TEX Reference CardRelations(for Plain TEX)

Greek Letters
αβγ
δ
²ε
ζη
θ
ϑ

\alpha\beta\gamma\delta\epsilon\varepsilon\zeta\eta\theta\vartheta

ι
κ
λµν
ξ
oπ$
ρ

\iota
\kappa\lambda\mu\nu\xi\o\pi\varpi\rho%σ
ς
τ
υ
φϕ
χ
ψ
ω

\varrho\sigma\varsigma\tau\upsilon\phi\varphi\chi\psi\omega

Γ
∆
Θ
Λ

\Gamma\Delta\Theta\Lambda

Ξ
Π
Σ
Υ

\Xi\Pi\Sigma\UpsilonΦΨΩ\Phi\Psi\Omega

Symbols of Type Ordℵ
h̄ı

`
℘
<=
∂∞\aleph\hbar\imath\jmath\ell\wp\Re\Im\partial\infty0
∅
∇
√
>
⊥
k6

4\\prime\emptyset\nabla\surd
\top
\bot
\|\angle\triangle\backslash

Large Operators

PQ
`
RH

T
S
F
W
V

\sum\prod\coprod\int\oint\bigcap\bigcup\bigsqcup\bigvee\bigwedge

∀
∃
¬
[\]
♣
♦
♥
♠

\forall\exists\neg or \lnot\flat\natural\sharp\clubsuit\diamondsuit\heartsuit\spadesuit

JN \bigodot
L \bigotimes
U \bigoplus\biguplus

Binary Operations
±
∓
\·×
∗
?
¦◦
•
÷

\pm
\mp
\setminus\cdot\times\ast\star\diamond\circ\bullet\div

∩
∪
]
ut/.
o°
45\cap\cup\uplus\sqcap\sqcup\triangleleft\triangleright\wr\bigcirc\bigtriangleup\bigtriangledown

∨∧
⊕
ª
⊗
®
¯
†
‡
q

\vee or \lor\wedge or \land\oplus\ominus\otimes\oslash\odot\dagger\ddagger\amalgPage Layout\hsize=hdimeni\vsize=hdimeni\displaywidth=hdimeni\hoffset=hdimeni\voffset=hdimeni

set width of page
set height of page
set width of math displays
move page horizontally
move page vertically

≤
≺
¹
¿
⊂
⊆
v
∈
`
^
_∝

Accents\leq or \le\prec\preceq\ll\subset\subseteq\sqsubseteq\in\vdash\smile\frown\propto

≥
Â
ºÀ
⊃
⊇
w
∈
/a|k\geq or \ge\succ\succeq\gg\supset\supseteq\sqsupseteq\notin\dashv\mid\parallel

≡
∼
'³≈
∼
=./
3
|=.
=
⊥\equiv\sim\simeq\asymp\approx\cong\bowtie\ni or \owns\models\doteq\perp

Most relations can be negated by prefixing them with \not.
6≡\not\equiv∈/\notin

6=\neArrows← \leftarrow or \gets←− \longleftarrow⇐ \Leftarrow⇐= \Longleftarrow→ \rightarrow or \to−→ \longrightarrow⇒ \Rightarrow=⇒ \Longrightarrow↔ \leftrightarrow←→ \longleftrightarrow⇔ \Leftrightarrow⇐⇒ \Longleftrightarrow
7→ \mapsto
7−→ \longmapsto←- \hookleftarrow,→\hookrightarrow↑\uparrow⇑\Uparrow↓\downarrow⇓\Downarrowl\updownarrow
m\Updownarrow% \nearrow&\searrow- \nwarrow.
\swarrow
The \buildrel macro puts one symbol over another. The format is \buildrelhsuperscripti\overhrelationi.
αβ−→
def

f (x) = x + 1\buildrel\alpha\beta\over\longrightarrow
f(x)\; {\buildrel\rm def\over=} \;x+1

Delimiters
[]
|k
[[]]

\lbrack or [\rbrack or ]\vert or |\Vert or \|[\![]\!]

{}
bc
(())

\lbrace or \{\rbrace or \}\lfloor\rfloor(\!()\!)

hidehhii\langle\rangle\lceil\rceil\langle\!\langle\rangle\!\rangle

Left and right delimiters will be enlarged if they are prefixedwith \left or \right. Each \left must have a matching\right, one of which may be an empty delimiter (\left. or\right.). To specify a particular size, use the following:\bigl, \bigr\Bigl, \Bigr\biggl, \biggr
You can also say \bigm for a large delimiter in the middle of aformula, or just \big for one that acts as an ordinary symbol.

Every Time Insertions\everypar\everymath\everydisplay\everycrinsert whenever a paragraph begins
insert whenever math in text begins
insert whenever displayed math begins
insert after every \cr

Type
hat
expanding hat
check
tilde
expanding tilde
acute
grave
dot
double dot
breve
bar
vectorExample
â
ac
bc
ǎ
ã
af
bc
á
à
ȧ
ä
ă
ā
~a

In Math\hat\widehat\check\tilde\widetilde\acute\grave\dot\ddot\breve\bar\vec

In Text\^none
\v
\~
none
\’\‘\.
\"\u\=
none

The \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 Sequences
overline a formula
underline a formulasquare root
higher order roots

x+y\overline{x+y}x+y\underline{x+y}√x+2\sqrt{x+2}√nx+2\root n\of{x+2}n+1fraction{n+1\over 3}
3n+1
fraction, no line{n+1\atop 3}
3 ¢
¡n +1
binomial coeff.
{n+1\choose 3}
3 ª
©n +1
braced fraction{n+1\brace 3}
3 ¤
£n +1
{n+1\brack 3}
bracketed fraction
3
The following specify a style for typesetting formulas.
\displaystyle \textstyle \scriptstyle \scriptscriptstyleNon-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 parentheses

The following examples use \mathop to create function names.
Example CommandPlain TEX Definition
lim\lim_{x\to2} \def\lim{\mathop{\rm lim}}
x→2

log2\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}

footnote
insert at top of page
insert on full page
insert middle of pageunderline text

c 2007 J.H. Silverman, Permissions on back. v1.5°
Send comments and corrections to J.H. Silverman, Math. Dept., Brown
Univ., Providence, RI 02912 USA. hjhs@math.brown.eduiUseful Parameters and Conversions

Indentation and Itemized Lists

Dimensions, Spacing, and Glue

\day,\month,\year\jobname\romannumeralhnumberi\uppercase{htoken listi}\lowercase{htoken listi}\indent\noindent\parindent=hdimeni\displayindent=hdimeni\leftskip=hdimeni\rightskip=hdimeni\narrower\item{hlabeli}\itemitem{hlabeli}\hangindent=hdimeni\hangafter=hnumberi

Dimensions are specified as hnumberihunit of measurei.
Glue is specified as hdimeni plushdimeni minushdimeni.
pcinchin centimeter cmpointpt pica
m width em x height exmath unit mu millimeter mm
1 pc = 12 pt 1 in = 72.72 pt 2.54 cm = 1 in 18 mu = 1 em
Horizontal Spacing:\quad (skip 1em) \qquad
Horizontal Spacing (Text): \thinspace \enspace \enskip\hskiphgluei \hfil \hfill \hfilneg
Horizontal Spacing (Math): thin space \, medium space \>thick space \; neg. thin space \! \mskiphmugluei

the current day, month, year
name of current job
convert to lower case roman nums.
convert to upper caseconvert to lower case

Fills, Leaders and Ellipses
Text or Math:
Math: . . . \ldots. . . \dots· · · \cdots.
.. \vdots

The following fill space with the indicated item.
\hrulefill \rightarrowfill \leftarrowfill..

. \ddots\dotfill

The general format for constructing leaders is\leadershbox or rulei\hskiphgluei repeat box or rule\leadershbox or rulei\hfill
fill space with box or rule

TEX Fonts and Magnification\rm\slRomanSlant\bf\itBold
Italic\tt\/Typewriter“italic correction”\magnification=hnumberiscale document by n/1000\magstephnumberi
scaling factor of √1.2n × 1000
\magstephalf
scaling factor of 1.2\font\FN=hfontnameiload a font, naming it \FN\font\FN=hfontnamei at hdimeni
scaled to dimension\font\FN=hfontnamei scaled hnumberi scaled by n/1000
true hdimeni
dimension with no scaling\char‘\cprint the character or symbol c

Alignment Displays\settabshnumberi\columns\settabs\+hsample linei\cr\+htext1 i&htext2 i&· · ·\cr
\halign\halign tohdimeni\openuphdimeni\noalign{hvmode materiali}\tabskip=hgluei\omit\span\multispanhnumberi\hidewidth\crcr

set equally spaced tabs
set tabs as per sample line
tabbed text to be typeset
horizontal alignment
horizontal alignment
add space between lines
insert material after any \cr
set glue at tab stops
omit the template for a column
span two columns
span several columns
ignore the width of an entry
insert \cr if one is not present

Boxes\hbox tohdimeni\vbox tohdimeni\vtop tohdimeni\vcenter tohdimeni\rlap\llaphbox of given dimension
vbox, bottom justified
vbox, top justified
vbox, center justified (math only)
right overlap material
left overlap material

Overfull Boxes\hfuzz\vfuzz\overfullrule

allowable excess in hboxes
allowable excess in vboxes
width of overfull box marker. To eliminate
entirely, set \overfullrule=0pt.

\parshape=hnumberi

indentdo not indent
set indentation of paragraphs
set indentation of math displays
skip space on left
skip space on rightmake paragraph narrower
singly indented itemized list
doubly indented itemized list
hanging indentation for paragraphstart hanging indent after line n.
If n < 0, indent first |n| lines.
general paragraph shaping macro

Headers, Footers, and Page Numbers\nopagenumbers\pageno\folio\footline\headline

turn off page numbering
current page number. To get roman nums,
set \pageno=hnegative numberi
current page number, roman num if < 0material to put at foot of pagematerial to put at top of page. To leave
space, 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=htokeni
give \cs token’s current meaning
Advanced Macro Definition Commands\long\defmacro whose args may include \par\outer\def
macro not allowed inside definitions\global\def or \gdef
definition that transcends grouping\edef
expand while defining macro\xdef or \global\edefglobal version of \edef\noexpandhtokeni
do not expand token\expandafterhtokeni
expand item after token first\futurelet\cshtok1 ihtok2 i equals \let\cs=htok2 ihtok1 ihtok2 i\csname. . . \endcsname
create a control sequence name\string\cslist characters in name, \ c s\numberhnumberi
list of characters in number\thehinternal quantityi
list of tokens giving value of quantity

Conditionals
The general format of a conditional is\ifhconditionihtrue texti\elsehfalse texti\fi\ifnumhnum1 ihrelationihnum2 icompare two integers\ifdimhdimen1 ihrelationihdimen2 icompare two dimensions\ifoddhnumi
test for an odd integer\ifmmode
test for math mode
\ifhtoken1 ihtoken2 itest if character codes agree\ifxhtoken1 ihtoken2 itest if tokens agree\ifdimhdim1 ihdim2 itest if dimensions agree\ifeofhnumberi
test for end of file\iftrue, \iffalse
always true, always false\ifcasehnumberihtext0 i\orhtext1 i\or· · ·\orhtextn i\elsehtexti\fichoose text by hnumberi\loop α \if. . . β \repeat
loop αβα · · · α until \if is false\newif\ifblob
create a new conditional called \ifblob\blobtrue, \blobfalse
set conditional \ifblob true, false

Vertical Spacing:\vskiphgluei \vfil \vfill\strut
box 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 right
Skip Space Between Lines: \smallskip \medskip \bigskip
encourage a break\smallbreak \medbreak \bigbreak
break if no room
\filbreakSet Line Spacing:\baselineskip = hgluei
single space\baselineskip = 12pt
1 1/2 space\baselineskip = 18pt
double space\baselineskip = 24pt
Increase Line Spacing\openuphdimeni
use \jot’s
1\jot = 3pt
Allow Unjustified Lines\raggedright
Allow Unjustified Pages\raggedbottom

Braces and Matrices\matrix
rectangular array of entries\pmatrix
matrix with parentheses\bordermatrix
matrix with labels on top and left
\overbrace
overbrace, may be superscripted\underbrace
underbrace, may be subscripted
For small matrices in text, use the following constructions:¡a b¢{a\,b \choose c\,d}
cd\left( {a\atop c} {b\atop d} \right)

Displayed Equations\eqno\leqno\eqalign\eqalignno\leqalignno\displaylines\cases\noalign\openuphdimeni

¡a b¢
cd

equation number at rightequation number at left
display several aligned equations
display aligned equations numbered at rightdisplay aligned equations numbered at left
display several equations, centeredcase by case definitions
to insert space between lines in displays,use \noalign{\vskiphgluei} after any \cr
add space between all lines in a display

c 2007 J.H. Silverman, January 2007 v1.5
Copyright °Math. Dept., Brown Univ., Providence, RI 02912 USA
TEX is a trademark of the American Mathematical Society
Permission is granted to make and distribute copies of this card provided the copyright notice and this permission notice are preserved on
all copies.