesim

equivclosed (THORN) 32er () 13es-zet see ss

ESC () 72Esc ( Esc ) 72

escapable characters 9esh (M) 13esh (s) 13esint (package) 28 119Estatically (J) 74estimated see textestimated

esvect (package) 61 119eta (η) 50etaup (η) 50ETB () 72eth (eth) 66eth () 13eth (d) 13ETX () 72eufrak (package) 68Euler Roman 51EUR (e ) 18EURcr (d) 18EURdig (D) 18EURhv (c) 18

Euro (yuml) 19euro 19euro signs 18 19

blackboard bold 68eurologo (() 19eurosym (package) 19 119 120EURtm (e) 18euscript (package) 68 119 120evaluated at see vert

evil spirits 98exclusive disjunction

see nleftrightarrow

nequiv and oplus

exclusive or 103exists (D) 52exists (exist) 51exists (exist) 52exp (exp) 49Explosionsafe (`) 74extarrows (package) 62 119 120extensible accents 59ndash61 63

108ndash109extensible arrows 59ndash63extensible symbols creating 107ndash

109extensible tildes 59 61extension characters 48 49extpfeil (package) 63 119 120extraipa (package) 16 119eye (E) 80

EyesDollar (brvbar) 18

Ff (esvect package option) 61faces 72 81 88 90 91 96 98fallingdotseq () 32fallingdotseq () 30fallingdotseq (≒) 32FallingEdge () 70fatbslash ()) 22fatsemi () 22fatslash (() 22FAX (u) 73fax (t) 73Faxmachine (v) 73fc (package) 10 14fcdice ( ) 92fclfont (package) 119fcscore ( ) 92feet see prime and

textquotesingle

FEMALE () 74Female (~) 74female 12 71 73 74female () 73FemaleFemale (bdquo) 74FemaleMale (hellip) 74

Ferli (aa) 89

Fermi (aa

) 89fermions 74feyn (package) 74 119 120Feynman slashed character nota-

tion 105Feynman-diagram symbols 74feyna ( a) 74feync (c) 74feynfd (d) 74feynflS (o) 74feynfl ( l) 74feynfs (k) 74feynfu (e) 74

feynfv ( b) 74feynf (f) 74

feyng1 ( q) 74feyngd (v) 74

feynglB () 74feynglS (|) 74feynglu (z) 74

feyngl ( y) 74feyngu (u) 74

feyngvs (s) 74

feyngv ( ) 74feyng (g) 74feynhd (j) 74feynhs (K) 74feynhu (i) 74feynh (h) 74feynms () 74feynm (m) 74feynP (P) 74

133

feynp (p) 74feynx ( x) 74FF () 72fge (package) 47 53 58 65 67

119 120fge-digits 65fgeA (A) 53fgebackslash (K) 67fgebaracute (M) 67fgebarcap (O) 67fgec (c) 53fgecap (S) 67fgecapbar (Q) 67fgecup (N) 67fgecupacute (R) 67fgecupbar (P) 67fged (p) 53fgee (e) 53fgeeszett (ı) 53fgeeta (rdquo) 53fgeF (F) 53fgef (f) 53fgeinfty (i) 67fgelangle (h) 67fgelb 53fgelb (rdquo) 53fgeleftB (D) 53fgeleftC (C) 53fgeN (rdquo) 53fgeoverU (rdquo) 53fgerightarrow () 47fgerightB (B) 53fges (s) 53fgestruckone (1) 65fgestruckzero (0) 65fgeU (U) 53fgeuparrow () 47fgeupbracket (L) 67FHBOLOGO (f) 90FHBOlogo (F) 90field (F) see alphabets mathfile (H) 93

FilledBigCircle (U) 79

FilledBigDiamondshape (V) 79

FilledBigSquare (P) 79

FilledBigTriangleDown (S) 79

FilledBigTriangleLeft (R) 79

FilledBigTriangleRight (T) 79

FilledBigTriangleUp (Q) 79

FilledCircle (e) 79FilledCloud ( ) 91filleddiamond () 25

FilledDiamondShadowA () 79

FilledDiamondShadowC () 79

FilledDiamondshape (f) 79

FilledHut () 91filledlargestar () 79filledlozenge (⧫) 79filledmedlozenge (⧫) 79

filledmedsquare (∎) 25filledmedtriangledown () 25

40filledmedtriangleleft () 25

40filledmedtriangleright ()

25 40filledmedtriangleup () 25

40FilledRainCloud () 91

FilledSectioningDiamond () 92

FilledSmallCircle (u) 79

FilledSmallDiamondshape (v) 79

FilledSmallSquare (p) 79

FilledSmallTriangleDown (s) 79

FilledSmallTriangleLeft (r) 79

FilledSmallTriangleRight

(t) 79

FilledSmallTriangleUp (q) 79

FilledSnowCloud ($) 91

FilledSquare (`) 79filledsquare (◾) 25

FilledSquareShadowA () 79

FilledSquareShadowC () 79

filledsquarewithdots (C) 80filledstar () 25

FilledSunCloud () 91

FilledTriangleDown (c) 79filledtriangledown () 25 40

FilledTriangleLeft (b) 79filledtriangleleft () 25 40

FilledTriangleRight (d) 79filledtriangleright () 25

40FilledTriangleUp (a) 79filledtriangleup () 25 40FilledWeakRainCloud () 91finger pointing see fistsfinite field (F) see alphabets

mathfinpartvoice (araquo) 16finpartvoiceless (araquo) 16

fint (gt

) 27

fint (ffl) 28

Finv (F) 52Finv (`) 52

Fire () 92fish hook see strictif

fists 76fivedots () 23 64

FiveFlowerOpen (R) 78

FiveFlowerPetal (P) 78

FiveStar (8) 78

FiveStarCenterOpen () 78

FiveStarConvex () 78

FiveStarLines (7) 78

FiveStarOpen (9) 78

FiveStarOpenCircled () 78

FiveStarOpenDotted (lt) 78

FiveStarOutline (=) 78

FiveStarOutlineHeavy (gt) 78

FiveStarShadow () 78Fixedbearing () 73

fixedddots ( ) 63

fixedvdots () 63

fixmath (package) 113fj (F) 13

Flag () 91flap (f) 13flapr (D) 13flat ([) 65 88flat () 66Flatsteel (ndash) 73fletched arrows 47 75fleurons 78 80florin see textflorin

floweroneleft (b) 78floweroneright (c) 78flowers 78Flynn Peter 104

Fog () 91font encodings

Latin 1 119font encodings 8 114 115

7-bit 88-bit 8ASCII 119document 115limiting scope of 8LY1 8OT1 8 10 14 107 114 115OT2 103T1 8 10 14 115T4 10 14 17T5 10 14TS1 115

fontdefdtx (file) 103 107fontenc (package) 8 10 14 115fontencoding 8fonts

Calligra 68Charter 18 30Computer Modern 100 102115

Courier 18Garamond 18 30Helvetica 18Symbol 51 103Times Roman 18 102Type 1 112Utopia 18 30Zapf Chancery 68Zapf Dingbats 75 77

134

fontsize 100 102fontspec (package) 118Football (o) 90forall (forall) 51forall (forall) 52Force (l) 73Forward (middot) 90ForwardToEnd (cedil) 90ForwardToIndex (sup1) 90

FourAsterisk (1) 78

FourClowerOpen (V) 78

FourClowerSolid (W) 78

Fourier ( ) 36fourier (package) 19 36 51 53

57 60 76 78 91 119

fourier ( ) 36Fourier transform (F) see

alphabets mathFourStar (5) 78

FourStarOpen (6) 78fourth (4) 66fractions 67fraktur see alphabets mathFreemasonrsquos cipher 98Frege logic symbols 47 53 65 67frown (_) 30frown () 48frown symbols 48frowneq () 48frowneqsmile () 48frownie () 88frownsmile () 48frownsmileeq ()) 48Frowny (sect) 90frowny faces 72 88 90 91FS () 72FullFHBO () 90fullmoon (M) 71fullmoon () 71fullnote () 88

GG (a) 14g (esvect package option) 61Game (G) 52Game (a) 52Gamma (Γ) 50gamma (γ) 50gammaup (γ) 50Ganz ( macr ) 89GaPa (lt) 89Garamond (font) 18 30gcd (gcd) 49ge see geq

Gemini (R) 71Gemini (acirc) 71gemini (^) 71genealogical symbols 88geneuro (AC) 19geneuronarrow (BC) 19geneurowide (CC) 19gensymb (package) 70

Gentsroom (x) 90geometric shapes 78ndash80 94geq (yen) 38geq (ge) 37 38geq (ge) 39geqclosed (⊵) 39 40geqdot (u) 39geqq (macr) 38geqq (=) 38geqq (≧) 39geqslant (gt) 38geqslant (⩾) 39geqslantdot (⪀) 39german (keystroke package option)

72gets see leftarrow

gg () 38gg () 37gg (≫) 39ggcurly (Iuml) 32ggg (Iuml) 38ggg (≫) 38ggg (≫ vs Iuml) 101ggg (⋙) 39gggtr see ggg

gggtr (⋙) 39ghosts 98Gibbons Jeremy 122gimel (ג) 51gimel (ℷ) 51girl (B) 71globe 90glotstop (b) 13glottal () 13gluon (QPPPPPPR) 70gluons 74gnapprox (Euml) 38gnapprox () 38gnapprox (⪊) 39gneq (shy) 38gneq (13) 38gneqq (sup3) 38gneqq () 38gneqq (≩) 39gnsim (Aring) 38gnsim () 38gnsim (≵) 39Go boards 94Go stones 94goban 94Goofy 96graphics (package) 47 103graphicx (package) 17 100 103grave (`) 57grave (a) see accentsgravis (a) 17greater-than signs see

inequalitiesgreatest lower bound see sqcap

Greek 50 51blackboard bold 68bold 50 113polytonic 50

upright 50 51greek (babel package option) 50

87Greek coins 19

Greenpoint () 98Gregorio Enrico 104 105grimace (M) 91GS () 72gtr (gt) 39gtrapprox (Ccedil) 38gtrapprox () 38gtrapprox (⪆) 39gtrclosed (⊳) 39 40gtrdot (Iacute) 38gtrdot (m) 38gtrdot (⋗) 39gtreqless (frac12) 38

gtreqless (R) 38

gtreqless (⋛) 39gtreqlessslant (O) 39

gtreqqless (iquest) 38

gtreqqless (T) 38

gtreqqless (⪌) 39

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

gtrneqqless (oacute) 39

gtrsim (Aacute) 38gtrsim (amp) 38gtrsim (≳) 39guillemotleft (laquo) 10 116guillemotright (raquo) 10 116guilsinglleft (lsaquo) 10 117guilsinglright (rsaquo) 10 117gvcropped () 74gvertneqq (micro) 38gvertneqq () 38gvertneqq (≩) 39

HH (a) 14h (esvect package option) 61

h (ả) 14HA (A) 82

Ha (a) 82hacek (a) see accents

Hail () 91Halb ( ˘ ldquo) 89half note see musical symbols

HalfCircleLeft (s) 80

HalfCircleRight (r) 80

HalfFilledHut () 91halflength (p) 18halfnote (13) 88

HalfSun () 91Hamiltonian (H) see alphabets

mathHandCuffLeft () 76

HandCuffLeftUp () 76

135

HandCuffRight (13) 76

HandCuffRightUp () 76

HandLeft () 76

HandLeftUp () 76

HandPencilLeft () 76

HandRight () 76

HandRightUp () 76hands see fistsHandwash (Uuml) 90HaPa (lt) 89harmony (package) 89 119 120harpoon (package) 47 119 121harpoons 41 43 46 47hash () 66hash mark see

hat (ˆ) 57hateq (≙) 32hausaB (B) 13hausab (b) 13hausaD (T) 13hausad (D) 13hausaK (K) 13hausak (k) 13

HB (B) 82

Hb (b) 82

HBar () 79hbar (~) 51 52 103hbipropto () 23HC (C) 82

Hc (c) 82hcrossing () 33

HCthousand (6) 82HD (D) 82

Hd (d) 82hdotdot () 23 64hdots (⋯) 64Hdual (cedil) 82HE (E) 82He (e) 82heads see facesHeart (Œ) 90hearts (suit) 65ndash67 80heartsuit (hearts) 65heartsuit () 66Hebrew 51 68Helvetica (font) 18hemiobelion (Α) 19HERMAPHRODITE () 74Hermaphrodite () 74hexagon (7) 78Hexasteel (rsquo) 73hexstar (A) 77HF (F) 70HF (F) 82Hf (f) 82hfermion (k) 74hfil 105HG (G) 82Hg (g) 82

HH 89

HH (H) 82Hh (h) 82hhcount (package) 92 119 121Hhundred (3) 82

HI (I) 82

Hi (i) 82

hiatus (H) 95Hibl (˝) 82

Hibp (ˆ) 82

Hibs (uml) 82

Hibw (˜) 82hieroglf (package) 82 119 120hieroglyphics 82Hilbert space (H) see alphabets

mathhill (a

) 16

HJ (J) 82Hj (j) 82HK (K) 82Hk (k) 82hksqrt (

radic) 106

HL (L) 82Hl (l) 82HM (M) 82

Hm (m) 82

Hman (ˇ) 82

Hmillion (7) 82

Hms (acute) 82HN (N) 82Hn (n) 82HO (O) 82

Ho (o) 82Holt Alexander 1 118

holter ( ) 63

holtpolt (package) 63 119hom (hom) 49Home ( Home ) 72

Homer (

) 96Hone (|) 82

hook accent (ả) see accentshookb () 13hookd () 13hookd (D) 13hookdownminus () 66hookg () 13hookh ($) 13hookheng () 13hookleftarrow (larr) 41hookleftarrow () 44hookrevepsilon () 13hookrightarrow (rarr) 41hookrightarrow () 44hookupminus (⨽) 66

Horn Berthold 69HP (P) 82Hp (p) 82Hplural (˙) 82

Hplus (+) 82HQ (Q) 82Hq (q) 82

Hquery () 82HR (R) 82Hr (r) 82HS (S) 82

Hs (s) 82

Hscribe (macr) 82

Hslash () 82hslash () 52Hsv (˚) 82HT (T) 82HT () 72Ht (t) 82Hten (2) 82

Hthousand (4) 82

Htongue (˘) 82

HU (U) 82

Hu (u) 82Hungarian umlaut (a) see accents

Hut () 91

HV (V) 82Hv (v) 82hv () 13Hvbar (|) 82HW (W) 82

Hw (w) 82HX (X) 82

Hx (x) 82

HXthousand (5) 82

HY (Y) 82

Hy (y) 82hyphen discretionary 115

HZ (Z) 82Hz (z) 82

Ii 14i (ı) 14ialign 104 106 108ibar ( i ) 13IBM PC 72 97 115Icelandic staves 97IceMountain () 91

iddots ( ) 64

iddots () 107

idotsint (intmiddot middotmiddotint

) 26

idotsint (

) 27

idotsint (Z) 29iff see Longleftrightarrow

136

ifsym (package) 70 79 91 92101 103 119 120

igo (package) 94 119igocircle () 94igocircle () 94igocross (|) 94igocross (|) 94igonone () 94igonone () 94igosquare (~) 94igosquare (~) 94igotriangle () 94igotriangle () 94

iiiint (intintintint

) 26

iiiint (

) 27

iiiint (ˇ

) 28

iiiint (⨌) 29iiint (

micro) 27

iiint (intintint

) 26

iiint (

) 26 27

iiint (˝

) 28

iiint (∭) 29iint (

acute) 27

iint (intint

) 26

iint (

) 26 28

iint (˜

) 28

iint (∬) 29Im (=) 51im (j) 52imath (ı) 51 57impliedby see Longleftarrow

implies see Longrightarrow

and vdash

impulse train see shain (P) 52in (isin) 51in (isin) 52in (isin) 52inches see second and

textquotedbl

incoh (˚) 36independence

probabilistic 106statistical 106stochastic see bot

independent (perpperp) 106Industry (I) 90inequalities 9 37ndash39inexact differential see dbar

inf (inf) 49infimum see inf and sqcap

infinity (infin) see infty

Info (lt) 98Info (i) 90information symbols 90informator symbols 93infty (8) 66infty (infin) 65infty (infin) 66inipartvoice (andash ) 16inipartvoiceless (andash ) 16

injlim (inj lim) 49

inplus (A) 31

inputenc (package) 117

Ins ( Ins ) 72

int (sup3) 27

int (int

) 25 26

int (r

) 26

int (int) 29

intclockwise () 30

INTEGER (iquest) 49

Integer (Uacute) 49

integers (Z) see alphabets math

integrals 25ndash30 66 105ndash106

integrals (wasysym package op-tion) 26

intercal (ᵀ) 22

intercal (⊺) 52

interleave (9) 22

intersection see cap

Interval () 91

inva () 13

invamp (M) 23

invbackneg (⨽) 66

INVd () 73

invdiameter () 88

inve (U) 13

inverse limit see varprojlim

InversTransformHoriz () 36

InversTransformVert () 36

inverted symbols 11ndash13 17 103

inverters 73

invf () 13

invglotstop (d) 13

invh (amp) 13

INVl () 73

invlegr (I) 13

invm (5) 13

invneg () 31

invneg (⨼) 66

INVr () 73

invr (G) 13

invscr (K) 13

invscripta () 13

INVu () 73

invv () 13

invw (Z) 13

invy () 13

iota (ι) 50

iota upside-down 103

iotaup (ι) 50

ipagamma ( ) 13

ipercatal (η) 95

IroningI (macr) 90

IroningII (deg) 90

IroningIII (plusmn) 90

irony mark ( ) 103

irrational numbers (J) seealphabets math

Irritant () 92ismodeledby (=|) 103ISO character entities 117isoent (package) 117

Jj () 14

JackStar (2) 78

JackStarBold (3) 78Jewish star 77 78jmath () 51 57Joch () 91Join (Z) 30 31Join (amp) 24joinrel 103joint denial see downarrow

junicode (package) 118Junicode-Regularttf (file) 118Jupiter (E) 71Jupiter (Aring) 71jupiter (X) 71

Kk ( a) 17k ( ˛) 14kappa (κ) 50kappaup (κ) 50ker (ker) 49ket 54Keyboard (Iuml) 72keyboard symbols 72keys computer 72keystroke (package) 72 119 120keystroke ( ) 72

king 94knight 94Knuth Donald E 8 114 122

symbols by 89Koppa (Ϙ) 87koppa (ϟ) 87Kr ( l) 89kreuz (6) 88Kronecker product see otimes

Kronecker sum see oplus

krouzek (a) see accentskside (O) 93Kutline (R) 75

LL ( L) 10l ( l) 10labdentalnas (4) 13labvel 16Ladiesroom (y) 90Lagrangian (L) see alphabets

mathLambda (Λ) 50lambda (λ) 50lambdabar (o) 66lambdaslash (n) 66

137

lambdaup (λ) 50Lamport Leslie 118 122land see wedge

landdownint () 28

landdownint (⨚) 29landupint (

) 28

landupint (⨙) 29Langle (lt) 68lAngle (〈〈) 56langle (〈) 21 54

langle (⟨) 55

langlebar (n) 55

Laplace ( ) 36

laplace ( ) 36Laplace transform (L) see

alphabets mathLaplacian (∆) see Delta

Laplacian (nabla2) see nabla

largecircle () 79largediamond () 79largelozenge (loz) 79

largepencil (W) 76

largepentagram () 79largesquare (◻) 79largestar () 79largestarofdavid () 79largetriangledown () 40largetriangleleft (◁) 40largetriangleright (▷) 40largetriangleup () 40LArrow ( larr ) 72

larrowfill 62Laserbeam (a) 74LATEX 1 8 14 26 30 49 54

63 65 73 75 100 103ndash109112 113 115 117ndash119 121122

LATEX 2ε 1 89 19 20 22 30 36 41 5863 65 69 73 100 101 103106 107 111 112 114ndash117122

latexsym (package) 22 30 36 4165 100 119

latfric () 13Latin 1 8 115 119

table 116laundry symbols 90Lbag (P) 53lbag (N) 53

lbrace (⎧⎪⎪⎨⎪⎪⎩

) 55Lbrack ([) 68lBrack ([[) 56LCD digits 70lCeil (dd) 56lceil (d) 54

lceil (⎡⎢⎢⎢⎢⎢⎢) 55

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

lcircleleftint (∲) 29

lcirclerightint (∲) 29lcm (lcm) 113lcorners (v) 53lcurvearrowdown (⤸) 43lcurvearrowleft (ordm) 43lcurvearrowne (frac14) 43lcurvearrownw (frac12) 43lcurvearrowright () 43lcurvearrowse (iquest) 43lcurvearrowsw (frac34) 43lcurvearrowup (sup1) 43ldbrack (v) 55ldotp () 63ldots ( ) 63le see leq

leadsto () 31 41leadsto () 44leaf see textleaf

leafleft (g) 78leafNE (f) 78leafright (h) 78leaves 78 80Lefschetz motive (L) see

alphabets mathLeft 96left 54 56 100 102LEFTarrow () 88Leftarrow (lArr) 21 41Leftarrow (lArr) 43leftarrow (ETH) 42leftarrow (larr) 41leftarrow (larr) 44leftarrowtail () 41leftarrowtail () 44leftarrowtriangle (^) 42leftbarharpoon (Uuml) 43LEFTCIRCLE (G) 88LEFTcircle (G) 88Leftcircle (I) 88

leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

leftfilledspoon (r) 47leftfootline (z) 33leftfree () 33lefthalfcap () 23lefthalfcup () 24lefthand (t) 76leftharpoonccw () 46leftharpooncw () 46leftharpoondown (acirc) 43leftharpoondown () 41leftharpoonup (agrave) 43leftharpoonup () 41leftleftarrows (ETH) 42leftleftarrows (hArr) 41

leftleftarrows () 44leftleftharpoons (Oslash) 43leftlsquigarrow (cent) 44leftmapsto () 44leftModels (ograve) 33leftmodels (acirc) 33leftmoon (K) 71leftmoon ($) 71leftp (v) 18leftpitchfork () 47leftpointright (R) 76leftpropto (prop) 33Leftrightarrow (hArr) 41Leftrightarrow (hArr) 44leftrightarrow (Oslash) 42leftrightarrow (harr) 41leftrightarrow (harr) 44leftrightarroweq (-) 42leftrightarrows (Ocirc) 42leftrightarrows () 41leftrightarrows () 44leftrightarrowtriangle (])

42leftrightharpoon (agrave) 43leftrightharpoondownup (⥊)

46leftrightharpoons (egrave) 43leftrightharpoons () 41leftrightharpoons () 46leftrightharpoonsfill 62leftrightharpoonupdown (⥋)

46Leftrightline (Ocirc) 33leftrightline (ETH) 33leftrightsquigarrow (uacute) 42leftrightsquigarrow () 41leftrightsquigarrow () 44leftrsquigarrow () 44Leftscissors (S) 75leftslice (2) 22leftslice (⪦) 33leftspoon (⟜) 47leftsquigarrow (oslash) 42leftsquigarrow (f) 42leftt (n) 18lefttherefore () 24 64leftthreetimes ($) 66leftthreetimes (h) 22leftthreetimes (⋋) 24leftthumbsdown (D) 76leftthumbsup (U) 76lefttorightarrow (uuml) 42Lefttorque (amp) 73leftturn () 88leftVdash (ecirc) 33leftvdash (⊣) 33

leftwave (

ETH

ETH

ETH

ETH

) 56

leftY () 24legal symbols 9 19 116legm (6) 13legr (E) 13

138

length (q) 18Leo (auml) 71leo () 71leq (curren) 38leq (le) 37 38leq (le) 39leqclosed (⊴) 39 40leqdot (t) 39leqq (reg) 38leqq (5) 38leqq (≦) 39leqslant (6) 38leqslant (⩽) 39leqslantdot (⩿) 39less (lt) 39less-than signs see inequalitieslessapprox (AElig) 38lessapprox () 38lessapprox (⪅) 39lessclosed (⊲) 39 40lessdot (Igrave) 38lessdot (l) 38lessdot (⋖) 39lesseqgtr (frac14) 38

lesseqgtr (Q) 38

lesseqgtr (⋚) 39lesseqgtrslant (N) 39

lesseqqgtr (frac34) 38

lesseqqgtr (S) 38

lesseqqgtr (⪋) 39

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

lessneqqgtr (ograve) 39

lesssim (Agrave) 38lesssim () 38lesssim (≲) 39Letter () 92Letter (B vs ) 101Letter (B) 73letter-like symbols 51ndash53letters see alphabets

barred 104non-ASCII 10slashed 105variant Latin 51

levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

LF () 72

lfilet (

7777) 55

lFloor (bb) 56lfloor (b) 54

lfloor (⎢⎢⎢⎢⎢⎢⎣) 55

lg (lg) 49

lgroup (

) 54

lgroup (⎧⎪⎪⎪⎪⎪⎩) 55

LHD () 23

lhd (C) 22 23lhd (⊲) 39 40lhdbend (~) 89lhookdownarrow (3) 44lhookleftarrow (2) 44lhooknearrow (4) 44lhooknwarrow (⤣) 44lhookrightarrow () 44lhooksearrow (⤥) 44lhookswarrow (6) 44lhookuparrow (1) 44Libra (aelig) 71libra (a) 71Lie derivative (L) see alphabets

mathlife-insurance symbols 108lightbulb (A) 112lightbulbmf (file) 109ndash111lightbulbsty (file) 112lightbulb102602gf (file) 111lightbulb10dvi (file) 111lightbulb10mf (file) 109ndash111lightbulb10tfm (file) 112

Lightning (E vs ) 101

Lightning () 91Lightning (E) 73lightning ( ) 42lightning ( vs ) 101lightning () 44lightning () 88lim (lim) 49 113liminf (lim inf) 49 113limits 49limsup (lim sup) 49 113linbfamily 85 86Linear A 82Linear B 85 86linear implication see multimap

linear logic symbols 21ndash23 2529ndash30 36 51 52

linearA (package) 82 119 121

LinearAC (c) 82LinearACC () 82LinearACCC (y) 82LinearACCCI (z) 82LinearACCCII () 82LinearACCCIII (|) 82LinearACCCIV () 82LinearACCCIX () 83LinearACCCL (laquo) 83LinearACCCLI (not) 83LinearACCCLII (shy) 83LinearACCCLIII (reg) 83LinearACCCLIV (macr) 83LinearACCCLIX (acute) 83LinearACCCLV (deg) 83LinearACCCLVI (plusmn) 83LinearACCCLVII (sup2) 83LinearACCCLVIII (sup3) 83LinearACCCLX (micro) 84LinearACCCLXI (para) 84LinearACCCLXII (middot) 84

LinearACCCLXIII (cedil) 84LinearACCCLXIV (sup1) 84LinearACCCLXIX (frac34) 84LinearACCCLXV (ordm) 84LinearACCCLXVI (raquo) 84LinearACCCLXVII (frac14) 84LinearACCCLXVIII (frac12) 84LinearACCCLXX (iquest) 84LinearACCCLXXI (Agrave) 84LinearACCCLXXII (Aacute) 84LinearACCCLXXIII (Acirc) 84LinearACCCLXXIV (Atilde) 84LinearACCCLXXIX (Egrave) 84LinearACCCLXXV (Auml) 84LinearACCCLXXVI (Aring) 84LinearACCCLXXVII (AElig) 84LinearACCCLXXVIII (Ccedil) 84LinearACCCLXXX (Eacute) 84LinearACCCLXXXI (Ecirc) 84LinearACCCLXXXII (Euml) 84LinearACCCLXXXIII (Igrave) 84LinearACCCLXXXIV (Iacute) 84LinearACCCLXXXIX (Ograve) 84LinearACCCLXXXV (Icirc) 84LinearACCCLXXXVI (Iuml) 84LinearACCCLXXXVII (ETH) 84LinearACCCLXXXVIII (Ntilde) 84LinearACCCV (~) 82LinearACCCVI () 82LinearACCCVII () 82LinearACCCVIII () 83LinearACCCX () 83LinearACCCXI () 83LinearACCCXII () 83LinearACCCXIII () 83LinearACCCXIV () 83LinearACCCXIX () 83LinearACCCXL (iexcl) 83LinearACCCXLI (cent) 83LinearACCCXLII (pound) 83LinearACCCXLIII (curren) 83LinearACCCXLIV (yen) 83LinearACCCXLIX (ordf) 83LinearACCCXLV (brvbar) 83LinearACCCXLVI (sect) 83LinearACCCXLVII (uml) 83LinearACCCXLVIII (copy) 83LinearACCCXV () 83LinearACCCXVI () 83LinearACCCXVII () 83LinearACCCXVIII () 83LinearACCCXX () 83LinearACCCXXI () 83LinearACCCXXII () 83LinearACCCXXIII () 83LinearACCCXXIV () 83LinearACCCXXIX () 83LinearACCCXXV () 83LinearACCCXXVI () 83LinearACCCXXVII () 83LinearACCCXXVIII () 83LinearACCCXXX () 83LinearACCCXXXI () 83

139

LinearACCCXXXII () 83LinearACCCXXXIII () 83LinearACCCXXXIV () 83LinearACCCXXXIX ( ) 83LinearACCCXXXV () 83LinearACCCXXXVI () 83LinearACCCXXXVII () 83LinearACCCXXXVIII () 83LinearACCI () 82LinearACCII () 82LinearACCIII () 82LinearACCIV () 82LinearACCIX () 82LinearACCL (G) 83LinearACCLI (H) 83LinearACCLII (I) 83LinearACCLIII (J) 83LinearACCLIV (K) 83LinearACCLIX (P) 83LinearACCLV (L) 83LinearACCLVI (M) 83LinearACCLVII (N) 83LinearACCLVIII (O) 83LinearACCLX (Q) 83LinearACCLXI (R) 83LinearACCLXII (S) 84LinearACCLXIII (T) 84LinearACCLXIV (U) 84LinearACCLXIX (Z) 84LinearACCLXV (V) 84LinearACCLXVI (W) 84LinearACCLXVII (X) 84LinearACCLXVIII (Y) 84LinearACCLXX ([) 84LinearACCLXXI () 84LinearACCLXXII (]) 84LinearACCLXXIII (^) 84LinearACCLXXIV (_) 84LinearACCLXXIX (d) 84LinearACCLXXV (`) 84LinearACCLXXVI (a) 84LinearACCLXXVII (b) 84LinearACCLXXVIII (c) 84LinearACCLXXX (e) 84LinearACCLXXXI (f) 84LinearACCLXXXII (g) 84LinearACCLXXXIII (h) 84LinearACCLXXXIV (i) 84LinearACCLXXXIX (n) 84LinearACCLXXXV (j) 84LinearACCLXXXVI (k) 84LinearACCLXXXVII (l) 84LinearACCLXXXVIII (m) 84LinearACCLXXXX (o) 84LinearACCV () 82LinearACCVI () 82LinearACCVII () 82LinearACCVIII () 82LinearACCX () 83LinearACCXCI (p) 84LinearACCXCII (q) 84LinearACCXCIII (r) 84LinearACCXCIV (s) 84

LinearACCXCIX (x) 82LinearACCXCV (t) 82LinearACCXCVI (u) 82LinearACCXCVII (v) 82LinearACCXCVIII (w) 82LinearACCXI ( ) 83LinearACCXII () 83LinearACCXIII () 83LinearACCXIV () 83LinearACCXIX (() 83LinearACCXL (=) 83LinearACCXLI (gt) 83LinearACCXLII () 83LinearACCXLIII () 83LinearACCXLIV (A) 83LinearACCXLIX (F) 83LinearACCXLV (B) 83LinearACCXLVI (C) 83LinearACCXLVII (D) 83LinearACCXLVIII (E) 83LinearACCXV ($) 83LinearACCXVI () 83LinearACCXVII (amp) 83LinearACCXVIII () 83LinearACCXX ()) 83LinearACCXXI () 83LinearACCXXII (+) 83LinearACCXXIII () 83LinearACCXXIV (-) 83

LinearACCXXIX (2) 83LinearACCXXV () 83LinearACCXXVI () 83LinearACCXXVII (0) 83LinearACCXXVIII (1) 83LinearACCXXX (3) 83LinearACCXXXI (4) 83LinearACCXXXII (5) 83LinearACCXXXIII (6) 83LinearACCXXXIV (7) 83LinearACCXXXIX (lt) 83LinearACCXXXV (8) 83LinearACCXXXVI (9) 83LinearACCXXXVII () 83LinearACCXXXVIII () 83LinearACI (d) 82LinearACII (e) 82LinearACIII (f) 82LinearACIV (g) 82LinearACIX (l) 82LinearACL () 83LinearACLI () 83LinearACLII () 83LinearACLIII () 83

LinearACLIV () 83LinearACLIX () 83LinearACLV () 83LinearACLVI () 83

LinearACLVII () 83LinearACLVIII () 83LinearACLX () 83LinearACLXI ( ) 83LinearACLXII (iexcl) 83

LinearACLXIII (cent) 83LinearACLXIV (pound) 84LinearACLXIX (uml) 84

LinearACLXV (curren) 84LinearACLXVI (yen) 84LinearACLXVII (brvbar) 84LinearACLXVIII (sect) 84LinearACLXX (copy) 84LinearACLXXI (ordf) 84LinearACLXXII (laquo) 84LinearACLXXIII (not) 84LinearACLXXIV (shy) 84

LinearACLXXIX () 84LinearACLXXV (reg) 84LinearACLXXVI (macr) 84LinearACLXXVII (deg) 84LinearACLXXVIII (plusmn) 84LinearACLXXX () 84LinearACLXXXI () 84LinearACLXXXII () 84LinearACLXXXIII () 84LinearACLXXXIV () 84LinearACLXXXIX () 84LinearACLXXXV () 84LinearACLXXXVI () 84LinearACLXXXVII () 84

LinearACLXXXVIII () 84LinearACLXXXX () 84LinearACV (h) 82LinearACVI (i) 82LinearACVII (j) 82LinearACVIII (k) 82LinearACX (m) 82LinearACXCI () 84LinearACXCII (13) 84LinearACXCIII () 84LinearACXCIV () 84LinearACXCIX () 82LinearACXCV () 84LinearACXCVI () 84LinearACXCVII () 82LinearACXCVIII () 82LinearACXI (n) 82LinearACXII (o) 83LinearACXIII (p) 83LinearACXIV (q) 83LinearACXIX (v) 83

LinearACXL () 83LinearACXLI () 83LinearACXLII () 83LinearACXLIII () 83LinearACXLIV () 83LinearACXLIX () 83LinearACXLV () 83LinearACXLVI () 83LinearACXLVII () 83LinearACXLVIII () 83LinearACXV (r) 83LinearACXVI (s) 83LinearACXVII (t) 83

LinearACXVIII (u) 83LinearACXX (w) 83

140

LinearACXXI (x) 83

LinearACXXII (y) 83LinearACXXIII (z) 83LinearACXXIV () 83

LinearACXXIX () 83

LinearACXXV (|) 83LinearACXXVI () 83LinearACXXVII (~) 83LinearACXXVIII () 83LinearACXXX () 83

LinearACXXXI () 83LinearACXXXII () 83

LinearACXXXIII () 83

LinearACXXXIV () 83LinearACXXXIX () 83LinearACXXXV () 83LinearACXXXVI () 83LinearACXXXVII () 83LinearACXXXVIII () 83

LinearAI () 82

LinearAII () 82LinearAIII () 82LinearAIV () 82LinearAIX () 82

LinearAL (1) 83LinearALI (2) 83LinearALII (3) 83LinearALIII (4) 83LinearALIV (5) 83

LinearALIX () 83

LinearALV (6) 83LinearALVI (7) 83LinearALVII (8) 83

LinearALVIII (9) 83

LinearALX () 83LinearALXI (lt) 83LinearALXII (=) 83LinearALXIII (gt) 83LinearALXIV () 83

LinearALXIX (D) 84LinearALXV () 83

LinearALXVI (A) 84LinearALXVII (B) 84

LinearALXVIII (C) 84LinearALXX (E) 84LinearALXXI (F) 84

LinearALXXII (G) 84LinearALXXIII (H) 84LinearALXXIV (I) 84

LinearALXXIX (N) 84LinearALXXV (J) 84

LinearALXXVI (K) 84LinearALXXVII (L) 84LinearALXXVIII (M) 84LinearALXXX (O) 84LinearALXXXI (P) 84

LinearALXXXII (Q) 84LinearALXXXIII (R) 84

LinearALXXXIV (S) 84LinearALXXXIX (X) 84

LinearALXXXV (T) 84LinearALXXXVI (U) 84

LinearALXXXVII (V) 84LinearALXXXVIII (W) 84LinearALXXXX (Y) 84LinearAV () 82

LinearAVI () 82LinearAVII () 82LinearAVIII () 82

LinearAX () 82

LinearAXCI (Z) 84LinearAXCII ([) 84LinearAXCIII () 84LinearAXCIV (]) 84

LinearAXCIX (b) 82LinearAXCV (^) 84LinearAXCVI (_) 84LinearAXCVII (`) 84LinearAXCVIII (a) 84LinearAXI () 82LinearAXII () 82LinearAXIII () 82LinearAXIV (13) 83LinearAXIX () 83

LinearAXL () 83LinearAXLI (() 83

LinearAXLII ()) 83LinearAXLIII () 83

LinearAXLIV (+) 83

LinearAXLIX (0) 83

LinearAXLV () 83

LinearAXLVI (-) 83LinearAXLVII () 83LinearAXLVIII () 83LinearAXV () 83

LinearAXVI () 83LinearAXVII () 83

LinearAXVIII () 83LinearAXX () 83LinearAXXI () 83

LinearAXXII () 83

LinearAXXIII () 83

LinearAXXIV () 83LinearAXXIX () 83LinearAXXV () 83LinearAXXVI () 83

LinearAXXVII () 83LinearAXXVIII () 83LinearAXXX () 83

LinearAXXXI () 83LinearAXXXII () 83LinearAXXXIII ( ) 83LinearAXXXIV () 83LinearAXXXIX (amp) 83LinearAXXXV () 83LinearAXXXVI () 83LinearAXXXVII ($) 83LinearAXXXVIII () 83linearb (package) 85 86 119 121Lineload (L) 73linguistic symbols 11ndash14

Lisa (

) 96lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 55

llap 106llbracket (~) 54

llbracket (

) 57

llceil (V) 53llcorner (z) 53llcorner (x) 53

llcorner () 55

llcurly (Icirc) 32Lleftarrow (W) 41Lleftarrow () 44llfloor (T) 53lll (Icirc) 38lll (≪) 38lll (≪ vs Icirc) 101lll (⋘) 39llless see lll

llless (⋘) 39llparenthesis (L) 53

lmoustache (

) 54

lmoustache (⎧⎪⎪⎪⎪⎪⎭) 55

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

lnot (not) 66lnsim (Auml) 38lnsim () 38lnsim (≴) 39local ring (O) see alphabets

mathlog (log) 49 113log-like symbols 49 113logic gates 73logical operators

and see wedge

not see neg and sim

or see vee

logof () 31lollipop see multimap

long division 59longa (λ) 95longcastling (O-O-O) 93longdiv (package) 59

141

Longleftarrow (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) 70LongPulseLow () 70Longrightarrow (=rArr) 41Longrightarrow (OcircrArr) 43longrightarrow (ETHrarr) 43longrightarrow (minusrarr) 41looparrowdownleft (icirc) 42looparrowdownright (iuml) 42looparrowleft (igrave) 42looparrowleft () 41looparrowleft () 43looparrowright (iacute) 42looparrowright () 41looparrowright () 43Loosebearing ($) 73lor see vee

LowerDiamond (o) 79lowering see textlowering

lozenge (diams) 65 66lozenge (loz) 79Lparen (() 68lrcorner () 53lrcorner (y) 53

lrcorner () 55

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 55

lsemantic see ldbrack

Lsh (egrave) 42Lsh () 41Lsh () 43Lsteel (trade) 73ltimes () 23ltimes (n) 22ltimes (⋉) 24ltriple 57Luecking Dan 106lVert () 54lVert (||) 56lvert (|) 54lvertneqq (acute) 38lvertneqq () 38lvertneqq (≨) 39

lwave (

ETH

ETH

ETH

ETH

) 56

lWavy (_______

) 55

lwavy (^^^) 55

lz (1) 13

MM 10M (

macr) 95

m 10m (

macr) 95

ma (times) 95macron (a) 17macron (a) see accents

Maggie ( ) 96

magical signs 97majuscules 50makeatletter 107makeatother 107MALE () 74Male (|) 74male 71 73 74male () 73MaleMale (ƒ) 74maltese (z) 10maltese () 66man 81 90manboldkidney () 89manconcentriccircles ($) 89manconcentricdiamond () 89mancone () 89mancube () 89manerrarrow (y) 89manfilledquartercircle () 89manfnt (package) 89 119 120manhpennib () 89manimpossiblecube () 89mankidney () 89manlhpenkidney () 89manpenkidney () 89

manquadrifolium (amp) 89manquartercircle ( ) 89

manrotatedquadrifolium () 89

manrotatedquartercircle () 89

manstar () 89mantiltpennib () 89mantriangledown (7) 89mantriangleright (x) 89mantriangleup (6) 89manvpennib () 89Mappedfromchar ( ) 48mappedfromchar ( ) 48Mapsfrom (lArr ) 42mapsfrom (larr [) 42Mapsfromchar (ucirc) 49Mapsfromchar () 48mapsfromchar (szlig) 49mapsfromchar ([) 48Mapsto ( rArr) 42mapsto ( 7rarr) 41mapsto (↦) 44

Mapstochar (uacute) 49Mapstochar () 48mapstochar (THORN) 49

Marge (

) 96markera (x) 93markerb (y) 93married see textmarried

Mars (D) 71Mars (Auml) 71mars () 71MartinVogel (yuml) 90marvosym (package) 18 65 67

71ndash75 90 101masonic cipher 98mate (m) 93material biconditional

see leftrightarrow andequiv

material conditional seerightarrow and supset

material equivalence see leftrightarrow andequiv

material implication seerightarrow and supset

material nonimplication see nrightarrow andnsupset

math alphabets 68mathabx (package) 21 23 25 26

30 32 36ndash38 40 42 43 4952ndash55 58 60 65 66 71 93100 101 119 120 123

mathaccent 104mathbb 68mathbbm 68mathbbmss 68mathbbmtt 68mathbbol (package) 68mathbf 113mathbin 112mathbold 113mathcal (euscript package option)

68mathcal 68mathcent (cent) 52mathchoice 105 106mathclose 112mathcomp (package) 65mathdesign (package) 18 24 30

52 56 67 119mathdollar ($) 21mathdots (package) 58 63 64

107 119 120mathds 68mathellipsis ( ) 21mathematical symbols 21ndash69mathfrak 68

142

mathit 68mathnormal 68mathop 112mathopen 112mathord 112mathpalette 106mathparagraph (para) 21mathpunct 112mathpzc 68mathrel 103 112mathring ( ) 57 58mathrm 68mathrsfs (package) 68 119mathscr (euscript package option)

68mathscr 68mathsection (sect) 21mathsterling (pound) 52mathsterling (pound) 21mathtools (package) 21 34 60

62 119 120mathunderscore ( ) 21max (max) 49Maxwell-Stefan diffusion coeffi-

cient seeDH

maya 65Mb (˘) 95mb (˘) 95Mbb (˘ ) 95mBb (˘ ) 95mbB (˘ ) 95mbb (˘ ) 95mbboard (package) 68 119mbbx (˘ macr

) 95mbox 106measuredangle (gt) 66measuredangle (]) 66measuredangle (∡) 66mechanical scaling 109 112medbackslash (∖) 24medbullet () 23medcirc () 23medcircle () 24meddiamond () 25medlozenge (loz) 79medslash (∕) 24medsquare (◻) 25medstar () 25medstarofdavid () 79medtriangledown () 25 40medtriangleleft (◁) 25 40medtriangleright (▷) 25 40medtriangleup () 25 40medvert (∣) 24medvertdot () 24membership see in

Mercury (A) 71Mercury (Acirc) 71mercury () 71merge () 22METAFONT 69 109ndash112METAFONTbook symbols 89

metre (package) 17 57 95 119120

metre 95metrical symbols 95mho (f) 65 66micro see textmu

micro (micro) 70

Microsoftreg Windowsreg 115mid (|) 30 56middle 54midtilde () 18MIL-STD-806 73millesimal sign see

textperthousand

milstd (package) 73 119min (min) 49 113minim see musical symbolsminus see textminus

minus (minus) 24minuscolon (minus) 36minuscoloncolon (minus) 36minusdot () 24minushookdown (not) 66minushookup (⨼) 66minuso () 22 104minutes angular see prime

miscellaneous symbols 65ndash67 8088ndash99

ldquoMissing $ insertedrdquo 21Mmappedfromchar () 48mmappedfromchar () 48Mmapstochar () 48mmapstochar () 48MnSymbol (package) 21

23ndash25 29 32ndash34 37 39 4043ndash48 51 52 55 58ndash60 6466 67 79 119 120

Mobilefone (H) 73mod 49models (|=) 30 103models (⊧) 33moduli space see alphabets

mathmonetary symbols 18 19 68monus see dotdiv

moo () 22Moon (K) 71Moon (Aacute) 71MoonPha 98morepawns (S) 93moreroom (U) 93Mountain () 91mouse see ComputerMouse

MoveDown (raquo) 90moverlay 107MoveUp (ordm) 90mp (∓) 22mp (∓) 24mu (micro) 50multimap (() 30 31multimap (⊸) 47multimapboth () 31

multimapbothvert () 31multimapdot () 31multimapdotboth () 31multimapdotbothA () 31multimapdotbothAvert () 31multimapdotbothB () 31multimapdotbothBvert () 31multimapdotbothvert () 31multimapdotinv () 31multimapinv () 31multiple accents per character 107multiplicative disjunction

see bindnasrepmainvamp and parr

Mundus (m) 90Museum of Icelandic Sorcery and

Witchcraft 98musical symbols 20 65 66 88

89musixtex (package) 89muup (micro) 50MVAt () 90MVEight (8) 65MVFive (5) 65MVFour (4) 65MVNine (9) 65MVOne (1) 65MVRightarrow () 90MVSeven (7) 65MVSix (6) 65MVThree (3) 65MVTwo (2) 65MVZero (0) 65

Nnabla (nabla) 65nabla (nabla) 66NAK () 72NAND gates 73

NANDd () 73

NANDl () 73

NANDr () 73

NANDu () 73napprox () 32napprox (≉) 33napproxeq (6) 31napproxeq () 33nasymp (-) 31nasymp (≭) 48nath (package) 53 56 57 119

NATURAL (frac14) 49

Natural (Icirc) 49natural () 65 88natural () 66natural numbers (N) see

alphabets math

143

navigation symbols 90nbackapprox () 33nbackapproxeq () 33nbackcong () 33nbackeqsim () 33nbacksim () 31nbacksim () 33nbacksimeq (+) 31nbacksimeq () 34nbacktriplesim () 34NBSP ( ) 72nBumpeq ()) 31nBumpeq () 34nbumpeq (() 31nbumpeq () 34ncirceq (sup3) 34ncirclearrowleft (ugrave) 46ncirclearrowright (yacute) 46nclosedequal (eacute) 34ncong () 32

ncong () 31

ncong (≇) 34ncurlyeqprec (cedil) 32ncurlyeqprec (ograve) 34ncurlyeqsucc (sup1) 32ncurlyeqsucc (oacute) 34ncurvearrowdownup (Euml) 44ncurvearrowleft (Acirc) 46ncurvearrowleftright (Egrave) 44ncurvearrownesw (Igrave) 44ncurvearrownwse (Iacute) 44ncurvearrowright (cedil) 46ncurvearrowrightleft (Ecirc) 44ncurvearrowsenw (Iuml) 44ncurvearrowswne (Icirc) 44ncurvearrowupdown (Eacute) 44ndasharrow (`) 46ndasheddownarrow (c) 45ndashedleftarrow (b) 45ndashednearrow (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 () 34ndoteq () 34ndoublefrown () 48ndoublefrowneq () 48ndoublesmile () 48

ndoublesmileeq () 48nDownarrow () 45ndownarrow () 45ndownarrowtail () 45ndowndownarrows () 45ndownfilledspoon (s) 47ndownfootline () 34ndownfree (⫝̸) 34ndownharpoonccw (C) 46ndownharpooncw (K) 46ndownlsquigarrow (pound) 45ndownmapsto (+) 45ndownModels (oacute) 34ndownmodels (atilde) 34ndownpitchfork () 47ndownrsquigarrow (laquo) 45ndownspoon (k) 47ndownuparrows () 45ndownupharpoons (]) 46ndownVdash (euml) 34ndownvdash (Ucirc) 34

ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq

ne (ne) 34Nearrow (t) 42Nearrow () 43nearrow (Otilde) 42nearrow () 41 106 107nearrow () 43nearrowtail ($) 43nefilledspoon (t) 47nefootline (|) 33nefree () 33neg (not) 65neg (not) 66negation see neg and sim

neharpoonccw (D) 46neharpooncw (L) 46nelsquigarrow (curren) 43nemapsto () 43neModels (ocirc) 33nemodels (auml) 33nenearrows () 43nepitchfork () 47Neptune (H) 71Neptune (Egrave) 71neptune ([) 71neq () 32neq () 37neq (ne) 34neqbump () 34neqcirc (sup2) 34neqdot () 34neqfrown () 48neqsim () 33neqslantgtr (sup1) 38neqslantgtr (ntilde) 39neqslantless (cedil) 38neqslantless (eth) 39

neqsmile () 48nequal (ne) 33nequalclosed (ecirc) 33nequiv () 31nequiv (≢) 33nequivclosed (euml) 33nersquigarrow (not) 43nespoon (l) 47Neswarrow () 43neswarrow () 106 107neswarrow (⤡) 43neswarrows () 43neswbipropto () 24neswcrossing () 33neswharpoonnwse (R) 46neswharpoons (Z) 46neswharpoonsenw (V) 46Neswline (Ouml) 33neswline (Ograve) 33Neutral () 74neVdash (igrave) 33nevdash (Uuml) 33newextarrow 63newmetrics 95newmoon (N) 71newmoon ( ) 71newtie (a) 14nexists (E) 52nexists () 52nexists (∄) 52nfallingdotseq () 33nfrown () 48nfrowneq () 48nfrowneqsmile () 48nfrownsmile () 48nfrownsmileeq (iexcl) 48NG (Ŋ) 10ng (ŋ) 10ngeq (sect) 38

ngeq () 38

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

ngeqq () 38

ngeqq (iquest) 39

ngeqslant () 38

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

ngtreqless (Atilde) 39

144

ngtreqlessslant (Ccedil) 39

ngtreqqless (Aring) 39

ngtrless (amp) 38

ngtrless (≹) 39

ngtrsim (Atilde) 38ngtrsim () 38nhateq (micro) 34nhookleftarrow () 46nhookrightarrow (0) 46ni (3) 51 105ni (ni) 52nialpha () 13nibar see ownsbar

nibeta () 13

NibLeft () 76

NibRight () 76nibs 76

NibSolidLeft ( ) 76

NibSolidRight () 76nicefrac (package) 67 119 121nichi ([) 13niepsilon () 13nigamma () 13niiota ()) 13nilambda (2) 13nin (notin) 52niomega (gt) 13niphi (C) 13niplus (B) 31nisigma (O) 13nitheta (S) 13niupsilon (V) 13niv ( ) 53nj (7) 13nlcirclearrowdown (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) 34nleftfree () 34nleftharpoonccw (B) 46nleftharpooncw (J) 46nleftleftarrows () 45nleftlsquigarrow (cent) 45

nleftmapsto () 45nleftModels (ograve) 34nleftmodels (acirc) 34nleftpitchfork () 47nLeftrightarrow (oslash) 42nLeftrightarrow (lt) 41nLeftrightarrow (⇎) 45nleftrightarrow (Uuml) 42nleftrightarrow (=) 21 41nleftrightarrow (↮) 45nleftrightarrows () 45nleftrightharpoondownup (T)

46nleftrightharpoons () 46nleftrightharpoonupdown (P)

46nLeftrightline (Ocirc) 34nleftrightline (ETH) 34nleftrightsquigarrow (deg) 46nleftrsquigarrow (ordf) 45nleftspoon (j) 47nleftVdash (ecirc) 34nleftvdash (Uacute) 34nleq (brvbar) 38

nleq () 38

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

nleqq () 38

nleqq (frac34) 39

nleqslant () 38

nleqslant (≰) 39nleqslantdot (icirc) 39nless (cent) 38nless (≮) 38nless (≮) 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) 39

nmapsto (() 46nmid (-) 31nmid (∤) 34nmodels (⊭) 34nmultimap (h) 47

nndtstile ( ) 35nNearrow () 44nnearrow (1) 42nnearrow () 44nnearrowtail ($) 45nnefilledspoon (t) 47nnefootline (|) 34nnefree () 34nneharpoonccw (D) 46nneharpooncw (L) 46nnelsquigarrow (curren) 45nnemapsto () 45nneModels (ocirc) 34nnemodels (auml) 34nnenearrows () 45nnepitchfork () 47nnersquigarrow (not) 45nnespoon (l) 47nNeswarrow () 45nneswarrow () 45nneswarrows () 45nneswharpoonnwse (R) 46nneswharpoons (Z) 46nneswharpoonsenw (V) 46nNeswline (Ouml) 34nneswline (Ograve) 34nneVdash (igrave) 34nnevdash (Uuml) 34

nnststile ( ) 35

nntstile ( ) 35

nnttstile ( ) 35nNwarrow (13) 45nnwarrow (0) 42nnwarrow () 45nnwarrowtail () 45nnwfilledspoon (u) 47nnwfootline () 34nnwfree () 34nnwharpoonccw (E) 46nnwharpooncw (M) 46nnwlsquigarrow (yen) 45nnwmapsto (-) 45nnwModels (otilde) 33nnwmodels (aring) 34nnwnwarrows () 45nnwpitchfork () 47nnwrsquigarrow (shy) 45nNwsearrow () 45nnwsearrow () 45nnwsearrows () 45nnwseharpoonnesw (S) 46nnwseharpoons (_) 46nnwseharpoonswne (W) 46nNwseline (times) 33nnwseline (Oacute) 33nnwspoon (m) 47nnwVdash (iacute) 33

145

nnwvdash (Yacute) 33no entry see noway

NoBleech (Igrave) 90NoChemicalCleaning (uml) 90nointegrals (wasysym package op-

tion) 26NoIroning (sup2) 90non-commutative division 63nonbreaking space 72NOR gates 73

NORd () 73

NORl () 73norm see lVert and rVert

NORr (13) 73

NORu () 73

NoSun () 91not see neg

not 32 105not equal ( = vs =) 32notasymp () 32notbackslash (minus) 71notbot (M) 52notdivides () 32notequiv () 32notin (R) 52notin (lt) 52notin ( 6isin) 52notin (notin) 52notni (=) 52notowner (S) 52notowns see notowner and

notni

notperp (M) 32notslash (minus) 71notsmallin () 52notsmallowns () 52nottop (L) 52NoTumbler () 90novelty (N) 93noway (A) 91nowns (∌) 52nparallel (∦) 31nparallel (∦) 34nparallelslant (Ocirc) 36nperp (Ugrave) 34npitchfork () 47nplus (`) 22nprec (cent) 32nprec (⊀) 31nprec (⊀) 33nprecapprox (Egrave) 32nprecapprox (7) 31nprecapprox (egrave) 33npreccurlyeq (brvbar) 32npreccurlyeq ($) 31npreccurlyeq (⋠) 34

npreceq (ordf) 32

npreceq () 31

npreceq (acirc) 34npreceqq (9) 31nprecsim (Acirc) 32nprecsim () 31nprecsim (aelig) 34nrcirclearrowdown (ucirc) 45nrcirclearrowleft (uacute) 45nrcirclearrowright (oslash) 45nrcirclearrowup (ugrave) 45nrcurvearrowdown (Atilde) 45nrcurvearrowleft (Acirc) 45nrcurvearrowne (Auml) 45nrcurvearrownw (Aring) 45nrcurvearrowright (Agrave) 45nrcurvearrowse (Ccedil) 45nrcurvearrowsw (AElig) 45nrcurvearrowup (Aacute) 45nRelbar (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) 34nrightfree () 34nrightharpoonccw () 46nrightharpooncw (H) 46nrightleftarrows () 44nrightleftharpoons (X) 46nrightlsquigarrow ( ) 44nrightmapsto (() 44nrightModels (⊯) 34nrightmodels (⊭) 34nrightpitchfork () 47nrightrightarrows () 44nrightrsquigarrow (uml) 44nrightspoon (h) 47nrightsquigarrow ( ) 46nrightVdash (⊮) 34nrightvdash (⊬) 34nrisingdotseq () 34nRrightarrow (ocirc) 44

nsdtstile ( ) 35nSearrow () 44nsearrow () 44nsearrowtail () 45nsefilledspoon (w) 47

nsefootline () 34nsefree () 34nseharpoonccw (G) 46nseharpooncw (O) 46nselsquigarrow (sect) 45nsemapsto () 45nseModels (divide) 34nsemodels (ccedil) 34nsenwarrows () 45nsenwharpoons ([) 46nsepitchfork () 47nsersquigarrow (macr) 45nsesearrows () 45nsespoon (o) 47nseVdash (iuml) 34nsevdash (szlig) 34nshortmid () 31nshortmid (∤) 34nshortparallel () 31nshortparallel (∦) 34nsim () 32nsim () 31nsim (≁) 34nsimeq () 32nsimeq () 31nsimeq (≄) 34nsmile () 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) 37nsqsubset (ETH) 37nsqsubseteq () 37nsqsubseteq () 37nsqsubseteq (⋢) 37nsqsubseteqq () 37nsqsubseteqq (Ocirc) 37nSqsupset (times) 37nsqSupset () 37nsqsupset () 37nsqsupset (b) 37nsqsupset (Ntilde) 37nsqsupseteq () 37nsqsupseteq (A) 37nsqsupseteq (⋣) 37

146

nsqsupseteqq () 37nsqsupseteqq (Otilde) 37nsqtriplefrown (sect) 48nsqtriplesmile (brvbar) 48nsquigarrowdownup (sup3) 45nsquigarrowleftright (deg) 45nsquigarrownesw (acute) 45nsquigarrownwse (micro) 45nsquigarrowrightleft (sup2) 45nsquigarrowsenw (middot) 45nsquigarrowswne (para) 45nsquigarrowupdown (plusmn) 45

nsststile ( ) 35

nststile ( ) 35

nsttstile ( ) 35nSubset () 37nSubset (gt) 37nSubset (THORN) 37nsubset () 37nsubset (nsub) 37nsubseteq () 37

nsubseteq () 36

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

nsucceq () 31

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

nsupseteq (+) 36

nsupseteq (⊉) 37nsupseteqq () 37nsupseteqq () 36nsupseteqq (Yacute) 37nSwarrow () 45nswarrow () 45nswarrowtail (amp) 45nswfilledspoon (v) 47nswfootline (~) 33nswfree () 33nswharpoonccw (F) 46nswharpooncw (N) 46

nswlsquigarrow (brvbar) 45nswmapsto () 45nswModels (ouml) 34nswmodels (aelig) 34nswnearrows () 45nswneharpoons (^) 46nswpitchfork () 47nswrsquigarrow (reg) 45nswspoon (n) 47nswswarrows () 45nswVdash (icirc) 34nswvdash (THORN) 34

ntdtstile ( ) 35

ntheorem (package) 65nthickapprox (5) 31nto (↛) 46ntriangleeq (acute) 40ntriangleleft () 40ntriangleleft (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 (~) 34ntriplesmile () 48

ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35

ntwoheaddownarrow () 45ntwoheadleftarrow (h) 31ntwoheadleftarrow () 45ntwoheadnearrow () 45ntwoheadnwarrow () 45ntwoheadrightarrow (g) 31ntwoheadrightarrow () 45ntwoheadsearrow () 45ntwoheadswarrow () 45ntwoheaduparrow () 45nu (ν) 50nuclear power plant see SNPP

NUL () 72null infinity see alphabets mathnull set 65 66number sets see alphabets mathnumber sign see textnumero

numbers see digitscircled 77 94

numeralsLinear B 85old style 20

NumLock ( Num ) 72

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

46nupdownharpoonrightleft (U)

46nupdownharpoons (Y) 46nUpdownline (∦) 34nupdownline (∤) 34nupfilledspoon (q) 47nupfootline (y) 34nupfree () 34nupharpoonccw (A) 46nupharpooncw (I) 46nuplsquigarrow (iexcl) 45nupmapsto ()) 45nupModels (ntilde) 34nupmodels (aacute) 34nuppitchfork () 47nuprsquigarrow (copy) 45nupspoon (i) 47nupuparrows () 45nupVdash (eacute) 34nupvdash (Ugrave) 34nuup (ν) 50nvargeq (laquo) 38nvarleq (ordf) 38nvarparallel () 31nvarparallelinv () 31nVDash () 32nVDash (3) 31nVDash (⊯) 34nVdash () 32nVdash (1) 31nVdash (⊮) 34nvDash () 32nvDash (2) 31nvDash (⊭) 34nvdash (amp) 32nvdash (0) 31nvdash (⊬) 34nVvash () 32Nwarrow (v) 42Nwarrow () 43nwarrow (Ocirc) 42nwarrow () 41 106nwarrow () 43nwarrowtail () 43nwfilledspoon (u) 47nwfootline () 32nwfree () 32nwharpoonccw (E) 46nwharpooncw (M) 46nwlsquigarrow (yen) 43nwmapsto (-) 43nwModels (otilde) 32nwmodels (aring) 32nwnwarrows () 43nwpitchfork () 47

147

nwrsquigarrow (shy) 43Nwsearrow () 43nwsearrow () 106nwsearrow (⤢) 43nwsearrows () 43nwsebipropto () 24nwsecrossing () 32nwseharpoonnesw (S) 46nwseharpoons (_) 46nwseharpoonswne (W) 46Nwseline (times) 32nwseline (Oacute) 32nwspoon (m) 47nwVdash (iacute) 32nwvdash (Yacute) 32

OO (Oslash) 10o (oslash) 10o (o) 50oast (⊛) 25oasterisk (f) 25obackslash (n) 25obackslash (⦸) 25obar () 22Obelus ( ) 95obelus ( ) 95Obelus ( middotmiddot ) 95obelus ( middotmiddot ) 95oblong () 22obot (k) 25obslash () 22oc () 21ocirc (e) 25ocirc (⊚) 25ocircle () 23ocoasterisk (g) 25octagon (8) 78octonions (O) see alphabets

mathOctosteel (lsquo) 73od (a

˚) 16

odiv (c) 25odot (d) 25odot () 22odot (⊙) 25odplus () 24OE (Œ) 10 117oe (œ) 10 117officialeuro (e) 19offinterlineskip 104ogonek (package) 17 119 121ogonek ( ˛) see accentsogreaterthan (=) 22ohill ( a) 16ohm see textohm

ohm (Ω) 70

Ohne (a ) 89

OHORN (Ơ) 10ohorn (ơ) 10

oiiint ()

) 28

oiiint (

) 30

oiiintclockwise (L

) 28

oiiintctrclockwise (D

) 28

oiint (middot

) 27

oiint (

) 26 28

oiint (sbquo

) 28

oiint (

) 30

oiint (∯) 29

oiintclockwise (H

) 28

oiintctrclockwise (

) 28

oint (para) 27

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27

ointclockwise (ı) 28

ointclockwise () 30

ointctrclockwise (

) 27

ointctrclockwise () 28


old-style digits 20oldstylenums 20oleft (h) 25olessthan (lt) 22Omega (Ω) 50omega (ω) 50omegaup (ω) 50ominus (a) 25ominus () 22ominus (⊖) 25onlymove (F) 93oo () 95oo () 13ooalign 104 105open (z) 18open unit disk (D) see

alphabets mathopenJoin ([) 31openo (=) 13openo (c) 13openo (l) 13opentimes (]) 31operators

binary 22ndash25logical see logical operatorsset see set operatorsunary 21

oplus (`) 25oplus (oplus) 21 22 103oplus (oplus) 25opposbishops (o) 93opposition (W) 71optical scaling 109options see package optionsor see vee

OR gates 73

ORd () 73oright (i) 25

ORl () 73

OrnamentDiamondSolid (q) 80ornaments 78 80

ORr () 73orthogonal to see bot

ORu () 73oslash (m) 25oslash () 22oslash (⊘) 25ostar () 25otimes (b) 25otimes (otimes) 22otimes (otimes) 25otop (j) 25otriangle (d) 25 40otriangleup (o) 25ovals 80ovee (gt) 22overarc (a_) 17

overbrace (hkkikkj

) 60

overbrace (copy

) 60

overbrace (︷︸︸︷

) 60


) 59

overbracket ( ) 60

overbracket ( ) 108 109overbridge (

rdquoa) 16

overgroup (hkkkkj

) 60

overgroup (sup3micro

) 60overleftarrow (larrminus) 59overleftharp () 47overleftharpdown () 47

overleftharpoon (ETH) 60overleftrightarrow (larrrarr) 59overline ( ) 21 59

overlinesegment (zx) 60

overparenthesis (︷︷

) 108 109Overrightarrow (=rArr) 59overrightarrow (package) 59 119overrightarrow (minusrarr) 59overrightharp () 47overrightharpdown () 47

overrightharpoon (ETH) 60overring (x) 18overset 104overt (⦶) 25ovoid (l) 25owedge () 22owns see ni

owns (Q) 52owns (3) 52owns (ni) 52ownsbar (W) 52

PP (para) 9 116p (

˙) 95

p 107

148

package optionsa (esvect) 61b (esvect) 61bbgreekl (mathbbol) 68c (esvect) 61crescent (fge) 58d (esvect) 61e (esvect) 61f (esvect) 61g (esvect) 61german (keystroke) 72greek (babel) 50 87h (esvect) 61integrals (wasysym) 26mathcal (euscript) 68mathscr (euscript) 68nointegrals (wasysym) 26polutonikogreek (babel) 50sans (dsfont) 68utf8x (inputenc) 117varg (txfontspxfonts) 51

packageslongdiv 59accents 58 107 119 121amsbsy 113amsfonts 22 30 36 41 6568

amsmath 8 49 58 104 112amssymb 8 22 30 36 4158 65 68 87 119 120 123

amstext 105 106ar 70 119arcs 17 119 120arev 67 88 119 120ascii 72 115 119 120babel 50 87bbding 75ndash78 80 101 119120

bbm 68 119bbold 68 119bm 113 119 121braket 54calligra 68 119 121calrsfs 68cancel 59cclicenses 19 119 120centernot 105chancery 119chemarr 62 119 120chemarrow 47 62 119china2e 19 49 68 98 119121

clock 92 119 120cmll 21 24 30 36 119colonequals 21 36 119 120combelow 17 119 121cypriot 86 119 121dblaccnt 107dictsym 96 119 120dingbat 76 80 101 119 120DotArrow 63 119 121dozenal 65 119dsfont 68 119

epsdice 92 119 120esint 28 119esvect 61 119eufrak 68eurosym 19 119 120euscript 68 119 120extarrows 62 119 120extpfeil 63 119 120extraipa 16 119fc 10 14fclfont 119feyn 74 119 120fge 47 53 58 65 67 119120

fixmath 113fontenc 8 10 14 115fontspec 118fourier 19 36 51 53 57 6076 78 91 119

gensymb 70graphics 47 103graphicx 17 100 103harmony 89 119 120harpoon 47 119 121hhcount 92 119 121hieroglf 82 119 120holtpolt 63 119ifsym 70 79 91 92 101103 119 120

igo 94 119inputenc 117isoent 117junicode 118keystroke 72 119 120latexsym 22 30 36 41 65100 119

linearA 82 119 121linearb 85 86 119 121manfnt 89 119 120marvosym 18 65 67 71ndash7590 101

mathabx 21 23 25 2630 32 36ndash38 40 42 43 4952ndash55 58 60 65 66 71 93100 101 119 120 123

mathbbol 68mathcomp 65mathdesign 18 24 30 5256 67 119

mathdots 58 63 64 107119 120

mathrsfs 68 119mathtools 21 34 60 62119 120

mbboard 68 119metre 17 57 95 119 120milstd 73 119MnSymbol 2123ndash25 29 32ndash34 37 39 4043ndash48 51 52 55 58ndash60 6466 67 79 119 120

musixtex 89nath 53 56 57 119

nicefrac 67 119 121ntheorem 65ogonek 17 119 121overrightarrow 59 119phaistos 81 119 120phonetic 13 16 103 119pict2e 70pifont 10 75ndash78 80 103119 120

pigpen 98 119 120pmboxdraw 97 119 120polynom 59protosem 81 119 120psnfss 77pxfonts 21ndash23 27 30 3136ndash38 41 42 48 50ndash52 6566 68 100 115

recycle 99 119rotating 19 72sarabian 87 119 121savesym 100semtrans 14 17 119 120shuffle 24 119 120simplewick 109simpsons 96 119skak 93 94 119 120skull 93 119 120slashed 105staves 97 119steinmetz 70 119 121stmaryrd 22 26 31 3740 42 48 53 54 101 104118ndash120

t4phonet 14 17 119 120teubner 19 64 87 95 119120

textcomp 8 9 14 18ndash20 4157 67 70 88 100 115 119

timing 70tipa 11 12 14ndash17 103 119120

tipx 12 119 120trfsigns 36 52 63 119trsym 36 119 120turnstile 35 119 120txfonts 21ndash2327 30 31 36ndash38 41 42 4850ndash52 65 66 68 100 102115 119 120

type1cm 100ucs 117 118ulsy 24 48 103 119underscore 9undertilde 61 119 120units 67universa 80 90 119 120universal 75 77 80 90 119120

upgreek 51 119 120upquote 115url 115ushort 61 119 121vietnam 119

149

vntex 10 14wasysym 13 18 2022 23 26 30 31 36ndash38 4164ndash66 70 71 73 77 78 88101 119 120

wsuipa 13 16 18 101 103107 119 120

xfrac 67yfonts 68 69 119 120yhmath 58 59 61 64 107119

Pakin Scott 1 108 118PaperLandscape () 92

PaperPortrait () 92par see bindnasrepma invamp

and parr

paragraph mark see P

parallel () 30 56parallel (∥) 33ParallelPort (Ntilde) 72parallelslant (Euml) 36parr (`) 24partial (B) 52partial (part) 51partial (part) 53partialslash (C) 52partialvardint (q) 67partialvardlanddownint (⨚) 67partialvardlandupint (⨙) 67partialvardlcircleleftint

(∲) 43partialvardlcircleleftint

(∲) 67partialvardlcirclerightint


(∲) 67partialvardoiint (∯) 67partialvardoint (∮) 67partialvardrcircleleftint

(∳) 43partialvardrcircleleftint

(∳) 67partialvardrcirclerightint


(∳) 67partialvardstrokedint (⨏) 67partialvardsumint (⨋) 67partialvartint (p) 67partialvartlanddownint (⨚) 67partialvartlandupint (⨙) 67partialvartlcircleleftint

(∲) 43partialvartlcircleleftint

(∲) 67partialvartlcirclerightint


(∲) 67partialvartoiint (∯) 67partialvartoint (∮) 67

partialvartrcircleleftint

(∳) 43partialvartrcircleleftint

(∳) 67partialvartrcirclerightint


(∳) 67partialvartstrokedint (⨏) 67partialvartsumint (⨋) 67particle-physics symbols 74parts per thousand see

textperthousand

partvoice (andash raquo) 16partvoiceless (andash raquo) 16

passedpawn (r) 93pawn 94pdfLATEX 118Peace () 80

PencilLeft () 76

PencilLeftDown () 76

PencilLeftUp () 76

PencilRight () 76

PencilRightDown () 76

PencilRightUp () 76pencils 76pentagon (D) 78pentagram () 25pentam (λθλθλ||λββλββλ)

95people see facespercent sign see

permil (h) 20Perp (y) 31perp (perp) 30 106perp (perp) 33perthousand (permil) 70Pfund (pound) 18PgDown ( Page darr ) 72

PgUp ( Page uarr ) 72

phaistos (package) 81 119 120Phaistos disk 81pharmaceutical prescription see

textrecipe

PHarrow (J) 81phase ( ) 70phasor 70

PHbee (h) 81

PHbeehive (X) 81

PHboomerang (R) 81

PHbow (K) 81

PHbullLeg (b) 81

PHcaptive (D) 81

PHcarpentryPlane (S) 81

PHcat (c) 81

PHchild (E) 81

PHclub (M) 81

PHcolumn (W) 81

PHcomb (U) 81

PHdolium (T) 81

PHdove (f) 81

PHeagle (e) 81

PHflute (o) 81

PHgaunlet (H) 81

PHgrater (p) 81

PHhelmet (G) 81

PHhide (a) 81

PHhorn (Z) 81

Phi (Φ) 50

phi (φ) 50

phiup (φ) 50

PHlid (Q) 81

PHlily (m) 81

PHmanacles (N) 81

PHmattock (O) 81

Phone () 80

phone () 88

PhoneHandset () 80

phonetic (package) 13 16 103119

phonetic symbols 11ndash14

photon () 70

photons 74

PHoxBack (n) 81

PHpapyrus (k) 81

PHpedestrian (A) 81

PHplaneTree (i) 81

PHplumedHead (B) 81

PHram (d) 81

PHrosette (l) 81

PHsaw (P) 81

PHshield (L) 81

PHship (Y) 81

PHsling (V) 81

PHsmallAxe (r) 81

PHstrainer (q) 81

PHtattooedHead (C) 81

150

PHtiara (I) 81PHtunny (g) 81

PHvine (j) 81

PHwavyBand (s) 81

PHwoman (F) 81physical symbols 70Pi (Π) 50pi (π) 50pi (π) 51Pickup (A) 73pict2e (package) 70pifont (package) 10 75ndash78 80

103 119 120pigpen (package) 98 119 120pigpen cipher 98

pigpenfont A (A) 98

pigpenfont B (B) 98

pigpenfont C (C) 98

pigpenfont D (D) 98

pigpenfont E (E) 98

pigpenfont F (F) 98

pigpenfont G (G) 98

pigpenfont H (H) 98

pigpenfont I (I) 98

pigpenfont J (J) 98

pigpenfont K (K) 98

pigpenfont L (L) 98

pigpenfont M (M) 98

pigpenfont N (N) 98

pigpenfont O (O) 98

pigpenfont P (P) 98

pigpenfont Q (Q) 98

pigpenfont R (R) 98

pigpenfont S (S) 98

pigpenfont T (T) 98

pigpenfont U (U) 98

pigpenfont V (V) 98

pigpenfont W (W) 98

pigpenfont X (X) 98

pigpenfont Y (Y) 98

pigpenfont Z (Z) 98pilcrow see P

pipe see textpipe

Pisces (euml) 71pisces (f) 71Pisymbol 103pitchfork (amp) 66pitchfork (t) 30pitchfork (⋔) 47pitchfork symbols 30 47 66Pitmanrsquos base-12 symbols 65piup (π) 50planck ( h) 13

Plane () 80

planets 71playing cards see card suitsPlimsoll line 104

Plus () 76plus (+) 24plus-or-minus sign see pm

PlusCenterOpen (() 76pluscirc () 23

PlusOutline (amp) 76plusses 76 77

PlusThinCenterOpen ()) 76Pluto (I) 71Pluto (Eacute) 71pluto () 71pm (plusmn) 22pm (plusmn) 24pm (

macr) 95

pmb 113pmboxdraw (package) 97 119

120pmod 49pod 49pointer () 88pointing finger see fistsPointinghand (Z) 90polishhook (~) 18

polter ( ) 63

polutonikogreek (babel package op-tion) 50

polygons 78 79polynom (package) 59polynomial division 59polytonic Greek 50

Postbox () 98PostScript 51 69 75 103 112PostScript fonts 75 103

Pound (thorn) 19pounds (pound) 9 115 116power set see alphabets mathpowerset (weierp) 52Pp (˙) 95pp ( ˙ ) 95ppm (

macr) 95

Ppp (˙˙) 95

ppp ( ˙˙

) 95Pppp (˙

˙) 95

pppp ( ˙˙

) 95Ppppp (˙

˙) 95

ppppp ( ˙˙

) 95Pr (Pr) 49prec (≺) 30prec (≺) 32precapprox (AElig) 32precapprox (w) 30precapprox (⪷) 33preccurlyeq (curren) 32preccurlyeq (4) 30preccurlyeq (≼) 33precdot (Igrave) 32preceq () 30

preceq (⪯) 33preceqq () 31precnapprox (Ecirc) 32precnapprox () 31precnapprox (⪹) 34precneq (not) 32precneqq () 31precnsim (Auml) 32precnsim () 31precnsim (⋨) 34precsim (Agrave) 32precsim (-) 30precsim (≾) 33prescription see textrecipe

present-value symbols 108prime (prime) 65prime (prime) 66Printer (Ograve) 72printerrsquos fist see fistsprobabilistic independence 106prod (

prod) 25

prod (prod) 29projective space (P) see

alphabets mathprojlim (proj lim) 49pronunciation symbols see

phonetic symbolsproof end of 65proper subsetsuperset see

subsetneqsupsetneqproper vertices 74propto (9) 66propto (prop) 30propto (prop) 33proto-Semitic symbols 81protosem (package) 81 119 120ProvidesPackage 119PrtSc ( PrtSc ) 72

ps ( ) 95pseudographics 97Psi (Ψ) 50psi (ψ) 50psiup (ψ) 50psnfss (package) 77Pu (permil ) 89pullback diagrams 106pulse diagram symbols 70PulseHigh ($) 70PulseLow () 70punctuation 10pushout diagrams 106pwedge (U) 13pxfonts (package) 21ndash23 27 30

31 36ndash38 41 42 48 50ndash5265 66 68 100 115

Pxp (˙) 95pxp ( ˙ ) 95

QQED 65qoppa (ϟ) 87qside (M) 93Quadrad (]]) 57

151

quadrad (]]) 57Quadras ([[) 57quadras ([[) 57quarter note see musical symbolsquarternote () 88quarternote () 88quaternions (H) see alphabets

mathquaver see musical symbolsqueen 94quotedblbase (bdquo) 10 117quotesinglbase (sbquo) 10 117

RR (sim

) 95r (a) 14r (sim

) 95

Radiation () 92radicals see sqrt and surd

Radioactivity (j) 74

Rain () 91

RainCloud () 91raising see textraising

RaisingEdge ( ) 70Rangle (gt) 68rAngle (〉〉) 56rangle (〉) 21 54

rangle (⟩) 55

ranglebar (s) 55

RArrow ( rarr ) 72

rarrowfill 62ratio () 36

RATIONAL (frac12) 49

Rational (Ntilde) 49rational numbers (Q) see

alphabets mathrationalized Planck constant see

hbar

Rbag (Q) 53rbag (O) 53

rbrace (⎫⎪⎪⎬⎪⎪⎭

) 55Rbrack (]) 68rBrack (]]) 56rc (a) 16rCeil (ee) 56rceil (e) 54

rceil (⎤⎥⎥⎥⎥⎥⎥) 55

rcirclearrowdown (ucirc) 44rcirclearrowleft (⟲) 44rcirclearrowright (⤿) 44rcirclearrowup () 44

rcircleleftint (∳) 29

rcirclerightint (∳) 29rcorners (w) 53rcurvearrowdown (⤹) 44rcurvearrowleft () 44rcurvearrowne (Auml) 44

rcurvearrownw (Aring) 44rcurvearrowright (Agrave) 44rcurvearrowse (Ccedil) 44rcurvearrowsw (AElig) 44rcurvearrowup (Aacute) 44rdbrack (w) 55Re (lt) 51

REAL (frac34) 49

Real (Ograve) 49real numbers (R) see alphabets

mathrecipe see textrecipe

recorder () 88

Rectangle (u) 80

RectangleBold (v) 80rectangles 80

RectangleThin (t) 80Rectpipe (˜) 73Rectsteel (rdquo) 73recycle (package) 99 119

recycle (A) 99recycling symbols 98 99reduced quadrupole moment see

rqm

reflectbox 103registered trademark see

textregistered

relational symbols 30binary 30ndash32 34ndash39 47 48negated binary 31ndash33triangle 39 40

Relbar (=) 48 103Relbar (Ocirc) 33relbar (minus) 48 103relbar (ETH) 33

Request (gt) 98resizebox 47 100Respondens (sim) 95respondens (sim) 95

response ( ) 118restoresymbol 100restriction see

upharpoonright

restriction (aelig) 42restriction () 46retracting see textretracting

Return ( larr ) 72

return see carriage return

revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

revD () 13

revddots ( ) 107

reve () 13reveject (f) 13revepsilon () 13 103reverse solidus see

textbackslash

reversed symbols 103

reversedvideodbend () 89revglotstop (c) 13Rewind (para) 90RewindToIndex (acute) 90RewindToStart (micro) 90

rfilet (

) 55

rFloor (cc) 56rfloor (c) 54

rfloor (⎥⎥⎥⎥⎥⎥⎦) 55

rgroup (

) 54

rgroup (⎫⎪⎪⎪⎪⎪⎭) 55

RHD () 23rhd (B) 22 23rhd (⊳) 39 40rho (ρ) 50rho (ρ) 51rhookdownarrow () 44rhookleftarrow () 44rhooknearrow (⤤) 44rhooknwarrow (=) 44rhookrightarrow (8) 44rhooksearrow () 44rhookswarrow (⤦) 43rhookuparrow (9) 43rhoup (ρ) 50right 54 56 100 102rightangle (∟) 67RIGHTarrow () 88Rightarrow (rArr) 21 41Rightarrow (rArr) 43rightarrow (Ntilde) 42rightarrow (rarr) 41rightarrow (rarr) 43rightarrowtail () 41rightarrowtail (↣) 43rightarrowtriangle (_) 42rightbarharpoon (Yacute) 43RIGHTCIRCLE (H) 88RIGHTcircle (H) 88Rightcircle (J) 88

RightDiamond () 79

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

rightfilledspoon (p) 47rightfootline (x) 33rightfree () 33righthalfcap () 24righthalfcup () 24righthand (u) 76rightharpoonccw () 46rightharpooncw () 46rightharpoondown (atilde) 43rightharpoondown () 41rightharpoonup (aacute) 43rightharpoonup () 41rightleftarrows (Otilde) 42rightleftarrows () 41rightleftarrows () 43rightleftharpoon (aacute) 43

152

rightleftharpoons (eacute) 43rightleftharpoons () 41rightleftharpoons () 41rightleftharpoons () 46rightleftharpoonsfill 62rightlsquigarrow () 43rightmapsto (↦) 43rightModels (⊫) 33rightmodels (⊧) 33rightmoon (L) 71rightmoon () 71rightp (w) 18rightpitchfork () 47rightpointleft (L) 76

rightpointright (N) 76rightpropto () 33rightrightarrows (Ntilde) 42rightrightarrows (rArr) 41rightrightarrows () 43rightrightharpoons (Ugrave) 43rightrsquigarrow (uml) 43Rightscissors (Q) 75rightslice (3) 22rightslice (⪧) 33rightspoon (⊸) 47rightsquigarrow (ugrave) 42rightsquigarrow ( ) 41rightsquigarrow () 44rightt (o) 18righttherefore () 23 64rightthreetimes () 66rightthreetimes (i) 22rightthreetimes (⋌) 23rightthumbsdown (d) 76rightthumbsup (u) 76righttoleftarrow (yacute) 42Righttorque () 73rightturn () 88rightVdash (⊩) 33rightvdash (⊢) 33

rightwave (

ETH

ETH

ETH

ETH

) 56

rightY (() 23ring ( ) 58ring (a) see accentsring equal to see circeq

ring in equal to see eqcirc

riota () 13rip (O) 93risingdotseq () 32risingdotseq () 30risingdotseq (≓) 33rJoin (Y) 31rlap 79 106

rmoustache (

) 54

rmoustache (⎫⎪⎪⎪⎪⎪⎩) 55

Roman coins 19Romanian comma-belo accent (a)

see accentsrook 94

roots see sqrt

rotatebox 17 103rotated symbols 11ndash13 17 103rotating (package) 19 72rotm (m) 13rotOmega () 13rotr (r) 13rotvara (A) 13rotw (w) 13roty (y) 13RoundedLsteel (Ÿ) 73RoundedTsteel () 73RoundedTTsteel () 73Rparen ()) 68rqm ( -I) 105

rrangle (⟫) 55

rrbracket () 54

rrbracket (

) 57

rrceil (W) 53rrfloor (U) 53Rrightarrow (V) 42Rrightarrow () 43rrparenthesis (M) 53RS () 72

rsem (MQQQQQO) 55

rsemantic see rdbrack

Rsh (eacute) 42Rsh () 41Rsh () 43rtimes () 23rtimes (o) 22rtimes (⋊) 23rtriple 57rVert (||) 56rVert () 54rvert (|) 54

rwave (

ETH

ETH

ETH

ETH

) 56

rWavy (_______

) 55

rwavy (^^^) 55

SS (sect) 9 116SAa (a) 87SAb (b) 87SAd (d) 87SAdb (D) 87SAdd (B) 87SAf (f) 87safety-related symbols 74SAg (g) 87SAga (G) 87Sagittarius (egrave) 71sagittarius (c) 71SAh (h) 87SAhd (H) 87SAhu (I) 87

SAk (k) 87SAl (l) 87SAlq (lsquo) 87SAm (m) 87samebishops (s) 93Sampi (Ϡ) 87sampi (ϡ) 87SAn (n) 87sans (dsfont package option) 68SAo (o) 87SAq (q) 87SAr (r) 87sarabfamily 87sarabian (package) 87 119 121SAs (s) 87SAsa (X) 87SAsd (x) 87SAsv (S) 87SAt (t) 87SAtb (J) 87SAtd (T) 87

satellitedish (I) 80satisfies see models

Saturn (F) 71Saturn (AElig) 71saturn (Y) 71savesym (package) 100savesymbol 100SAw (w) 87SAy (y) 87SAz (z) 87SAzd (Z) 87Sborder (S) 80scalebox 100scaling

mechanical 109 112optical 109

scd () 13scg () 13schwa () 13schwa (e) 13Schwartz distribution spaces see

alphabets mathsci () 13scientific symbols 70ndash74

ScissorHollowLeft () 75

ScissorHollowRight () 75

ScissorLeft () 75

ScissorLeftBrokenBottom () 75

ScissorLeftBrokenTop () 75

ScissorRight () 75ScissorRightBrokenBottom

() 75

ScissorRightBrokenTop () 75scissors 75scn () 13scoh (˝) 36Scorpio (ccedil) 71scorpio (b) 71scr (J) 13

153

script letters see alphabets mathscripta () 13scriptg () 13scriptscriptstyle 105 106scriptstyle 105 106scriptv (Y) 13Scroll ( Scroll ) 72

scu (W) 13scy (]) 13

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35

seagull see textseagull

Searrow (u) 42Searrow () 43searrow (times) 42searrow () 41 106searrow () 43searrowtail () 43sec (sec) 49

Sech ( ˇ ldquo) ) 89

SechBL ( ˇ ldquo====

) 89

SechBl ( ˇ ldquo===

) 89

SechBR ( ˇ ldquo====) 89

SechBr ( ˇ ldquo===) 89

second (2) 66seconds angular see second

secstress (i) 18section mark see S

SectioningDiamond () 92sedenions (S) see alphabets

mathsefilledspoon (w) 47sefootline () 33sefree () 33segmented digits 70seharpoonccw (G) 46seharpooncw (O) 46selectfont 8selsquigarrow (sect) 43semantic valuation 54ndash57semapsto () 43semibreve see musical symbolssemidirect products 22 23 66semiquaver see musical symbolssemitic transliteration 14 17seModels (divide) 33semodels (ccedil) 33semtrans (package) 14 17 119

120senwarrows () 43senwharpoons ([) 46

SePa ( ) 89separated () 33sepitchfork () 47seppawns (q) 93SerialInterface (Icirc) 72SerialPort (ETH) 72

sersquigarrow (macr) 43sesearrows () 43sespoon (o) 47set operators


membership see in

union see cup

setminus () 22setminus (∖) 24seVdash (iuml) 32sevdash (szlig) 33SGML 117sha (X) 103sharp (]) 65 88sharp (♯) 66shfermion ( l) 74Shift ( Shift uArr ) 72

shift (˜) 21Shilling (iexcl) 18shneg (ˆ) 21shortcastling (O-O) 93shortdownarrow () 42ShortFifty (times) 90ShortForty (Ugrave) 90shortleftarrow () 42shortmid (p) 30shortmid (∣) 24ShortNinetyFive (Ocirc) 90shortparallel (q) 30shortparallel (∥) 32ShortPulseHigh () 70ShortPulseLow () 70shortrightarrow () 42ShortSixty (Ouml) 90ShortThirty (Ucirc) 90shortuparrow () 42showclock 91shpos (acute) 21shuffle (package) 24 119 120shuffle () 24shuffle product () 24SI () 72Sigma (Σ) 50sigma (σ) 50sigmaup (σ) 50sim (sim) 30 104 115sim (sim) 32simcolon (sim) 36simcoloncolon (sim) 36simeq () 30simeq (≃) 32simplewick (package) 109simpsons (package) 96 119Simpsons characters 96sin (sin) 49sincoh (ˇ) 36sinh (sinh) 49

SixFlowerAlternate (O) 78

SixFlowerAltPetal (U) 78

SixFlowerOpenCenter (M) 78

SixFlowerPetalDotted (Q) 78

SixFlowerPetalRemoved (L) 78SixFlowerRemovedOpenPetal

([) 78

SixStar (G) 78

SixteenStarLight (K) 78sixteenth note see musical

symbolssixteenthnote () 88skak (package) 93 94 119 120skull (package) 93 119 120

skull (A) 93slash () 115slashb () 13slashc () 13slashd () 13slashdiv () 23slashed (package) 105slashed 105slashed letters 105slashedsty (file) 105slashu (U) 13

Sleet () 91sliding (a) 16smallbosonloop ( |) 74smallbosonloopA ( ) 74smallbosonloopV ( ) 74

SmallCircle (E) 79

SmallCross () 79smalldiamond () 25

SmallDiamondshape (F) 79smallfrown (a) 30smallfrown () 48

SmallHBar () 79smallin () 52smallint (int) 66

SmallLowerDiamond () 79smalllozenge (loz) 79smallowns () 52smallpencil (P) 76smallprod (prod) 23

SmallRightDiamond (O) 79smallsetminus (r) 22smallsetminus (∖) 24smallsmile (`) 30smallsmile () 48

SmallSquare () 79smallsquare (◽) 25smallstar () 25

SmallTriangleDown (C) 79smalltriangledown () 25smalltriangledown () 25 40

SmallTriangleLeft (B) 79smalltriangleleft () 25smalltriangleleft () 25 40

SmallTriangleRight (D) 79smalltriangleright () 25smalltriangleright () 25 40

SmallTriangleUp (A) 79smalltriangleup () 25

154

smalltriangleup () 25 40

SmallVBar () 79smile (^) 30smile () 48smile symbols 48smileeq ( ) 48smileeqfrown (amp) 48smilefrown (≍) 48smilefrowneq (() 48Smiley (copy) 90smiley () 88smiley faces 72 88 90 98

sndtstile ( ) 35

Snow () 91

SnowCloud () 91

Snowflake (`) 78

SnowflakeChevron (^) 78

SnowflakeChevronBold (_) 78snowflakes 78

SNPP () 96

snststile ( ) 35

sntstile ( ) 35

snttstile ( ) 35SO () 72SOH () 72South Arabian alphabet 87space

thin 113visible seetextvisiblespace

Spacebar ( ) 72

spades (suit) 65ndash67 80spadesuit (spades) 65spadesuit (spades) 66

Sparkle (]) 78

SparkleBold () 78sparkles 78ldquospecialrdquo characters 9SpecialForty (Uacute) 90sphericalangle () 66sphericalangle (^) 66sphericalangle (∢) 66

SpinDown () 79

SpinUp ()) 79spirituslenis (andash) 58spirituslenis (mdash) 58splitvert (brvbar) 72spoon symbols 47spreadlips (a) 16sqbullet (13) 23sqcap ([) 23sqcap (u) 22sqcap (⊓) 23sqcapdot (E) 23sqcapplus () 23sqcapplus (G) 23sqcup () 23sqcup (t) 21 22sqcup (⊔) 23

sqcupdot (D) 24sqcupplus (|) 23sqcupplus (F) 24sqdoublecap (^) 23sqdoublecup (_) 23sqdoublefrown (-) 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

sqrt (radic

) 59 106sqsmile () 48sqsmileeq (2) 48sqsmileeqfrown (8) 48sqsmilefrown (0) 48Sqsubset (^) 37sqSubset () 37sqsubset () 37sqsubset () 36 37sqsubset (⊏) 37sqsubseteq () 37sqsubseteq (v) 36sqsubseteq (⊑) 37sqsubseteqq () 37sqsubseteqq () 37sqsubsetneq () 37sqsubsetneq (⋤) 37sqsubsetneqq () 37sqsubsetneqq (ouml) 37Sqsupset (_) 37sqSupset () 37sqsupset () 37sqsupset (A) 36 37sqsupset (⊐) 37sqsupseteq () 37sqsupseteq (w) 36sqsupseteq (⊒) 37sqsupseteqq () 37sqsupseteqq (]) 37sqsupsetneq () 37sqsupsetneq (⋥) 37sqsupsetneqq () 37sqsupsetneqq (divide) 37sqtriplefrown () 48sqtriplesmile () 48

Square (0) 79

Square ( vs f vs 0) 101Square () 77

Square (f) 80square () 23square () 66

square (◻) 25square root see sqrt

hooked see hksqrt

SquareCastShadowBottomRight

(k) 80

SquareCastShadowTopLeft (m) 80

SquareCastShadowTopRight

(l) 80Squaredot (divide) 67squaredots (∷) 24 64Squarepipe (mdash) 73squares 79ndash80 94

SquareShadowA () 79

SquareShadowB () 79

SquareShadowBottomRight (h) 80

SquareShadowC () 79

SquareShadowTopLeft (j) 80

SquareShadowTopRight (i) 80

SquareSolid (g) 80Squaresteel (ldquo) 73

squarewithdots (B) 80squigarrowdownup (sup3) 43squigarrowleftright () 43squigarrownesw (acute) 43squigarrownwse (micro) 43squigarrowrightleft (sup2) 43squigarrowsenw (middot) 43squigarrowswne (para) 43squigarrowupdown (plusmn) 43squplus (]) 23SS (SS) 10ss (szlig) 10

ssdtstile ( ) 35ssearrow () 42sslash () 22

ssststile ( ) 35

sststile ( ) 35

ssttstile ( ) 35sswarrow ($) 42stackrel 21 104 108standard state 104star () 22 107star (⋆) 25Star of David 77 78starredbullet (d) 78stars 66 77ndash79stater (῝) 19statistical independence 106

staveI () 97

staveII () 97

staveIII () 97

staveIV () 97

staveIX () 97

staveL (1) 97 98

155

staveLI (2) 97

staveLII (3) 97

staveLIII (4) 97

staveLIV (5) 97

staveLIX () 98

staveLV (6) 97

staveLVI (7) 97

staveLVII (8) 97

staveLVIII (9) 98staveLX () 98

staveLXI (lt) 98

staveLXII (=) 98

staveLXIII (gt) 98

staveLXIV () 98

staveLXV () 98

staveLXVI (A) 98

staveLXVII (B) 98

staveLXVIII (C) 98staves 97staves (package) 97 119

staveV () 97

staveVI () 97

staveVII () 97

staveVIII () 97

staveX () 97

staveXI () 97

staveXII () 98

staveXIII () 98

staveXIV (13) 98staveXIX () 98

staveXL () 98

staveXLI (() 98

staveXLII ()) 98

staveXLIII () 98staveXLIV (+) 98

staveXLIX (0) 97

staveXLV () 98

staveXLVI (-) 98

staveXLVII () 97

staveXLVIII () 97

staveXV () 98

staveXVI () 98

staveXVII () 98

staveXVIII () 98

staveXX () 98staveXXI () 98

staveXXII () 98

staveXXIII () 98

staveXXIV () 97

staveXXIX () 97

staveXXV () 97

staveXXVI () 97

staveXXVII () 97

staveXXVIII () 97

staveXXX () 97

staveXXXI () 97

staveXXXII () 97

staveXXXIII ( ) 97

staveXXXIV () 97

staveXXXIX (amp) 98

staveXXXV () 98

staveXXXVI () 98staveXXXVII ($) 98staveXXXVIII () 98

stdtstile ( ) 35

steaming () 67steinmetz (package) 70 119 121Steinmetz phasor notation 70sterling see pounds

stick figures 81Stigma (Ϛ) 87stigma (ϛ) 87stmaryrd (package) 22 26 31 37

40 42 48 53 54 101 104118ndash120

stochastic independence see bot

StoneMan () 91Stopsign () 74

StopWatchEnd () 91

StopWatchStart () 91stress (h) 18strictfi (K) 31strictif (J) 31strictiff (L) 31

strokedint (⨏) 29

StrokeFive () 92

StrokeFour () 92

StrokeOne () 92

StrokeThree () 92

StrokeTwo () 92stst (minus ) 104

stststile ( ) 35

sttstile ( ) 35

stttstile ( ) 35

STX () 72SUB () 72subatomic particles 74subcorner (a

^) 16

subdoublebar (amacr) 16

subdoublevert (a) 16

sublptr (aiexcl) 16

subrptr (aiquest) 16

subscriptsnew symbols used in 105

Subset () 37Subset (b) 36Subset (⋐) 37subset () 37subset (sub) 36subset (sub) 37subseteq () 37subseteq (sube) 36subseteq (sube) 37subseteqq () 37subseteqq (j) 36subseteqq (⫅) 37subsetneq () 37subsetneq (() 36subsetneq (⊊) 37subsetneqq () 37

subsetneqq ($) 36subsetneqq (⫋) 37subsetplus (D) 37subsetpluseq (F) 37subsets 36 37succ () 30succ (≻) 32succapprox (Ccedil) 32succapprox (v) 30succapprox (⪸) 32succcurlyeq (yen) 32succcurlyeq (lt) 30succcurlyeq (≽) 32succdot (Iacute) 32succeq () 30succeq (⪰) 32succeqq () 31succnapprox (Euml) 32succnapprox () 31succnapprox (⪺) 34succneq (shy) 32succneqq () 31succnsim (Aring) 32succnsim () 31succnsim (⋩) 34succsim (Aacute) 32succsim () 30

156

succsim (≿) 32such that 103 105suchthat (3minusminus) 105sum (

sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 91

SummitSign () 91Sun () 71

Sun (Agrave vs vs ) 101

Sun () 91Sun (Agrave) 71sun () 88

SunCloud () 91

SunshineOpenCircled (T) 80sup (sup) 49superscripts

new symbols used in 105supersets 36 37supremum see sup

Supset () 37Supset (c) 36Supset (⋑) 37supset () 37supset (sup) 36supset (sup) 37supseteq () 37supseteq (supe) 36supseteq (supe) 37supseteqq () 37supseteqq (k) 36supseteqq (⫆) 37supsetneq () 37supsetneq ()) 36supsetneq (⊋) 37supsetneqq () 37

supsetneqq () 36supsetneqq (⫌) 37supsetplus (E) 37supsetpluseq (G) 37surd (

`) 65

SurveySign () 91Swarrow (w) 42Swarrow () 43swarrow (Ouml) 42swarrow () 41 106 107swarrow () 43swarrowtail (amp) 43swfilledspoon (v) 47swfootline (~) 32swfree () 33swharpoonccw (F) 46swharpooncw (N) 46swlsquigarrow (brvbar) 43swmapsto () 43swModels (ouml) 33swmodels (aelig) 33swnearrows () 43swneharpoons (^) 46swords 91swpitchfork () 47

swrsquigarrow (reg) 43swspoon (n) 47swswarrows () 43swung dash see sim

swVdash (icirc) 33swvdash (THORN) 33syl (a) 16syllabic (j) 18

symA (Aacute) 68

symAE (Ucirc) 68

symB (Acirc) 68symbishop (B) 94Symbol (font) 51 103symbols

actuarial 108alpine 91ancient language 81ndash87annuity 108APL 71astrological 71astronomical 71 98biological 74block-element 97body-text 9ndash20bold 113box-drawing 97chess 93 94cipher 98clock 88 90ndash92communication 73computer hardware 72contradiction 21 48currency 18 19 68dangerous bend 89definition 21 108dictionary 11ndash14 96dingbat 75ndash80dot 9 63 64 107electrical 70engineering 70 73extensible 47 59ndash63 70102 107ndash109

Feynman diagram 74Frege logic 47 53 65 67frown 48gates digital logic 73genealogical 88general 88Go stones 94information 90informator 93inverted 11ndash13 17 103keyboard 72Knuthrsquos 89laundry 90legal 9 19 116letter-like 51ndash53life insurance 108linear logic 21ndash23 2529ndash30 36 51 52

linguistic 11ndash14log-like 49 113

logic 73magical signs 97mathematical 21ndash69METAFONTbook 89metrical 95miscellaneous 65ndash67 8088ndash99

monetary 18 19 68musical 20 65 66 88 89navigation 90non-commutative division 63particle physics 74Phaistos disk 81phonetic 11ndash14physical 70pitchfork 30 47 66Pitmanrsquos base-12 65present value 108proto-Semitic 81pulse diagram 70recycling 98 99relational 30reversed 103rotated 11ndash13 17 103safety-related 74scientific 70ndash74Simpsons characters 96smile 48spoon 47staves 97subset and superset 36 37technological 70ndash74TEXbook 89transliteration 14upside-down 11ndash13 17 103114

variable-sized 25ndash30 100102

weather 91zodiacal 71

symbolstex (file) 100 119

symC (Atilde) 68symking (K) 94symknight (N) 94

symOE (Uuml) 68sympawn (p) 94symqueen (Q) 94symrook (R) 94

symUE (Yacute) 68SYN () 72

TT 10T ( a) 17T (otimes

) 95t ( a) 14t (otimes

) 95t4phonet (package) 14 17 119

120Tab ( minusminusrarrminusminusrarr ) 72

tabcolsep 104tacks 30 51

157

taild () 13tailinvr (H) 13taill (0) 13tailn (9) 13tailr (F) 13tails (L) 13tailt (P) 13tailz (_) 13Takt 89talloblong (8) 22tally markers 85 92tan (tan) 49tanh (tanh) 49

Tape () 80

Taschenuhr () 91Tate-Shafarevich group see shatau (τ) 50Taurus (Q) 71Taurus (aacute) 71taurus (]) 71tautology see top

tauup (τ) 50tccentigrade () 65tcmu (micro) 65tcohm (Ω) 65tcpertenthousand () 65tcperthousand (permil) 65td (a) 16

tddtstile ( ) 35

tdststile ( ) 35

tdtstile ( ) 35

tdttstile ( ) 35

technological symbols 70ndash74Telefon (T) 73

Telephone (() 92

Telephone () 98Tennent Bob 21

Tent () 91Terminus (otimes) 95terminus (otimes) 95Terminus (oplus) 95terminus (oplus) 95tesh (Q) 13testfontdvi (file) 111testfonttex (file) 111 112tetartemorion (Β) 19teubner (package) 19 64 87 95

119 120TEX 40 47 64 70 97 100

103ndash109 111ndash113 115 117118 122

TEXbook The 103ndash107 109 112symbols from 89

text 21 105 106textacutedbl (˝) 18textacutemacron (acutea) 15textacutewedge (acutea) 15textadvancing (affi) 15textaolig () 12textasciiacute (acute) 18 116

textasciibreve (˘) 18textasciicaron (ˇ) 18textasciicircum (ˆ) 9 115

117textasciidieresis (uml) 18 116textasciigrave (`) 18textasciimacron 115textasciimacron (macr) 18 116textasciitilde (˜) 9 115 117textasteriskcentered (lowast) 9

20textbabygamma (Egrave) 11textbackslash () 9 114 115textbaht (฿) 18textbar (|) 9 114textbarb (b) 11textbarc (c) 11textbard (d) 11textbardbl () 20textbardotlessj (eacute) 11textbarg (g) 11textbarglotstop (Uuml) 11textbari (1) 11textbarl (ł) 11textbaro (8) 11textbarrevglotstop (Yacute) 11textbaru (0) 11textbeltl (igrave) 11textbenttailyogh (B) 12textbeta (B) 11textbigcircle () 20textbktailgamma () 12textblank () 20textblock ( ) 97textborn (b) 88textbottomtiebar (alt) 15

textbraceleft () 9textbraceright () 9textbrevemacron (˘a) 15textbrokenbar (brvbar) 20 116textbullet (bull) 9 20 117textbullseye (ograve) 11textcelsius () 70 117textceltpal ( ) 11textcent (cent) 18 116textcentoldstyle () 18

textchi () 11textcircled (copy) 14textcircledP () 19textcircumacute (Ża) 15textcircumdot (â) 15textcloseepsilon (Aring) 11textcloseomega (Ntilde) 11textcloserevepsilon (AElig) 11textcolonmonetary (₡) 18textcommatailz (THORN) 11textcomp (package) 8

9 14 18ndash20 41 57 67 7088 100 115 119

textcopyleft (laquo) 19textcopyright (copy) 9 19 116textcorner (^) 11

textcrb (ă) 11textcrd (ą) 11textcrd () 14textcrg (g) 11textcrh (egrave) 11textcrh (sect) 14textcrinvglotstop (Ucirc) 11textcrlambda (ň) 11textcrtwo (2) 11textctc (C) 11textctd (ć) 11textctdctzlig (ćyacute) 11textctesh (š) 11textctinvglotstop (D) 12textctj (J) 11textctjvar (2) 12textctn (ő) 11textctstretchc () 12textctstretchcvar (amp) 12textctt (ť) 11textcttctclig (ťC) 11textctturnt () 12textctyogh (yuml) 11textctz (yacute) 11textcurrency (curren) 18 116textcypr 86textdagger (dagger) 9 20textdaggerdbl (Dagger) 9 20

textdbend (

) 89textdblhyphen (-) 20textdblhyphenchar () 20textdblig ()) 12textdctzlig (dyacute) 11textdegree (deg) 67 116textdied (d) 88textdiscount () 20textdiv (divide) 67textdivorced (c) 88textdkshade ( ) 97textdnblock ( ) 97textdollar ($) 9 18textdollaroldstyle () 18textdong (₫) 18textdotacute (secta) 15textdotbreve ( ˙a) 15textdoublebaresh (S) 11textdoublebarpipe () 11textdoublebarpipevar (H) 12textdoublebarslash (= ) 11textdoublegrave (sbquoa) 15textdoublegrave (a) 17textdoublepipe () 11textdoublepipevar (G) 12textdoublevbaraccent (İa) 15textdoublevbaraccent (frac14a) 17textdoublevertline (Ş) 11textdownarrow (darr) 41textdownfullarrow (ˇ) 12textdownstep (Ť) 11textdyoghlig (Atilde) 11textdzlig (dz) 11texteightoldstyle () 20

158

textellipsis ( ) 9textemdash (mdash) 9textendash (ndash) 9textepsilon (E) 11textepsilon (cent) 14textesh (S) 12textesh (not) 14textestimated () 20texteuro (euro) 19texteuro (euro) 18texteuro (euro) 18 115 117textexclamdown (iexcl) 9textfemale (7) 12textfishhookr (R) 12textfiveoldstyle () 20textfjlig () 14textflorin (ƒ) 18textfouroldstyle () 20textfractionsolidus (frasl) 67textfrak 68textfrbarn (5) 12textfrhookd (rsquo) 12textfrhookdvar (() 12textfrhookt () 12textfrtailgamma (-) 12textg (ě) 12textgamma (G) 12textglobfall (Ů) 12textglobrise (Ű) 12textglotstop (P) 11textglotstopvari (T) 12textglotstopvarii (U) 12textglotstopvariii (V) 12textgoth 68textgravecircum (Ža) 15textgravedbl () 18textgravedot (đa) 15textgravemacron (à) 15textgravemid (Źa) 15textgreater (gt) 9 114textgrgamma () 12textguarani () 18texthalflength () 11texthardsign (ż) 11textheng (0) 12texthmlig (4) 12texthooktop () 11texthtb (aacute) 11texthtb ( ) 14texthtbardotlessj (ecirc) 11texthtbardotlessjvar (3) 12texthtc (Aacute) 11texthtc (deg) 14texthtd (acirc) 11texthtd (iexcl) 14texthtg (auml) 11texthth (H) 11texththeng (Ecirc) 11texthtk (Icirc) 11texthtk (uml) 14texthtp (Ograve) 11texthtp (plusmn) 14texthtq (Oacute) 11

texthtrtaild (č) 11texthtscg (Eacute) 11texthtt (Ouml) 11texthtt (ordm) 14texthvlig (szlig) 11textifsym 70textinterrobang () 20textinterrobangdown () 20textinvglotstop (Ucirc) 11textinvomega () 12textinvsca (p) 12textinvscr (K) 11textinvscripta () 12textinvsubbridge (abdquo) 15textiota (Igrave) 11textiota (agrave) 14textlambda (ń) 11textlangle (lang) 57 114textlbrackdbl (〚) 57textleaf (l) 88textleftarrow (larr) 41textlengthmark () 11textless (lt) 9 114textlfblock ( ) 97textlfishhookrlig (I) 12

textlhdbend (~

) 89textlhookfour () 12textlhookp (lt) 12textlhookt (ş) 11textlhti (1) 12textlhtlongi (ę) 11textlhtlongy (ű) 11textlinb 85 86textlira (₤) 18textlnot (not) 67 116textlonglegr (Ocirc) 11textlooptoprevesh (gt) 12textlowering (afl) 15textlptr (iexcl) 11textlquill (⁅) 57textltailm (M) 11textltailn (ntilde) 11textltailn (copy) 14textltilde (euml) 11textltshade ( ) 97textlyoghlig (ETH) 11textmarried (m) 88textmho () 70textmidacute (Ÿa) 15textminus (minus) 67textmu (micro) 70 116textmusicalnote () 20textnaira (₦) 18textnineoldstyle () 20textnrleg (6) 12textnumero () 20textObardotlessj (Iacute) 11textObullseye (9) 12textohm (Ω) 70textOlyoghlig (ŋ) 11textomega (ř) 11textonehalf (frac12) 67 116

textoneoldstyle 20textoneoldstyle () 20textonequarter (frac14) 67 116textonesuperior (sup1) 67 116textopenbullet () 20textopencorner (_) 11textopeno (O) 11textopeno (ordf) 14textordfeminine (ordf) 9 20 116textordmasculine (ordm) 9 20

116textovercross (permila) 15textoverw (

mdasha) 15

textpalhook () 11textpalhooklong (ˆ) 12textpalhookvar (˜) 12textparagraph (para) 9 20textperiodcentered (middot) 9 20

116textpertenthousand () 20textperthousand (permil) 20 117textpeso () 18textphi (F) 11textpilcrow (para) 20textpipe (|) 11textpipe (|) 14textpipevar (F) 12textpm (plusmn) 67 116textpmhg 82textpolhook (a) 15textprimstress () 11textproto 81textqplig (=) 12textquestiondown (iquest) 9textquotedbl () 10 114textquotedblleft (ldquo) 9textquotedblright (rdquo) 9textquoteleft (lsquo) 9textquoteright (rsquo) 9textquotesingle () 20 114textquotestraightbase (sbquo) 20textquotestraightdblbase (bdquo)

20textraiseglotstop (ĳ) 11textraisevibyi (ğ) 11textraising (afi) 15textramshorns (7) 11textrangle (rang) 57 114textrbrackdbl (〛) 57textrecipe () 20 102textrectangle (uml) 12textreferencemark () 20 21textregistered (reg) 9 19 116textretracting (affl) 15textretractingvar (˚) 12textrevapostrophe () 11textreve (9) 11textrevepsilon (3) 11 103

textreversedvideodbend (

) 89

textrevglotstop (Q) 11textrevscl (v) 12

159

textrevscr (z) 12textrevyogh (ź) 11textrhooka ( ) 12textrhooke () 12textrhookepsilon (+) 12textrhookopeno () 12textrhookrevepsilon (Ccedil) 12textrhookschwa (Auml) 12textrhoticity (~) 12textrightarrow (rarr) 41textringmacron (a) 15textroundcap (ldquoa) 15textrptr (iquest) 12textrquill (⁆) 57textrtaild (atilde) 12textrtaild (eth) 14textrtailhth () 12textrtaill (iacute) 12textrtailn (iuml) 11textrtailr (oacute) 11textrtails (ugrave) 11textrtailt (uacute) 11textrtailt (raquo) 14textrtailz (uuml) 11textrtblock ( ) 97textrthook ($) 11textrthooklong (acute) 12textsarab 87textsca (Agrave) 11textscaolig (q) 12textscb (agrave) 11textscdelta (r) 12textsce (ď) 11textscf (s) 12textscg (aring) 11textsch (Euml) 11textschwa () 11textschwa (iexcl) 14textsci (I) 11textscj (ĺ) 11textsck (t) 12textscl (Iuml) 11textscm (w) 12textscn (eth) 11textscoelig (Œ) 11textscomega (ś) 11textscp (x) 12textscq (y) 12textscr (ouml) 11textscripta (A) 11textscriptg (g) 11textscriptv (V) 11textscriptv (not) 14textscu (Uacute) 11textscy (Y) 11textseagull (a) 15textsecstress (shy) 11textsection (sect) 9 20textservicemark () 19textsevenoldstyle () 20textSFi ( ) 97textSFii ( ) 97textSFiii ( ) 97

textSFiv ( ) 97textSFix ( ) 97textSFl ( ) 97textSFli ( ) 97textSFlii ( ) 97textSFliii ( ) 97textSFliv ( ) 97textSFv ( ) 97textSFvi ( ) 97textSFvii ( ) 97textSFviii ( ) 97textSFx ( ) 97textSFxi ( ) 97textSFxix ( ) 97textSFxl ( ) 97textSFxli ( ) 97textSFxlii ( ) 97textSFxliii ( ) 97textSFxliv ( ) 97textSFxlix ( ) 97textSFxlv ( ) 97textSFxlvi ( ) 97textSFxlvii ( ) 97textSFxlviii ( ) 97textSFxx ( ) 97textSFxxi ( ) 97textSFxxii ( ) 97textSFxxiii ( ) 97textSFxxiv ( ) 97textSFxxv ( ) 97textSFxxvi ( ) 97textSFxxvii ( ) 97textSFxxviii ( ) 97textSFxxxix ( ) 97textSFxxxvi ( ) 97textSFxxxvii ( ) 97textSFxxxviii ( ) 97textshade ( ) 97textsixoldstyle () 20textsoftsign (ž) 11textspleftarrow (˝) 12textsterling (pound) 9 18textstretchc (Acirc) 11textstretchcvar ($) 12textstyle 105 106 113textsubacute (a

rsaquo) 15

textsubarch (aldquo) 15

textsubbar (amacr) 15

textsubbridge (ardquo) 15textsubcircum (a

ˆ) 15

textsubdot (a˙) 15

textsubdoublearrow (˙) 12textsubgrave (a

lsaquo) 15

textsublhalfring (andash) 15textsubplus (aff) 15textsubrhalfring (araquo) 15textsubrightarrow (macr) 12textsubring (a

˚) 15

textsubsquare (alaquo) 15textsubtilde (a

˜) 15

textsubumlaut (auml) 15

textsubw (amdash) 16textsubwedge (a

ˇ) 16

textsuperimposetilde (aamp) 16

textsuperscript 16textsurd (radic) 67textswab 68textsyllabic (a

) 16

texttctclig (tC) 11textteshlig (Ugrave) 11textteshlig () 14texttheta (T) 11textthing (N) 91textthorn (thorn) 11textthornvari (P) 12textthornvarii (Q) 12textthornvariii (R) 12textthornvariv (S) 12textthreeoldstyle () 20textthreequarters (frac34) 67 116textthreequartersemdash ()

20textthreesuperior (sup3) 67 116texttildedot (ã) 16texttildelow (~) 20 115texttimes (times) 67texttoneletterstem (pound) 11texttoptiebar (gta) 16texttrademark (trade) 9 19 117texttslig (ţ) 11textturna (5) 11textturncelig (ŕ) 11textturnglotstop (E) 12textturnh (4) 11textturnk (ľ) 11textturnlonglegr (Otilde) 11textturnm (W) 11textturnmrleg (icirc) 11textturnr (ocirc) 11textturnrrtail (otilde) 11textturnsck (u) 12textturnscripta (6) 11textturnscu () 12textturnt (Oslash) 11textturnthree (C) 12textturntwo (A) 12textturnv (2) 11textturnw (ucirc) 11textturny (L) 11texttwelveudash () 20texttwooldstyle 20texttwooldstyle () 20texttwosuperior (sup2) 67 116textuncrfemale (8) 12textunderscore ( ) 9textuparrow (uarr) 41textupblock ( ) 97textupfullarrow (˘) 12textupsilon (U) 11textupstep (Ţ) 11textvbaraccent (Ĳa) 16textvbaraccent (iquesta) 17textvertline (Š) 12textvibyi (ğ) 12textvibyy (ů) 12

160

textvisiblespace ( ) 9textwon (₩) 18textwynn (szlig) 12textxswdown (U) 91textxswup (T) 91textyen (yen) 18 116textyogh (Z) 12textyogh (para) 14textzerooldstyle () 20TH (THORN) 10 116th (thorn) 10 116

Thanh Han Thacutee 107therefore (6) 32therefore (there4) 30 64therefore (there4) 64Thermo 91Theta (Θ) 50theta (θ) 50thetaup (θ) 50thething (N) 91thickapprox (asymp) 30thicksim (sim) 30thickvert (~) 55thin space 113

ThinFog () 91thinstar (⋆) 25third (3) 66thirty-second note see musical

symbolsThorn (THORN) 13thorn (B) 13thorn (p) 13thorn (thorn) 13thousandths see

textperthousand

threesim (simsimsim) 104tick see check markstilde 9 11 13 15ndash16 18 20 57

59 61 107 115extensible 59 61vertically centered 115

tilde (˜) 57 107tildel (-) 13time of day 91 92timelimit (T) 93times (times) 22times (times) 24Times Roman (font) 18 102timing (package) 70tipa (package) 11 12 14ndash17 103

119 120tipx (package) 12 119 120

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35

tnttstile ( ) 35to see rightarrow

ToBottom (frac12) 90tone 12top (gt) 22 51 105top (⊺) 52

topbot (perpgt) 105 107topdoteq () 32torus (T) see alphabets mathToTop (frac14) 90trademark see texttrademark

TransformHoriz () 36transforms 36 63

TransformVert () 36transliteration

semitic 14 17transliteration symbols 14transpose 22transversal intersection see

pitchfork

trema (a) see accentstrfsigns (package) 36 52 63 119triangle (4) 65triangle () 40triangle relations 39 40

TriangleDown (3) 79

TriangleDown (o vs 3) 101

TriangleDown (o) 80triangledown (O) 66triangledown () 40triangleeq (≜) 40

TriangleLeft (2) 79triangleleft () 40triangleleft () 22triangleleft (◁) 40trianglelefteq () 40trianglelefteq (E) 39trianglelefteq (⊴) 39 40trianglelefteqslant (P) 40

triangleq () 21 39triangleq (≜) 40

TriangleRight (4) 79triangleright () 40triangleright () 22triangleright (▷) 40trianglerighteq () 40trianglerighteq (D) 39trianglerighteq (⊵) 39 40trianglerighteqslant (Q) 40triangles 66 73 79ndash80 94

TriangleUp (1) 79

TriangleUp (n vs 1) 101

TriangleUp (n) 80triple 57triplefrown () 48triplesim (≋) 33triplesmile () 48trsym (package) 36 119 120tsbm ( ) 95

tsdtstile ( ) 35tsmb ( ) 95tsmm ( ) 95

tsststile ( ) 35Tsteel (œ) 73

tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 73

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35

TUGboat 59Tumbler () 90turnstile (package) 35 119 120

TwelweStar (J) 78twiddle see tildetwoheaddownarrow () 43twoheadleftarrow () 41twoheadleftarrow () 44twoheadnearrow () 44twoheadnwarrow () 44twoheadrightarrow () 41twoheadrightarrow (↠) 44twoheadsearrow () 44twoheadswarrow () 44twoheaduparrow () 44twonotes () 88txfonts (package) 21ndash23

27 30 31 36ndash38 41 42 4850ndash52 65 66 68 100 102115 119 120

type1cm (package) 100Type 1 (font) 112

UU (a

˘) 17

U (frac14a) 14u (a) 14UArrow ( uarr ) 72

UB (lt) 89ubar (u) 13ubarbbrevis (ε) 95ubarbrevis (δ) 95ubarsbrevis (φ) 95ubrevislonga (κ) 95ubulbfd (file) 111 112ucs (package) 117 118udesc (u) 13udot () 23udotdot () 24 64udots (⋰) 64udtimes (]) 24

UHORN (Ư) 10uhorn (ư) 10ulcorner (x) 53ulcorner (p) 53

ulcorner () 55

ullcorner (6) 55

ulrcorner () 55

ulsy (package) 24 48 103 119

Umd ( a) 89umlaut (a) see accents

161

unary operators 21unclear (k) 93underaccent 107underarc (a) 17underarch (a) 16underbrace (loomoon) 60

underbrace (reg) 60

underbrace (︸︷︷︸) 60


underbracket ( ) 60

underbracket ( ) 108 109

underdots (r) 18undergroup (loooon) 60

undergroup (acutepara) 60

underleftarrow (larrminus) 59

underleftharp () 47

underleftharpdown () 47

underleftrightarrow (larrrarr) 59

underline 9 21 59 61underline ( ) 59underlinesegment (zx) 60

underparenthesis (︸︸) 108 109

underrightarrow (minusrarr) 59

underrightharp () 47

underrightharpdown () 47

underring (y) 18underscore see underlineunderscore (package) 9underset 104undertilde (package) 61 119 120undertilde (|) 18underwedge () 18Unicode 8 97 117ndash118union see cup

unit disk (D) see alphabetsmath

unitedpawns (u) 93units (package) 67unity (1) see alphabets mathuniversa (package) 80 90 119

120universal (package) 75 77 80 90

119 120unlhd (E) 22 23unlhd (⊴) 39 40unrhd (D) 22 23unrhd (⊵) 39 40upalpha (α) 51UParrow (K) 88Uparrow (uArr) 41 54Uparrow (uArr) 44uparrow (uarr) 41 54 100uparrow (uarr) 44uparrowtail () 44upbar 16upbeta (β) 51upbracketfill 109upchi (χ) 51

Updelta (∆) 51updelta (δ) 51Updownarrow (m) 41 54Updownarrow () 44updownarrow (l) 41 54updownarrow () 44updownarrows (Ouml) 42updownarrows () 44updownharpoonleftright (Q) 46updownharpoonrightleft (U) 46updownharpoons (ecirc) 43updownharpoons (⥮) 46Updownline (∥) 33updownline (∣) 33upepsilon (ε) 51upeta (η) 51upfilledspoon (q) 47upfootline (y) 33upfree () 33Upgamma (Γ) 51upgamma (γ) 51upgreek (package) 51 119 120upharpoonccw () 46upharpooncw () 46upharpoonleft (auml) 43upharpoonleft () 41upharpoonright (aelig) 43upharpoonright () 41upiota (ι) 51upkappa (κ) 51Uplambda (Λ) 51uplambda (λ) 51uplett 16uplsquigarrow (iexcl) 44uplus (Z) 23uplus (]) 22uplus (⊎) 24upmapsto () 44upModels (ntilde) 33upmodels (aacute) 33upmu (micro) 51upnu (ν) 51Upomega (Ω) 51upomega (ω) 51upp (t) 18upparenthfill 109Upphi (Φ) 51upphi (φ) 51Uppi (Π) 51uppi (π) 51uppitchfork (⋔) 47uppropto () 33Uppsi (Ψ) 51uppsi (ψ) 51upquote (package) 115uprho (ρ) 51upright Greek letters 50 51uprsquigarrow (copy) 44upside-down symbols 114upside-down symbols 11ndash13 17

103Upsigma (Σ) 51upsigma (σ) 51

Upsilon (Υ) 50upsilon (υ) 50upsilonup (υ) 50upslice (Agrave) 25upspoon (⫯) 47upt (l) 18uptau (τ) 51uptherefore (there4) 24 64Uptheta (Θ) 51uptheta (θ) 51uptodownarrow (thorn) 42upuparrows (Ograve) 42upuparrows () 41upuparrows () 44upupharpoons (Uacute) 43Upupsilon (Υ) 51upupsilon (υ) 51upvarepsilon (ε) 51upvarphi (ϕ) 51upvarpi (ϖ) 51upvarrho (ρ) 51upvarsigma (σ) 51upvartheta (ϑ) 51upVdash () 33upvdash (perp) 33Upxi (Ξ) 51upxi (ξ) 51upY ()) 24upzeta (ζ) 51Uranus (G) 71Uranus (Ccedil) 71uranus (Z) 71urcorner (y) 53urcorner (q) 53

urcorner () 55

url (package) 115US () 72usepackage 8ushort (package) 61 119 121ushort ( ) 61ushortdw ( ) 61

ushortw ( ) 61ut (a

˜) 16

UTF-8 117 118utf8x (inputenc package option)

117utilde (˜) 61

utimes (^) 24utimes ($) 24Utopia (font) 18 30

Vv (a) 14vara (a) 13varangle () 66varbigcirc () 22

VarClock () 91varclub () 67varclubsuit (p) 66varcoppa (ϙ) 87varcurlyvee () 22

162

varcurlywedge () 22vardiamond (diams) 67vardiamondsuit (q) 66varEarth (J) 71varepsilon (ε) 50varepsilonup (ε) 50

VarFlag () 91varg (txfontspxfonts package op-

tion) 51varg (1) 51varg (G) 13vargeq (copy) 38varhash () 66varheart (hearts) 67varheartsuit (r) 66varhexagon (9) 78varhexstar (B) 77vari (i) 13variable-sized symbols 25ndash30

100 102VarIceMountain () 91varinjlim (limminusrarr) 49

varint (r

) 26various (R) 93varkappa (κ) 50varleq (uml) 38varliminf (lim) 49

varlimsup (lim) 49varmathbb 68VarMountain () 91varnothing (empty) 21 65 66varnothing (empty) 66varnotin (T) 52varnotowner (U) 52varoast () 22varobar () 22varobslash () 22varocircle () 22varodot () 22varogreaterthan (5) 22

varoiiintclockwise (F

) 27

varoiiintctrclockwise (N

)

28varoiint (

) 28

varoiintclockwise (B

) 28

varoiintctrclockwise (J

) 28

varoint (u

) 26

varointclockwise (-

) 28

varointclockwise (ff) 28

varointctrclockwise (+

) 28

varointctrclockwise (fl) 28

varolessthan (4) 22varomega () 13varominus () 22varopeno (C) 13varoplus () 22varoslash () 22varotimes () 22varovee (6) 22varowedge (7) 22varparallel (∥) 31

varparallelinv () 31varpartialdiff (Ccedil) 53varphi (ϕ) 50varphiup (ϕ) 50varpi ($) 50varpi ($) 51varpiup ($) 50varprod (

) 28

varprojlim (limlarrminus) 49

varpropto (prop) 30varpropto (prop) 33varQ () 90varrho () 50varrho () 51varrhoup () 50varsigma (ς) 50varsigmaup (ς) 50varspade () 67varspadesuit (s) 66varsqsubsetneq () 37varsqsubsetneqq () 37varsqsupsetneq () 37varsqsupsetneqq () 37varstar () 23varstigma (ϛ) 87varsubsetneq () 37varsubsetneq ( ) 36varsubsetneq (⊊) 37varsubsetneqq () 37varsubsetneqq (amp) 36varsubsetneqq (⫋) 37

VarSummit () 91varsupsetneq () 37varsupsetneq () 36varsupsetneq (⊋) 37varsupsetneqq () 37varsupsetneqq () 36varsupsetneqq (⫌) 37

VarTaschenuhr () 91vartheta (ϑ) 50varthetaup (ϑ) 50vartimes () 22vartriangle (M) 66vartriangle () 40vartriangleleft () 40vartriangleleft (C) 39vartriangleleft (⊲) 39 40vartriangleright () 40vartriangleright (B) 39vartriangleright (⊳) 39 40varv (3) 51varvarpi (Egrave) 51varvarrho (AElig) 51varw (4) 51vary (2) 51

VBar () 79vbipropto () 24vcentcolon () 34vcenter 104vcrossing () 33VDash (() 32

VDash (⊫) 33Vdash () 32Vdash (13) 30Vdash (⊩) 33vDash (() 32vDash () 30vDash (⊧) 33vdash (`) 30vdash (⊢) 33vdotdot (∶) 24 64

vdots () 63

vdots (⋮) 64vec () 58vec (~) 57Vectorarrow ( p) 67

Vectorarrowhigh ( P) 67vee (_) 23vee (or) 22vee (or) 24veebar (Y) 23veebar (Y) 22veedot () 24veedoublebar ([) 23Venus (B) 71Venus (Atilde) 71venus () 71vernal () 71

versicle ( ) 118

VERT (

) 57

Vert () 54 56vert (|) 54 56vertbowtie (⧖) 24vertdiv () 24VHF () 70Vier ( ˇ ldquo) 89vietnam (package) 119

Village () 91

vin ( ) 53vinculum see overline

ViPa ( gt ) 89Virgo (aring) 71virgo (`) 71VM (gt) 89vntex (package) 10 14vod (v

˚) 13

voicedh (h) 13vppm (

macr) 95

vpppm (macr

) 95vrule 97VT () 72vv ( raquo) 61VvDash () 31Vvdash () 32Vvdash () 30Vvdash (⊪) 33vvvert (~) 55

WWashCotton (permil) 90WashSynthetics (Š) 90

163

WashWool (lsaquo) 90wasylozenge (loz) 88wasypropto () 31wasysym (package) 13 18 20

22 23 26 30 31 36ndash38 4164ndash66 70 71 73 77 78 88101 119 120

wasytherefore (there4) 64wavy-line delimiters 55 56wbetter (f) 93wdecisive (h) 93weakpt (J) 93

WeakRain () 91WeakRainCloud () 91weather symbols 91

Wecker () 91wedge (^) 23wedge (and) 22wedge (and) 24wedgedot () 24Weierstrass weierp function see wp

wfermion (d) 74Wheelchair (w) 90whfermion (m) 74whistle (a

Ţ) 16

WhiteBishopOnBlack (A) 94

WhiteBishopOnWhite (B) 94WhiteEmptySquare (0) 94

WhiteKingOnBlack (J) 94

WhiteKingOnWhite (K) 94

WhiteKnightOnBlack (M) 94

WhiteKnightOnWhite (N) 94

WhitePawnOnBlack (O) 94

WhitePawnOnWhite (P) 94

WhiteQueenOnBlack (L) 94

WhiteQueenOnWhite (Q) 94

WhiteRookOnBlack (S) 94

WhiteRookOnWhite (R) 94whitestone 94whole note see musical symbolsWick contractions 109widearc (Oslash) 60widearrow (t) 60widebar (s) 60widecheck (q) 60widehat () 60widehat () 59wideOarc (auml) 60wideparen (u) 60

wideparen () 60wideparen (Igrave) 60wideparen (Ucirc) 59

widering (u) 60

widering () 60

widering (Ucirc) 59widetilde () 60widetilde (˜) 59 61widetriangle (Ecirc) 59wind 91window 90

Windowsreg 115with (amp) 24with (v) 93withattack (A) 93withidea (E) 93withinit (C) 93without (w) 93wn () 21woman 81 90Womanface (thorn) 90won see textwon

world 90wp (weierp) 51wp (weierp) 52wr (o) 22wr (≀) 24wreath (≀) 24wreath product see wr

Writinghand (b) 90wsuipa (package) 13 16 18 101

103 107 119 120wupperhand (c) 93

Xx (X) 65x (

˙˙) 95

XBox (4) 77Xdvi 47 103X ELATEX 118xfrac (package) 67

xhookleftarrow (larrminus) 62

xhookrightarrow (minusrarr) 62Xi (Ξ) 50xi (ξ) 50xiup (ξ) 50

xLeftarrow (lArr=) 62

xleftarrow (larrminus) 61

xleftharpoondown (minus) 62

xleftharpoonup (minus) 62

xLeftrightarrow (lArrrArr) 62


xleftrightarrow (larrrarr) 62


xleftrightharpoons (minusminus) 62

xlongequal (===) 63

xlongequal (===) 62

xLongleftarrow (lArr==) 62

xlongleftarrow (larrminusminus) 62

xLongleftrightarrow (lArr==rArr) 62

xlongleftrightarrow (larrminusminusrarr) 62

xLongrightarrow (==rArr) 62

xlongrightarrow (minusminusrarr) 62

xmapsto ( 7minusrarr) 62

xmapsto ( 7minusrarr) 63XML 117

xRightarrow (=rArr) 62

xrightarrow (minusrarr) 61

xrightharpoondown (minus) 62

xrightharpoonup (minus) 62

xrightleftharpoons (minusminus) 62


Xs 77 90

XSolid () 77

XSolidBold ($) 77

XSolidBrush () 77xswordsdown (U) 91xswordsup (T) 91

xtwoheadleftarrow (minusminusminus) 63

xtwoheadrightarrow (minusminusminus) 63XY-pic 106

YYdown () 22yen see textyen

yfonts (package) 68 69 119 120yhmath (package) 58 59 61 64

107 119Yinyang (Y) 90Yleft () 22yogh (`) 13yogh (x) 13Yright () 22Yu Billy 108Yup () 22

ZZapf Chancery (font) 68Zapf Dingbats (font) 75 77Zborder (Z) 80zeta (ζ) 50zetaup (ζ) 50Zodiac 71zodiacal symbols 71

Ztransf ( ) 36

ztransf ( ) 36zugzwang (D) 93

Zwdr ( ˇ ldquo ) 89

ZwPa ( A ) 89

164

Contents

Introduction

Document Usage

Frequently Requested Symbols

Body-text symbols

LaTeX2e Escapable ``Special Characters

Predefined LaTeX2e Text-mode Commands

LaTeX2e Commands Defined to Work in Both Math and Text Mode

AMS Commands Defined to Work in Both Math and Text Mode

Non-ASCII Letters (Excluding Accented Letters)

Letters Used to Typeset African Languages

Letters Used to Typeset Vietnamese

Punctuation Marks Not Found in OT1

pifont Decorative Punctuation Marks

tipa Phonetic Symbols

tipx Phonetic Symbols

wsuipa Phonetic Symbols

wasysym Phonetic Symbols

phonetic Phonetic Symbols

t4phonet Phonetic Symbols

semtrans Transliteration Symbols

Text-mode Accents

tipa Text-mode Accents

extraipa Text-mode Accents

wsuipa Text-mode Accents

phonetic Text-mode Accents

metre Text-mode Accents

t4phonet Text-mode Accents

arcs Text-mode Accents

semtrans Accents

ogonek Accents

combelow Accents

wsuipa Diacritics

textcomp Diacritics

textcomp Currency Symbols

marvosym Currency Symbols

wasysym Currency Symbols

C25exh2exi6exnA2e Currency Symbols

teubner Currency Symbols

eurosym Euro Signs

fourier Euro Signs

textcomp Legal Symbols

cclicenses Creative Commons License Icons

textcomp Old-style Numerals

Miscellaneous textcomp Symbols

Miscellaneous wasysym Text-mode Symbols

Mathematical symbols

Math-Mode Versions of Text Symbols

cmll Unary Operators

Binary Operators

AMS Binary Operators

stmaryrd Binary Operators

wasysym Binary Operators

txfontspxfonts Binary Operators

mathabx Binary Operators

MnSymbol Binary Operators

mathdesign Binary Operators

cmll Binary Operators

shuffle Binary Operators

ulsy Geometric Binary Operators

mathabx Geometric Binary Operators

MnSymbol Geometric Binary Operators

Variable-sized Math Operators

AMS Variable-sized Math Operators

stmaryrd Variable-sized Math Operators

wasysym Variable-sized Math Operators

mathabx Variable-sized Math Operators

txfontspxfonts Variable-sized Math Operators

esint Variable-sized Math Operators

MnSymbol Variable-sized Math Operators

mathdesign Variable-sized Math Operators

cmll Large Math Operators

Binary Relations

AMS Binary Relations

AMS Negated Binary Relations

stmaryrd Binary Relations

wasysym Binary Relations

txfontspxfonts Binary Relations

txfontspxfonts Negated Binary Relations

mathabx Binary Relations

mathabx Negated Binary Relations

MnSymbol Binary Relations

MnSymbol Negated Binary Relations

mathtools Binary Relations

turnstile Binary Relations

trsym Binary Relations

trfsigns Binary Relations

cmll Binary Relations

colonequals Binary Relations

fourier Binary Relations

Subset and Superset Relations

AMS Subset and Superset Relations

stmaryrd Subset and Superset Relations

wasysym Subset and Superset Relations

txfontspxfonts Subset and Superset Relations

mathabx Subset and Superset Relations

MnSymbol Subset and Superset Relations

Inequalities

AMS Inequalities

wasysym Inequalities

txfontspxfonts Inequalities

mathabx Inequalities

MnSymbol Inequalities

AMS Triangle Relations

stmaryrd Triangle Relations

mathabx Triangle Relations

MnSymbol Triangle Relations

Arrows

Harpoons

textcomp Text-mode Arrows

AMS Arrows

AMS Negated Arrows

AMS Harpoons

stmaryrd Arrows

txfontspxfonts Arrows

mathabx Arrows

mathabx Negated Arrows

mathabx Harpoons

MnSymbol Arrows

MnSymbol Negated Arrows

MnSymbol Harpoons

MnSymbol Negated Harpoons

harpoon Extensible Harpoons

chemarrow Arrows

fge Arrows

MnSymbol Spoons

MnSymbol Pitchforks

MnSymbol Smiles and Frowns

ulsy Contradiction Symbols

Extension Characters

stmaryrd Extension Characters

txfontspxfonts Extension Characters

mathabx Extension Characters

Log-like Symbols

AMS Log-like Symbols

C25exh2exi6exnA2e Number Sets

Greek Letters

AMS Greek Letters

txfontspxfonts Upright Greek Letters

upgreek Upright Greek Letters

fourier Variant Greek Letters

txfontspxfonts Variant Latin Letters

AMS Hebrew Letters

MnSymbol Hebrew Letters

Letter-like Symbols

AMS Letter-like Symbols

txfontspxfonts Letter-like Symbols

mathabx Letter-like Symbols

MnSymbol Letter-like Symbols

trfsigns Letter-like Symbols

mathdesign Letter-like Symbols

fge Letter-like Symbols

fourier Letter-like Symbols

AMS Delimiters

stmaryrd Delimiters

mathabx Delimiters

nath Delimiters

Variable-sized Delimiters

Large Variable-sized Delimiters

AMS Variable-sized Delimiters

stmaryrd Variable-sized Delimiters

mathabx Variable-sized Delimiters

MnSymbol Variable-sized Delimiters

mathdesign Variable-sized Delimiters

nath Variable-sized Delimiters (Double)

nath Variable-sized Delimiters (Triple)

fourier Variable-sized Delimiters

textcomp Text-mode Delimiters

metre Text-mode Delimiters

Math-mode Accents

AMS Math-mode Accents

MnSymbol Math-mode Accents

fge Math-mode Accents

yhmath Math-mode Accents

Extensible Accents

overrightarrow Extensible Accents

yhmath Extensible Accents

AMS Extensible Accents

MnSymbol Extensible Accents

mathtools Extensible Accents

mathabx Extensible Accents

fourier Extensible Accents

esvect Extensible Accents

undertilde Extensible Accents

ushort Extensible Accents

AMS Extensible Arrows

mathtools Extensible Arrows

chemarr Extensible Arrows

chemarrow Extensible Arrows

extarrows Extensible Arrows

extpfeil Extensible Arrows

DotArrow Extensible Arrows

trfsigns Extensible Transform Symbols

holtpolt Non-commutative Division Symbols

Dots

AMS Dots

wasysym Dots

MnSymbol Dots

mathdots Dots

yhmath Dots

teubner Dots

mathcomp Math Symbols

marvosym Digits

fge Digits

dozenal Base-12 Digits

mathabx Mayan Digits

Miscellaneous LaTeX2e Math Symbols

Miscellaneous AMS Math Symbols

Miscellaneous wasysym Math Symbols

Miscellaneous txfontspxfonts Math Symbols

Miscellaneous mathabx Math Symbols

Miscellaneous MnSymbol Math Symbols

Miscellaneous Internal MnSymbol Math Symbols

Miscellaneous textcomp Text-mode Math Symbols

Miscellaneous marvosym Math Symbols

Miscellaneous fge Math Symbols

Miscellaneous mathdesign Math Symbols

Miscellaneous arev Math Symbols

Math Alphabets

Science and technology symbols

gensymb Symbols Defined to Work in Both Math and Text Mode

wasysym Electrical and Physical Symbols

ifsym Pulse Diagram Symbols

ar Aspect Ratio Symbol

textcomp Text-mode Science and Engineering Symbols

steinmetz Extensible Phasor Symbol

wasysym Astronomical Symbols

marvosym Astronomical Symbols

mathabx Astronomical Symbols

wasysym APL Symbols

wasysym APL Modifiers

marvosym Computer Hardware Symbols

keystroke Computer Keys

ascii Control Characters (CP437)

milstd Logic Gates

marvosym Communication Symbols

marvosym Engineering Symbols

wasysym Biological Symbols

marvosym Biological Symbols

marvosym Safety-related Symbols

feyn Feynman Diagram Symbols

Dingbats

bbding Arrows

pifont Arrows

universal Arrows

marvosym Scissors

bbding Scissors

pifont Scissors

dingbat Pencils

bbding Pencils and Nibs

pifont Pencils and Nibs

dingbat Fists

bbding Fists

pifont Fists

fourier Fists

bbding Crosses and Plusses

pifont Crosses and Plusses

bbding Xs and Check Marks

pifont Xs and Check Marks

wasysym Xs and Check Marks

universal Xs

pifont Circled Numbers

wasysym Stars

bbding Stars Flowers and Similar Shapes

pifont Stars Flowers and Similar Shapes

fourier Ornaments

wasysym Geometric Shapes

MnSymbol Geometric Shapes

ifsym Geometric Shapes

bbding Geometric Shapes

pifont Geometric Shapes

universa Geometric Shapes

universal Geometric Shapes

Miscellaneous dingbat Dingbats

Miscellaneous bbding Dingbats

Miscellaneous pifont Dingbats

Ancient languages

phaistos Symbols from the Phaistos Disk

protosem Proto-Semitic Characters

hieroglf Hieroglyphics

linearA Linear A Script

linearb Linear B Basic and Optional Letters

linearb Linear B Numerals

linearb Linear B Weights and Measures

linearb Linear B Ideograms

linearb Unidentified Linear B Symbols

cypriot Cypriot Letters

sarabian South Arabian Letters

teubner Archaic Greek Letters and Greek Numerals

Other symbols

textcomp Genealogical Symbols

wasysym General Symbols

wasysym Circles

wasysym Musical Symbols

arev Musical Symbols

harmony Musical Symbols

harmony Musical Accents

manfnt Dangerous Bend Symbols

Miscellaneous manfnt Symbols

marvosym Navigation Symbols

marvosym Laundry Symbols

marvosym Information Symbols

Other marvosym Symbols

Miscellaneous universa Symbols

Miscellaneous universal Symbols

Miscellaneous fourier Symbols

ifsym Weather Symbols

ifsym Alpine Symbols

ifsym Clocks

Other ifsym Symbols

clock Clocks

epsdice Dice

hhcount Dice

hhcount Tally Markers

skull Symbols

Non-Mathematical mathabx Symbols

skak Chess Informator Symbols

skak Chess Pieces and Chessboard Squares

igo Go Stones

metre Metrical Symbols

metre Small and Large Metrical Symbols

teubner Metrical Symbols

dictsym Dictionary Symbols

simpsons Characters from The Simpsons

pmboxdraw Box-Drawing Symbols

staves Magical Staves

pigpen Cipher Symbols

C25exh2exi6exnA2e Phases of the Moon

Other C25exh2exi6exnA2e Symbols

recycle Recycling Symbols

Additional Information

Symbol Name Clashes

Resizing symbols

Where can I find the symbol for hellip

Math-mode spacing

Bold mathematical symbols

ASCII and Latin 1 quick reference

Unicode characters

About this document

Copyright and license

References

Index

Symbols

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

Table 28 wsuipa Diacritics 18Table 29 textcomp Diacritics 18Table 30 textcomp Currency Symbols 18Table 31 marvosym Currency Symbols 18Table 32 wasysym Currency Symbols 18Table 33 ChinA2e Currency Symbols 19Table 34 teubner Currency Symbols 19Table 35 eurosym Euro Signs 19Table 36 fourier Euro Signs 19Table 37 textcomp Legal Symbols 19Table 38 cclicenses Creative Commons License Icons 19Table 39 textcomp Old-style Numerals 20Table 40 Miscellaneous textcomp Symbols 20Table 41 Miscellaneous wasysym Text-mode Symbols 20

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

2


3


4




5




6



References 122

Index 123

7

1 Introduction





11 Document Usage








cent 18

e 18


permil 20 27

there4 30

B and F 31

and amp 38

64


L F etc 68

N Z R etc 68

r 68

minusint

105




8

2 Body-text symbols


















9





















10





11






12







˚vod


13





Alif Ayn





Aa =A=a Amacr

amacr







14












Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



15



Aˇ

aˇ



Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



16


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast



A a kAka


A a cbAcba


17



















18
















Ccopy ccsalowast


19











h permil

20





∐rdquo (coprod)











21












22











23











cshuffle shuffle


odplus

24








and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint

25


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint




notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





26



Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint




bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint



27


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28






















29


intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)


˙bigparr

˘bigwith







30




A inplus B niplus








31









32








33









34


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

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

def

ttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef


35





dfourier Dfourier

fourier Fourier













36




sqsubset A sqsupset










37













apprge gt apprle

















38

























39









40

Table 102 Arrows






Table 103 Harpoons










41









42






43









44




45












46






A chemarrow










47












48













49











50

















51












e e j im




52














niv vin

53



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

54


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert

55



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





56




triplegt

[[[[[[

triple[ ]]]]]]

triple]






llbracket

rrbracket

VERT








57


a ddddota





a veca


Andash




a ringa


58














˚abc wideringabc




59














abc widearrowabc





60












abcrsaquo utildeabc








61












abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG








62









a dfta a DFTa


abcdef

holterabcdefabcdef

polterabcdef

Table 189 Dots





63

Table 190 AMS Dots












iddots


adots


antilabe

64








X x E e





`surd





65













66
















67
















68



69















A AR




abc phaseabc


70




















71



















72


ANDd BUFu NANDl ORd


ANDr INVd NANDu ORr

ANDu INVl NORd ORu

BUFd INVr NORl

BUFl INVu 13 NORr

BUFr NANDd NORu









female male

73



















74

5 Dingbats



















75

























76











baucross







77
























78





























79
























80

6 Ancient languages





















81


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








82








83




84




























85






























86








87

7 Other symbols














88








Aa

aa


Aa

aa


Alal KrAKra



a












89










bauforms bauhead



90
























91





Cube1 Cube3 Cube5

Cube2 Cube4 Cube6





0 i i01 i1 i102 i2 i203 i3 i30










92


A skull


O rip



93






















94


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









95




Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart

96





























97






























98


A recycleA Recycle

A RECYCLE



99









82 Resizing symbols






100

Table

321

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

101



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


102

















103







endtabular












104

















105





one (ldquo=int





















106



makeatother








makeatother








e






107


makeatother




endarray










makeatother

108






ABCD









109













endcharend


110




1

2

3

4

5

6677

8







111


0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F
















112













Package Code Output



113




















114













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 330 presents thecharacters with which CP1252 augments the standard Latin 1 table





115




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


116

















117

usepackagetextcomp



which produces

It was a balmy 21








which produces






118















Name Date



119


Name Date



120


Name Date









121

References











122

Index




( (() 55

) ()) 54

) ()) 55

() 23 113- (-) 115 116 (a) 14 () 54

() 55

( ) 64

() 64

lt (⟨) 55

() 64

[ ([) 54

[ (⎡⎢⎢⎢⎢⎢⎣) 55

104] (]) 54

] (⎤⎥⎥⎥⎥⎥⎦) 55

^ (a) 14^ (ˆ) 9 115| () 54| () 54 56| (iquesta) 14= (a) 14= (macr) 115

| (

RRRRRRR) 55| (|) 30 54 56 57_ ( ) 9 115 () 9 54 115 () 9 54 115lsquo (a) 14~ (a) 14~ (˜) 9 115


) 95

AA (A) 10aa (a) 10

AAaleph (A) 81

AAayin (O) 81

AAbeth (B) 81


) 89

AAdaleth (D) 81

AAhe (E) 81

AAhelmet (V) 81

AAheth (h) 81

AAkaph (K) 81

AAlamed (L) 81

Aaleph (a) 81

AApe (P) 81

AAqoph (Q) 81

AAresh (R) 81

AAsade (X) 81

Aayin (o) 81

AAyod (Y) 81

Abeth (b) 81



AC () 70

acarc 16

acbar 16




arc (a) 14ndash17 59 60


caron (a) 14 18 57 60

cedilla (cedil) 14


comma-below (a) 17







hook (ả) 14



macron (a) 14 17 18 5759 60



ring (a) 14ndash16 18 57 58




accentset 107


AchtBL ( ˇ ldquo==

) 89




Adobe Acrobat 112

adots ( ) 64 107





African 10


123




and |

AltGr ( AltGr ) 72


AMS 8 10 22 26 30 31 3638 39 41 49ndash54 58 59 6164ndash66 69 100 118




41 58 65 68 87 119 120123



AND gates 73

ANDd () 73

ANDl () 73

ANDr () 73



text mode see AA
















Arrowvert (ww) 54

Arrowvert (

XXXXXXX) 55

arrowvert () 54

arrowvert (


117 119table 114



AsteriskBold (A) 78



AsteriskThin (C) 78



124



(EGGGGGGGGGGC) 62



(GGGGGBFGGGGG) 62



macr) 14

b (˘) 95


backslash () 55


Baii () 85





Bart (






tion) 68BBm (

macr) 95

Bbm (macr

) 95bBm (

macr) 95


bbm (macr

) 95bbmb ( ˘) 95bbmx (


Bda (d) 85


Bdi (f) 85

Bdo (g) 85

Bdu (x) 85

Bdwe (gt) 85

Bdwo () 85


Bi (i) 85bibridge (

rdquoardquo) 16



bigbosonloop ( ) 74



e) 26



THORN) 27

bigboxbot (Ucirc

) 27bigboxcirc (

Otilde) 27


) 27bigboxdiv (

Oacute) 27

bigboxdot (Ocirc

) 27bigboxleft (

Oslash) 27

bigboxminus (Ntilde

) 27bigboxplus (

ETH) 27

125

bigboxright (Ugrave

) 27bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 27

bigcap (⋂



) 27


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 26


) 26


AElig) 27



Euml) 27

bigocirc (Aring


Ccedil) 27

bigodiv (Atilde

) 27bigodot (

⊙) 25


Egrave) 27

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


bigotimes (otimes


Ecirc) 26


Iuml) 26


Igrave) 27

bigparallel (f) 26

bigparr (˙

) 30bigplus (

) 27

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 27


) 27

bigtimes (⨉) 29


`) 26






a) 26



⊎) 25



or) 25


and) 25


bigwith (˘





Bja (j) 85

Bje (J) 85

Bjo (b) 85

Bju (L) 85

Bka (k) 85

Bke (K) 85

Bki (c) 85

Bko (h) 85

Bku (v) 85















126

blank see textblank


macr) 95

bm (package) 113 119 121bm 113bm (

macr) 95

Bma (m) 85

Bme (M) 85

Bmi (y) 85

Bmo (A) 85bmod 49

Bmu (B) 85

Bna (n) 85

BNc (laquo) 85

BNcc (raquo) 85

BNccc (ndash) 85

BNcd (mdash) 85

BNcm (ff) 85

BNd (zwnj) 85

BNdc (permil) 85

BNdcc (ı) 85

BNdccc (ȷ) 85

Bne (N) 85

BNi (acute) 85

Bni (C) 85

BNii (ˆ) 85

BNiii (˜) 85

BNiv (uml) 85

BNix (macr) 85

BNl (lsaquo) 85

BNlx (rsaquo) 85

BNlxx (ldquo) 85

BNlxxx (rdquo) 85

BNm (fi) 85

Bno (E) 85

Bnu (F) 85

BNv (˝) 85

BNvi (˚) 85

BNvii (ˇ) 85

BNviii (˘) 85

Bnwa () 85

BNx (˙) 85

BNxc (bdquo) 85

BNxl (sbquo) 85

BNxx (cedil) 85

BNxxx (˛) 85





boy (D) 71

Bpa (p) 85

Bpaiii ([) 85

BPamphora (Ž) 86

BParrow (ĳ) 86

BPbarley (Ş) 86

BPbilly (ť) 86

BPboar (ľ) 86

BPbronze (Ű) 86

BPbull (ň) 86

BPcauldroni (đ) 86


BPchariot (yuml) 86

BPchassis (ź) 86

BPcloth (Ř) 86

BPcow (ŋ) 86

BPcup (Ÿ) 86

Bpe (P) 85

BPewe (š) 86

BPfoal (ě) 86

BPgoat (ş) 86

BPgoblet (Ź) 86

BPgold (Ů) 86

BPhorse (ď) 86

Bpi (G) 85

BPman (ă) 86

BPnanny (ț) 86

Bpo (H) 85

BPolive (Ț) 86

BPox (ń) 86

BPpig (ĺ) 86

BPram (ś) 86

BPsheep (ř) 86

BPsow (ł) 86

BPspear (iexcl) 86

BPsword (ż) 86

BPtalent (Ď) 85

Bpte (]) 85

Bpu (I) 85

Bpuii () 85

BPvola (Ĺ) 85

BPvolb (Ľ) 85

BPvolcd (Ł) 85

BPvolcf (Ń) 85

BPwheat (Š) 86

BPwheel (ž) 86

BPwine (Ť) 86

BPwineiih (Ż) 86

BPwineiiih (Ĳ) 86

BPwineivh (İ) 86

BPwoman (ą) 86

BPwool (Ś) 86

127

BPwta (Ă) 85

BPwtb (Ą) 85

BPwtc (Ć) 85

BPwtd (Č) 85

Bqa (q) 85

Bqe (Q) 85

Bqi (X) 85

Bqo (8) 85

Bra (r) 85

bra 54

braceld (︷) 109

bracerd (︷) 109

bracevert () 54

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 55


Braii (^) 85

Braiii (_) 85

braket (package) 54

Bre (R) 85

Break ( Break ) 72

breve (˘) 57

breve (a) 17


brevis (β) 95

Bri (O) 85

Bro (U) 85

Broii (lsquo) 85

brokenvert (|) 88

Bronger Torsten 105

Bru (V) 85

BS () 72

Bsa (s) 85

Bse (S) 85

BSEfree (n) 74

Bsi (Y) 85

Bso (1) 85


Bsu (2) 85

Bswa () 85

Bswi (|) 85

Bta (t) 85

Btaii () 85

Bte (T) 85

Bti (3) 85

Bto (4) 85

Btu (5) 85

Btwe (shy) 86

Btwo (~) 85

Bu (u) 85

BUFd () 73

buffers 73

BUFl () 73

BUFr () 73

BUFu () 73

BUi (fl) 86

BUii (ffi) 86

BUiii (ffl) 86

BUiv () 86



Burns (

) 96BusWidth () 73

BUv () 86

BUvi () 86

BUvii () 86

BUviii ($) 86

BUx (amp) 86

BUxi (rsquo) 86

BUxii (shy) 86

Bwa (w) 85

Bwe (W) 85

Bwi (6) 85

Bwo (7) 85

Bza (z) 85

Bze (Z) 85

Bzo (9) 85













CEsign (C) 74



Checkmark () 77

128



checkmark (D) 80


119 121chiup (χ) 50


Circle (5) 79








circledvee (U) 23


CircleShadow (d) 80


Cja (j) 86

Cjo (b) 86

Cka (k) 86

Cke (K) 86

Cki (c) 86

Cko (h) 86

Cku (v) 86

Cla (l) 86




clock (i1) 92



Cma (m) 86

Cme (M) 86


Cmo (A) 86

Cmu (B) 86

Cna (n) 86

Cne (N) 86

Cni (C) 86

Cno (E) 86

Cnu (F) 86






COMPLEX (raquo) 49

Complex (Atilde) 49

129



work 1 8 59 69 100117ndash119




and amp





∐) 21 25


Cpa (p) 86

Cpe (P) 86

Cpi (G) 86

Cpo (H) 86

Cpu (I) 86CR () 72cr 104

Cra (r) 86


Cri (O) 86

Cro (U) 86

Cross () 79



crossb () 13






Ŕa) 16




Csi (Y) 86

Cso (1) 86

Csu (2) 86



Cti (3) 86


Ctu (5) 86

Cu (u) 86





Cutright (q) 75

Cwa (w) 86

Cwe (W) 86

Cwi (6) 86

Cwo (7) 86

Cxa (x) 86

Cxe (X) 86

Cya (j) 86


Cza (g) 86

Czo (9) 86

DD (a

uml) 17




130


dashint (minusint

) 106


DavidStar (0) 78


ddashint (=int

) 106

ddddot (

) 58dddot (

) 58

dddtstile ( ) 35

ddigamma (ϝ) 87


ddots ( ) 63 107

ddots (⋱) 64

ddststile ( ) 35

ddtstile ( ) 35

ddttstile ( ) 35




DEL () 72Del ( Del ) 72






Dfourier ( ) 36

dfourier ( ) 36

DFT ( ) 63

















non-commutative 63

131




dndtstile ( ) 35

dnststile ( ) 35

dntstile ( ) 35




does not imply 105


dollar sign see $








macr) 28


dottedtilde (a) 16


doublecap see Cap






dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35


dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35







EightStar (H) 78





132

ell (`) 51





Enter ( Enter ) 72






ESC () 72Esc ( Esc ) 72






see nleftrightarrow

nequiv and oplus






textquotesingle


Ferli (aa) 89

Fermi (aa







feyngvs (s) 74


133



























(t) 79













fint (gt

) 27

fint (ffl) 28






FiveStar (8) 78




FiveStarOpen (9) 78






fixedddots ( ) 63

fixedvdots () 63










134


FourAsterisk (1) 78




57 60 76 78 91 119













87Greek coins 19


gtreqless (R) 38



gtreqqless (T) 38

gtreqqless (⪌) 39





h (ả) 14HA (A) 82









135



HandLeft () 76

HandLeftUp () 76


HandRight () 76



HB (B) 82

Hb (b) 82





HH 89


HI (I) 82

Hi (i) 82


Hibp (ˆ) 82

Hibs (uml) 82


mathhill (a

) 16


radic) 106

HL (L) 82Hl (l) 82HM (M) 82

Hm (m) 82

Hman (ˇ) 82

Hmillion (7) 82



holter ( ) 63


Homer (

) 96Hone (|) 82



Hplus (+) 82HQ (Q) 82Hq (q) 82


Hs (s) 82

Hscribe (macr) 82


Hthousand (4) 82

Htongue (˘) 82

HU (U) 82


Hut () 91


Hw (w) 82HX (X) 82

Hx (x) 82

HXthousand (5) 82

HY (Y) 82


HZ (Z) 82Hz (z) 82


iddots ( ) 64

iddots () 107


) 26

idotsint (

) 27


136

ifsym (package) 70 79 91 92101 103 119 120



) 26

iiiint (

) 27

iiiint (ˇ

) 28


micro) 27

iiint (intintint

) 26

iiint (

) 26 27

iiint (˝

) 28


acute) 27

iint (intint

) 26

iint (

) 26 28

iint (˜

) 28



and vdash


textquotedbl







injlim (inj lim) 49

inplus (A) 31


Ins ( Ins ) 72

int (sup3) 27

int (int

) 25 26

int (r

) 26

int (int) 29

intclockwise () 30

INTEGER (iquest) 49

Integer (Uacute) 49




intercal (ᵀ) 22

intercal (⊺) 52

interleave (9) 22


Interval () 91

inva () 13

invamp (M) 23

invbackneg (⨽) 66

INVd () 73

invdiameter () 88

inve (U) 13





inverters 73

invf () 13

invglotstop (d) 13

invh (amp) 13

INVl () 73

invlegr (I) 13

invm (5) 13

invneg () 31

invneg (⨼) 66

INVr () 73

invr (G) 13

invscr (K) 13

invscripta () 13

INVu () 73

invv () 13

invw (Z) 13

invy () 13

iota (ι) 50


iotaup (ι) 50

ipagamma ( ) 13

ipercatal (η) 95

IroningI (macr) 90

IroningII (deg) 90


irony mark ( ) 103



Jj () 14

JackStar (2) 78










137


landdownint () 28


) 28


langle (⟨) 55

langlebar (n) 55

Laplace ( ) 36





largepencil (W) 76



63 65 73 75 100 103ndash109112 113 115 117ndash119 121122

LATEX 2ε 1 89 19 20 22 30 36 41 5863 65 69 73 100 101 103106 107 111 112 114ndash117122






lceil (⎡⎢⎢⎢⎢⎢⎢) 55







leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56






leftwave (

ETH

ETH

ETH

ETH

) 56


138


lesseqgtr (Q) 38



lesseqqgtr (S) 38

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

LF () 72

lfilet (

7777) 55


lfloor (⎢⎢⎢⎢⎢⎢⎣) 55

lg (lg) 49

lgroup (

) 54

lgroup (⎧⎪⎪⎪⎪⎪⎩) 55

LHD () 23









139












140

LinearACXXI (x) 83


LinearACXXIX () 83





LinearAI () 82



LinearALIX () 83


LinearALVIII (9) 83













LinearAX () 82





LinearAXLIV (+) 83

LinearAXLIX (0) 83

LinearAXLV () 83




LinearAXXII () 83

LinearAXXIII () 83




Lisa (

) 96lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 55


llbracket (

) 57


llcorner () 55



lmoustache (

) 54





and see wedge

not see neg and sim

or see vee



141




lrcorner () 55

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 55



lwave (

ETH

ETH

ETH

ETH

) 56

lWavy (_______

) 55

lwavy (^^^) 55

lz (1) 13

MM 10M (

macr) 95

m 10m (

macr) 95


Maggie ( ) 96







Marge (










30 32 36ndash38 40 42 43 4952ndash55 58 60 65 66 71 93100 101 119 120 123





142




cient seeDH




metre (package) 17 57 95 119120


micro (micro) 70


textperthousand
















NANDd () 73

NANDl () 73

NANDr () 73


NATURAL (frac14) 49


alphabets math

143


ncong () 31


nddtstile ( ) 35



ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 38


ngeqq () 38

ngeqq (iquest) 39

ngeqslant () 38



144



ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 13

NibLeft () 76


NibSolidLeft ( ) 76





nleq () 38


nleqq () 38

nleqq (frac34) 39

nleqslant () 38





nlessgtr () 38

nlessgtr (≸) 39




nnststile ( ) 35

nntstile ( ) 35


145




NORd () 73


NORr (13) 73

NORu () 73



notni


npreceq (ordf) 32

npreceq () 31




146


nsststile ( ) 35

nststile ( ) 35


nsubseteq () 36


nsucceq () 31


nsupseteq (+) 36



ntdtstile ( ) 35






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35





NumLock ( Num ) 72




147




˚) 16


ohm (Ω) 70

Ohne (a ) 89


oiiint ()

) 28

oiiint (

) 30

oiiintclockwise (L

) 28


) 28

oiint (middot

) 27

oiint (

) 26 28

oiint (sbquo

) 28

oiint (

) 30

oiint (∯) 29

oiintclockwise (H

) 28

oiintctrclockwise (

) 28

oint (para) 27

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 30

ointctrclockwise (

) 27







OR gates 73


ORl () 73




overbrace (hkkikkj

) 60

overbrace (copy

) 60


) 60


) 59

overbracket ( ) 60


rdquoa) 16

overgroup (hkkkkj

) 60









PP (para) 9 116p (

˙) 95

p 107

148



amsmath 8 49 58 104 112amssymb 8 22 30 36 4158 65 68 87 119 120 123











mathdots 58 63 64 107119 120







t4phonet 14 17 119 120teubner 19 64 87 95 119120

textcomp 8 9 14 18ndash20 4157 67 70 88 100 115 119





149


wsuipa 13 16 18 101 103107 119 120




and parr




















textperthousand



PencilLeft () 76


PencilLeftUp () 76

PencilRight () 76







textrecipe


PHbee (h) 81

PHbeehive (X) 81

PHboomerang (R) 81

PHbow (K) 81

PHbullLeg (b) 81

PHcaptive (D) 81


PHcat (c) 81

PHchild (E) 81

PHclub (M) 81

PHcolumn (W) 81

PHcomb (U) 81

PHdolium (T) 81

PHdove (f) 81

PHeagle (e) 81

PHflute (o) 81

PHgaunlet (H) 81

PHgrater (p) 81

PHhelmet (G) 81

PHhide (a) 81

PHhorn (Z) 81

Phi (Φ) 50

phi (φ) 50

phiup (φ) 50

PHlid (Q) 81

PHlily (m) 81

PHmanacles (N) 81

PHmattock (O) 81

Phone () 80

phone () 88

PhoneHandset () 80



photon () 70

photons 74

PHoxBack (n) 81

PHpapyrus (k) 81

PHpedestrian (A) 81

PHplaneTree (i) 81

PHplumedHead (B) 81

PHram (d) 81

PHrosette (l) 81

PHsaw (P) 81

PHshield (L) 81

PHship (Y) 81

PHsling (V) 81

PHsmallAxe (r) 81

PHstrainer (q) 81


150


PHvine (j) 81

PHwavyBand (s) 81



pigpenfont A (A) 98

pigpenfont B (B) 98

pigpenfont C (C) 98

pigpenfont D (D) 98

pigpenfont E (E) 98

pigpenfont F (F) 98

pigpenfont G (G) 98

pigpenfont H (H) 98

pigpenfont I (I) 98

pigpenfont J (J) 98

pigpenfont K (K) 98

pigpenfont L (L) 98

pigpenfont M (M) 98

pigpenfont N (N) 98

pigpenfont O (O) 98

pigpenfont P (P) 98

pigpenfont Q (Q) 98

pigpenfont R (R) 98

pigpenfont S (S) 98

pigpenfont T (T) 98

pigpenfont U (U) 98

pigpenfont V (V) 98

pigpenfont W (W) 98

pigpenfont X (X) 98

pigpenfont Y (Y) 98


pipe see textpipe


Plane () 80






macr) 95



polter ( ) 63





macr) 95

Ppp (˙˙) 95

ppp ( ˙˙

) 95Pppp (˙

˙) 95

pppp ( ˙˙

) 95Ppppp (˙

˙) 95

ppppp ( ˙˙




prod) 25






31 36ndash38 41 42 48 50ndash5265 66 68 100 115

Pxp (˙) 95pxp ( ˙ ) 95


151



RR (sim

) 95r (a) 14r (sim

) 95



Rain () 91



rangle (⟩) 55

ranglebar (s) 55

RArrow ( rarr ) 72





hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 55





REAL (frac34) 49



recorder () 88

Rectangle (u) 80




rqm


textregistered





upharpoonright


Return ( larr ) 72


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

revD () 13

revddots ( ) 107


textbackslash



rfilet (

) 55


rfloor (⎥⎥⎥⎥⎥⎥⎦) 55

rgroup (

) 54

rgroup (⎫⎪⎪⎪⎪⎪⎭) 55


RightDiamond () 79

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56


152



rightwave (

ETH

ETH

ETH

ETH

) 56




rmoustache (

) 54



see accentsrook 94

roots see sqrt


rrangle (⟫) 55

rrbracket () 54

rrbracket (

) 57


rsem (MQQQQQO) 55



rwave (

ETH

ETH

ETH

ETH

) 56

rWavy (_______

) 55

rwavy (^^^) 55










ScissorLeft () 75




() 75


153


scu (W) 13scy (]) 13

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 89


) 89











membership see in

union see cup








([) 78

SixStar (G) 78





SmallCircle (E) 79











154



sndtstile ( ) 35

Snow () 91

SnowCloud () 91

Snowflake (`) 78



SNPP () 96

snststile ( ) 35

sntstile ( ) 35



Spacebar ( ) 72


Sparkle (]) 78


SpinDown () 79



sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

sqrt (radic


Square (0) 79




hooked see hksqrt


(k) 80




SquareShadowA () 79

SquareShadowB () 79


SquareShadowC () 79






ssststile ( ) 35

sststile ( ) 35


staveI () 97

staveII () 97

staveIII () 97

staveIV () 97

staveIX () 97

staveL (1) 97 98

155

staveLI (2) 97

staveLII (3) 97

staveLIII (4) 97

staveLIV (5) 97

staveLIX () 98

staveLV (6) 97

staveLVI (7) 97

staveLVII (8) 97


staveLXI (lt) 98

staveLXII (=) 98

staveLXIII (gt) 98

staveLXIV () 98

staveLXV () 98

staveLXVI (A) 98

staveLXVII (B) 98


staveV () 97

staveVI () 97

staveVII () 97

staveVIII () 97

staveX () 97

staveXI () 97

staveXII () 98

staveXIII () 98


staveXL () 98

staveXLI (() 98

staveXLII ()) 98


staveXLIX (0) 97

staveXLV () 98

staveXLVI (-) 98

staveXLVII () 97

staveXLVIII () 97

staveXV () 98

staveXVI () 98

staveXVII () 98

staveXVIII () 98


staveXXII () 98

staveXXIII () 98

staveXXIV () 97

staveXXIX () 97

staveXXV () 97

staveXXVI () 97

staveXXVII () 97

staveXXVIII () 97

staveXXX () 97

staveXXXI () 97

staveXXXII () 97

staveXXXIII ( ) 97

staveXXXIV () 97

staveXXXIX (amp) 98

staveXXXV () 98


stdtstile ( ) 35



40 42 48 53 54 101 104118ndash120



StopWatchEnd () 91


strokedint (⨏) 29

StrokeFive () 92

StrokeFour () 92

StrokeOne () 92

StrokeThree () 92


stststile ( ) 35

sttstile ( ) 35

stttstile ( ) 35


^) 16



sublptr (aiexcl) 16





156


sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 91




SunCloud () 91





`) 65




symA (Aacute) 68

symAE (Ucirc) 68


















157


Tape () 80



tddtstile ( ) 35

tdststile ( ) 35

tdtstile ( ) 35

tdttstile ( ) 35


Telephone (() 92



119 120TEX 40 47 64 70 97 100

103ndash109 111ndash113 115 117118 122








9 14 18ndash20 41 57 67 7088 100 115 119



textdbend (


158



textlhdbend (~




mdasha) 15





) 89


159



rsaquo) 15




ˆ) 15

textsubdot (a˙) 15


lsaquo) 15


˚) 15


˜) 15



ˇ) 16



) 16



160





textperthousand




119 120tipx (package) 12 119 120

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35







pitchfork


TriangleDown (3) 79






TriangleUp (1) 79





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 73

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



27 30 31 36ndash38 41 42 4850ndash52 65 66 68 100 102115 119 120


UU (a

˘) 17




ulcorner () 55

ullcorner (6) 55

ulrcorner () 55

ulsy (package) 24 48 103 119


161


underbrace (reg) 60



underbracket ( ) 60





underleftharp () 47
















urcorner () 55


ushortw ( ) 61ut (a

˜) 16


117utilde (˜) 61




162





varint (r




) 27


)

28varoiint (

) 28


) 28


) 28

varoint (u

) 26

varointclockwise (-

) 28



) 28




) 28







vdots () 63



versicle ( ) 118

VERT (

) 57


Village () 91



˚) 13


macr) 95

vpppm (macr



163


22 23 26 30 31 36ndash38 4164ndash66 70 71 73 77 78 88101 119 120





Ţ) 16














widering (u) 60

widering () 60





103 107 119 120wupperhand (c) 93

Xx (X) 65x (

˙˙) 95













xlongequal (===) 63

xlongequal (===) 62















Xs 77 90

XSolid () 77

XSolidBold ($) 77








Ztransf ( ) 36



ZwPa ( A ) 89

164

Contents

Introduction

Document Usage


Body-text symbols

















Text-mode Accents








semtrans Accents

ogonek Accents

combelow Accents

wsuipa Diacritics

textcomp Diacritics






eurosym Euro Signs

fourier Euro Signs









Binary Operators























Binary Relations

























Inequalities

AMS Inequalities









Arrows

Harpoons


AMS Arrows

AMS Negated Arrows

AMS Harpoons

stmaryrd Arrows


mathabx Arrows


mathabx Harpoons

MnSymbol Arrows


MnSymbol Harpoons



chemarrow Arrows

fge Arrows

MnSymbol Spoons

MnSymbol Pitchforks







Log-like Symbols



Greek Letters

AMS Greek Letters





AMS Hebrew Letters


Letter-like Symbols









AMS Delimiters

stmaryrd Delimiters

mathabx Delimiters

nath Delimiters













Math-mode Accents





Extensible Accents




















Dots

AMS Dots

wasysym Dots

MnSymbol Dots

mathdots Dots

yhmath Dots

teubner Dots


marvosym Digits

fge Digits















Math Alphabets











wasysym APL Symbols





milstd Logic Gates







Dingbats

bbding Arrows

pifont Arrows

universal Arrows

marvosym Scissors

bbding Scissors

pifont Scissors

dingbat Pencils



dingbat Fists

bbding Fists

pifont Fists

fourier Fists






universal Xs


wasysym Stars



fourier Ornaments











Ancient languages













Other symbols



wasysym Circles
















ifsym Clocks

Other ifsym Symbols

clock Clocks

epsdice Dice

hhcount Dice


skull Symbols




igo Go Stones













Symbol Name Clashes

Resizing symbols


Math-mode spacing



Unicode characters

About this document


References

Index

Symbols

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z


3


4




5




6



References 122

Index 123

7

1 Introduction





11 Document Usage








cent 18

e 18


permil 20 27

there4 30

B and F 31

and amp 38

64


L F etc 68

N Z R etc 68

r 68

minusint

105




8

2 Body-text symbols


















9





















10





11






12







˚vod


13





Alif Ayn





Aa =A=a Amacr

amacr







14












Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



15



Aˇ

aˇ



Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



16


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast



A a kAka


A a cbAcba


17



















18
















Ccopy ccsalowast


19











h permil

20





∐rdquo (coprod)











21












22











23











cshuffle shuffle


odplus

24








and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint

25


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint




notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





26



Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint




bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint



27


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28






















29


intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)


˙bigparr

˘bigwith







30




A inplus B niplus








31









32








33









34


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

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

def

ttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef


35





dfourier Dfourier

fourier Fourier













36




sqsubset A sqsupset










37













apprge gt apprle

















38

























39









40

Table 102 Arrows






Table 103 Harpoons










41









42






43









44




45












46






A chemarrow










47












48













49











50

















51












e e j im




52














niv vin

53



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

54


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert

55



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





56




triplegt

[[[[[[

triple[ ]]]]]]

triple]






llbracket

rrbracket

VERT








57


a ddddota





a veca


Andash




a ringa


58














˚abc wideringabc




59














abc widearrowabc





60












abcrsaquo utildeabc








61












abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG








62









a dfta a DFTa


abcdef

holterabcdefabcdef

polterabcdef

Table 189 Dots





63

Table 190 AMS Dots












iddots


adots


antilabe

64








X x E e





`surd





65













66
















67
















68



69















A AR




abc phaseabc


70




















71



















72


ANDd BUFu NANDl ORd


ANDr INVd NANDu ORr

ANDu INVl NORd ORu

BUFd INVr NORl

BUFl INVu 13 NORr

BUFr NANDd NORu









female male

73



















74

5 Dingbats



















75

























76











baucross







77
























78





























79
























80

6 Ancient languages





















81


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








82








83




84




























85






























86








87

7 Other symbols














88








Aa

aa


Aa

aa


Alal KrAKra



a












89










bauforms bauhead



90
























91





Cube1 Cube3 Cube5

Cube2 Cube4 Cube6





0 i i01 i1 i102 i2 i203 i3 i30










92


A skull


O rip



93






















94


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









95




Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart

96





























97






























98


A recycleA Recycle

A RECYCLE



99









82 Resizing symbols






100

Table

321

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

101



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


102

















103







endtabular












104

















105





one (ldquo=int





















106



makeatother








makeatother








e






107


makeatother




endarray










makeatother

108






ABCD









109













endcharend


110




1

2

3

4

5

6677

8







111


0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F
















112













Package Code Output



113




















114


















115




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


116

















117

usepackagetextcomp



which produces

It was a balmy 21








which produces






118















Name Date



119


Name Date



120


Name Date









121

References











122

Index




( (() 55

) ()) 54

) ()) 55

() 23 113- (-) 115 116 (a) 14 () 54

() 55

( ) 64

() 64

lt (⟨) 55

() 64

[ ([) 54

[ (⎡⎢⎢⎢⎢⎢⎣) 55

104] (]) 54

] (⎤⎥⎥⎥⎥⎥⎦) 55

^ (a) 14^ (ˆ) 9 115| () 54| () 54 56| (iquesta) 14= (a) 14= (macr) 115

| (

RRRRRRR) 55| (|) 30 54 56 57_ ( ) 9 115 () 9 54 115 () 9 54 115lsquo (a) 14~ (a) 14~ (˜) 9 115


) 95

AA (A) 10aa (a) 10

AAaleph (A) 81

AAayin (O) 81

AAbeth (B) 81


) 89

AAdaleth (D) 81

AAhe (E) 81

AAhelmet (V) 81

AAheth (h) 81

AAkaph (K) 81

AAlamed (L) 81

Aaleph (a) 81

AApe (P) 81

AAqoph (Q) 81

AAresh (R) 81

AAsade (X) 81

Aayin (o) 81

AAyod (Y) 81

Abeth (b) 81



AC () 70

acarc 16

acbar 16




arc (a) 14ndash17 59 60


caron (a) 14 18 57 60

cedilla (cedil) 14


comma-below (a) 17







hook (ả) 14



macron (a) 14 17 18 5759 60



ring (a) 14ndash16 18 57 58




accentset 107


AchtBL ( ˇ ldquo==

) 89




Adobe Acrobat 112

adots ( ) 64 107





African 10


123




and |

AltGr ( AltGr ) 72


AMS 8 10 22 26 30 31 3638 39 41 49ndash54 58 59 6164ndash66 69 100 118




41 58 65 68 87 119 120123



AND gates 73

ANDd () 73

ANDl () 73

ANDr () 73



text mode see AA
















Arrowvert (ww) 54

Arrowvert (

XXXXXXX) 55

arrowvert () 54

arrowvert (


117 119table 114



AsteriskBold (A) 78



AsteriskThin (C) 78



124



(EGGGGGGGGGGC) 62



(GGGGGBFGGGGG) 62



macr) 14

b (˘) 95


backslash () 55


Baii () 85





Bart (






tion) 68BBm (

macr) 95

Bbm (macr

) 95bBm (

macr) 95


bbm (macr

) 95bbmb ( ˘) 95bbmx (


Bda (d) 85


Bdi (f) 85

Bdo (g) 85

Bdu (x) 85

Bdwe (gt) 85

Bdwo () 85


Bi (i) 85bibridge (

rdquoardquo) 16



bigbosonloop ( ) 74



e) 26



THORN) 27

bigboxbot (Ucirc

) 27bigboxcirc (

Otilde) 27


) 27bigboxdiv (

Oacute) 27

bigboxdot (Ocirc

) 27bigboxleft (

Oslash) 27

bigboxminus (Ntilde

) 27bigboxplus (

ETH) 27

125

bigboxright (Ugrave

) 27bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 27

bigcap (⋂



) 27


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 26


) 26


AElig) 27



Euml) 27

bigocirc (Aring


Ccedil) 27

bigodiv (Atilde

) 27bigodot (

⊙) 25


Egrave) 27

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


bigotimes (otimes


Ecirc) 26


Iuml) 26


Igrave) 27

bigparallel (f) 26

bigparr (˙

) 30bigplus (

) 27

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 27


) 27

bigtimes (⨉) 29


`) 26






a) 26



⊎) 25



or) 25


and) 25


bigwith (˘





Bja (j) 85

Bje (J) 85

Bjo (b) 85

Bju (L) 85

Bka (k) 85

Bke (K) 85

Bki (c) 85

Bko (h) 85

Bku (v) 85















126

blank see textblank


macr) 95

bm (package) 113 119 121bm 113bm (

macr) 95

Bma (m) 85

Bme (M) 85

Bmi (y) 85

Bmo (A) 85bmod 49

Bmu (B) 85

Bna (n) 85

BNc (laquo) 85

BNcc (raquo) 85

BNccc (ndash) 85

BNcd (mdash) 85

BNcm (ff) 85

BNd (zwnj) 85

BNdc (permil) 85

BNdcc (ı) 85

BNdccc (ȷ) 85

Bne (N) 85

BNi (acute) 85

Bni (C) 85

BNii (ˆ) 85

BNiii (˜) 85

BNiv (uml) 85

BNix (macr) 85

BNl (lsaquo) 85

BNlx (rsaquo) 85

BNlxx (ldquo) 85

BNlxxx (rdquo) 85

BNm (fi) 85

Bno (E) 85

Bnu (F) 85

BNv (˝) 85

BNvi (˚) 85

BNvii (ˇ) 85

BNviii (˘) 85

Bnwa () 85

BNx (˙) 85

BNxc (bdquo) 85

BNxl (sbquo) 85

BNxx (cedil) 85

BNxxx (˛) 85





boy (D) 71

Bpa (p) 85

Bpaiii ([) 85

BPamphora (Ž) 86

BParrow (ĳ) 86

BPbarley (Ş) 86

BPbilly (ť) 86

BPboar (ľ) 86

BPbronze (Ű) 86

BPbull (ň) 86

BPcauldroni (đ) 86


BPchariot (yuml) 86

BPchassis (ź) 86

BPcloth (Ř) 86

BPcow (ŋ) 86

BPcup (Ÿ) 86

Bpe (P) 85

BPewe (š) 86

BPfoal (ě) 86

BPgoat (ş) 86

BPgoblet (Ź) 86

BPgold (Ů) 86

BPhorse (ď) 86

Bpi (G) 85

BPman (ă) 86

BPnanny (ț) 86

Bpo (H) 85

BPolive (Ț) 86

BPox (ń) 86

BPpig (ĺ) 86

BPram (ś) 86

BPsheep (ř) 86

BPsow (ł) 86

BPspear (iexcl) 86

BPsword (ż) 86

BPtalent (Ď) 85

Bpte (]) 85

Bpu (I) 85

Bpuii () 85

BPvola (Ĺ) 85

BPvolb (Ľ) 85

BPvolcd (Ł) 85

BPvolcf (Ń) 85

BPwheat (Š) 86

BPwheel (ž) 86

BPwine (Ť) 86

BPwineiih (Ż) 86

BPwineiiih (Ĳ) 86

BPwineivh (İ) 86

BPwoman (ą) 86

BPwool (Ś) 86

127

BPwta (Ă) 85

BPwtb (Ą) 85

BPwtc (Ć) 85

BPwtd (Č) 85

Bqa (q) 85

Bqe (Q) 85

Bqi (X) 85

Bqo (8) 85

Bra (r) 85

bra 54

braceld (︷) 109

bracerd (︷) 109

bracevert () 54

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 55


Braii (^) 85

Braiii (_) 85

braket (package) 54

Bre (R) 85

Break ( Break ) 72

breve (˘) 57

breve (a) 17


brevis (β) 95

Bri (O) 85

Bro (U) 85

Broii (lsquo) 85

brokenvert (|) 88

Bronger Torsten 105

Bru (V) 85

BS () 72

Bsa (s) 85

Bse (S) 85

BSEfree (n) 74

Bsi (Y) 85

Bso (1) 85


Bsu (2) 85

Bswa () 85

Bswi (|) 85

Bta (t) 85

Btaii () 85

Bte (T) 85

Bti (3) 85

Bto (4) 85

Btu (5) 85

Btwe (shy) 86

Btwo (~) 85

Bu (u) 85

BUFd () 73

buffers 73

BUFl () 73

BUFr () 73

BUFu () 73

BUi (fl) 86

BUii (ffi) 86

BUiii (ffl) 86

BUiv () 86



Burns (

) 96BusWidth () 73

BUv () 86

BUvi () 86

BUvii () 86

BUviii ($) 86

BUx (amp) 86

BUxi (rsquo) 86

BUxii (shy) 86

Bwa (w) 85

Bwe (W) 85

Bwi (6) 85

Bwo (7) 85

Bza (z) 85

Bze (Z) 85

Bzo (9) 85













CEsign (C) 74



Checkmark () 77

128



checkmark (D) 80


119 121chiup (χ) 50


Circle (5) 79








circledvee (U) 23


CircleShadow (d) 80


Cja (j) 86

Cjo (b) 86

Cka (k) 86

Cke (K) 86

Cki (c) 86

Cko (h) 86

Cku (v) 86

Cla (l) 86




clock (i1) 92



Cma (m) 86

Cme (M) 86


Cmo (A) 86

Cmu (B) 86

Cna (n) 86

Cne (N) 86

Cni (C) 86

Cno (E) 86

Cnu (F) 86






COMPLEX (raquo) 49

Complex (Atilde) 49

129



work 1 8 59 69 100117ndash119




and amp





∐) 21 25


Cpa (p) 86

Cpe (P) 86

Cpi (G) 86

Cpo (H) 86

Cpu (I) 86CR () 72cr 104

Cra (r) 86


Cri (O) 86

Cro (U) 86

Cross () 79



crossb () 13






Ŕa) 16




Csi (Y) 86

Cso (1) 86

Csu (2) 86



Cti (3) 86


Ctu (5) 86

Cu (u) 86





Cutright (q) 75

Cwa (w) 86

Cwe (W) 86

Cwi (6) 86

Cwo (7) 86

Cxa (x) 86

Cxe (X) 86

Cya (j) 86


Cza (g) 86

Czo (9) 86

DD (a

uml) 17




130


dashint (minusint

) 106


DavidStar (0) 78


ddashint (=int

) 106

ddddot (

) 58dddot (

) 58

dddtstile ( ) 35

ddigamma (ϝ) 87


ddots ( ) 63 107

ddots (⋱) 64

ddststile ( ) 35

ddtstile ( ) 35

ddttstile ( ) 35




DEL () 72Del ( Del ) 72






Dfourier ( ) 36

dfourier ( ) 36

DFT ( ) 63

















non-commutative 63

131




dndtstile ( ) 35

dnststile ( ) 35

dntstile ( ) 35




does not imply 105


dollar sign see $








macr) 28


dottedtilde (a) 16


doublecap see Cap






dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35


dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35







EightStar (H) 78





132

ell (`) 51





Enter ( Enter ) 72






ESC () 72Esc ( Esc ) 72






see nleftrightarrow

nequiv and oplus






textquotesingle


Ferli (aa) 89

Fermi (aa







feyngvs (s) 74


133



























(t) 79













fint (gt

) 27

fint (ffl) 28






FiveStar (8) 78




FiveStarOpen (9) 78






fixedddots ( ) 63

fixedvdots () 63










134


FourAsterisk (1) 78




57 60 76 78 91 119













87Greek coins 19


gtreqless (R) 38



gtreqqless (T) 38

gtreqqless (⪌) 39





h (ả) 14HA (A) 82









135



HandLeft () 76

HandLeftUp () 76


HandRight () 76



HB (B) 82

Hb (b) 82





HH 89


HI (I) 82

Hi (i) 82


Hibp (ˆ) 82

Hibs (uml) 82


mathhill (a

) 16


radic) 106

HL (L) 82Hl (l) 82HM (M) 82

Hm (m) 82

Hman (ˇ) 82

Hmillion (7) 82



holter ( ) 63


Homer (

) 96Hone (|) 82



Hplus (+) 82HQ (Q) 82Hq (q) 82


Hs (s) 82

Hscribe (macr) 82


Hthousand (4) 82

Htongue (˘) 82

HU (U) 82


Hut () 91


Hw (w) 82HX (X) 82

Hx (x) 82

HXthousand (5) 82

HY (Y) 82


HZ (Z) 82Hz (z) 82


iddots ( ) 64

iddots () 107


) 26

idotsint (

) 27


136

ifsym (package) 70 79 91 92101 103 119 120



) 26

iiiint (

) 27

iiiint (ˇ

) 28


micro) 27

iiint (intintint

) 26

iiint (

) 26 27

iiint (˝

) 28


acute) 27

iint (intint

) 26

iint (

) 26 28

iint (˜

) 28



and vdash


textquotedbl







injlim (inj lim) 49

inplus (A) 31


Ins ( Ins ) 72

int (sup3) 27

int (int

) 25 26

int (r

) 26

int (int) 29

intclockwise () 30

INTEGER (iquest) 49

Integer (Uacute) 49




intercal (ᵀ) 22

intercal (⊺) 52

interleave (9) 22


Interval () 91

inva () 13

invamp (M) 23

invbackneg (⨽) 66

INVd () 73

invdiameter () 88

inve (U) 13





inverters 73

invf () 13

invglotstop (d) 13

invh (amp) 13

INVl () 73

invlegr (I) 13

invm (5) 13

invneg () 31

invneg (⨼) 66

INVr () 73

invr (G) 13

invscr (K) 13

invscripta () 13

INVu () 73

invv () 13

invw (Z) 13

invy () 13

iota (ι) 50


iotaup (ι) 50

ipagamma ( ) 13

ipercatal (η) 95

IroningI (macr) 90

IroningII (deg) 90


irony mark ( ) 103



Jj () 14

JackStar (2) 78










137


landdownint () 28


) 28


langle (⟨) 55

langlebar (n) 55

Laplace ( ) 36





largepencil (W) 76



63 65 73 75 100 103ndash109112 113 115 117ndash119 121122

LATEX 2ε 1 89 19 20 22 30 36 41 5863 65 69 73 100 101 103106 107 111 112 114ndash117122






lceil (⎡⎢⎢⎢⎢⎢⎢) 55







leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56






leftwave (

ETH

ETH

ETH

ETH

) 56


138


lesseqgtr (Q) 38



lesseqqgtr (S) 38

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

LF () 72

lfilet (

7777) 55


lfloor (⎢⎢⎢⎢⎢⎢⎣) 55

lg (lg) 49

lgroup (

) 54

lgroup (⎧⎪⎪⎪⎪⎪⎩) 55

LHD () 23









139












140

LinearACXXI (x) 83


LinearACXXIX () 83





LinearAI () 82



LinearALIX () 83


LinearALVIII (9) 83













LinearAX () 82





LinearAXLIV (+) 83

LinearAXLIX (0) 83

LinearAXLV () 83




LinearAXXII () 83

LinearAXXIII () 83




Lisa (

) 96lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 55


llbracket (

) 57


llcorner () 55



lmoustache (

) 54





and see wedge

not see neg and sim

or see vee



141




lrcorner () 55

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 55



lwave (

ETH

ETH

ETH

ETH

) 56

lWavy (_______

) 55

lwavy (^^^) 55

lz (1) 13

MM 10M (

macr) 95

m 10m (

macr) 95


Maggie ( ) 96







Marge (










30 32 36ndash38 40 42 43 4952ndash55 58 60 65 66 71 93100 101 119 120 123





142




cient seeDH




metre (package) 17 57 95 119120


micro (micro) 70


textperthousand
















NANDd () 73

NANDl () 73

NANDr () 73


NATURAL (frac14) 49


alphabets math

143


ncong () 31


nddtstile ( ) 35



ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 38


ngeqq () 38

ngeqq (iquest) 39

ngeqslant () 38



144



ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 13

NibLeft () 76


NibSolidLeft ( ) 76





nleq () 38


nleqq () 38

nleqq (frac34) 39

nleqslant () 38





nlessgtr () 38

nlessgtr (≸) 39




nnststile ( ) 35

nntstile ( ) 35


145




NORd () 73


NORr (13) 73

NORu () 73



notni


npreceq (ordf) 32

npreceq () 31




146


nsststile ( ) 35

nststile ( ) 35


nsubseteq () 36


nsucceq () 31


nsupseteq (+) 36



ntdtstile ( ) 35






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35





NumLock ( Num ) 72




147




˚) 16


ohm (Ω) 70

Ohne (a ) 89


oiiint ()

) 28

oiiint (

) 30

oiiintclockwise (L

) 28


) 28

oiint (middot

) 27

oiint (

) 26 28

oiint (sbquo

) 28

oiint (

) 30

oiint (∯) 29

oiintclockwise (H

) 28

oiintctrclockwise (

) 28

oint (para) 27

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 30

ointctrclockwise (

) 27







OR gates 73


ORl () 73




overbrace (hkkikkj

) 60

overbrace (copy

) 60


) 60


) 59

overbracket ( ) 60


rdquoa) 16

overgroup (hkkkkj

) 60









PP (para) 9 116p (

˙) 95

p 107

148



amsmath 8 49 58 104 112amssymb 8 22 30 36 4158 65 68 87 119 120 123











mathdots 58 63 64 107119 120







t4phonet 14 17 119 120teubner 19 64 87 95 119120

textcomp 8 9 14 18ndash20 4157 67 70 88 100 115 119





149


wsuipa 13 16 18 101 103107 119 120




and parr




















textperthousand



PencilLeft () 76


PencilLeftUp () 76

PencilRight () 76







textrecipe


PHbee (h) 81

PHbeehive (X) 81

PHboomerang (R) 81

PHbow (K) 81

PHbullLeg (b) 81

PHcaptive (D) 81


PHcat (c) 81

PHchild (E) 81

PHclub (M) 81

PHcolumn (W) 81

PHcomb (U) 81

PHdolium (T) 81

PHdove (f) 81

PHeagle (e) 81

PHflute (o) 81

PHgaunlet (H) 81

PHgrater (p) 81

PHhelmet (G) 81

PHhide (a) 81

PHhorn (Z) 81

Phi (Φ) 50

phi (φ) 50

phiup (φ) 50

PHlid (Q) 81

PHlily (m) 81

PHmanacles (N) 81

PHmattock (O) 81

Phone () 80

phone () 88

PhoneHandset () 80



photon () 70

photons 74

PHoxBack (n) 81

PHpapyrus (k) 81

PHpedestrian (A) 81

PHplaneTree (i) 81

PHplumedHead (B) 81

PHram (d) 81

PHrosette (l) 81

PHsaw (P) 81

PHshield (L) 81

PHship (Y) 81

PHsling (V) 81

PHsmallAxe (r) 81

PHstrainer (q) 81


150


PHvine (j) 81

PHwavyBand (s) 81



pigpenfont A (A) 98

pigpenfont B (B) 98

pigpenfont C (C) 98

pigpenfont D (D) 98

pigpenfont E (E) 98

pigpenfont F (F) 98

pigpenfont G (G) 98

pigpenfont H (H) 98

pigpenfont I (I) 98

pigpenfont J (J) 98

pigpenfont K (K) 98

pigpenfont L (L) 98

pigpenfont M (M) 98

pigpenfont N (N) 98

pigpenfont O (O) 98

pigpenfont P (P) 98

pigpenfont Q (Q) 98

pigpenfont R (R) 98

pigpenfont S (S) 98

pigpenfont T (T) 98

pigpenfont U (U) 98

pigpenfont V (V) 98

pigpenfont W (W) 98

pigpenfont X (X) 98

pigpenfont Y (Y) 98


pipe see textpipe


Plane () 80






macr) 95



polter ( ) 63





macr) 95

Ppp (˙˙) 95

ppp ( ˙˙

) 95Pppp (˙

˙) 95

pppp ( ˙˙

) 95Ppppp (˙

˙) 95

ppppp ( ˙˙




prod) 25






31 36ndash38 41 42 48 50ndash5265 66 68 100 115

Pxp (˙) 95pxp ( ˙ ) 95


151



RR (sim

) 95r (a) 14r (sim

) 95



Rain () 91



rangle (⟩) 55

ranglebar (s) 55

RArrow ( rarr ) 72





hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 55





REAL (frac34) 49



recorder () 88

Rectangle (u) 80




rqm


textregistered





upharpoonright


Return ( larr ) 72


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

revD () 13

revddots ( ) 107


textbackslash



rfilet (

) 55


rfloor (⎥⎥⎥⎥⎥⎥⎦) 55

rgroup (

) 54

rgroup (⎫⎪⎪⎪⎪⎪⎭) 55


RightDiamond () 79

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56


152



rightwave (

ETH

ETH

ETH

ETH

) 56




rmoustache (

) 54



see accentsrook 94

roots see sqrt


rrangle (⟫) 55

rrbracket () 54

rrbracket (

) 57


rsem (MQQQQQO) 55



rwave (

ETH

ETH

ETH

ETH

) 56

rWavy (_______

) 55

rwavy (^^^) 55










ScissorLeft () 75




() 75


153


scu (W) 13scy (]) 13

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 89


) 89











membership see in

union see cup








([) 78

SixStar (G) 78





SmallCircle (E) 79











154



sndtstile ( ) 35

Snow () 91

SnowCloud () 91

Snowflake (`) 78



SNPP () 96

snststile ( ) 35

sntstile ( ) 35



Spacebar ( ) 72


Sparkle (]) 78


SpinDown () 79



sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

sqrt (radic


Square (0) 79




hooked see hksqrt


(k) 80




SquareShadowA () 79

SquareShadowB () 79


SquareShadowC () 79






ssststile ( ) 35

sststile ( ) 35


staveI () 97

staveII () 97

staveIII () 97

staveIV () 97

staveIX () 97

staveL (1) 97 98

155

staveLI (2) 97

staveLII (3) 97

staveLIII (4) 97

staveLIV (5) 97

staveLIX () 98

staveLV (6) 97

staveLVI (7) 97

staveLVII (8) 97


staveLXI (lt) 98

staveLXII (=) 98

staveLXIII (gt) 98

staveLXIV () 98

staveLXV () 98

staveLXVI (A) 98

staveLXVII (B) 98


staveV () 97

staveVI () 97

staveVII () 97

staveVIII () 97

staveX () 97

staveXI () 97

staveXII () 98

staveXIII () 98


staveXL () 98

staveXLI (() 98

staveXLII ()) 98


staveXLIX (0) 97

staveXLV () 98

staveXLVI (-) 98

staveXLVII () 97

staveXLVIII () 97

staveXV () 98

staveXVI () 98

staveXVII () 98

staveXVIII () 98


staveXXII () 98

staveXXIII () 98

staveXXIV () 97

staveXXIX () 97

staveXXV () 97

staveXXVI () 97

staveXXVII () 97

staveXXVIII () 97

staveXXX () 97

staveXXXI () 97

staveXXXII () 97

staveXXXIII ( ) 97

staveXXXIV () 97

staveXXXIX (amp) 98

staveXXXV () 98


stdtstile ( ) 35



40 42 48 53 54 101 104118ndash120



StopWatchEnd () 91


strokedint (⨏) 29

StrokeFive () 92

StrokeFour () 92

StrokeOne () 92

StrokeThree () 92


stststile ( ) 35

sttstile ( ) 35

stttstile ( ) 35


^) 16



sublptr (aiexcl) 16





156


sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 91




SunCloud () 91





`) 65




symA (Aacute) 68

symAE (Ucirc) 68


















157


Tape () 80



tddtstile ( ) 35

tdststile ( ) 35

tdtstile ( ) 35

tdttstile ( ) 35


Telephone (() 92



119 120TEX 40 47 64 70 97 100

103ndash109 111ndash113 115 117118 122








9 14 18ndash20 41 57 67 7088 100 115 119



textdbend (


158



textlhdbend (~




mdasha) 15





) 89


159



rsaquo) 15




ˆ) 15

textsubdot (a˙) 15


lsaquo) 15


˚) 15


˜) 15



ˇ) 16



) 16



160





textperthousand




119 120tipx (package) 12 119 120

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35







pitchfork


TriangleDown (3) 79






TriangleUp (1) 79





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 73

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



27 30 31 36ndash38 41 42 4850ndash52 65 66 68 100 102115 119 120


UU (a

˘) 17




ulcorner () 55

ullcorner (6) 55

ulrcorner () 55

ulsy (package) 24 48 103 119


161


underbrace (reg) 60



underbracket ( ) 60





underleftharp () 47
















urcorner () 55


ushortw ( ) 61ut (a

˜) 16


117utilde (˜) 61




162





varint (r




) 27


)

28varoiint (

) 28


) 28


) 28

varoint (u

) 26

varointclockwise (-

) 28



) 28




) 28







vdots () 63



versicle ( ) 118

VERT (

) 57


Village () 91



˚) 13


macr) 95

vpppm (macr



163


22 23 26 30 31 36ndash38 4164ndash66 70 71 73 77 78 88101 119 120





Ţ) 16














widering (u) 60

widering () 60





103 107 119 120wupperhand (c) 93

Xx (X) 65x (

˙˙) 95













xlongequal (===) 63

xlongequal (===) 62















Xs 77 90

XSolid () 77

XSolidBold ($) 77








Ztransf ( ) 36



ZwPa ( A ) 89

164

Contents

Introduction

Document Usage


Body-text symbols

















Text-mode Accents








semtrans Accents

ogonek Accents

combelow Accents

wsuipa Diacritics

textcomp Diacritics






eurosym Euro Signs

fourier Euro Signs









Binary Operators























Binary Relations

























Inequalities

AMS Inequalities









Arrows

Harpoons


AMS Arrows

AMS Negated Arrows

AMS Harpoons

stmaryrd Arrows


mathabx Arrows


mathabx Harpoons

MnSymbol Arrows


MnSymbol Harpoons



chemarrow Arrows

fge Arrows

MnSymbol Spoons

MnSymbol Pitchforks







Log-like Symbols



Greek Letters

AMS Greek Letters





AMS Hebrew Letters


Letter-like Symbols









AMS Delimiters

stmaryrd Delimiters

mathabx Delimiters

nath Delimiters













Math-mode Accents





Extensible Accents




















Dots

AMS Dots

wasysym Dots

MnSymbol Dots

mathdots Dots

yhmath Dots

teubner Dots


marvosym Digits

fge Digits















Math Alphabets











wasysym APL Symbols





milstd Logic Gates







Dingbats

bbding Arrows

pifont Arrows

universal Arrows

marvosym Scissors

bbding Scissors

pifont Scissors

dingbat Pencils



dingbat Fists

bbding Fists

pifont Fists

fourier Fists






universal Xs


wasysym Stars



fourier Ornaments











Ancient languages













Other symbols



wasysym Circles
















ifsym Clocks

Other ifsym Symbols

clock Clocks

epsdice Dice

hhcount Dice


skull Symbols




igo Go Stones













Symbol Name Clashes

Resizing symbols


Math-mode spacing



Unicode characters

About this document


References

Index

Symbols

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z


4




5




6



References 122

Index 123

7

1 Introduction





11 Document Usage








cent 18

e 18


permil 20 27

there4 30

B and F 31

and amp 38

64


L F etc 68

N Z R etc 68

r 68

minusint

105




8

2 Body-text symbols


















9





















10





11






12







˚vod


13





Alif Ayn





Aa =A=a Amacr

amacr







14












Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



15



Aˇ

aˇ



Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



16


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast



A a kAka


A a cbAcba


17



















18
















Ccopy ccsalowast


19











h permil

20





∐rdquo (coprod)











21












22











23











cshuffle shuffle


odplus

24








and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint

25


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint




notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





26



Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint




bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint



27


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28






















29


intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)


˙bigparr

˘bigwith







30




A inplus B niplus








31









32








33









34


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

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

def

ttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef


35





dfourier Dfourier

fourier Fourier













36




sqsubset A sqsupset










37













apprge gt apprle

















38

























39









40

Table 102 Arrows






Table 103 Harpoons










41









42






43









44




45












46






A chemarrow










47












48













49











50

















51












e e j im




52














niv vin

53



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

54


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert

55



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





56




triplegt

[[[[[[

triple[ ]]]]]]

triple]






llbracket

rrbracket

VERT








57


a ddddota





a veca


Andash




a ringa


58














˚abc wideringabc




59














abc widearrowabc





60












abcrsaquo utildeabc








61












abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG








62









a dfta a DFTa


abcdef

holterabcdefabcdef

polterabcdef

Table 189 Dots





63

Table 190 AMS Dots












iddots


adots


antilabe

64








X x E e





`surd





65













66
















67
















68



69















A AR




abc phaseabc


70




















71


















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

72


ANDd BUFu NANDl ORd


ANDr INVd NANDu ORr

ANDu INVl NORd ORu

BUFd INVr NORl

BUFl INVu 13 NORr

BUFr NANDd NORu









female male

73



















74

5 Dingbats



















75

























76











baucross







77
























78





























79
























80

6 Ancient languages





















81


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








82








83




84




























85






























86








87

7 Other symbols














88








Aa

aa


Aa

aa


Alal KrAKra



a












89










bauforms bauhead



90
























91





Cube1 Cube3 Cube5

Cube2 Cube4 Cube6





0 i i01 i1 i102 i2 i203 i3 i30










92


A skull


O rip



93






















94


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









95




Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart

96





























97






























98


A recycleA Recycle

A RECYCLE



99









82 Resizing symbols






100

Table

321

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

101



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


102

















103







endtabular












104

















105





one (ldquo=int





















106



makeatother








makeatother








e






107


makeatother




endarray










makeatother

108






ABCD









109













endcharend


110




1

2

3

4

5

6677

8







111


0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F
















112













Package Code Output



113




















114


















115




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


116

















117

usepackagetextcomp



which produces

It was a balmy 21








which produces






118















Name Date



119


Name Date



120


Name Date









121

References











122

Index




( (() 55

) ()) 54

) ()) 55

() 23 113- (-) 115 116 (a) 14 () 54

() 55

( ) 64

() 64

lt (⟨) 55

() 64

[ ([) 54

[ (⎡⎢⎢⎢⎢⎢⎣) 55

104] (]) 54

] (⎤⎥⎥⎥⎥⎥⎦) 55

^ (a) 14^ (ˆ) 9 115| () 54| () 54 56| (iquesta) 14= (a) 14= (macr) 115

| (

RRRRRRR) 55| (|) 30 54 56 57_ ( ) 9 115 () 9 54 115 () 9 54 115lsquo (a) 14~ (a) 14~ (˜) 9 115


) 95

AA (A) 10aa (a) 10

AAaleph (A) 81

AAayin (O) 81

AAbeth (B) 81


) 89

AAdaleth (D) 81

AAhe (E) 81

AAhelmet (V) 81

AAheth (h) 81

AAkaph (K) 81

AAlamed (L) 81

Aaleph (a) 81

AApe (P) 81

AAqoph (Q) 81

AAresh (R) 81

AAsade (X) 81

Aayin (o) 81

AAyod (Y) 81

Abeth (b) 81



AC () 70

acarc 16

acbar 16




arc (a) 14ndash17 59 60


caron (a) 14 18 57 60

cedilla (cedil) 14


comma-below (a) 17







hook (ả) 14



macron (a) 14 17 18 5759 60



ring (a) 14ndash16 18 57 58




accentset 107


AchtBL ( ˇ ldquo==

) 89




Adobe Acrobat 112

adots ( ) 64 107





African 10


123




and |

AltGr ( AltGr ) 72


AMS 8 10 22 26 30 31 3638 39 41 49ndash54 58 59 6164ndash66 69 100 118




41 58 65 68 87 119 120123



AND gates 73

ANDd () 73

ANDl () 73

ANDr () 73



text mode see AA
















Arrowvert (ww) 54

Arrowvert (

XXXXXXX) 55

arrowvert () 54

arrowvert (


117 119table 114



AsteriskBold (A) 78



AsteriskThin (C) 78



124



(EGGGGGGGGGGC) 62



(GGGGGBFGGGGG) 62



macr) 14

b (˘) 95


backslash () 55


Baii () 85





Bart (






tion) 68BBm (

macr) 95

Bbm (macr

) 95bBm (

macr) 95


bbm (macr

) 95bbmb ( ˘) 95bbmx (


Bda (d) 85


Bdi (f) 85

Bdo (g) 85

Bdu (x) 85

Bdwe (gt) 85

Bdwo () 85


Bi (i) 85bibridge (

rdquoardquo) 16



bigbosonloop ( ) 74



e) 26



THORN) 27

bigboxbot (Ucirc

) 27bigboxcirc (

Otilde) 27


) 27bigboxdiv (

Oacute) 27

bigboxdot (Ocirc

) 27bigboxleft (

Oslash) 27

bigboxminus (Ntilde

) 27bigboxplus (

ETH) 27

125

bigboxright (Ugrave

) 27bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 27

bigcap (⋂



) 27


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 26


) 26


AElig) 27



Euml) 27

bigocirc (Aring


Ccedil) 27

bigodiv (Atilde

) 27bigodot (

⊙) 25


Egrave) 27

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


bigotimes (otimes


Ecirc) 26


Iuml) 26


Igrave) 27

bigparallel (f) 26

bigparr (˙

) 30bigplus (

) 27

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 27


) 27

bigtimes (⨉) 29


`) 26






a) 26



⊎) 25



or) 25


and) 25


bigwith (˘





Bja (j) 85

Bje (J) 85

Bjo (b) 85

Bju (L) 85

Bka (k) 85

Bke (K) 85

Bki (c) 85

Bko (h) 85

Bku (v) 85















126

blank see textblank


macr) 95

bm (package) 113 119 121bm 113bm (

macr) 95

Bma (m) 85

Bme (M) 85

Bmi (y) 85

Bmo (A) 85bmod 49

Bmu (B) 85

Bna (n) 85

BNc (laquo) 85

BNcc (raquo) 85

BNccc (ndash) 85

BNcd (mdash) 85

BNcm (ff) 85

BNd (zwnj) 85

BNdc (permil) 85

BNdcc (ı) 85

BNdccc (ȷ) 85

Bne (N) 85

BNi (acute) 85

Bni (C) 85

BNii (ˆ) 85

BNiii (˜) 85

BNiv (uml) 85

BNix (macr) 85

BNl (lsaquo) 85

BNlx (rsaquo) 85

BNlxx (ldquo) 85

BNlxxx (rdquo) 85

BNm (fi) 85

Bno (E) 85

Bnu (F) 85

BNv (˝) 85

BNvi (˚) 85

BNvii (ˇ) 85

BNviii (˘) 85

Bnwa () 85

BNx (˙) 85

BNxc (bdquo) 85

BNxl (sbquo) 85

BNxx (cedil) 85

BNxxx (˛) 85





boy (D) 71

Bpa (p) 85

Bpaiii ([) 85

BPamphora (Ž) 86

BParrow (ĳ) 86

BPbarley (Ş) 86

BPbilly (ť) 86

BPboar (ľ) 86

BPbronze (Ű) 86

BPbull (ň) 86

BPcauldroni (đ) 86


BPchariot (yuml) 86

BPchassis (ź) 86

BPcloth (Ř) 86

BPcow (ŋ) 86

BPcup (Ÿ) 86

Bpe (P) 85

BPewe (š) 86

BPfoal (ě) 86

BPgoat (ş) 86

BPgoblet (Ź) 86

BPgold (Ů) 86

BPhorse (ď) 86

Bpi (G) 85

BPman (ă) 86

BPnanny (ț) 86

Bpo (H) 85

BPolive (Ț) 86

BPox (ń) 86

BPpig (ĺ) 86

BPram (ś) 86

BPsheep (ř) 86

BPsow (ł) 86

BPspear (iexcl) 86

BPsword (ż) 86

BPtalent (Ď) 85

Bpte (]) 85

Bpu (I) 85

Bpuii () 85

BPvola (Ĺ) 85

BPvolb (Ľ) 85

BPvolcd (Ł) 85

BPvolcf (Ń) 85

BPwheat (Š) 86

BPwheel (ž) 86

BPwine (Ť) 86

BPwineiih (Ż) 86

BPwineiiih (Ĳ) 86

BPwineivh (İ) 86

BPwoman (ą) 86

BPwool (Ś) 86

127

BPwta (Ă) 85

BPwtb (Ą) 85

BPwtc (Ć) 85

BPwtd (Č) 85

Bqa (q) 85

Bqe (Q) 85

Bqi (X) 85

Bqo (8) 85

Bra (r) 85

bra 54

braceld (︷) 109

bracerd (︷) 109

bracevert () 54

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 55


Braii (^) 85

Braiii (_) 85

braket (package) 54

Bre (R) 85

Break ( Break ) 72

breve (˘) 57

breve (a) 17


brevis (β) 95

Bri (O) 85

Bro (U) 85

Broii (lsquo) 85

brokenvert (|) 88

Bronger Torsten 105

Bru (V) 85

BS () 72

Bsa (s) 85

Bse (S) 85

BSEfree (n) 74

Bsi (Y) 85

Bso (1) 85


Bsu (2) 85

Bswa () 85

Bswi (|) 85

Bta (t) 85

Btaii () 85

Bte (T) 85

Bti (3) 85

Bto (4) 85

Btu (5) 85

Btwe (shy) 86

Btwo (~) 85

Bu (u) 85

BUFd () 73

buffers 73

BUFl () 73

BUFr () 73

BUFu () 73

BUi (fl) 86

BUii (ffi) 86

BUiii (ffl) 86

BUiv () 86



Burns (

) 96BusWidth () 73

BUv () 86

BUvi () 86

BUvii () 86

BUviii ($) 86

BUx (amp) 86

BUxi (rsquo) 86

BUxii (shy) 86

Bwa (w) 85

Bwe (W) 85

Bwi (6) 85

Bwo (7) 85

Bza (z) 85

Bze (Z) 85

Bzo (9) 85













CEsign (C) 74



Checkmark () 77

128



checkmark (D) 80


119 121chiup (χ) 50


Circle (5) 79








circledvee (U) 23


CircleShadow (d) 80


Cja (j) 86

Cjo (b) 86

Cka (k) 86

Cke (K) 86

Cki (c) 86

Cko (h) 86

Cku (v) 86

Cla (l) 86




clock (i1) 92



Cma (m) 86

Cme (M) 86


Cmo (A) 86

Cmu (B) 86

Cna (n) 86

Cne (N) 86

Cni (C) 86

Cno (E) 86

Cnu (F) 86






COMPLEX (raquo) 49

Complex (Atilde) 49

129



work 1 8 59 69 100117ndash119




and amp





∐) 21 25


Cpa (p) 86

Cpe (P) 86

Cpi (G) 86

Cpo (H) 86

Cpu (I) 86CR () 72cr 104

Cra (r) 86


Cri (O) 86

Cro (U) 86

Cross () 79



crossb () 13






Ŕa) 16




Csi (Y) 86

Cso (1) 86

Csu (2) 86



Cti (3) 86


Ctu (5) 86

Cu (u) 86





Cutright (q) 75

Cwa (w) 86

Cwe (W) 86

Cwi (6) 86

Cwo (7) 86

Cxa (x) 86

Cxe (X) 86

Cya (j) 86


Cza (g) 86

Czo (9) 86

DD (a

uml) 17




130


dashint (minusint

) 106


DavidStar (0) 78


ddashint (=int

) 106

ddddot (

) 58dddot (

) 58

dddtstile ( ) 35

ddigamma (ϝ) 87


ddots ( ) 63 107

ddots (⋱) 64

ddststile ( ) 35

ddtstile ( ) 35

ddttstile ( ) 35




DEL () 72Del ( Del ) 72






Dfourier ( ) 36

dfourier ( ) 36

DFT ( ) 63

















non-commutative 63

131




dndtstile ( ) 35

dnststile ( ) 35

dntstile ( ) 35




does not imply 105


dollar sign see $








macr) 28


dottedtilde (a) 16


doublecap see Cap






dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35


dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35







EightStar (H) 78





132

ell (`) 51





Enter ( Enter ) 72






ESC () 72Esc ( Esc ) 72






see nleftrightarrow

nequiv and oplus






textquotesingle


Ferli (aa) 89

Fermi (aa







feyngvs (s) 74


133



























(t) 79













fint (gt

) 27

fint (ffl) 28






FiveStar (8) 78




FiveStarOpen (9) 78






fixedddots ( ) 63

fixedvdots () 63










134


FourAsterisk (1) 78




57 60 76 78 91 119













87Greek coins 19


gtreqless (R) 38



gtreqqless (T) 38

gtreqqless (⪌) 39





h (ả) 14HA (A) 82









135



HandLeft () 76

HandLeftUp () 76


HandRight () 76



HB (B) 82

Hb (b) 82





HH 89


HI (I) 82

Hi (i) 82


Hibp (ˆ) 82

Hibs (uml) 82


mathhill (a

) 16


radic) 106

HL (L) 82Hl (l) 82HM (M) 82

Hm (m) 82

Hman (ˇ) 82

Hmillion (7) 82



holter ( ) 63


Homer (

) 96Hone (|) 82



Hplus (+) 82HQ (Q) 82Hq (q) 82


Hs (s) 82

Hscribe (macr) 82


Hthousand (4) 82

Htongue (˘) 82

HU (U) 82


Hut () 91


Hw (w) 82HX (X) 82

Hx (x) 82

HXthousand (5) 82

HY (Y) 82


HZ (Z) 82Hz (z) 82


iddots ( ) 64

iddots () 107


) 26

idotsint (

) 27


136

ifsym (package) 70 79 91 92101 103 119 120



) 26

iiiint (

) 27

iiiint (ˇ

) 28


micro) 27

iiint (intintint

) 26

iiint (

) 26 27

iiint (˝

) 28


acute) 27

iint (intint

) 26

iint (

) 26 28

iint (˜

) 28



and vdash


textquotedbl







injlim (inj lim) 49

inplus (A) 31


Ins ( Ins ) 72

int (sup3) 27

int (int

) 25 26

int (r

) 26

int (int) 29

intclockwise () 30

INTEGER (iquest) 49

Integer (Uacute) 49




intercal (ᵀ) 22

intercal (⊺) 52

interleave (9) 22


Interval () 91

inva () 13

invamp (M) 23

invbackneg (⨽) 66

INVd () 73

invdiameter () 88

inve (U) 13





inverters 73

invf () 13

invglotstop (d) 13

invh (amp) 13

INVl () 73

invlegr (I) 13

invm (5) 13

invneg () 31

invneg (⨼) 66

INVr () 73

invr (G) 13

invscr (K) 13

invscripta () 13

INVu () 73

invv () 13

invw (Z) 13

invy () 13

iota (ι) 50


iotaup (ι) 50

ipagamma ( ) 13

ipercatal (η) 95

IroningI (macr) 90

IroningII (deg) 90


irony mark ( ) 103



Jj () 14

JackStar (2) 78










137


landdownint () 28


) 28


langle (⟨) 55

langlebar (n) 55

Laplace ( ) 36





largepencil (W) 76



63 65 73 75 100 103ndash109112 113 115 117ndash119 121122

LATEX 2ε 1 89 19 20 22 30 36 41 5863 65 69 73 100 101 103106 107 111 112 114ndash117122






lceil (⎡⎢⎢⎢⎢⎢⎢) 55







leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56






leftwave (

ETH

ETH

ETH

ETH

) 56


138


lesseqgtr (Q) 38



lesseqqgtr (S) 38

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

LF () 72

lfilet (

7777) 55


lfloor (⎢⎢⎢⎢⎢⎢⎣) 55

lg (lg) 49

lgroup (

) 54

lgroup (⎧⎪⎪⎪⎪⎪⎩) 55

LHD () 23









139












140

LinearACXXI (x) 83


LinearACXXIX () 83





LinearAI () 82



LinearALIX () 83


LinearALVIII (9) 83













LinearAX () 82





LinearAXLIV (+) 83

LinearAXLIX (0) 83

LinearAXLV () 83




LinearAXXII () 83

LinearAXXIII () 83




Lisa (

) 96lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 55


llbracket (

) 57


llcorner () 55



lmoustache (

) 54





and see wedge

not see neg and sim

or see vee



141




lrcorner () 55

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 55



lwave (

ETH

ETH

ETH

ETH

) 56

lWavy (_______

) 55

lwavy (^^^) 55

lz (1) 13

MM 10M (

macr) 95

m 10m (

macr) 95


Maggie ( ) 96







Marge (










30 32 36ndash38 40 42 43 4952ndash55 58 60 65 66 71 93100 101 119 120 123





142




cient seeDH




metre (package) 17 57 95 119120


micro (micro) 70


textperthousand
















NANDd () 73

NANDl () 73

NANDr () 73


NATURAL (frac14) 49


alphabets math

143


ncong () 31


nddtstile ( ) 35



ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 38


ngeqq () 38

ngeqq (iquest) 39

ngeqslant () 38



144



ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 13

NibLeft () 76


NibSolidLeft ( ) 76





nleq () 38


nleqq () 38

nleqq (frac34) 39

nleqslant () 38





nlessgtr () 38

nlessgtr (≸) 39




nnststile ( ) 35

nntstile ( ) 35


145




NORd () 73


NORr (13) 73

NORu () 73



notni


npreceq (ordf) 32

npreceq () 31




146


nsststile ( ) 35

nststile ( ) 35


nsubseteq () 36


nsucceq () 31


nsupseteq (+) 36



ntdtstile ( ) 35






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35





NumLock ( Num ) 72




147




˚) 16


ohm (Ω) 70

Ohne (a ) 89


oiiint ()

) 28

oiiint (

) 30

oiiintclockwise (L

) 28


) 28

oiint (middot

) 27

oiint (

) 26 28

oiint (sbquo

) 28

oiint (

) 30

oiint (∯) 29

oiintclockwise (H

) 28

oiintctrclockwise (

) 28

oint (para) 27

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 30

ointctrclockwise (

) 27







OR gates 73


ORl () 73




overbrace (hkkikkj

) 60

overbrace (copy

) 60


) 60


) 59

overbracket ( ) 60


rdquoa) 16

overgroup (hkkkkj

) 60









PP (para) 9 116p (

˙) 95

p 107

148



amsmath 8 49 58 104 112amssymb 8 22 30 36 4158 65 68 87 119 120 123











mathdots 58 63 64 107119 120







t4phonet 14 17 119 120teubner 19 64 87 95 119120

textcomp 8 9 14 18ndash20 4157 67 70 88 100 115 119





149


wsuipa 13 16 18 101 103107 119 120




and parr




















textperthousand



PencilLeft () 76


PencilLeftUp () 76

PencilRight () 76







textrecipe


PHbee (h) 81

PHbeehive (X) 81

PHboomerang (R) 81

PHbow (K) 81

PHbullLeg (b) 81

PHcaptive (D) 81


PHcat (c) 81

PHchild (E) 81

PHclub (M) 81

PHcolumn (W) 81

PHcomb (U) 81

PHdolium (T) 81

PHdove (f) 81

PHeagle (e) 81

PHflute (o) 81

PHgaunlet (H) 81

PHgrater (p) 81

PHhelmet (G) 81

PHhide (a) 81

PHhorn (Z) 81

Phi (Φ) 50

phi (φ) 50

phiup (φ) 50

PHlid (Q) 81

PHlily (m) 81

PHmanacles (N) 81

PHmattock (O) 81

Phone () 80

phone () 88

PhoneHandset () 80



photon () 70

photons 74

PHoxBack (n) 81

PHpapyrus (k) 81

PHpedestrian (A) 81

PHplaneTree (i) 81

PHplumedHead (B) 81

PHram (d) 81

PHrosette (l) 81

PHsaw (P) 81

PHshield (L) 81

PHship (Y) 81

PHsling (V) 81

PHsmallAxe (r) 81

PHstrainer (q) 81


150


PHvine (j) 81

PHwavyBand (s) 81



pigpenfont A (A) 98

pigpenfont B (B) 98

pigpenfont C (C) 98

pigpenfont D (D) 98

pigpenfont E (E) 98

pigpenfont F (F) 98

pigpenfont G (G) 98

pigpenfont H (H) 98

pigpenfont I (I) 98

pigpenfont J (J) 98

pigpenfont K (K) 98

pigpenfont L (L) 98

pigpenfont M (M) 98

pigpenfont N (N) 98

pigpenfont O (O) 98

pigpenfont P (P) 98

pigpenfont Q (Q) 98

pigpenfont R (R) 98

pigpenfont S (S) 98

pigpenfont T (T) 98

pigpenfont U (U) 98

pigpenfont V (V) 98

pigpenfont W (W) 98

pigpenfont X (X) 98

pigpenfont Y (Y) 98


pipe see textpipe


Plane () 80






macr) 95



polter ( ) 63





macr) 95

Ppp (˙˙) 95

ppp ( ˙˙

) 95Pppp (˙

˙) 95

pppp ( ˙˙

) 95Ppppp (˙

˙) 95

ppppp ( ˙˙




prod) 25






31 36ndash38 41 42 48 50ndash5265 66 68 100 115

Pxp (˙) 95pxp ( ˙ ) 95


151



RR (sim

) 95r (a) 14r (sim

) 95



Rain () 91



rangle (⟩) 55

ranglebar (s) 55

RArrow ( rarr ) 72





hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 55





REAL (frac34) 49



recorder () 88

Rectangle (u) 80




rqm


textregistered





upharpoonright


Return ( larr ) 72


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

revD () 13

revddots ( ) 107


textbackslash



rfilet (

) 55


rfloor (⎥⎥⎥⎥⎥⎥⎦) 55

rgroup (

) 54

rgroup (⎫⎪⎪⎪⎪⎪⎭) 55


RightDiamond () 79

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56


152



rightwave (

ETH

ETH

ETH

ETH

) 56




rmoustache (

) 54



see accentsrook 94

roots see sqrt


rrangle (⟫) 55

rrbracket () 54

rrbracket (

) 57


rsem (MQQQQQO) 55



rwave (

ETH

ETH

ETH

ETH

) 56

rWavy (_______

) 55

rwavy (^^^) 55










ScissorLeft () 75




() 75


153


scu (W) 13scy (]) 13

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 89


) 89











membership see in

union see cup








([) 78

SixStar (G) 78





SmallCircle (E) 79











154



sndtstile ( ) 35

Snow () 91

SnowCloud () 91

Snowflake (`) 78



SNPP () 96

snststile ( ) 35

sntstile ( ) 35



Spacebar ( ) 72


Sparkle (]) 78


SpinDown () 79



sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

sqrt (radic


Square (0) 79




hooked see hksqrt


(k) 80




SquareShadowA () 79

SquareShadowB () 79


SquareShadowC () 79






ssststile ( ) 35

sststile ( ) 35


staveI () 97

staveII () 97

staveIII () 97

staveIV () 97

staveIX () 97

staveL (1) 97 98

155

staveLI (2) 97

staveLII (3) 97

staveLIII (4) 97

staveLIV (5) 97

staveLIX () 98

staveLV (6) 97

staveLVI (7) 97

staveLVII (8) 97


staveLXI (lt) 98

staveLXII (=) 98

staveLXIII (gt) 98

staveLXIV () 98

staveLXV () 98

staveLXVI (A) 98

staveLXVII (B) 98


staveV () 97

staveVI () 97

staveVII () 97

staveVIII () 97

staveX () 97

staveXI () 97

staveXII () 98

staveXIII () 98


staveXL () 98

staveXLI (() 98

staveXLII ()) 98


staveXLIX (0) 97

staveXLV () 98

staveXLVI (-) 98

staveXLVII () 97

staveXLVIII () 97

staveXV () 98

staveXVI () 98

staveXVII () 98

staveXVIII () 98


staveXXII () 98

staveXXIII () 98

staveXXIV () 97

staveXXIX () 97

staveXXV () 97

staveXXVI () 97

staveXXVII () 97

staveXXVIII () 97

staveXXX () 97

staveXXXI () 97

staveXXXII () 97

staveXXXIII ( ) 97

staveXXXIV () 97

staveXXXIX (amp) 98

staveXXXV () 98


stdtstile ( ) 35



40 42 48 53 54 101 104118ndash120



StopWatchEnd () 91


strokedint (⨏) 29

StrokeFive () 92

StrokeFour () 92

StrokeOne () 92

StrokeThree () 92


stststile ( ) 35

sttstile ( ) 35

stttstile ( ) 35


^) 16



sublptr (aiexcl) 16





156


sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 91




SunCloud () 91





`) 65




symA (Aacute) 68

symAE (Ucirc) 68


















157


Tape () 80



tddtstile ( ) 35

tdststile ( ) 35

tdtstile ( ) 35

tdttstile ( ) 35


Telephone (() 92



119 120TEX 40 47 64 70 97 100

103ndash109 111ndash113 115 117118 122








9 14 18ndash20 41 57 67 7088 100 115 119



textdbend (


158



textlhdbend (~




mdasha) 15





) 89


159



rsaquo) 15




ˆ) 15

textsubdot (a˙) 15


lsaquo) 15


˚) 15


˜) 15



ˇ) 16



) 16



160





textperthousand




119 120tipx (package) 12 119 120

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35







pitchfork


TriangleDown (3) 79






TriangleUp (1) 79





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 73

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



27 30 31 36ndash38 41 42 4850ndash52 65 66 68 100 102115 119 120


UU (a

˘) 17




ulcorner () 55

ullcorner (6) 55

ulrcorner () 55

ulsy (package) 24 48 103 119


161


underbrace (reg) 60



underbracket ( ) 60





underleftharp () 47
















urcorner () 55


ushortw ( ) 61ut (a

˜) 16


117utilde (˜) 61




162





varint (r




) 27


)

28varoiint (

) 28


) 28


) 28

varoint (u

) 26

varointclockwise (-

) 28



) 28




) 28







vdots () 63



versicle ( ) 118

VERT (

) 57


Village () 91



˚) 13


macr) 95

vpppm (macr



163


22 23 26 30 31 36ndash38 4164ndash66 70 71 73 77 78 88101 119 120





Ţ) 16














widering (u) 60

widering () 60





103 107 119 120wupperhand (c) 93

Xx (X) 65x (

˙˙) 95













xlongequal (===) 63

xlongequal (===) 62















Xs 77 90

XSolid () 77

XSolidBold ($) 77








Ztransf ( ) 36



ZwPa ( A ) 89

164

Contents

Introduction

Document Usage


Body-text symbols

















Text-mode Accents








semtrans Accents

ogonek Accents

combelow Accents

wsuipa Diacritics

textcomp Diacritics






eurosym Euro Signs

fourier Euro Signs









Binary Operators























Binary Relations

























Inequalities

AMS Inequalities









Arrows

Harpoons


AMS Arrows

AMS Negated Arrows

AMS Harpoons

stmaryrd Arrows


mathabx Arrows


mathabx Harpoons

MnSymbol Arrows


MnSymbol Harpoons



chemarrow Arrows

fge Arrows

MnSymbol Spoons

MnSymbol Pitchforks







Log-like Symbols



Greek Letters

AMS Greek Letters





AMS Hebrew Letters


Letter-like Symbols









AMS Delimiters

stmaryrd Delimiters

mathabx Delimiters

nath Delimiters













Math-mode Accents





Extensible Accents




















Dots

AMS Dots

wasysym Dots

MnSymbol Dots

mathdots Dots

yhmath Dots

teubner Dots


marvosym Digits

fge Digits















Math Alphabets











wasysym APL Symbols





milstd Logic Gates







Dingbats

bbding Arrows

pifont Arrows

universal Arrows

marvosym Scissors

bbding Scissors

pifont Scissors

dingbat Pencils



dingbat Fists

bbding Fists

pifont Fists

fourier Fists






universal Xs


wasysym Stars



fourier Ornaments











Ancient languages













Other symbols



wasysym Circles
















ifsym Clocks

Other ifsym Symbols

clock Clocks

epsdice Dice

hhcount Dice


skull Symbols




igo Go Stones













Symbol Name Clashes

Resizing symbols


Math-mode spacing



Unicode characters

About this document


References

Index

Symbols

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z




5




6



References 122

Index 123

7

1 Introduction





11 Document Usage








cent 18

e 18


permil 20 27

there4 30

B and F 31

and amp 38

64


L F etc 68

N Z R etc 68

r 68

minusint

105




8

2 Body-text symbols


















9





















10





11






12







˚vod


13





Alif Ayn





Aa =A=a Amacr

amacr







14












Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



15



Aˇ

aˇ



Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



16


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast



A a kAka


A a cbAcba


17



















18
















Ccopy ccsalowast


19











h permil

20





∐rdquo (coprod)











21












22











23











cshuffle shuffle


odplus

24








and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint

25


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint




notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





26



Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint




bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint



27


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28






















29


intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)


˙bigparr

˘bigwith







30




A inplus B niplus








31









32








33









34


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

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

def

ttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef


35





dfourier Dfourier

fourier Fourier













36




sqsubset A sqsupset










37













apprge gt apprle

















38

























39









40

Table 102 Arrows






Table 103 Harpoons










41









42






43









44




45












46






A chemarrow










47












48













49











50

















51












e e j im




52














niv vin

53



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

54


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert

55



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





56




triplegt

[[[[[[

triple[ ]]]]]]

triple]






llbracket

rrbracket

VERT








57


a ddddota





a veca


Andash




a ringa


58














˚abc wideringabc




59














abc widearrowabc





60












abcrsaquo utildeabc








61












abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG








62









a dfta a DFTa


abcdef

holterabcdefabcdef

polterabcdef

Table 189 Dots





63

Table 190 AMS Dots












iddots


adots


antilabe

64








X x E e





`surd





65













66
















67
















68



69















A AR




abc phaseabc


70




















71



















72


ANDd BUFu NANDl ORd


ANDr INVd NANDu ORr

ANDu INVl NORd ORu

BUFd INVr NORl

BUFl INVu 13 NORr

BUFr NANDd NORu









female male

73



















74

5 Dingbats



















75

























76











baucross







77
























78





























79
























80

6 Ancient languages





















81


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








82








83




84




























85






























86








87

7 Other symbols














88








Aa

aa


Aa

aa


Alal KrAKra



a












89










bauforms bauhead



90
























91





Cube1 Cube3 Cube5

Cube2 Cube4 Cube6





0 i i01 i1 i102 i2 i203 i3 i30










92


A skull


O rip



93






















94


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









95




Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart

96





























97






























98


A recycleA Recycle

A RECYCLE



99









82 Resizing symbols






100

Table

321

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

101



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


102

















103







endtabular












104

















105





one (ldquo=int





















106



makeatother








makeatother








e






107


makeatother




endarray










makeatother

108






ABCD









109













endcharend


110




1

2

3

4

5

6677

8







111


0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F
















112













Package Code Output



113




















114


















115




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


116

















117

usepackagetextcomp



which produces

It was a balmy 21








which produces






118















Name Date



119


Name Date



120


Name Date









121

References











122

Index




( (() 55

) ()) 54

) ()) 55

() 23 113- (-) 115 116 (a) 14 () 54

() 55

( ) 64

() 64

lt (⟨) 55

() 64

[ ([) 54

[ (⎡⎢⎢⎢⎢⎢⎣) 55

104] (]) 54

] (⎤⎥⎥⎥⎥⎥⎦) 55

^ (a) 14^ (ˆ) 9 115| () 54| () 54 56| (iquesta) 14= (a) 14= (macr) 115

| (

RRRRRRR) 55| (|) 30 54 56 57_ ( ) 9 115 () 9 54 115 () 9 54 115lsquo (a) 14~ (a) 14~ (˜) 9 115


) 95

AA (A) 10aa (a) 10

AAaleph (A) 81

AAayin (O) 81

AAbeth (B) 81


) 89

AAdaleth (D) 81

AAhe (E) 81

AAhelmet (V) 81

AAheth (h) 81

AAkaph (K) 81

AAlamed (L) 81

Aaleph (a) 81

AApe (P) 81

AAqoph (Q) 81

AAresh (R) 81

AAsade (X) 81

Aayin (o) 81

AAyod (Y) 81

Abeth (b) 81



AC () 70

acarc 16

acbar 16




arc (a) 14ndash17 59 60


caron (a) 14 18 57 60

cedilla (cedil) 14


comma-below (a) 17







hook (ả) 14



macron (a) 14 17 18 5759 60



ring (a) 14ndash16 18 57 58




accentset 107


AchtBL ( ˇ ldquo==

) 89




Adobe Acrobat 112

adots ( ) 64 107





African 10


123




and |

AltGr ( AltGr ) 72


AMS 8 10 22 26 30 31 3638 39 41 49ndash54 58 59 6164ndash66 69 100 118




41 58 65 68 87 119 120123



AND gates 73

ANDd () 73

ANDl () 73

ANDr () 73



text mode see AA
















Arrowvert (ww) 54

Arrowvert (

XXXXXXX) 55

arrowvert () 54

arrowvert (


117 119table 114



AsteriskBold (A) 78



AsteriskThin (C) 78



124



(EGGGGGGGGGGC) 62



(GGGGGBFGGGGG) 62



macr) 14

b (˘) 95


backslash () 55


Baii () 85





Bart (






tion) 68BBm (

macr) 95

Bbm (macr

) 95bBm (

macr) 95


bbm (macr

) 95bbmb ( ˘) 95bbmx (


Bda (d) 85


Bdi (f) 85

Bdo (g) 85

Bdu (x) 85

Bdwe (gt) 85

Bdwo () 85


Bi (i) 85bibridge (

rdquoardquo) 16



bigbosonloop ( ) 74



e) 26



THORN) 27

bigboxbot (Ucirc

) 27bigboxcirc (

Otilde) 27


) 27bigboxdiv (

Oacute) 27

bigboxdot (Ocirc

) 27bigboxleft (

Oslash) 27

bigboxminus (Ntilde

) 27bigboxplus (

ETH) 27

125

bigboxright (Ugrave

) 27bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 27

bigcap (⋂



) 27


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 26


) 26


AElig) 27



Euml) 27

bigocirc (Aring


Ccedil) 27

bigodiv (Atilde

) 27bigodot (

⊙) 25


Egrave) 27

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


bigotimes (otimes


Ecirc) 26


Iuml) 26


Igrave) 27

bigparallel (f) 26

bigparr (˙

) 30bigplus (

) 27

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 27


) 27

bigtimes (⨉) 29


`) 26






a) 26



⊎) 25



or) 25


and) 25


bigwith (˘





Bja (j) 85

Bje (J) 85

Bjo (b) 85

Bju (L) 85

Bka (k) 85

Bke (K) 85

Bki (c) 85

Bko (h) 85

Bku (v) 85















126

blank see textblank


macr) 95

bm (package) 113 119 121bm 113bm (

macr) 95

Bma (m) 85

Bme (M) 85

Bmi (y) 85

Bmo (A) 85bmod 49

Bmu (B) 85

Bna (n) 85

BNc (laquo) 85

BNcc (raquo) 85

BNccc (ndash) 85

BNcd (mdash) 85

BNcm (ff) 85

BNd (zwnj) 85

BNdc (permil) 85

BNdcc (ı) 85

BNdccc (ȷ) 85

Bne (N) 85

BNi (acute) 85

Bni (C) 85

BNii (ˆ) 85

BNiii (˜) 85

BNiv (uml) 85

BNix (macr) 85

BNl (lsaquo) 85

BNlx (rsaquo) 85

BNlxx (ldquo) 85

BNlxxx (rdquo) 85

BNm (fi) 85

Bno (E) 85

Bnu (F) 85

BNv (˝) 85

BNvi (˚) 85

BNvii (ˇ) 85

BNviii (˘) 85

Bnwa () 85

BNx (˙) 85

BNxc (bdquo) 85

BNxl (sbquo) 85

BNxx (cedil) 85

BNxxx (˛) 85





boy (D) 71

Bpa (p) 85

Bpaiii ([) 85

BPamphora (Ž) 86

BParrow (ĳ) 86

BPbarley (Ş) 86

BPbilly (ť) 86

BPboar (ľ) 86

BPbronze (Ű) 86

BPbull (ň) 86

BPcauldroni (đ) 86


BPchariot (yuml) 86

BPchassis (ź) 86

BPcloth (Ř) 86

BPcow (ŋ) 86

BPcup (Ÿ) 86

Bpe (P) 85

BPewe (š) 86

BPfoal (ě) 86

BPgoat (ş) 86

BPgoblet (Ź) 86

BPgold (Ů) 86

BPhorse (ď) 86

Bpi (G) 85

BPman (ă) 86

BPnanny (ț) 86

Bpo (H) 85

BPolive (Ț) 86

BPox (ń) 86

BPpig (ĺ) 86

BPram (ś) 86

BPsheep (ř) 86

BPsow (ł) 86

BPspear (iexcl) 86

BPsword (ż) 86

BPtalent (Ď) 85

Bpte (]) 85

Bpu (I) 85

Bpuii () 85

BPvola (Ĺ) 85

BPvolb (Ľ) 85

BPvolcd (Ł) 85

BPvolcf (Ń) 85

BPwheat (Š) 86

BPwheel (ž) 86

BPwine (Ť) 86

BPwineiih (Ż) 86

BPwineiiih (Ĳ) 86

BPwineivh (İ) 86

BPwoman (ą) 86

BPwool (Ś) 86

127

BPwta (Ă) 85

BPwtb (Ą) 85

BPwtc (Ć) 85

BPwtd (Č) 85

Bqa (q) 85

Bqe (Q) 85

Bqi (X) 85

Bqo (8) 85

Bra (r) 85

bra 54

braceld (︷) 109

bracerd (︷) 109

bracevert () 54

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 55


Braii (^) 85

Braiii (_) 85

braket (package) 54

Bre (R) 85

Break ( Break ) 72

breve (˘) 57

breve (a) 17


brevis (β) 95

Bri (O) 85

Bro (U) 85

Broii (lsquo) 85

brokenvert (|) 88

Bronger Torsten 105

Bru (V) 85

BS () 72

Bsa (s) 85

Bse (S) 85

BSEfree (n) 74

Bsi (Y) 85

Bso (1) 85


Bsu (2) 85

Bswa () 85

Bswi (|) 85

Bta (t) 85

Btaii () 85

Bte (T) 85

Bti (3) 85

Bto (4) 85

Btu (5) 85

Btwe (shy) 86

Btwo (~) 85

Bu (u) 85

BUFd () 73

buffers 73

BUFl () 73

BUFr () 73

BUFu () 73

BUi (fl) 86

BUii (ffi) 86

BUiii (ffl) 86

BUiv () 86



Burns (

) 96BusWidth () 73

BUv () 86

BUvi () 86

BUvii () 86

BUviii ($) 86

BUx (amp) 86

BUxi (rsquo) 86

BUxii (shy) 86

Bwa (w) 85

Bwe (W) 85

Bwi (6) 85

Bwo (7) 85

Bza (z) 85

Bze (Z) 85

Bzo (9) 85













CEsign (C) 74



Checkmark () 77

128



checkmark (D) 80


119 121chiup (χ) 50


Circle (5) 79








circledvee (U) 23


CircleShadow (d) 80


Cja (j) 86

Cjo (b) 86

Cka (k) 86

Cke (K) 86

Cki (c) 86

Cko (h) 86

Cku (v) 86

Cla (l) 86




clock (i1) 92



Cma (m) 86

Cme (M) 86


Cmo (A) 86

Cmu (B) 86

Cna (n) 86

Cne (N) 86

Cni (C) 86

Cno (E) 86

Cnu (F) 86






COMPLEX (raquo) 49

Complex (Atilde) 49

129



work 1 8 59 69 100117ndash119




and amp





∐) 21 25


Cpa (p) 86

Cpe (P) 86

Cpi (G) 86

Cpo (H) 86

Cpu (I) 86CR () 72cr 104

Cra (r) 86


Cri (O) 86

Cro (U) 86

Cross () 79



crossb () 13






Ŕa) 16




Csi (Y) 86

Cso (1) 86

Csu (2) 86



Cti (3) 86


Ctu (5) 86

Cu (u) 86





Cutright (q) 75

Cwa (w) 86

Cwe (W) 86

Cwi (6) 86

Cwo (7) 86

Cxa (x) 86

Cxe (X) 86

Cya (j) 86


Cza (g) 86

Czo (9) 86

DD (a

uml) 17




130


dashint (minusint

) 106


DavidStar (0) 78


ddashint (=int

) 106

ddddot (

) 58dddot (

) 58

dddtstile ( ) 35

ddigamma (ϝ) 87


ddots ( ) 63 107

ddots (⋱) 64

ddststile ( ) 35

ddtstile ( ) 35

ddttstile ( ) 35




DEL () 72Del ( Del ) 72






Dfourier ( ) 36

dfourier ( ) 36

DFT ( ) 63

















non-commutative 63

131




dndtstile ( ) 35

dnststile ( ) 35

dntstile ( ) 35




does not imply 105


dollar sign see $








macr) 28


dottedtilde (a) 16


doublecap see Cap






dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35


dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35







EightStar (H) 78





132

ell (`) 51





Enter ( Enter ) 72






ESC () 72Esc ( Esc ) 72






see nleftrightarrow

nequiv and oplus






textquotesingle


Ferli (aa) 89

Fermi (aa







feyngvs (s) 74


133



























(t) 79













fint (gt

) 27

fint (ffl) 28






FiveStar (8) 78




FiveStarOpen (9) 78






fixedddots ( ) 63

fixedvdots () 63










134


FourAsterisk (1) 78




57 60 76 78 91 119













87Greek coins 19


gtreqless (R) 38



gtreqqless (T) 38

gtreqqless (⪌) 39





h (ả) 14HA (A) 82









135



HandLeft () 76

HandLeftUp () 76


HandRight () 76



HB (B) 82

Hb (b) 82





HH 89


HI (I) 82

Hi (i) 82


Hibp (ˆ) 82

Hibs (uml) 82


mathhill (a

) 16


radic) 106

HL (L) 82Hl (l) 82HM (M) 82

Hm (m) 82

Hman (ˇ) 82

Hmillion (7) 82



holter ( ) 63


Homer (

) 96Hone (|) 82



Hplus (+) 82HQ (Q) 82Hq (q) 82


Hs (s) 82

Hscribe (macr) 82


Hthousand (4) 82

Htongue (˘) 82

HU (U) 82


Hut () 91


Hw (w) 82HX (X) 82

Hx (x) 82

HXthousand (5) 82

HY (Y) 82


HZ (Z) 82Hz (z) 82


iddots ( ) 64

iddots () 107


) 26

idotsint (

) 27


136

ifsym (package) 70 79 91 92101 103 119 120



) 26

iiiint (

) 27

iiiint (ˇ

) 28


micro) 27

iiint (intintint

) 26

iiint (

) 26 27

iiint (˝

) 28


acute) 27

iint (intint

) 26

iint (

) 26 28

iint (˜

) 28



and vdash


textquotedbl







injlim (inj lim) 49

inplus (A) 31


Ins ( Ins ) 72

int (sup3) 27

int (int

) 25 26

int (r

) 26

int (int) 29

intclockwise () 30

INTEGER (iquest) 49

Integer (Uacute) 49




intercal (ᵀ) 22

intercal (⊺) 52

interleave (9) 22


Interval () 91

inva () 13

invamp (M) 23

invbackneg (⨽) 66

INVd () 73

invdiameter () 88

inve (U) 13





inverters 73

invf () 13

invglotstop (d) 13

invh (amp) 13

INVl () 73

invlegr (I) 13

invm (5) 13

invneg () 31

invneg (⨼) 66

INVr () 73

invr (G) 13

invscr (K) 13

invscripta () 13

INVu () 73

invv () 13

invw (Z) 13

invy () 13

iota (ι) 50


iotaup (ι) 50

ipagamma ( ) 13

ipercatal (η) 95

IroningI (macr) 90

IroningII (deg) 90


irony mark ( ) 103



Jj () 14

JackStar (2) 78










137


landdownint () 28


) 28


langle (⟨) 55

langlebar (n) 55

Laplace ( ) 36





largepencil (W) 76



63 65 73 75 100 103ndash109112 113 115 117ndash119 121122

LATEX 2ε 1 89 19 20 22 30 36 41 5863 65 69 73 100 101 103106 107 111 112 114ndash117122






lceil (⎡⎢⎢⎢⎢⎢⎢) 55







leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56






leftwave (

ETH

ETH

ETH

ETH

) 56


138


lesseqgtr (Q) 38



lesseqqgtr (S) 38

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

LF () 72

lfilet (

7777) 55


lfloor (⎢⎢⎢⎢⎢⎢⎣) 55

lg (lg) 49

lgroup (

) 54

lgroup (⎧⎪⎪⎪⎪⎪⎩) 55

LHD () 23









139












140

LinearACXXI (x) 83


LinearACXXIX () 83





LinearAI () 82



LinearALIX () 83


LinearALVIII (9) 83













LinearAX () 82





LinearAXLIV (+) 83

LinearAXLIX (0) 83

LinearAXLV () 83




LinearAXXII () 83

LinearAXXIII () 83




Lisa (

) 96lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 55


llbracket (

) 57


llcorner () 55



lmoustache (

) 54





and see wedge

not see neg and sim

or see vee



141




lrcorner () 55

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 55



lwave (

ETH

ETH

ETH

ETH

) 56

lWavy (_______

) 55

lwavy (^^^) 55

lz (1) 13

MM 10M (

macr) 95

m 10m (

macr) 95


Maggie ( ) 96







Marge (










30 32 36ndash38 40 42 43 4952ndash55 58 60 65 66 71 93100 101 119 120 123





142




cient seeDH




metre (package) 17 57 95 119120


micro (micro) 70


textperthousand
















NANDd () 73

NANDl () 73

NANDr () 73


NATURAL (frac14) 49


alphabets math

143


ncong () 31


nddtstile ( ) 35



ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 38


ngeqq () 38

ngeqq (iquest) 39

ngeqslant () 38



144



ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 13

NibLeft () 76


NibSolidLeft ( ) 76





nleq () 38


nleqq () 38

nleqq (frac34) 39

nleqslant () 38





nlessgtr () 38

nlessgtr (≸) 39




nnststile ( ) 35

nntstile ( ) 35


145




NORd () 73


NORr (13) 73

NORu () 73



notni


npreceq (ordf) 32

npreceq () 31




146


nsststile ( ) 35

nststile ( ) 35


nsubseteq () 36


nsucceq () 31


nsupseteq (+) 36



ntdtstile ( ) 35






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35





NumLock ( Num ) 72




147




˚) 16


ohm (Ω) 70

Ohne (a ) 89


oiiint ()

) 28

oiiint (

) 30

oiiintclockwise (L

) 28


) 28

oiint (middot

) 27

oiint (

) 26 28

oiint (sbquo

) 28

oiint (

) 30

oiint (∯) 29

oiintclockwise (H

) 28

oiintctrclockwise (

) 28

oint (para) 27

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 30

ointctrclockwise (

) 27







OR gates 73


ORl () 73




overbrace (hkkikkj

) 60

overbrace (copy

) 60


) 60


) 59

overbracket ( ) 60


rdquoa) 16

overgroup (hkkkkj

) 60









PP (para) 9 116p (

˙) 95

p 107

148



amsmath 8 49 58 104 112amssymb 8 22 30 36 4158 65 68 87 119 120 123











mathdots 58 63 64 107119 120







t4phonet 14 17 119 120teubner 19 64 87 95 119120

textcomp 8 9 14 18ndash20 4157 67 70 88 100 115 119





149


wsuipa 13 16 18 101 103107 119 120




and parr




















textperthousand



PencilLeft () 76


PencilLeftUp () 76

PencilRight () 76







textrecipe


PHbee (h) 81

PHbeehive (X) 81

PHboomerang (R) 81

PHbow (K) 81

PHbullLeg (b) 81

PHcaptive (D) 81


PHcat (c) 81

PHchild (E) 81

PHclub (M) 81

PHcolumn (W) 81

PHcomb (U) 81

PHdolium (T) 81

PHdove (f) 81

PHeagle (e) 81

PHflute (o) 81

PHgaunlet (H) 81

PHgrater (p) 81

PHhelmet (G) 81

PHhide (a) 81

PHhorn (Z) 81

Phi (Φ) 50

phi (φ) 50

phiup (φ) 50

PHlid (Q) 81

PHlily (m) 81

PHmanacles (N) 81

PHmattock (O) 81

Phone () 80

phone () 88

PhoneHandset () 80



photon () 70

photons 74

PHoxBack (n) 81

PHpapyrus (k) 81

PHpedestrian (A) 81

PHplaneTree (i) 81

PHplumedHead (B) 81

PHram (d) 81

PHrosette (l) 81

PHsaw (P) 81

PHshield (L) 81

PHship (Y) 81

PHsling (V) 81

PHsmallAxe (r) 81

PHstrainer (q) 81


150


PHvine (j) 81

PHwavyBand (s) 81



pigpenfont A (A) 98

pigpenfont B (B) 98

pigpenfont C (C) 98

pigpenfont D (D) 98

pigpenfont E (E) 98

pigpenfont F (F) 98

pigpenfont G (G) 98

pigpenfont H (H) 98

pigpenfont I (I) 98

pigpenfont J (J) 98

pigpenfont K (K) 98

pigpenfont L (L) 98

pigpenfont M (M) 98

pigpenfont N (N) 98

pigpenfont O (O) 98

pigpenfont P (P) 98

pigpenfont Q (Q) 98

pigpenfont R (R) 98

pigpenfont S (S) 98

pigpenfont T (T) 98

pigpenfont U (U) 98

pigpenfont V (V) 98

pigpenfont W (W) 98

pigpenfont X (X) 98

pigpenfont Y (Y) 98


pipe see textpipe


Plane () 80






macr) 95



polter ( ) 63





macr) 95

Ppp (˙˙) 95

ppp ( ˙˙

) 95Pppp (˙

˙) 95

pppp ( ˙˙

) 95Ppppp (˙

˙) 95

ppppp ( ˙˙




prod) 25






31 36ndash38 41 42 48 50ndash5265 66 68 100 115

Pxp (˙) 95pxp ( ˙ ) 95


151



RR (sim

) 95r (a) 14r (sim

) 95



Rain () 91



rangle (⟩) 55

ranglebar (s) 55

RArrow ( rarr ) 72





hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 55





REAL (frac34) 49



recorder () 88

Rectangle (u) 80




rqm


textregistered





upharpoonright


Return ( larr ) 72


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

revD () 13

revddots ( ) 107


textbackslash



rfilet (

) 55


rfloor (⎥⎥⎥⎥⎥⎥⎦) 55

rgroup (

) 54

rgroup (⎫⎪⎪⎪⎪⎪⎭) 55


RightDiamond () 79

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56


152



rightwave (

ETH

ETH

ETH

ETH

) 56




rmoustache (

) 54



see accentsrook 94

roots see sqrt


rrangle (⟫) 55

rrbracket () 54

rrbracket (

) 57


rsem (MQQQQQO) 55



rwave (

ETH

ETH

ETH

ETH

) 56

rWavy (_______

) 55

rwavy (^^^) 55










ScissorLeft () 75




() 75


153


scu (W) 13scy (]) 13

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 89


) 89











membership see in

union see cup








([) 78

SixStar (G) 78





SmallCircle (E) 79











154



sndtstile ( ) 35

Snow () 91

SnowCloud () 91

Snowflake (`) 78



SNPP () 96

snststile ( ) 35

sntstile ( ) 35



Spacebar ( ) 72


Sparkle (]) 78


SpinDown () 79



sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

sqrt (radic


Square (0) 79




hooked see hksqrt


(k) 80




SquareShadowA () 79

SquareShadowB () 79


SquareShadowC () 79






ssststile ( ) 35

sststile ( ) 35


staveI () 97

staveII () 97

staveIII () 97

staveIV () 97

staveIX () 97

staveL (1) 97 98

155

staveLI (2) 97

staveLII (3) 97

staveLIII (4) 97

staveLIV (5) 97

staveLIX () 98

staveLV (6) 97

staveLVI (7) 97

staveLVII (8) 97


staveLXI (lt) 98

staveLXII (=) 98

staveLXIII (gt) 98

staveLXIV () 98

staveLXV () 98

staveLXVI (A) 98

staveLXVII (B) 98


staveV () 97

staveVI () 97

staveVII () 97

staveVIII () 97

staveX () 97

staveXI () 97

staveXII () 98

staveXIII () 98


staveXL () 98

staveXLI (() 98

staveXLII ()) 98


staveXLIX (0) 97

staveXLV () 98

staveXLVI (-) 98

staveXLVII () 97

staveXLVIII () 97

staveXV () 98

staveXVI () 98

staveXVII () 98

staveXVIII () 98


staveXXII () 98

staveXXIII () 98

staveXXIV () 97

staveXXIX () 97

staveXXV () 97

staveXXVI () 97

staveXXVII () 97

staveXXVIII () 97

staveXXX () 97

staveXXXI () 97

staveXXXII () 97

staveXXXIII ( ) 97

staveXXXIV () 97

staveXXXIX (amp) 98

staveXXXV () 98


stdtstile ( ) 35



40 42 48 53 54 101 104118ndash120



StopWatchEnd () 91


strokedint (⨏) 29

StrokeFive () 92

StrokeFour () 92

StrokeOne () 92

StrokeThree () 92


stststile ( ) 35

sttstile ( ) 35

stttstile ( ) 35


^) 16



sublptr (aiexcl) 16





156


sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 91




SunCloud () 91





`) 65




symA (Aacute) 68

symAE (Ucirc) 68


















157


Tape () 80



tddtstile ( ) 35

tdststile ( ) 35

tdtstile ( ) 35

tdttstile ( ) 35


Telephone (() 92



119 120TEX 40 47 64 70 97 100

103ndash109 111ndash113 115 117118 122








9 14 18ndash20 41 57 67 7088 100 115 119



textdbend (


158



textlhdbend (~




mdasha) 15





) 89


159



rsaquo) 15




ˆ) 15

textsubdot (a˙) 15


lsaquo) 15


˚) 15


˜) 15



ˇ) 16



) 16



160





textperthousand




119 120tipx (package) 12 119 120

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35







pitchfork


TriangleDown (3) 79






TriangleUp (1) 79





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 73

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



27 30 31 36ndash38 41 42 4850ndash52 65 66 68 100 102115 119 120


UU (a

˘) 17




ulcorner () 55

ullcorner (6) 55

ulrcorner () 55

ulsy (package) 24 48 103 119


161


underbrace (reg) 60



underbracket ( ) 60





underleftharp () 47
















urcorner () 55


ushortw ( ) 61ut (a

˜) 16


117utilde (˜) 61




162





varint (r




) 27


)

28varoiint (

) 28


) 28


) 28

varoint (u

) 26

varointclockwise (-

) 28



) 28




) 28







vdots () 63



versicle ( ) 118

VERT (

) 57


Village () 91



˚) 13


macr) 95

vpppm (macr



163


22 23 26 30 31 36ndash38 4164ndash66 70 71 73 77 78 88101 119 120





Ţ) 16














widering (u) 60

widering () 60





103 107 119 120wupperhand (c) 93

Xx (X) 65x (

˙˙) 95













xlongequal (===) 63

xlongequal (===) 62















Xs 77 90

XSolid () 77

XSolidBold ($) 77








Ztransf ( ) 36



ZwPa ( A ) 89

164

Contents

Introduction

Document Usage


Body-text symbols

















Text-mode Accents








semtrans Accents

ogonek Accents

combelow Accents

wsuipa Diacritics

textcomp Diacritics






eurosym Euro Signs

fourier Euro Signs









Binary Operators























Binary Relations

























Inequalities

AMS Inequalities









Arrows

Harpoons


AMS Arrows

AMS Negated Arrows

AMS Harpoons

stmaryrd Arrows


mathabx Arrows


mathabx Harpoons

MnSymbol Arrows


MnSymbol Harpoons



chemarrow Arrows

fge Arrows

MnSymbol Spoons

MnSymbol Pitchforks







Log-like Symbols



Greek Letters

AMS Greek Letters





AMS Hebrew Letters


Letter-like Symbols









AMS Delimiters

stmaryrd Delimiters

mathabx Delimiters

nath Delimiters













Math-mode Accents





Extensible Accents




















Dots

AMS Dots

wasysym Dots

MnSymbol Dots

mathdots Dots

yhmath Dots

teubner Dots


marvosym Digits

fge Digits















Math Alphabets











wasysym APL Symbols





milstd Logic Gates







Dingbats

bbding Arrows

pifont Arrows

universal Arrows

marvosym Scissors

bbding Scissors

pifont Scissors

dingbat Pencils



dingbat Fists

bbding Fists

pifont Fists

fourier Fists






universal Xs


wasysym Stars



fourier Ornaments











Ancient languages













Other symbols



wasysym Circles
















ifsym Clocks

Other ifsym Symbols

clock Clocks

epsdice Dice

hhcount Dice


skull Symbols




igo Go Stones













Symbol Name Clashes

Resizing symbols


Math-mode spacing



Unicode characters

About this document


References

Index

Symbols

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z




6



References 122

Index 123

7

1 Introduction





11 Document Usage








cent 18

e 18


permil 20 27

there4 30

B and F 31

and amp 38

64


L F etc 68

N Z R etc 68

r 68

minusint

105




8

2 Body-text symbols


















9





















10





11






12







˚vod


13





Alif Ayn





Aa =A=a Amacr

amacr







14












Arsaquo

arsaquo


Aldquo

aldquo


Amacr

amacr



Aˆ

aˆ


A˙a˙


Alsaquo

alsaquo





A˚

a˚



A˜

a˜


Auml

auml



15



Aˇ

aˇ



Aa




rdquoArdquo



â^



amacr



a



sublptrAsublptra




ŢaŢ

whistleAwhistlea






Aa


a˜

utAuta

A˚

a˚



16


Aa acutusAacutusa







A_




Auml

auml

DADa A˘

a˘

UAUa

Aa TATalowast



A a kAka


A a cbAcba


17



















18
















Ccopy ccsalowast


19











h permil

20





∐rdquo (coprod)











21












22











23











cshuffle shuffle


odplus

24








and andbigwedge

prodprodprod⋃ ⋃

bigcup⊔ ⊔

bigsqcup∐∐

coprodsumsum

sum⊙⊙bigodot

⊎ ⊎biguplus


bigoplusor or

bigvee∮ ∮

oint

25


intint intintiint





idotsint


embigbox

g obiginterleave

bigsqcap

bjbigcurlyvee

bignplus

`hbigtriangledown

ckbigcurlywedge

f nbigparallel

aibigtriangleup


r wintdagger

iint

$iiint

r wvarintlowast

u zvarointlowast

oiint




notbigcurlyvee



brvbarbigsqcap



laquobigcurlywedge


Ecircecircbigotop





26



Uumluumlbigboxvoid


Ucircucircbigboxbot

centbigcomplementop

bigplus



umlbigsquplus



iexclbigtimes


Eumleumlbigobot

microfrac12iiint

Ocircocircbigboxdot

Aringaringbigocirc

acute frac14iint



sup3 raquoint


Atildeatildebigodiv

middot iquestoiint

ETHethbigboxplus


para frac34oint




bigsqcapplus

13ointclockwise

bigsqcupplus

ointctrclockwise

gt fint

R Ssqiiint

(idotsint

P Qsqiint

ampiiiint

sqint

$iiint



27


iint


L Moiiintclockwise




) oiiint

- varointclockwise

H Ioiintclockwise


Aoiintctrclockwise

varprod

oiint


macr ˙dotsint

ı ointclockwise

ffl fint


ˇ ˘iiiint

rdquo bdquosqiint

˝ ˚iiint

rsaquo ldquosqint

˜ umliint

varoiint

amplanddownint


$landupint


sbquo lsaquooiint

28






















29


intclockwise

ointclockwise

oiiint

ointctrclockwise

oiint


int

) Garamond (int

) and

Charter (int

)


˙bigparr

˘bigwith







30




A inplus B niplus








31









32








33









34


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

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

def

ttststileabcdef

abc


defssdtstileabcdef

abc

def

tttstileabcdef

abc


defssststileabcdef

abc

def

ttttstileabcdef

abc


defsststileabcdef

abc


defssttstileabcdef


35





dfourier Dfourier

fourier Fourier













36




sqsubset A sqsupset










37













apprge gt apprle

















38

























39









40

Table 102 Arrows






Table 103 Harpoons










41









42






43









44




45












46






A chemarrow










47












48













49











50

















51












e e j im




52














niv vin

53



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

54


v1

ldbrack w9

rdbrack


~ thickvert ~

vvvert








^ ^^^

lwavy^ ^

^^


__________

lWavy___


( ( ( ) ) )⎧⎪⎩

⎧⎪⎪⎪⎪⎪⎩ lgroup⎫⎪⎭


⟦LPPPPPN

lsem ⟧MQQQQQO







[⎡⎢⎢⎢⎢⎢⎣

[ ]⎤⎥⎥⎥⎥⎥⎦


∣RRRRRRR | ∥



XXXXXXX Arrowvert

55



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





56




triplegt

[[[[[[

triple[ ]]]]]]

triple]






llbracket

rrbracket

VERT








57


a ddddota





a veca


Andash




a ringa


58














˚abc wideringabc




59














abc widearrowabc





60












abcrsaquo utildeabc








61












abcDGGGGGGG


abcGGGGGGGA


abcEGGGGGGGGGGGGGGC


abcGGGGGGGBFGGGGGGG








62









a dfta a DFTa


abcdef

holterabcdefabcdef

polterabcdef

Table 189 Dots





63

Table 190 AMS Dots












iddots


adots


antilabe

64








X x E e





`surd





65













66
















67
















68



69















A AR




abc phaseabc


70




















71



















72


ANDd BUFu NANDl ORd


ANDr INVd NANDu ORr

ANDu INVl NORd ORu

BUFd INVr NORl

BUFl INVu 13 NORr

BUFr NANDd NORu









female male

73



















74

5 Dingbats



















75

























76











baucross







77
























78





























79
























80

6 Ancient languages





















81


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








82








83




84




























85






























86








87

7 Other symbols














88








Aa

aa


Aa

aa


Alal KrAKra



a












89










bauforms bauhead



90
























91





Cube1 Cube3 Cube5

Cube2 Cube4 Cube6





0 i i01 i1 i102 i2 i203 i3 i30










92


A skull


O rip



93






















94


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









95




Bart

Homer Maggie SNPP

Burns

Lisa

Marge


LeftBart

96





























97






























98


A recycleA Recycle

A RECYCLE



99









82 Resizing symbols






100

Table

321

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

101



R R Rtextrecipe



trade

uparrow uarrx x x

xxuarr

minusrarr

top


middle


bottom


102

















103







endtabular












104

















105





one (ldquo=int





















106



makeatother








makeatother








e






107


makeatother




endarray










makeatother

108






ABCD









109













endcharend


110




1

2

3

4

5

6677

8







111


0 1 2 3 4 5 6 710x A ˝4x11x

˝8 ˝9 ˝A ˝B ˝C ˝D ˝E ˝F
















112













Package Code Output



113




















114


















115




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


116

















117

usepackagetextcomp



which produces

It was a balmy 21








which produces






118















Name Date



119


Name Date



120


Name Date









121

References











122

Index




( (() 55

) ()) 54

) ()) 55

() 23 113- (-) 115 116 (a) 14 () 54

() 55

( ) 64

() 64

lt (⟨) 55

() 64

[ ([) 54

[ (⎡⎢⎢⎢⎢⎢⎣) 55

104] (]) 54

] (⎤⎥⎥⎥⎥⎥⎦) 55

^ (a) 14^ (ˆ) 9 115| () 54| () 54 56| (iquesta) 14= (a) 14= (macr) 115

| (

RRRRRRR) 55| (|) 30 54 56 57_ ( ) 9 115 () 9 54 115 () 9 54 115lsquo (a) 14~ (a) 14~ (˜) 9 115


) 95

AA (A) 10aa (a) 10

AAaleph (A) 81

AAayin (O) 81

AAbeth (B) 81


) 89

AAdaleth (D) 81

AAhe (E) 81

AAhelmet (V) 81

AAheth (h) 81

AAkaph (K) 81

AAlamed (L) 81

Aaleph (a) 81

AApe (P) 81

AAqoph (Q) 81

AAresh (R) 81

AAsade (X) 81

Aayin (o) 81

AAyod (Y) 81

Abeth (b) 81



AC () 70

acarc 16

acbar 16




arc (a) 14ndash17 59 60


caron (a) 14 18 57 60

cedilla (cedil) 14


comma-below (a) 17







hook (ả) 14



macron (a) 14 17 18 5759 60



ring (a) 14ndash16 18 57 58




accentset 107


AchtBL ( ˇ ldquo==

) 89




Adobe Acrobat 112

adots ( ) 64 107





African 10


123




and |

AltGr ( AltGr ) 72


AMS 8 10 22 26 30 31 3638 39 41 49ndash54 58 59 6164ndash66 69 100 118




41 58 65 68 87 119 120123



AND gates 73

ANDd () 73

ANDl () 73

ANDr () 73



text mode see AA
















Arrowvert (ww) 54

Arrowvert (

XXXXXXX) 55

arrowvert () 54

arrowvert (


117 119table 114



AsteriskBold (A) 78



AsteriskThin (C) 78



124



(EGGGGGGGGGGC) 62



(GGGGGBFGGGGG) 62



macr) 14

b (˘) 95


backslash () 55


Baii () 85





Bart (






tion) 68BBm (

macr) 95

Bbm (macr

) 95bBm (

macr) 95


bbm (macr

) 95bbmb ( ˘) 95bbmx (


Bda (d) 85


Bdi (f) 85

Bdo (g) 85

Bdu (x) 85

Bdwe (gt) 85

Bdwo () 85


Bi (i) 85bibridge (

rdquoardquo) 16



bigbosonloop ( ) 74



e) 26



THORN) 27

bigboxbot (Ucirc

) 27bigboxcirc (

Otilde) 27


) 27bigboxdiv (

Oacute) 27

bigboxdot (Ocirc

) 27bigboxleft (

Oslash) 27

bigboxminus (Ntilde

) 27bigboxplus (

ETH) 27

125

bigboxright (Ugrave

) 27bigboxslash (

Yacute) 26

bigboxtimes (Ograve

) 26bigboxtop (

Uacute) 26


) 26bigboxvoid (

Uuml) 27

bigcap (⋂



) 27


⋃) 25



) 26

bigcurlyvee (b


) 26

bigcurlywedge (c




g) 26


) 26


AElig) 27



Euml) 27

bigocirc (Aring


Ccedil) 27

bigodiv (Atilde

) 27bigodot (

⊙) 25


Egrave) 27

bigominus (Aacute


oplus) 25


Eacute) 26

bigoslash (Iacute


bigotimes (otimes


Ecirc) 26


Iuml) 26


Igrave) 27

bigparallel (f) 26

bigparr (˙

) 30bigplus (

) 27

bigplus (+) 29


) 26

bigsqcap (


) 27


⊔) 25


) 27

bigsqcupplus (2) 29


) 27


) 27

bigtimes (⨉) 29


`) 26






a) 26



⊎) 25



or) 25


and) 25


bigwith (˘





Bja (j) 85

Bje (J) 85

Bjo (b) 85

Bju (L) 85

Bka (k) 85

Bke (K) 85

Bki (c) 85

Bko (h) 85

Bku (v) 85















126

blank see textblank


macr) 95

bm (package) 113 119 121bm 113bm (

macr) 95

Bma (m) 85

Bme (M) 85

Bmi (y) 85

Bmo (A) 85bmod 49

Bmu (B) 85

Bna (n) 85

BNc (laquo) 85

BNcc (raquo) 85

BNccc (ndash) 85

BNcd (mdash) 85

BNcm (ff) 85

BNd (zwnj) 85

BNdc (permil) 85

BNdcc (ı) 85

BNdccc (ȷ) 85

Bne (N) 85

BNi (acute) 85

Bni (C) 85

BNii (ˆ) 85

BNiii (˜) 85

BNiv (uml) 85

BNix (macr) 85

BNl (lsaquo) 85

BNlx (rsaquo) 85

BNlxx (ldquo) 85

BNlxxx (rdquo) 85

BNm (fi) 85

Bno (E) 85

Bnu (F) 85

BNv (˝) 85

BNvi (˚) 85

BNvii (ˇ) 85

BNviii (˘) 85

Bnwa () 85

BNx (˙) 85

BNxc (bdquo) 85

BNxl (sbquo) 85

BNxx (cedil) 85

BNxxx (˛) 85





boy (D) 71

Bpa (p) 85

Bpaiii ([) 85

BPamphora (Ž) 86

BParrow (ĳ) 86

BPbarley (Ş) 86

BPbilly (ť) 86

BPboar (ľ) 86

BPbronze (Ű) 86

BPbull (ň) 86

BPcauldroni (đ) 86


BPchariot (yuml) 86

BPchassis (ź) 86

BPcloth (Ř) 86

BPcow (ŋ) 86

BPcup (Ÿ) 86

Bpe (P) 85

BPewe (š) 86

BPfoal (ě) 86

BPgoat (ş) 86

BPgoblet (Ź) 86

BPgold (Ů) 86

BPhorse (ď) 86

Bpi (G) 85

BPman (ă) 86

BPnanny (ț) 86

Bpo (H) 85

BPolive (Ț) 86

BPox (ń) 86

BPpig (ĺ) 86

BPram (ś) 86

BPsheep (ř) 86

BPsow (ł) 86

BPspear (iexcl) 86

BPsword (ż) 86

BPtalent (Ď) 85

Bpte (]) 85

Bpu (I) 85

Bpuii () 85

BPvola (Ĺ) 85

BPvolb (Ľ) 85

BPvolcd (Ł) 85

BPvolcf (Ń) 85

BPwheat (Š) 86

BPwheel (ž) 86

BPwine (Ť) 86

BPwineiih (Ż) 86

BPwineiiih (Ĳ) 86

BPwineivh (İ) 86

BPwoman (ą) 86

BPwool (Ś) 86

127

BPwta (Ă) 85

BPwtb (Ą) 85

BPwtc (Ć) 85

BPwtd (Č) 85

Bqa (q) 85

Bqe (Q) 85

Bqi (X) 85

Bqo (8) 85

Bra (r) 85

bra 54

braceld (︷) 109

bracerd (︷) 109

bracevert () 54

bracevert (

⎪⎪⎪⎪⎪⎪⎪) 55


Braii (^) 85

Braiii (_) 85

braket (package) 54

Bre (R) 85

Break ( Break ) 72

breve (˘) 57

breve (a) 17


brevis (β) 95

Bri (O) 85

Bro (U) 85

Broii (lsquo) 85

brokenvert (|) 88

Bronger Torsten 105

Bru (V) 85

BS () 72

Bsa (s) 85

Bse (S) 85

BSEfree (n) 74

Bsi (Y) 85

Bso (1) 85


Bsu (2) 85

Bswa () 85

Bswi (|) 85

Bta (t) 85

Btaii () 85

Bte (T) 85

Bti (3) 85

Bto (4) 85

Btu (5) 85

Btwe (shy) 86

Btwo (~) 85

Bu (u) 85

BUFd () 73

buffers 73

BUFl () 73

BUFr () 73

BUFu () 73

BUi (fl) 86

BUii (ffi) 86

BUiii (ffl) 86

BUiv () 86



Burns (

) 96BusWidth () 73

BUv () 86

BUvi () 86

BUvii () 86

BUviii ($) 86

BUx (amp) 86

BUxi (rsquo) 86

BUxii (shy) 86

Bwa (w) 85

Bwe (W) 85

Bwi (6) 85

Bwo (7) 85

Bza (z) 85

Bze (Z) 85

Bzo (9) 85













CEsign (C) 74



Checkmark () 77

128



checkmark (D) 80


119 121chiup (χ) 50


Circle (5) 79








circledvee (U) 23


CircleShadow (d) 80


Cja (j) 86

Cjo (b) 86

Cka (k) 86

Cke (K) 86

Cki (c) 86

Cko (h) 86

Cku (v) 86

Cla (l) 86




clock (i1) 92



Cma (m) 86

Cme (M) 86


Cmo (A) 86

Cmu (B) 86

Cna (n) 86

Cne (N) 86

Cni (C) 86

Cno (E) 86

Cnu (F) 86






COMPLEX (raquo) 49

Complex (Atilde) 49

129



work 1 8 59 69 100117ndash119




and amp





∐) 21 25


Cpa (p) 86

Cpe (P) 86

Cpi (G) 86

Cpo (H) 86

Cpu (I) 86CR () 72cr 104

Cra (r) 86


Cri (O) 86

Cro (U) 86

Cross () 79



crossb () 13






Ŕa) 16




Csi (Y) 86

Cso (1) 86

Csu (2) 86



Cti (3) 86


Ctu (5) 86

Cu (u) 86





Cutright (q) 75

Cwa (w) 86

Cwe (W) 86

Cwi (6) 86

Cwo (7) 86

Cxa (x) 86

Cxe (X) 86

Cya (j) 86


Cza (g) 86

Czo (9) 86

DD (a

uml) 17




130


dashint (minusint

) 106


DavidStar (0) 78


ddashint (=int

) 106

ddddot (

) 58dddot (

) 58

dddtstile ( ) 35

ddigamma (ϝ) 87


ddots ( ) 63 107

ddots (⋱) 64

ddststile ( ) 35

ddtstile ( ) 35

ddttstile ( ) 35




DEL () 72Del ( Del ) 72






Dfourier ( ) 36

dfourier ( ) 36

DFT ( ) 63

















non-commutative 63

131




dndtstile ( ) 35

dnststile ( ) 35

dntstile ( ) 35




does not imply 105


dollar sign see $








macr) 28


dottedtilde (a) 16


doublecap see Cap






dststile ( ) 35

dsttstile ( ) 35

dtdtstile ( ) 35


dtststile ( ) 35

dttstile ( ) 35

dtttstile ( ) 35







EightStar (H) 78





132

ell (`) 51





Enter ( Enter ) 72






ESC () 72Esc ( Esc ) 72






see nleftrightarrow

nequiv and oplus






textquotesingle


Ferli (aa) 89

Fermi (aa







feyngvs (s) 74


133



























(t) 79













fint (gt

) 27

fint (ffl) 28






FiveStar (8) 78




FiveStarOpen (9) 78






fixedddots ( ) 63

fixedvdots () 63










134


FourAsterisk (1) 78




57 60 76 78 91 119













87Greek coins 19


gtreqless (R) 38



gtreqqless (T) 38

gtreqqless (⪌) 39





h (ả) 14HA (A) 82









135



HandLeft () 76

HandLeftUp () 76


HandRight () 76



HB (B) 82

Hb (b) 82





HH 89


HI (I) 82

Hi (i) 82


Hibp (ˆ) 82

Hibs (uml) 82


mathhill (a

) 16


radic) 106

HL (L) 82Hl (l) 82HM (M) 82

Hm (m) 82

Hman (ˇ) 82

Hmillion (7) 82



holter ( ) 63


Homer (

) 96Hone (|) 82



Hplus (+) 82HQ (Q) 82Hq (q) 82


Hs (s) 82

Hscribe (macr) 82


Hthousand (4) 82

Htongue (˘) 82

HU (U) 82


Hut () 91


Hw (w) 82HX (X) 82

Hx (x) 82

HXthousand (5) 82

HY (Y) 82


HZ (Z) 82Hz (z) 82


iddots ( ) 64

iddots () 107


) 26

idotsint (

) 27


136

ifsym (package) 70 79 91 92101 103 119 120



) 26

iiiint (

) 27

iiiint (ˇ

) 28


micro) 27

iiint (intintint

) 26

iiint (

) 26 27

iiint (˝

) 28


acute) 27

iint (intint

) 26

iint (

) 26 28

iint (˜

) 28



and vdash


textquotedbl







injlim (inj lim) 49

inplus (A) 31


Ins ( Ins ) 72

int (sup3) 27

int (int

) 25 26

int (r

) 26

int (int) 29

intclockwise () 30

INTEGER (iquest) 49

Integer (Uacute) 49




intercal (ᵀ) 22

intercal (⊺) 52

interleave (9) 22


Interval () 91

inva () 13

invamp (M) 23

invbackneg (⨽) 66

INVd () 73

invdiameter () 88

inve (U) 13





inverters 73

invf () 13

invglotstop (d) 13

invh (amp) 13

INVl () 73

invlegr (I) 13

invm (5) 13

invneg () 31

invneg (⨼) 66

INVr () 73

invr (G) 13

invscr (K) 13

invscripta () 13

INVu () 73

invv () 13

invw (Z) 13

invy () 13

iota (ι) 50


iotaup (ι) 50

ipagamma ( ) 13

ipercatal (η) 95

IroningI (macr) 90

IroningII (deg) 90


irony mark ( ) 103



Jj () 14

JackStar (2) 78










137


landdownint () 28


) 28


langle (⟨) 55

langlebar (n) 55

Laplace ( ) 36





largepencil (W) 76



63 65 73 75 100 103ndash109112 113 115 117ndash119 121122

LATEX 2ε 1 89 19 20 22 30 36 41 5863 65 69 73 100 101 103106 107 111 112 114ndash117122






lceil (⎡⎢⎢⎢⎢⎢⎢) 55







leftevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56






leftwave (

ETH

ETH

ETH

ETH

) 56


138


lesseqgtr (Q) 38



lesseqqgtr (S) 38

lesseqqgtr (⪋) 39





levaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

LF () 72

lfilet (

7777) 55


lfloor (⎢⎢⎢⎢⎢⎢⎣) 55

lg (lg) 49

lgroup (

) 54

lgroup (⎧⎪⎪⎪⎪⎪⎩) 55

LHD () 23









139












140

LinearACXXI (x) 83


LinearACXXIX () 83





LinearAI () 82



LinearALIX () 83


LinearALVIII (9) 83













LinearAX () 82





LinearAXLIV (+) 83

LinearAXLIX (0) 83

LinearAXLV () 83




LinearAXXII () 83

LinearAXXIII () 83




Lisa (

) 96lJoin (X) 31ll () 38ll () 37ll (≪) 39

llangle (⟪) 55


llbracket (

) 57


llcorner () 55



lmoustache (

) 54





and see wedge

not see neg and sim

or see vee



141




lrcorner () 55

lrJoin see Join

lrtimes () 31

lsem (LPPPPPN) 55



lwave (

ETH

ETH

ETH

ETH

) 56

lWavy (_______

) 55

lwavy (^^^) 55

lz (1) 13

MM 10M (

macr) 95

m 10m (

macr) 95


Maggie ( ) 96







Marge (










30 32 36ndash38 40 42 43 4952ndash55 58 60 65 66 71 93100 101 119 120 123





142




cient seeDH




metre (package) 17 57 95 119120


micro (micro) 70


textperthousand
















NANDd () 73

NANDl () 73

NANDr () 73


NATURAL (frac14) 49


alphabets math

143


ncong () 31


nddtstile ( ) 35



ndststile ( ) 35

ndtstile ( ) 35

ndttstile ( ) 35

ne see neq




ngeq () 38


ngeqq () 38

ngeqq (iquest) 39

ngeqslant () 38



144



ngtrless (amp) 38

ngtrless (≹) 39


nibeta () 13

NibLeft () 76


NibSolidLeft ( ) 76





nleq () 38


nleqq () 38

nleqq (frac34) 39

nleqslant () 38





nlessgtr () 38

nlessgtr (≸) 39




nnststile ( ) 35

nntstile ( ) 35


145




NORd () 73


NORr (13) 73

NORu () 73



notni


npreceq (ordf) 32

npreceq () 31




146


nsststile ( ) 35

nststile ( ) 35


nsubseteq () 36


nsucceq () 31


nsupseteq (+) 36



ntdtstile ( ) 35






ntststile ( ) 35

nttstile ( ) 35

ntttstile ( ) 35





NumLock ( Num ) 72




147




˚) 16


ohm (Ω) 70

Ohne (a ) 89


oiiint ()

) 28

oiiint (

) 30

oiiintclockwise (L

) 28


) 28

oiint (middot

) 27

oiint (

) 26 28

oiint (sbquo

) 28

oiint (

) 30

oiint (∯) 29

oiintclockwise (H

) 28

oiintctrclockwise (

) 28

oint (para) 27

oint (∮

) 25

oint (∮) 29

ointclockwise (

) 27


ointclockwise () 30

ointctrclockwise (

) 27







OR gates 73


ORl () 73




overbrace (hkkikkj

) 60

overbrace (copy

) 60


) 60


) 59

overbracket ( ) 60


rdquoa) 16

overgroup (hkkkkj

) 60









PP (para) 9 116p (

˙) 95

p 107

148



amsmath 8 49 58 104 112amssymb 8 22 30 36 4158 65 68 87 119 120 123











mathdots 58 63 64 107119 120







t4phonet 14 17 119 120teubner 19 64 87 95 119120

textcomp 8 9 14 18ndash20 4157 67 70 88 100 115 119





149


wsuipa 13 16 18 101 103107 119 120




and parr




















textperthousand



PencilLeft () 76


PencilLeftUp () 76

PencilRight () 76







textrecipe


PHbee (h) 81

PHbeehive (X) 81

PHboomerang (R) 81

PHbow (K) 81

PHbullLeg (b) 81

PHcaptive (D) 81


PHcat (c) 81

PHchild (E) 81

PHclub (M) 81

PHcolumn (W) 81

PHcomb (U) 81

PHdolium (T) 81

PHdove (f) 81

PHeagle (e) 81

PHflute (o) 81

PHgaunlet (H) 81

PHgrater (p) 81

PHhelmet (G) 81

PHhide (a) 81

PHhorn (Z) 81

Phi (Φ) 50

phi (φ) 50

phiup (φ) 50

PHlid (Q) 81

PHlily (m) 81

PHmanacles (N) 81

PHmattock (O) 81

Phone () 80

phone () 88

PhoneHandset () 80



photon () 70

photons 74

PHoxBack (n) 81

PHpapyrus (k) 81

PHpedestrian (A) 81

PHplaneTree (i) 81

PHplumedHead (B) 81

PHram (d) 81

PHrosette (l) 81

PHsaw (P) 81

PHshield (L) 81

PHship (Y) 81

PHsling (V) 81

PHsmallAxe (r) 81

PHstrainer (q) 81


150


PHvine (j) 81

PHwavyBand (s) 81



pigpenfont A (A) 98

pigpenfont B (B) 98

pigpenfont C (C) 98

pigpenfont D (D) 98

pigpenfont E (E) 98

pigpenfont F (F) 98

pigpenfont G (G) 98

pigpenfont H (H) 98

pigpenfont I (I) 98

pigpenfont J (J) 98

pigpenfont K (K) 98

pigpenfont L (L) 98

pigpenfont M (M) 98

pigpenfont N (N) 98

pigpenfont O (O) 98

pigpenfont P (P) 98

pigpenfont Q (Q) 98

pigpenfont R (R) 98

pigpenfont S (S) 98

pigpenfont T (T) 98

pigpenfont U (U) 98

pigpenfont V (V) 98

pigpenfont W (W) 98

pigpenfont X (X) 98

pigpenfont Y (Y) 98


pipe see textpipe


Plane () 80






macr) 95



polter ( ) 63





macr) 95

Ppp (˙˙) 95

ppp ( ˙˙

) 95Pppp (˙

˙) 95

pppp ( ˙˙

) 95Ppppp (˙

˙) 95

ppppp ( ˙˙




prod) 25






31 36ndash38 41 42 48 50ndash5265 66 68 100 115

Pxp (˙) 95pxp ( ˙ ) 95


151



RR (sim

) 95r (a) 14r (sim

) 95



Rain () 91



rangle (⟩) 55

ranglebar (s) 55

RArrow ( rarr ) 72





hbar




rceil (⎤⎥⎥⎥⎥⎥⎥) 55





REAL (frac34) 49



recorder () 88

Rectangle (u) 80




rqm


textregistered





upharpoonright


Return ( larr ) 72


revaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56

revD () 13

revddots ( ) 107


textbackslash



rfilet (

) 55


rfloor (⎥⎥⎥⎥⎥⎥⎦) 55

rgroup (

) 54

rgroup (⎫⎪⎪⎪⎪⎪⎭) 55


RightDiamond () 79

rightevaw (

Ntilde

Ntilde

Ntilde

Ntilde

) 56


152



rightwave (

ETH

ETH

ETH

ETH

) 56




rmoustache (

) 54



see accentsrook 94

roots see sqrt


rrangle (⟫) 55

rrbracket () 54

rrbracket (

) 57


rsem (MQQQQQO) 55



rwave (

ETH

ETH

ETH

ETH

) 56

rWavy (_______

) 55

rwavy (^^^) 55










ScissorLeft () 75




() 75


153


scu (W) 13scy (]) 13

sddtstile ( ) 35

sdststile ( ) 35

sdtstile ( ) 35

sdttstile ( ) 35





) 89


) 89











membership see in

union see cup








([) 78

SixStar (G) 78





SmallCircle (E) 79











154



sndtstile ( ) 35

Snow () 91

SnowCloud () 91

Snowflake (`) 78



SNPP () 96

snststile ( ) 35

sntstile ( ) 35



Spacebar ( ) 72


Sparkle (]) 78


SpinDown () 79



sqiiint (R

) 27

sqiint (P

) 27

sqiint (rdquo

) 28

sqint (

) 27

sqint (rsaquo) 28

sqrt (radic


Square (0) 79




hooked see hksqrt


(k) 80




SquareShadowA () 79

SquareShadowB () 79


SquareShadowC () 79






ssststile ( ) 35

sststile ( ) 35


staveI () 97

staveII () 97

staveIII () 97

staveIV () 97

staveIX () 97

staveL (1) 97 98

155

staveLI (2) 97

staveLII (3) 97

staveLIII (4) 97

staveLIV (5) 97

staveLIX () 98

staveLV (6) 97

staveLVI (7) 97

staveLVII (8) 97


staveLXI (lt) 98

staveLXII (=) 98

staveLXIII (gt) 98

staveLXIV () 98

staveLXV () 98

staveLXVI (A) 98

staveLXVII (B) 98


staveV () 97

staveVI () 97

staveVII () 97

staveVIII () 97

staveX () 97

staveXI () 97

staveXII () 98

staveXIII () 98


staveXL () 98

staveXLI (() 98

staveXLII ()) 98


staveXLIX (0) 97

staveXLV () 98

staveXLVI (-) 98

staveXLVII () 97

staveXLVIII () 97

staveXV () 98

staveXVI () 98

staveXVII () 98

staveXVIII () 98


staveXXII () 98

staveXXIII () 98

staveXXIV () 97

staveXXIX () 97

staveXXV () 97

staveXXVI () 97

staveXXVII () 97

staveXXVIII () 97

staveXXX () 97

staveXXXI () 97

staveXXXII () 97

staveXXXIII ( ) 97

staveXXXIV () 97

staveXXXIX (amp) 98

staveXXXV () 98


stdtstile ( ) 35



40 42 48 53 54 101 104118ndash120



StopWatchEnd () 91


strokedint (⨏) 29

StrokeFive () 92

StrokeFour () 92

StrokeOne () 92

StrokeThree () 92


stststile ( ) 35

sttstile ( ) 35

stttstile ( ) 35


^) 16



sublptr (aiexcl) 16





156


sum) 25

sum (sum) 29

sumint (⨋) 29

Summit () 91




SunCloud () 91





`) 65




symA (Aacute) 68

symAE (Ucirc) 68


















157


Tape () 80



tddtstile ( ) 35

tdststile ( ) 35

tdtstile ( ) 35

tdttstile ( ) 35


Telephone (() 92



119 120TEX 40 47 64 70 97 100

103ndash109 111ndash113 115 117118 122








9 14 18ndash20 41 57 67 7088 100 115 119



textdbend (


158



textlhdbend (~




mdasha) 15





) 89


159



rsaquo) 15




ˆ) 15

textsubdot (a˙) 15


lsaquo) 15


˚) 15


˜) 15



ˇ) 16



) 16



160





textperthousand




119 120tipx (package) 12 119 120

tndtstile ( ) 35

tnststile ( ) 35

tntstile ( ) 35







pitchfork


TriangleDown (3) 79






TriangleUp (1) 79





tststile ( ) 35

tsttstile ( ) 35

ttdtstile ( ) 35

TTsteel (š) 73

ttststile ( ) 35

tttstile ( ) 35

ttttstile ( ) 35



27 30 31 36ndash38 41 42 4850ndash52 65 66 68 100 102115 119 120


UU (a

˘) 17




ulcorner () 55

ullcorner (6) 55

ulrcorner () 55

ulsy (package) 24 48 103 119


161


underbrace (reg) 60



underbracket ( ) 60





underleftharp () 47
















urcorner () 55


ushortw ( ) 61ut (a

˜) 16


117utilde (˜) 61




162





varint (r




) 27


)

28varoiint (

) 28


) 28


) 28

varoint (u

) 26

varointclockwise (-

) 28



) 28




) 28







vdots () 63



versicle ( ) 118

VERT (

) 57


Village () 91



˚) 13


macr) 95

vpppm (macr



163


22 23 26 30 31 36ndash38 4164ndash66 70 71 73 77 78 88101 119 120





Ţ) 16














widering (u) 60

widering () 60





103 107 119 120wupperhand (c) 93

Xx (X) 65x (

˙˙) 95













xlongequal (===) 63

xlongequal (===) 62















Xs 77 90

XSolid () 77

XSolidBold ($) 77








Ztransf ( ) 36



ZwPa ( A ) 89

164

Contents

Introduction

Document Usage


Body-text symbols

















Text-mode Accents








semtrans Accents

ogonek Accents

combelow Accents

wsuipa Diacritics

textcomp Diacritics






eurosym Euro Signs

fourier Euro Signs









Binary Operators























Binary Relations

























Inequalities

AMS Inequalities









Arrows

Harpoons


AMS Arrows

AMS Negated Arrows

AMS Harpoons

stmaryrd Arrows


mathabx Arrows


mathabx Harpoons

MnSymbol Arrows


MnSymbol Harpoons



chemarrow Arrows

fge Arrows

MnSymbol Spoons

MnSymbol Pitchforks







Log-like Symbols



Greek Letters

AMS Greek Letters





AMS Hebrew Letters


Letter-like Symbols









AMS Delimiters

stmaryrd Delimiters

mathabx Delimiters

nath Delimiters













Math-mode Accents





Extensible Accents




















Dots

AMS Dots

wasysym Dots

MnSymbol Dots

mathdots Dots

yhmath Dots

teubner Dots


marvosym Digits

fge Digits















Math Alphabets











wasysym APL Symbols





milstd Logic Gates







Dingbats

bbding Arrows

pifont Arrows

universal Arrows

marvosym Scissors

bbding Scissors

pifont Scissors

dingbat Pencils



dingbat Fists

bbding Fists

pifont Fists

fourier Fists






universal Xs


wasysym Stars



fourier Ornaments











Ancient languages













Other symbols



wasysym Circles
















ifsym Clocks

Other ifsym Symbols

clock Clocks

epsdice Dice

hhcount Dice


skull Symbols




igo Go Stones













Symbol Name Clashes

Resizing symbols


Math-mode spacing



Unicode characters

About this document


References

Index

Symbols

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

The Comprehensive LaTeX Symbol List - The UK TeX Archive Web pages

Documents

Transcript of The Comprehensive LaTeX Symbol List - The UK TeX Archive Web pages