Help:Displaying a formula

Accents/Diacritics

Standard functions

Modular arithmetic

Derivatives

Sets

Operators

Logic

Root

Relations

Geometric

Arrows

Special

[edit] Larger Expressions

[edit] Subscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
		HTML	PNG
Superscript	a^2
Subscript	a_2
Grouping	a^{2+2}
	a_{i,j}
Combining sub & super without and with horizontal separation	x_2^3
	{x_2}^3
Super super	10^{10^{ \,\!{8} }
Super super (wrong in HTML in some browsers)	10^{10^8}
Preceding and/or Additional sub & super
	{}_1^2\!\Omega_3^4
Derivative (forced PNG)	x', y'', f', f''\!
Derivative (f in italics may overlap primes in HTML)	x', y'', f', f''
Derivative (wrong in HTML)	x^\prime, y^{\prime\prime}
Derivative (wrong in PNG)	x\prime, y\prime\prime
Derivative dots	\dot{x}, \ddot{x}
Underlines, overlines, vectors	\hat a \ \bar b \ \vec c
	\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}
	\overline{g h i} \ \underline{j k l}
Overbraces	\overbrace{ 1+2+\cdots+100 }^{5050}
Underbraces	\underbrace{ a+b+\cdots+z }_{26}
Sum	\sum_{k=1}^N k^2
Sum (force \textstyle)	\textstyle \sum_{k=1}^N k^2
Product	\prod_{i=1}^N x_i
Product (force \textstyle)	\textstyle \prod_{i=1}^N x_i
Coproduct	\coprod_{i=1}^N x_i
Coproduct (force \textstyle)	\textstyle \coprod_{i=1}^N x_i
Limit	\lim_{n \to \infty}x_n
Limit (force \textstyle)	\textstyle \lim_{n \to \infty}x_n
Integral	\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx
Integral (alternate limits style)	\int_{1}^{3}\frac{e^3/x}{x^2}\, dx
Integral (force \textstyle)	\textstyle \int\limits_{-N}^{N} e^x\, dx
Integral (force \textstyle, alternate limits style)	\textstyle \int_{-N}^{N} e^x\, dx
Double integral	\iint\limits_D \, dx\,dy
Triple integral	\iiint\limits_E \, dx\,dy\,dz
Quadruple integral	\iiiint\limits_F \, dx\,dy\,dz\,dt
Line or path integral	\int_C x^3\, dx + 4y^2\, dy
Closed line or path integral	\oint_C x^3\, dx + 4y^2\, dy
Intersections	\bigcap_1^n p
Unions	\bigcup_1^k p

[edit] Fractions, matrices, multilines

Feature	Syntax	How it looks rendered
Fractions	\frac{1}{2}=0.5
Large (nested) Fractions	\cfrac{2}{c + \cfrac{2}{d + \cfrac{1}{2}}} = a
Matrices	\begin{matrix} x & y \\ z & v \end{matrix}
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}
	\begin{pmatrix} x & y \\ z & v \end{pmatrix}
	Case distinctions	f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}
Breaking up a long expression so that it wraps when necessary.	<math>f(x) \,\!</math> <math>= \sum_{n=0}^\infty a_n x^n </math> <math>= a_0+a_1x+a_2x^2+\cdots</math>
Simultaneous equations	\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}

[edit] Parenthesizing big expressions, brackets, bars

Feature	Syntax	How it looks rendered
Bad	( \frac{1}{2} )
Good	\left ( \frac{1}{2} \right )

You can use various delimiters with \left and \right:

Feature	Syntax	How it looks rendered
Parentheses	\left ( \frac{a}{b} \right )
Brackets	\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack
Braces	\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace
Angle brackets	\left \langle \frac{a}{b} \right \rangle
Bars and double bars	\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|
Floor and ceiling functions:	\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil
Slashes and backslashes	\left / \frac{a}{b} \right \backslash
Up, down and up-down arrows	\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow
Delimiters can be mixed, as long as \left and \right match	\left [ 0,1 \right )</code> <br/> <code>\left \langle \psi \right |
Use \left. and \right. if you don't want a delimiter to appear:	\left . \frac{A}{B} \right \} \to X
Size of the delimiters	\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]/<code>
	<code>\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle
	\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|
	\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil
	\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow
	\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow
	\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash

[edit] Alphabets and typefaces

Texvc cannot render arbitrary Unicode characters. Those it can handle can be entered by the expressions below. For others, such as Cyrillic, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas.

Greek alphabet
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta
\Eta \Theta \Iota \Kappa \Lambda \Mu
\Nu \Xi \Pi \Rho \Sigma \Tau
\Upsilon \Phi \Chi \Psi \Omega
\alpha \beta \gamma \delta \epsilon \zeta
\eta \theta \iota \kappa \lambda \mu
\nu \xi \pi \rho \sigma \tau
\upsilon \phi \chi \psi \omega
\varepsilon \digamma \vartheta \varkappa
\varpi \varrho \varsigma \varphi
Blackboard Bold/Scripts
\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G}
\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M}
\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T}
\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}
boldface (vectors)
\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G}
\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M}
\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T}
\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z}
\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g}
\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m}
\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t}
\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z}
\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4}
\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}
Boldface (greek)
\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta}
\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}
\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}
\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}
\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}
\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}
\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}
\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}
\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa}
\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}
Italics
\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G}
\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M}
\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T}
\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z}
\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g}
\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m}
\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t}
\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z}
\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4}
\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}
Roman typeface
\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G}
\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M}
\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T}
\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z}
\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}
\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m}
\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t}
\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z}
\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4}
\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}
Fraktur typeface
\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G}
\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M}
\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T}
\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z}
\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g}
\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m}
\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t}
\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z}
\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4}
\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}
Calligraphy/Script
\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G}
\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M}
\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T}
\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}
Hebrew
\aleph \beth \gimel \daleth

Feature	Syntax	How it looks rendered
non-italicised characters	\mbox{abc}
mixed italics (bad)	\mbox{if} n \mbox{is even}
mixed italics (good)	\mbox{if }n\mbox{ is even}
mixed italics (more legible: ~ is a non-breaking space, while "\ " forces a space)	\mbox{if}~n\ \mbox{is even}

[edit] Color

Equations can use color:

• {\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}

  

• x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}

  

See here for all named colors supported by LaTeX.

Note that color should not be used as the only way to identify something, because it will become meaningless on black-and-white media or for color-blind people.

[edit] Formatting issues

[edit] Spacing

Note that TeX handles most spacing automatically, but you may sometimes want manual control.

Feature	Syntax	How it looks rendered
double quad space	a \qquad b
quad space	a \quad b
text space	a\ b
text space without PNG conversion	a \mbox{ } b
large space	a\;b
medium space	a\>b	[not supported]
small space	a\,b
no space	ab
small negative space	a\!b

Automatic spacing may be broken in very long expressions (because they produce an overfull hbox in TeX):

<math>0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots</math>

This can be remedied by putting a pair of braces { } around the whole expression:

<math>{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}</math>

[edit] Alignment with normal text flow

Due to the default css

img.tex { vertical-align: middle; }

an inline expression like should look good.

If you need to align it otherwise, use <math style="vertical-align:-100%;">...</math> and play with the vertical-align argument until you get it right; however, how it looks may depend on the browser and the browser settings.

Also note that if you rely on this workaround, if/when the rendering on the server gets fixed in future releases, as a result of this extra manual offset your formulae will suddenly be aligned incorrectly. So use it sparingly, if at all.

[edit] Forced PNG rendering

To force the formula to render as PNG, add \, (small space) at the end of the formula (where it is not rendered). This will force PNG if the user is in "HTML if simple" mode, but not for "HTML if possible" mode (math rendering settings in preferences).

You can also use \,\! (small space and negative space, which cancel out) anywhere inside the math tags. This does force PNG even in "HTML if possible" mode, unlike \,.

This could be useful to keep the rendering of formulae in a proof consistent, for example, or to fix formulae that render incorrectly in HTML (at one time, a^{2+2} rendered with an extra underscore), or to demonstrate how something is rendered when it would normally show up as HTML (as in the examples above).

For instance:

Syntax	How it looks rendered
a^{c+2}
a^{c+2} \,
a^{\,\!c+2}
a^{b^{c+2}}	(WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}} \,	(WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}}\approx 5	(due to "" correctly displayed, no code "\,\!" needed)
a^{b^{\,\!c+2}}
\int_{-N}^{N} e^x\, dx

This has been tested with most of the formulae on this page, and seems to work perfectly.

You might want to include a comment in the HTML so people don't "correct" the formula by removing it:

<!-- The \,\! is to keep the formula rendered as PNG instead of HTML. Please don't remove it.-->

[edit] Commutative diagrams

To make a commutative diagram, there are three steps:

• Write the diagram in TeX
• Convert to SVG
• Upload the file.

[edit] Diagrams in TeX

Xy-pic (online manual) is the most powerful and general-purpose diagram package in TeX.

Simpler packages include:

• AMS's amscd
• Paul Taylor's diagrams
• François Borceux Diagrams

The following is a template for Xy-pic, together with a hack to increase the margins in dvips, so that the diagram is not truncated by over-eager cropping (suggested in TUGboat:kpss TUGboat, Volume 17 1996, No. 3):

\documentclass{amsart}
\usepackage[all, ps, dvips]{xy} % Loading the XY-Pic package 
                                % Using postscript driver for smoother curves
\usepackage{color}              % For invisible frame
\begin{document}
\thispagestyle{empty} % No page numbers
\SelectTips{eu}{}     % Euler arrowheads (tips)
\setlength{\fboxsep}{0pt} % Frame box margin
{\color{white}\framebox{{\color{black}$$ % Frame for margin

\xymatrix{ % The diagram is a 3x3 matrix
%%% Diagram goes here %%%
}

$$}}} % end math, end frame
\end{document}

[edit] Convert to SVG

Once you have produced your diagram in LaTeX (or TeX), you can convert it to an SVG file using the following sequence of commands:

pdflatex file.tex
pdfcrop --clip file.pdf tmp.pdf
pdf2svg tmp.pdf file.svg
  (rm tmp.pdf at the end)

If you do not have pdflatex (which is unlikely) you can also use the commands

latex file.tex
dvipdfm file.dvi

to get a PDF version of your diagram. The pdfcrop and pdf2svg utilities are needed for this procedure.

An alternative, which goes via PS rather than PDF, is:

latex comm.tex
dvips -E -y 2500 -o comm.eps comm.dvi
eps2eps -dNOCACHE comm.eps comm2.eps
pstoedit -f sk comm2.eps comm.sk
inkscape -z -f comm.sk -l comm.svg

These produce a DVI file, convert it to EPS (rescaling by 2.5x), convert fonts to outlines, and convert to SVG via Sketch. One advantage is that rescaling makes smaller or more complex diagrams more legible, as xy-pic normally sizes for printed matter.

[edit] Programs

In general, you will not be able to get anywhere with diagrams without TeX and Ghostscript, and the inkscape program is a useful tool for creating or modifying your diagrams by hand. There is also a utility pstoedit which supports direct conversion from Postscript files to many vector graphics formats, but it requires a non-free plugin to convert to SVG, and regardless of the format, this editor has not been successful in using it to convert diagrams with diagonal arrows from TeX-created files.

These programs are:

• a working TeX distribution, such as TeX Live
• Ghostscript
• pstoedit
• Inkscape

[edit] Upload the file

As the diagram is your own work, upload it.

Check size

Before uploading, check that the default size of the image is neither too large nor too small by opening in an SVG application and viewing at default size (100% scaling), otherwise adjust the -y option to dvips.

Name

Make sure the file has a meaningful name.

Upload!

== LaTeX source ==
<source lang="latex">
% LaTeX source here
</source>

== [[Commons:Copyright tags|Licensing]]: ==
{{self|PD-self (or other license)|author=[[User:YourUserName|Your Real Name]]}}

[[Category:Descriptive categories, such as "Group theory"]]
[[Category:Commutative diagrams]]

Source code

• Include the source code in the image page, in a LaTeX source section, so that the diagram can be edited in future.
• Include the complete .tex file, not just the fragment, so future editors do not need to reconstruct a compilable file.

License

The most common license for commutative diagrams is PD-self; some use PD-ineligible, especially for simple diagrams, or other licenses. Please do not use the GFDL, as it requires the entire text of the GFDL to be attached to any document that uses the diagram.

Description

If possible, link to a Wikipedia page relevant to the diagram.

Category

Include [[Category:Commutative diagrams]], so that it appears in commons:Category:Commutative diagrams. There are also subcategories, which you may choose to use.

Include image

Now include the image on the original page via [[Image:Diagram.svg]]

[edit] Examples

A sample conforming diagram is commons:Image:PSU-PU.svg.

[edit] Examples

<math>ax^2 + bx + c = 0</math>

<math>ax^2 + bx + c = 0\,\!</math>

<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

<math>2 = \left(
 \frac{\left(3-x\right) \times 2}{3-x}
 \right)</math>

 <math>S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}</math>
 

<math>\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds
 = \int_a^x f(y)(x-y)\,dy</math>

<math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
 {3^m\left(m\,3^n+n\,3^m\right)}</math>

<math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math>

<math>|\bar{z}| = |z|,
 |(\bar{z})^n| = |z|^n,
 \arg(z^n) = n \arg(z)</math>

<math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math>

<math>\phi_n(\kappa) =
 \frac{1}{4\pi^2\kappa^2} \int_0^\infty
 \frac{\sin(\kappa R)}{\kappa R}
 \frac{\partial}{\partial R}
 \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math>

<math>\phi_n(\kappa) = 
 0.033C_n^2\kappa^{-11/3},\quad
 \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>

<math>
 f(x) =
 \begin{cases}
 1 & -1 \le x < 0 \\
 \frac{1}{2} & x = 0 \\
 1 - x^2 & \mbox{otherwise}
 \end{cases}
 </math>

 <math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
 = \sum_{n=0}^\infty
 \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}
 \frac{z^n}{n!}</math>

   
<math> \frac {a}{b}\  \tfrac {a}{b} </math>

[edit] External links

• A LaTeX tutorial.
• A paper introducing TeX—see page 39 onwards for a good introduction to the maths side of things.
• A paper introducing LaTeX—skip to page 49 for the math section. See page 63 for a complete reference list of symbols included in LaTeX and AMS-LaTeX.
• The Comprehensive LaTeX Symbol List.
• AMS-LaTeX guide.
• A set of public domain fixed-size math symbol bitmaps.
• MathML: A product of the W3C Math working group, is a low-level specification for describing mathematics as a basis for machine to machine communication.