Table Of ContentTEX Reference Card Relations Accents
(forPlainTEX) \leqor\le \geqor\ge \equiv Type Example InMath InText
≤ ≥ ≡
\prec \succ \sim hat aˆ \hat \^
Greek Letters ≺ (cid:31) ∼
\preceq \succeq \simeq expandinghat abc \widehat none
(cid:22) (cid:23) (cid:39)
α \alpha ι \iota (cid:37) \varrho (cid:28) \ll (cid:29) \gg (cid:16) \asymp check (cid:100)aˇ \check \v
\subset \supset \approx tilde a˜ \tilde \~
β \beta κ \kappa σ \sigma ⊂ ⊃ ≈
γ \gamma λ \lambda ς \varsigma ⊆ \subseteq ⊇ \supseteq ∼= \cong expandingtilde abc \widetilde none
δ \delta µ \mu τ \tau (cid:118) \sqsubseteq (cid:119) \sqsupseteq (cid:46)(cid:47) \bowtie acute (cid:103)a´ \acute \’
\in / \notin \nior\owns grave a` \grave \‘
(cid:15) \epsilon ν \nu υ \upsilon ∈ ∈ (cid:51)
\vdash \dashv = \models dot a˙ \dot \.
ε \varepsilon ξ \xi φ \phi (cid:96) (cid:97) |.
(cid:94) \smile \mid = \doteq doubledot a¨ \ddot \"
ζ \zeta o \o ϕ \varphi |
(cid:95) \frown \parallet \perp breve a˘ \breve \u
η \eta π \pi χ \chi (cid:107) ⊥
\propto bar a¯ \bar \=
θ \theta (cid:36) \varpi ψ \psi ∝
vector (cid:126)a \vec none
ϑ \vartheta ρ \rho ω \omega Mostrelationscanbenegated byprefixingthemwith\not.
The \skew number command shifts accents for proper posi-
Γ \Gamma Ξ \Xi Φ \Phi \not\equiv / \notin = \ne (cid:104) (cid:105)
(cid:54)≡ ∈ (cid:54) tioning,thelargerthe number ,themorerighttheshift. Com-
∆ \Delta Π \Pi Ψ \Psi Arrows pare (cid:104) (cid:105)
Θ \Theta Σ \Sigma Ω \Omega
Λ \Lambda Υ \Upsilon \leftarrow or\gets \longleftarrow \hat{\hat A}givesAˆˆ, \skew6\hat{\hat A}gives Aˆˆ.
← ←−
Symbols of Type Ord ⇐ \Leftarrow ⇐= \Longleftarrow Elementary Math Control Sequences
\rightarrow or\to \longrightarrow
→ −→
ℵ \aleph (cid:48) \prime ∀ \forall ⇒ \Rightarrow =⇒ \Longrightarrow overlineaformula x+y \overline{x+y}
h¯ı \\hibmaarth ∅ \\enmapbtlyaset ∃ \\enxeigsotrs\lnot ↔ \\lLeeffttrriigghhttaarrrrooww ←→ \\lLoonngglleeffttrriigghhttaarrrrooww underlineaformula x+y \underline{x+y}
(cid:96) \\ejlmlath ∇√ \\tsouprd ¬(cid:92)(cid:91) \\nfaltautral ⇔(cid:55)→(cid:45) \\hmoaopkslteoftarrow ⇐(cid:44)(cid:55)−→⇒ \\hlooonkgrmiagphsttaorrow hsqiguhaerreorordoetrroots √√nxx++22 \\srqorott{xn+\2o}f{x+2}
(cid:62) ← → n+1
℘ \wp \bot (cid:93) \sharp \uparrow \Uparrow fraction {n+1\over 3}
\Re ⊥ \| \clubsuit ↑ \downarrow ⇑ \Downarrow 3
(cid:60) \Im (cid:107)(cid:54) \angle ♣ \diamondsuit ↓ \updownarrow ⇓ \Updownarrow fraction,noline n+1 {n+1\atop 3}
∂(cid:61) \partial \triangle ♦ \heartsuit (cid:108) \nearrow (cid:109) \searrow 3
\infty (cid:52) \backslash ♥ \spadesuit (cid:37) \nwarrow (cid:38) \swarrow binomialcoeff. n+1 {n+1\choose 3}
L∞arge Operat\ors ♠ (cid:45)The\buildrel macroputsonesy(cid:46)mboloveranother. Thefor- (cid:16)n+3 1(cid:17)
matis\buildrel(cid:104)superscript(cid:105)\over(cid:104)relation(cid:105). bracedfraction (cid:110) 3 (cid:111) {n+1\brace 3}
\sum \bigcap \bigodot αβ \buildrel\alpha\beta\over\longrightarrow n+1
(cid:81)(cid:80) \\cporpordod (cid:83)(cid:84) \\bbiiggscqucpup (cid:78)(cid:74) \\bbiiggooptliumses f(x)−d=e→fx+1 f(x)\; {\buildrel\rm def\over=} \;x+1 Tbrhaeckfeotlleodwfirnagctsipoencifyastyle(cid:104)for3typ(cid:105)esetting f{onrm+1u\lbarsa.ck 3}
(cid:96) \int (cid:70) \bigvee (cid:76) \biguplus Delimeters
(cid:82) \oint (cid:87) \bigwedge (cid:85) \displaystyle \textstyle \scriptstyle \scriptscriptstyle
(cid:72) (cid:86) [ \lbrack or[ \lbrace or\{ \langle Non-Italic Function Names
Binary Operations ] \rbrack or] { \rbrace or\} (cid:104) \rangle
\vertor| } \lfloor (cid:105) \lceil \arccos \cos \csc \exp \ker \limsup \min \sinh
\pm \cap \veeor\lor | (cid:98) (cid:100)
± ∩ ∨ \Vertor\| \rfloor \rceil \arcsin \cosh \deg \gcd \lg \ln \Pr \sup
∓ \mp ∪ \cup ∧ \wedgeor\land (cid:107)[[ [\![ (cid:99)(( (\!( (cid:101) \langle\!\langle \arctan \cot \det \hom \lim \log \sec \tan
\ \setminus (cid:93) \uplus ⊕ \oplus ]] ]\!] )) )\!) (cid:104)(cid:104) \rangle\!\rangle \arg \coth \dim \inf \liminf \max \sin \tanh
\cdot \sqcap \ominus (cid:105)(cid:105) a \pmod{m} a (modm) modwithparentheses
· \times (cid:117) \sqcup (cid:9) \otimes Left and right delimeters willbe enlarged ifthey are prefixed a \bmod m amodm modwithoutparentheses
× \ast (cid:116)(cid:47) \triangleleft ⊗ \oslash with \left or \right. Each \left must have a matching
∗(cid:63) \star (cid:46) \triangleright (cid:11) \odot \right, one of which may be an empty delimeter (\left. or Thefollowingexamplesuse\mathoptocreatefunctionnames.
\diamond \wr (cid:12) \dagger \right.). Tospecifyaparticularsize,usethefollowing: Elixmample C\loimm_m{axn\dto2} \Pdlaeifn\lTiEmX{\Dmaetfihnoitpi{o\nrm lim}}
(cid:5) \circ (cid:111) \bigcirc † \ddagger \bigl,\bigr \Bigl,\Bigr \biggl,\biggr x→2
◦ \bullet (cid:13) \bigtriangleup ‡ \amalg Youcanalsosay\bigmforalargedelimenterinthemiddleofa log2 \log_2 \def\log{\mathop{\rm log}\nolimits}
• \div (cid:52) \bigtriangledown (cid:113) formula,orjust\bigforonethatactsasanordinarysymbol.
÷ (cid:53) Footnotes, Insertions, and Underlines
Page Layout Every Time Insertions
\footnote marker { text } footnote
\hsize= dimen setwidthofpage \everypar insertwheneveraparagraphbegins \topinsert(cid:104) vmode(cid:105)m(cid:104)ater(cid:105)ial \endinsert insertattopofpage
\vsize=(cid:104)dimen(cid:105) setheightofpage \everymath insertwhenevermathintextbegins \pageinsert(cid:104) vmode materia(cid:105)l \endinsert insertonfullpage
\display(cid:104)width=(cid:105) dimen setwidthofmathdisplays \everydisplay insertwheneverdisplayedmathbegins \midinsert v(cid:104)mode material \(cid:105)endinsert insertmiddleofpage
\hoffset= dime(cid:104)n (cid:105) movepagehorizontally \everycr insertafterevery\cr \underbar{(cid:104)text } (cid:105) underlinetext
\voffset=(cid:104)dimen(cid:105) movepagevertically (cid:104) (cid:105)
(cid:104) (cid:105)
(cid:13)c 1998J.H.Silverman,Permissionsonback. v1.3
SendcommentsandcorrectionstoJ.H.Silverman,Math.Dept.,Brown
Univ.,Providence,RI02912USA.(cid:104)[email protected](cid:105)
1 2 3
Useful Parameters and Conversions Indentation and Itemized Lists Dimensions, Spacing, and Glue
\day,\month,\year thecurrentday,month,year \indent indent Dimensionsarespecifiedas number unit ofmeasure .
\jobname nameofcurrentjob \noindent donotindent Glueisspecifiedas dimen (cid:104)plus dim(cid:105)(cid:104)en minus dimen(cid:105).
\romannumeral(cid:104)number(cid:105) converttolowercaseromannums. \parindent=(cid:104)dimen(cid:105) setindentationofparagraphs point pt pica (cid:104) pc(cid:105) inc(cid:104)h (cid:105) in c(cid:104)entime(cid:105)ter cm
\uppercase{ token list } converttouppercase \displayindent= dimen setindentationofmathdisplays
\lowercase{(cid:104)token list(cid:105)} converttolowercase \leftskip= dime(cid:104)n (cid:105) skipspaceonleft mwidth em xheight ex mathunit mu millimeter mm
(cid:104) (cid:105) \rightskip=(cid:104) dimen(cid:105) skipspaceonright 1pc=12pt 1in=72.72pt 2.54cm=1in 18mu=1em
Fills, Leaders and Ellipses (cid:104) (cid:105)
\narrower makeparagraphnarrower HorizontalSpacing: \quad(skip1em) \qquad
MTeaxttho:rM..a.t\hl:dots ·.·.·. \\cddoottss ... \vdots ... \ddots \\\ihitatenemgm{ii(cid:104)ntldeaembn{et(cid:104)ll(cid:105)=a}bdeilm(cid:105)}en hdsiaonnuggblyilnyignindindedennetnetedtdaittiieotemnmifziozereddplailsritsatgraph \HHhoosrrkiizzioopnn(cid:104)gttaalulleSS(cid:105)ppaacc\iihnnfggil((MTea\xthth)f):i:llt\htih\nihnfsspiplaancceeeg\,\enmsepdaicuems\peancseki\p>
Thefollowingfillspacewiththeindicateditem. \hangafter= n(cid:104)umber(cid:105) starthangingindentafterlinen. thickspace\; neg.thinspace\! \mskip muglue
\hrulefill \rightarrowfill \leftarrowfill \dotfill (cid:104) (cid:105) Ifn<0,indentfirst n lines. (cid:104) (cid:105)
| | VerticalSpacing: \vskip glue \vfil \vfill
Thegeneralformatforconstructing leadersis \parshape=(cid:104)number(cid:105) generalparagraphshapingmacro \strut boxw/hta(cid:104)ndd(cid:105)epthof“(”,zerowidth
\\lleeaaddeerrss(cid:104)bbooxx oorrrruullee(cid:105)\\hhfsiklilp(cid:104)glue(cid:105) rfielplespatacbeowxiotrhrbuolxe orrule Headers, Footers, and Page Numbers \\vpphhaannttoomm{{(cid:104)tetxext(cid:105)t}} binovxiswib/lehbto&xwdeitphthdiomf otefx(cid:104)tte,xzt(cid:105)erowidth
(cid:104) (cid:105) \nopagenumbers turnoffpagenumbering (cid:104) (cid:105) (cid:104) (cid:105)
TEX Fonts and Magnification \pageno currentpagenumber. Togetromannums, \hphantom{(cid:104)text(cid:105)} boxw/widthof(cid:104)text(cid:105),zeroht&depth
\smash{ text } typeset text ,setht&depthtozero
set\pageno= negative number (cid:104) (cid:105) (cid:104) (cid:105)
\rm Roman \bf Bold \tt Typewriter (cid:104) (cid:105) \raise dimen \hbox{ text } raiseboxup
\folio currentpagenumber,romannumif <0 (cid:104) (cid:105) (cid:104) (cid:105)
\sl Slant \it Italic \/ “italiccorrection” \lower dimen \hbox{ text } lowerboxdown
\footline materialtoputatfootofpage (cid:104) (cid:105) (cid:104) (cid:105)
\moveleft dimen \vbox{ text } moveboxleft
\magnification= number scaledocument byn/1000 \headline materialtoputattopofpage. Toleave (cid:104) (cid:105) (cid:104) (cid:105)
\magstep number(cid:104) (cid:105) scalingfactorof1.2n 1000 space,set\voffset=2\baselineskip, make \moveright(cid:104)dimen(cid:105)\vbox{(cid:104)text(cid:105)} moveboxright
(cid:104) (cid:105) × SkipSpaceBetweenLines: \smallskip \medskip \bigskip
\magstephalf scallingfactorof√1.2 roomwith\advance\vsize by-\voffset. encourageabreak \smallbreak \medbreak \bigbreak
\font\FN=(cid:104)fontname(cid:105) loadafont,namingit\FN Macro Definitions breakifnoroom \filbreak
\font\FN=(cid:104)fontname(cid:105) at(cid:104)dimenlo(cid:105)adfontscaledtodimension \def\cs{ replacement text } definethemacro\cs SetLsiinneglSepsapcaicneg: \\bbaasseelliinneesskkiipp ==(cid:104)1g2lupte(cid:105)
\font\FN=(cid:104)fontname(cid:105) scaled(cid:104)nlouamdbfeorn(cid:105)tscaledbyn/1000 \\ldeetf\\ccss=#(cid:104)1t·o·k·e#nn{(cid:104)repl.tegxit(cid:105)v(cid:105)e}\cstomkaecnr’oscwuirtrhenptarmameaentienrgs d1o1u/b2lespsapcaece \\bbaasseelliinneesskkiipp == 1284pptt
true(cid:104)dimen(cid:105) dimensionwithnoscaling Advanced(cid:104)Macr(cid:105)oDefinitionCommands IncreaseLineSpacing \openup(cid:104)dimen(cid:105)
Alignment Displays \long\def macrowhoseargsmayinclude\par use\jot’s 1\jot = 3pt
\outer\def macronotallowedinsidedefinitions AllowUnjustifiedLines \raggedright
\settabs number \columns setequallyspacedtabs \global\def or\gdef definitionthattranscendsgrouping AllowUnjustifiedPages \raggedbottom
\settabs\(cid:104)+ sampl(cid:105)e line \cr settabsaspersampleline \edef expandwhiledefiningmacro Braces and Matrices
\+ text1 & t(cid:104)ext2 & \cr(cid:105) tabbedtexttobetypeset \xdefor\global\edef globalversionof\edef \matrix rectangulararrayofentries
\ha(cid:104)lign(cid:105) (cid:104) (cid:105) ··· horizontalalignment \noexpand token donotexpandtoken \pmatrix matrixwithparentheses
(cid:104) (cid:105)
\halign to dimen horizontalalignment \expandafter token expanditemaftertokenfirst \bordermatrix matrixwithlabelsontopandleft
\openup dim(cid:104)en (cid:105) addspacebetweenlines \futurelet\cs(cid:104) tok1(cid:105) tok2 equals\let\cs= tok2 tok1 tok2 \overbrace overbrace,maybesuperscripted
\noalig(cid:104)n{ vmo(cid:105)de material } insertmaterialafterany\cr \csname...\end(cid:104)csnam(cid:105)(cid:104)e (cid:105)createacontrolseq(cid:104)uenc(cid:105)e(cid:104)name(cid:105)(cid:104) (cid:105) \underbrace underbrace,maybesubscripted
\tabskip=(cid:104)glue (cid:105) setglueattabstops \string\cs listcharactersinname,\cs Forsmallmatricesintext,usethefollowingconstructions:
\omit (cid:104) (cid:105) omitthetemplateforacolumn \number number listofcharactersinnumber ab
\span spantwocolumns \the int(cid:104)ernal qu(cid:105)antity listoftokensgivingvalueofquantity {a\,b \choose c\,d} (cid:0)cd(cid:1)
(cid:104) (cid:105) ab
\multispan(cid:104)number(cid:105) spanseveralcolumns Conditionals \left( {a\atop c} {b\atop d} \right) (cid:16)cd(cid:17)
\hidewidth ignorethewidthofanentry Displayed Equations
\crcr insert\crifoneisnotpresent Thegeneralformatofaconditionalis
\eqno equationnumberatright
\if condition true text \else false text \fi
Boxes (cid:104) (cid:105)(cid:104) (cid:105) (cid:104) (cid:105) \leqno equationnumberatleft
\ifnum(cid:104)num1(cid:105)(cid:104)relation(cid:105)(cid:104)num2(cid:105) comparetwointegers \eqalign displayseveralalignedequations
\\vhbbooxx ttoo(cid:104)ddiimmeenn(cid:105) vhbbooxx,obfogtitvoemndjuimsteifinesdion \\iiffdoidmd(cid:104)dnuimmen1(cid:105)(cid:104)relation(cid:105)(cid:104)dimen2(cid:105) tceosmtpfoarreantwoodddiminetnegsieorns \eqalignno displayalignedequationsnumberedatright
\vtop to(cid:104)dimen(cid:105) vbox,topjustified \ifmmod(cid:104)e (cid:105) testformathmode \leqalignno displayalignedequationsnumberedatleft
\\vrcleanpter(cid:104)to(cid:104)dim(cid:105)en(cid:105) vribgohxt,ocveenrtlearpjmusattiefireidal(mathonly) \\iiffd(cid:104)tiomken1(cid:105)(cid:104)token2(cid:105) cteosmtpifarcehatrwaoctdeirmceondseisonasgree \\cdaissepslaylines dcaisspelabyysceavseeradlefieqnuitaiotinosns,centered
\noalign toinsertspacebetween linesindisplays,
\llap leftoverlapmaterial \ifx token1 token2 testiftokensagree
(cid:104) (cid:105)(cid:104) (cid:105) use\noalign{\vskip glue } afterany\cr
\ifeof number testforendoffile (cid:104) (cid:105)
Overfull Boxes (cid:104) (cid:105) \openup dimen addspacebetweenalllinesinadisplay
\iftrue,\iffalse alwaystrue,alwaysfalse (cid:104) (cid:105)
\hfuzz allowableexcessinhboxes \ifcase number text0 \or text1 \or Copyright(cid:13)c 1998J.H.Silverman,November1998v1.3
(cid:104) (cid:105)(cid:104) (cid:105) (cid:104) (cid:105) ··· Math.Dept.,BrownUniv.,Providence,RI02912USA
\vfuzz allowableexcessinvboxes \or(cid:104)textn(cid:105)\else(cid:104)text(cid:105)\fi choosetextby(cid:104)number(cid:105) TEXisatrademarkoftheAmericanMathematicalSociety
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