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TEX Reference CardRelations(for Plain TEX)Greek Lettersαβγδεζηθϑ\alpha\beta\gamma\delta\epsilon\varepsilon\zeta\eta\theta\varthetaικλµνξoπ$ρ\iota\kappa\lambda\mu\nu\xi\o\pi\varpi\rho%σςτυφϕχψω\varrho\sigma\varsigma\tau\upsilon\phi\varphi\chi\psi\omegaΓ∆ΘΛ\Gamma\Delta\Theta\LambdaΞΠΣΥ\Xi\Pi\Sigma\UpsilonΦΨΩ\Phi\Psi\OmegaSymbols of Type Ordℵh̄ı`℘<=∂∞0∅∇√\aleph\hbar\imath\jmath\ell\wp\Re\Im\partial\infty>⊥k64\\prime\emptyset\nabla\surd\top\bot\|\angle\triangle\backslashLarge OperatorsPQ`RHTSFWV\sum\prod\coprod\int\oint\bigcap\bigcup\bigsqcup\bigvee\bigwedge∀∃¬[\]♣♦♥♠\forall\exists\neg or \lnot\flat\natural\sharp\clubsuit\diamondsuit\heartsuit\spadesuitJNLU\bigodot\bigotimes\bigoplus\biguplusBinary Operations±∓\·×∗?◦•÷\pm\mp\setminus\cdot\times\ast\star\diamond\circ\bullet\div∩∪]ut/.o45\cap\cup\uplus\sqcap\sqcup\triangleleft\triangleright\wr\bigcirc\bigtriangleup\bigtriangledown∨∧⊕⊗†‡q\vee or \lor\wedge or \land\oplus\ominus\otimes\oslash\odot\dagger\ddagger\amalg\leq or \le\prec\preceq\ll\subset\subseteq\sqsubseteq\in\vdash\smile\frown\propto6≡\not\equiv≥⊃⊇w∈/a|k≡∼'≈∼=./3|=.=⊥\geq or \ge\succ\succeq\gg\supset\supseteq\sqsupseteq\notin\dashv\mid\parallet\equiv\sim\simeq\asymp\approx\cong\bowtie\ni or \owns\models\doteq\perpMost relations can be negated by prefixing them with \not.∈/6=\notin\neArrows←⇐→⇒↔⇔7→←↑↓l%Themat\leftarrow or \gets←− \longleftarrow\Leftarrow⇐= \Longleftarrow\rightarrow or \to−→ \longrightarrow\Rightarrow=⇒ \Longrightarrow\leftrightarrow←→ \longleftrightarrow\Leftrightarrow⇐⇒ \Longleftrightarrow\mapsto7−→ \longmapsto\hookleftarrow,→\hookrightarrow\uparrow⇑\Uparrow\downarrow⇓\Downarrow\updownarrowm\Updownarrow\nearrow&\searrow\nwarrow.\swarrow\buildrel macro puts one symbol over another.

The foris \buildrelhsuperscripti\overhrelationi.αβ−→deff (x) = x + 1\buildrel\alpha\beta\over\longrightarrowf(x)\; {\buildrel\rm def\over=} \;x+1Delimeters[]|k[[]]\lbrack or [\rbrack or ]\vert or |\Vert or \|[\![]\!]{}bc(())\lbrace or \{\rbrace or \}\lfloor\rfloor(\!()\!)hidehhii\langle\rangle\lceil\rceil\langle\!\langle\rangle\!\rangleLeft and right delimeters will be enlarged if they are prefixedwith \left or \right.

Each \left must have a matching\right, one of which may be an empty delimeter (\left. or\right.). To specify a particular size, use the following:\bigl, \bigr\Bigl, \Bigr\biggl, \biggrYou can also say \bigm for a large delimenter in the middle of aformula, or just \big for one that acts as an ordinary symbol.Every Time InsertionsPage Layout\hsize=hdimeni\vsize=hdimeni\displaywidth=hdimeni\hoffset=hdimeni\voffset=hdimeniAccents≤≺⊂⊆v∈`^_∝set width of pageset height of pageset width of math displaysmove page horizontallymove page vertically\everypar\everymath\everydisplay\everycrinsertinsertinsertinsertwhenever a paragraph beginswhenever math in text beginswhenever displayed math beginsafter every \crTypehatexpanding hatchecktildeexpanding tildeacutegravedotdouble dotbrevebarvectorExampleâdabcǎãgabcáàȧäăā~aIn Math\hat\widehat\check\tilde\widetilde\acute\grave\dot\ddot\breve\bar\vecIn Text\^none\v\~none\’\‘\.\"\u\=noneThe \skewhnumberi command shifts accents for proper positioning, the larger the hnumberi, the more right the shift.

Compareˆˆ\hat{\hat A} gives Â,\skew6\hat{\hat A} gives Â.Elementary Math Control Sequencesx+y\overline{x+y}x+y\underline{x+y}√x+2\sqrt{x+2}√nx+2\root n\of{x+2}n+1{n+1\over 3}fraction3n+1fraction, no line{n+1\atop 3}3 n +1binomial coeff.{n+1\choose 3}3 onn +1braced fraction{n+1\brace 3}3 ihn +1bracketed fraction{n+1\brack 3}3The following specify a style for typesetting formulas.\displaystyle \textstyle \scriptstyle \scriptscriptstyleoverline a formulaunderline a formulasquare roothigher order rootsNon-Italic Function Names\arccos \cos\arcsin \cosh\arctan \cot\arg\cotha \pmod{m}a \bmod m\csc \exp \ker\limsup \min \sinh\deg \gcd \lg\ln\Pr \sup\det \hom \lim\log\sec \tan\dim \inf \liminf \max\sin \tanha (mod m)mod with parenthesesa mod mmod without parenthesesThe following examples use \mathop to create function names.Example CommandPlain TEX Definitionlim\lim_{x\to2} \def\lim{\mathop{\rm lim}}x→2log2\log_2\def\log{\mathop{\rm log}\nolimits}Footnotes, Insertions, and Underlines\footnotehmarkeri{htexti}\topinserthvmode materiali\endinsert\pageinserthvmode materiali\endinsert\midinserthvmode materiali\endinsert\underbar{htexti}footnoteinsert at top of pageinsert on full pageinsert middle of pageunderline textc 1998 J.H.

Silverman, Permissions on back. v1.3Send comments and corrections to J.H. Silverman, Math. Dept., BrownUniv., Providence, RI 02912 USA. hjhs@math.brown.edui123Useful Parameters and Conversionsthe current day, month, yearname of current jobconvert to lower case roman nums.convert to upper caseconvert to lower case\day,\month,\year\jobname\romannumeralhnumberi\uppercase{htoken listi}\lowercase{htoken listi}Fills, Leaders and EllipsesText or Math:Math: . .

. \ldots. . . \dots· · · \cdots... \vdotsThe following fill space with the indicated item.\hrulefill \rightarrowfill \leftarrowfill... \ddotsIndentation and Itemized Lists\indent\noindent\parindent=hdimeni\displayindent=hdimeni\leftskip=hdimeni\rightskip=hdimeni\narrower\item{hlabeli}\itemitem{hlabeli}\hangindent=hdimeni\hangafter=hnumberi\dotfill\parshape=hnumberiindentdo not indentset indentation of paragraphsset indentation of math displaysskip space on leftskip space on rightmake paragraph narrowersingly indented itemized listdoubly indented itemized listhanging indentation for paragraphstart hanging indent after line n.If n < 0, indent first |n| lines.general paragraph shaping macroThe general format for constructing leaders is\leadershbox or rulei\hskiphgluei repeat box or rule\leadershbox or rulei\hfillfill space with box or ruleHeaders, Footers, and Page NumbersTEX Fonts and Magnification\nopagenumbers\pageno\rm\slRomanSlant\bf\itBoldItalic\tt\/Typewriter“italic correction”\magnification=hnumberiscale document by n/1000n\magstephnumberiscaling factor of 1.2√ × 1000\magstephalfscalling factor of 1.2\font\FN=hfontnameiload a font, naming it \FN\font\FN=hfontnamei at hdimeniload font scaled to dimension\font\FN=hfontnamei scaled hnumberiload font scaled by n/1000true hdimenidimension with no scalingAlignment Displaysset equally spaced tabsset tabs as per sample linetabbed text to be typesethorizontal alignmenthorizontal alignmentadd space between linesinsert material after any \crset glue at tab stopsomit the template for a columnspan two columnsspan several columnsignore the width of an entryinsert \cr if one is not present\settabshnumberi\columns\settabs\+hsample linei\cr\+htext1 i&htext2 i&· · ·\cr\halign\halign tohdimeni\openuphdimeni\noalign{hvmode materiali}\tabskip=hgluei\omit\span\multispanhnumberi\hidewidth\crcrBoxes\hbox tohdimeni\vbox tohdimeni\vtop tohdimeni\vcenter tohdimeni\rlap\llaphbox of given dimensionvbox, bottom justifiedvbox, top justifiedvbox, center justified (math only)right overlap materialleft overlap materialOverfull Boxes\hfuzz\vfuzz\overfullruleallowable excess in hboxesallowable excess in vboxeswidth of overfull box marker.

To eliminateentirely, set \overfullrule=0pt.\folio\footline\headlineturn off page numberingcurrent page number. To get roman nums,set \pageno=hnegative numbericurrent page number, roman num if < 0material to put at foot of pagematerial to put at top of page. To leavespace, set \voffset=2\baselineskip, makeroom with \advance\vsize by-\voffset.Macro Definitions\def\cs{hreplacement texti}define the macro \cs\def\cs#1 · · · #n{hrepl. texti}macro with parameters\let\cs=htokenigive \cs token’s current meaningAdvanced Macro Definition Commands\long\defmacro whose args may include \par\outer\defmacro not allowed inside definitions\global\def or \gdefdefinition that transcends grouping\edefexpand while defining macro\xdef or \global\edefglobal version of \edef\noexpandhtokenido not expand token\expandafterhtokeniexpand item after token first\futurelet\cshtok1 ihtok2 i equals \let\cs=htok2 ihtok1 ihtok2 i\csname. .

. \endcsnamecreate a control sequence name\string\cslist characters in name, \ c s\numberhnumberilist of characters in number\thehinternal quantityilist of tokens giving value of quantityConditionalsThe general format of a conditional is\ifhconditionihtrue texti\elsehfalse texti\fi\ifnumhnum1 ihrelationihnum2 icompare two integers\ifdimhdimen1 ihrelationihdimen2 icompare two dimensions\ifoddhnumitest for an odd integer\ifmmodetest for math mode\ifhtoken1 ihtoken2 itest if character codes agree\ifdimcompare two dimensions\ifxhtoken1 ihtoken2 itest if tokens agree\ifeofhnumberitest for end of file\iftrue, \iffalsealways true, always false\ifcasehnumberihtext0 i\orhtext1 i\or· · ·\orhtextn i\elsehtexti\fichoose text by hnumberi\loop α \if.

. . β \repeatloop αβα · · · α until \if is false\newif\ifblobcreate a new conditional called \ifblob\blobtrue, \blobfalseset conditional \ifblob true, falseDimensions, Spacing, and GlueDimensions are specified as hnumberihunit of measurei.Glue is specified as hdimeni plushdimeni minushdimeni.pcinchin centimeter cmpointpt picamath unit mu millimeter mmm width em x height ex1 pc = 12 pt 1 in = 72.72 pt 2.54 cm = 1 in 18 mu = 1 emHorizontal Spacing:\quad (skip 1em) \qquadHorizontal Spacing (Text): \thinspace \enspace \enskip\hskiphgluei \hfil \hfill \hfilnegHorizontal Spacing (Math): thin space \, medium space \>thick space \; neg. thin space \! \mskiphmuglueiVertical Spacing:\vskiphgluei \vfil \vfill\strutbox w/ ht and depth of “(”, zero width\phantom{htexti}invisible box with dim of htexti\vphantom{htexti} box w/ ht & depth of htexti, zero width\hphantom{htexti} box w/ width of htexti, zero ht & depth\smash{htexti}typeset htexti, set ht & depth to zero\raisehdimeni\hbox{htexti}raise box up\lowerhdimeni\hbox{htexti}lower box down\movelefthdimeni\vbox{htexti}move box left\moverighthdimeni\vbox{htexti} move box rightSkip Space Between Lines: \smallskip \medskip \bigskipencourage a break\smallbreak \medbreak \bigbreakbreak if no room\filbreakSet Line Spacing:\baselineskip = hglueisingle space\baselineskip = 12pt1 1/2 space\baselineskip = 18ptdouble space\baselineskip = 24ptIncrease Line Spacing\openuphdimeniuse \jot’s1\jot = 3ptAllow Unjustified Lines\raggedrightAllow Unjustified Pages\raggedbottomBraces and Matrices\matrixrectangular array of entries\pmatrixmatrix with parentheses\bordermatrixmatrix with labels on top and left\overbraceoverbrace, may be superscripted\underbraceunderbrace, may be subscriptedFor small matrices in text, use the following constructions:a b{a\,b \choose c\,d}c d ab\left( {a\atop c} {b\atop d} \right)cdDisplayed Equations\eqno\leqno\eqalign\eqalignno\leqalignno\displaylines\cases\noalign\openuphdimeniequation number at rightequation number at leftdisplay several aligned equationsdisplay aligned equations numbered at rightdisplay aligned equations numbered at leftdisplay several equations, centeredcase by case definitionsto insert space between lines in displays,use \noalign{\vskiphgluei} after any \cradd space between all lines in a displayc 1998 J.H.

Silverman, November 1998 v1.3Copyright Math. Dept., Brown Univ., Providence, RI 02912 USATEX is a trademark of the American Mathematical SocietyPermission is granted to make and distribute copies of this card provided the copyright notice and this permission notice are preserved onall copies.Published by Ford & Mason Ltd, GL19 3JB, UK. Further copies of thiscard can be ordered through our web site: http://www.refcards.com.456.