Help:Displaying a formula

MediaWiki uses a subset of TeX markup, including some extensions from LaTeX and AMS-Latex, for mathematical formulae. It generates either PNG images or simple HTML markup, depending on user preferences and the complexity of the expression. In the future, as more browsers are smarter, it will be able to generate enhanced HTML or even MathML in many cases.

More precisely, MediaWiki filters the markup through Texvc, which in turn passes the commands to TeX for the actual rendering. Thus, only a limited part of the full TeX language is supported; see below for details.

Technicals

Syntax

Math markup goes inside <math> ... </math>. The edit toolbar has a button for this..

Similar to HTML, in TeX extra spaces and newlines are ignored.

The TeX code has to be put literally: MediaWiki templates, predefined templates, and parameters cannot be used within math tags: pairs of double braces are ignored and "#" gives an error message. However, math tags work in the then and else part of #if, etc.

Rendering

The PNG images are black on white (not transparent). These colors, as well as font sizes and types, are independent of browser settings or CSS. Font sizes and types will often deviate from what HTML renders. Vertical alignment with the surrounding text can also be a problem. The css selector of the images is img.tex. It should be pointed out that solutions to most of these shortcomings have been proposed but have not been implemented yet.

The alt attribute of the PNG images (the text that is displayed if your browser can't display images; Internet Explorer shows it up in the hover box) is the wikitext that produced them, excluding the <math> and </math>.

Apart from function and operator names, as is customary in mathematics for variables, letters are in italics; digits are not. Other text is not supported.

TeX vs HTML

Before introducing TeX markup for producing special characters, it should be noted that, as this comparison table shows, sometimes similar results can be achieved in HTML (see Help:Special characters).

TeX Syntax (forcing PNG)	TeX Rendering	HTML Syntax	HTML Rendering
<math>\alpha\,\!</math>	$\alpha\,\!$	{{math|<VAR>&alpha;</VAR>}}	α
<math>\sqrt{2}</math>	$\sqrt{2}$	{{math|{{radical|2}}}}	√2
<math>\sqrt{1-e^2}</math>	$\sqrt{1-e^2}\!$	{{math|{{radical|1 − ''e''²}}}}	√1 − e²

The codes on the left produce the symbols on the right, but the latter can also be put directly in the wikitext, except for ‘=’.

α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ ς τ υ φ χ ψ ω Γ Δ Θ Λ Ξ Π Σ Φ Ψ Ω	α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ ς τ υ φ χ ψ ω Γ Δ Θ Λ Ξ Π Σ Φ Ψ Ω
∫ ∑ ∏ √ − ± ∞ ≈ ∝ {{=}} ≡ ≠ ≤ ≥ × · ÷ ∂ ′ ″ ∇ ‰ ° ∴ Ø ø ∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇ ¬ ∧ ∨ ∃ ∀ ⇒ ⇔ → ↔ ↑ ℵ - – —	∫ ∑ ∏ √ − ± ∞ ≈ ∝ = ≡ ≠ ≤ ≥ × · ÷ ∂ ′ ″ ∇ ‰ ° ∴ Ø ø ∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇ ¬ ∧ ∨ ∃ ∀ ⇒ ⇔ → ↔ ↑ ℵ - – —

The use of HTML instead of TeX is still under discussion. The arguments either way can be summarised as follows.

Pros of HTML

1. In-line HTML formulae always align properly with the rest of the HTML text.
2. The formula’s background and font size match the rest of HTML contents and the appearance respects CSS and browser settings while the typeface is conveniently altered to help you identify formulae.
3. Pages using HTML code for formulae will load faster and they will create less clutter on your hard disk.
4. Formulae typeset with HTML code will be accessible to client-side script links (a.k.a. scriptlets).
5. The display of a formula entered using mathematical templates can be conveniently altered by modifying the templates involved; this modification will affect all relevant formulae without any manual intervention.
6. The HTML code, if entered diligently, will contain all semantic information to transform the equation back to TeX or any other code as needed. It can even contain differences TeX does not normally catch, e.g. {{math|''i''}} for the imaginary unit and {{math|<VAR>i</VAR>}} for an arbitrary index variable.

Pros of TeX

1. TeX is semantically superior to HTML. In TeX, "<math>x</math>" means "mathematical variable $x$", whereas in HTML "x" could mean anything. Information has been irrevocably lost.
2. On the other hand, if you encode the same formula as "{{math|<VAR>x</VAR>}}", you get the same visual result x and no information is lost. This requires diligence and more typing that could make the formula harder to understand as you type it. However, since there are far more readers than editors, this effort is worth considering.
3. TeX has been specifically designed for typesetting formulae, so input is easier and more natural if you are accustomed to it, and output is more aesthetically pleasing if you focus on a single formula rather than on the whole containing page.
4. One consequence of point 1 is that TeX code can be transformed into HTML, but not vice-versa.^[1] This means that on the server side we can always transform a formula, based on its complexity and location within the text, user preferences, type of browser, etc. Therefore, where possible, all the benefits of HTML can be retained, together with the benefits of TeX. It is true that the current situation is not ideal, but that is not a good reason to drop information/contents. It is more a reason to help improve the situation.
5. Another consequence of point 1 is that TeX can be converted to MathML for browsers which support it, thus keeping its semantics and allowing the rendering to be better suited for the reader’s graphic device.
6. When writing in TeX, editors need not worry about whether this or that version of this or that browser supports this or that HTML entity. The burden of these decisions is put on the software. This does not hold for HTML formulae, which can easily end up being rendered wrongly or differently from the editor’s intentions on a different browser.^[2]
7. More importantly, the serif font used for rendering formulae is browser-dependent and it may be missing some important glyphs. While the browser generally capable to substitute a matching glyph from a different font family, it need not be the case for combined glyphs (compare ‘ a̅ ’ and ‘ a̅ ’).
8. TeX is the preferred text formatting language of most professional mathematicians, scientists, and engineers. It is easier to persuade them to contribute if they can write in TeX.

Note:dilHTML unless your wikitext follows the style of point 2

Note:browsupp The entity support problem is not limited to mathematical formulae though; it can be easily solved by using the corresponding characters instead of entities, as the character repertoire links do, except for cases where the corresponding glyphs are visually indiscernible (e.g. – for ‘–’ and − for ‘−’).

Functions, symbols, special characters

Accents/Diacritics
\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}	$\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}\,\!$
\check{a} \bar{a} \ddot{a} \dot{a}	$\check{a} \bar{a} \ddot{a} \dot{a}\!$
Standard functions
\sin a \cos b \tan c	$\sin a \cos b \tan c\!$
\sec d \csc e \cot f	$\sec d \csc e \cot f\,\!$
\arcsin h \arccos i \arctan j	$\arcsin h \arccos i \arctan j\,\!$
\sinh k \cosh l \tanh m \coth n\!	$\sinh k \cosh l \tanh m \coth n\!$
\operatorname{sh}\,o\,\operatorname{ch}\,p\,\operatorname{th}\,q\!	$\operatorname{sh}\,o\,\operatorname{ch}\,p\,\operatorname{th}\,q\!$
\operatorname{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,t	$\operatorname{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,t\,\!$
\lim u \limsup v \liminf w \min x \max y\!	$\lim u \limsup v \liminf w \min x \max y\!$
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g\!	$\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g\!$
\deg h \gcd i \Pr j \det k \hom l \arg m \dim n	$\deg h \gcd i \Pr j \det k \hom l \arg m \dim n\!$
Modular arithmetic
s_k \equiv 0 \pmod{m}	$s_k \equiv 0 \pmod{m}\,\!$
a\,\bmod\,b	$a\,\bmod\,b\,\!$
Derivatives
\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}	$\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}$
Sets
\forall \exists \empty \emptyset \varnothing	$\forall \exists \empty \emptyset \varnothing\,\!$
\in \ni \not \in \notin \subset \subseteq \supset \supseteq	$\in \ni \not \in \notin \subset \subseteq \supset \supseteq\,\!$
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus	$\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus\,\!$
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup	$\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup\,\!$
Operators
+ \oplus \bigoplus \pm \mp -	$+ \oplus \bigoplus \pm \mp - \,\!$
\times \otimes \bigotimes \cdot \circ \bullet \bigodot	$\times \otimes \bigotimes \cdot \circ \bullet \bigodot\,\!$
\star * / \div \frac{1}{2}	$\star * / \div \frac{1}{2}\,\!$
Logic
\land (or \and) \wedge \bigwedge \bar{q} \to p	$\land \wedge \bigwedge \bar{q} \to p\,\!$
\lor \vee \bigvee \lnot \neg q \And	$\lor \vee \bigvee \lnot \neg q \And\,\!$
Root
\sqrt{2} \sqrt[n]{x}	$\sqrt{2} \sqrt[n]{x}\,\!$
Relations
\approx \simeq \cong \dot= {=}	$\approx \simeq \cong \dot= {=}\,\!$
\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto	$\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto\,\!$
Geometric
\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ	$\Diamond \, \Box \, \triangle \, \angle \perp \, \mid \; \nmid \, \| 45^\circ\,\!$
Arrows
\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \nrightarrow \leftrightarrow \longleftarrow \longrightarrow	$\leftarrow \rightarrow \nleftarrow \nrightarrow \leftrightarrow \longleftarrow \longrightarrow \,\!$
\Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow (or \iff)	$\Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow \!$
\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow	$\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow \!$
\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright	$\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \,\!$
\mapsto \longmapsto \hookrightarrow \hookleftarrow	$\mapsto \longmapsto \hookrightarrow \hookleftarrow \,\!$
Special
\And \eth \S \P \% \dagger \ddagger \ldots \cdots	$\And \eth \S \P \% \dagger \ddagger \ldots \cdots\,\!$
\smile \frown \wr \triangleleft \triangleright \infty \bot \top	$\smile \frown \wr \triangleleft \triangleright \infty \bot \top\,\!$
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar	$\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar\,\!$
\ell \mho \Finv \Re \Im \wp \complement	$\ell \mho \Finv \Re \Im \wp \complement\,\!$
\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp	$\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp\,\!$
Larger Expressions Subscripts, superscripts, integrals Feature Syntax How it looks rendered HTML PNG Superscript a^2 $a^2$ $a^2 \,\!$ Subscript a_2 $a_2$ $a_2 \,\!$ Grouping a^{2+2} $a^{2+2}$ $a^{2+2}\,\!$ a_{i,j} $a_{i,j}$ $a_{i,j}\,\!$ Combining sub & super without and with horizontal separation x_2^3 $x_2^3$ $x_2^3 \,\!$ {x_2}^3 ${x_2}^3$ ${x_2}^3 \,\!$ Super super 10^{10^{ \,\!{8} } $10^{10^{ \,\! 8 } }$ Super super (wrong in HTML in some browsers) 10^{10^8} $10^{10^8}$ Preceding and/or Additional sub & super {}_1^2\!\Omega_3^4 ${}_1^2\!\Omega_3^4$ Derivative (forced PNG) x', y'', f', f''\!   $x', y'', f', f''\!$ Derivative (f in italics may overlap primes in HTML) x', y'', f', f'' $x', y'', f', f''$ $x', y'', f', f''\!$ Derivative (wrong in HTML) x^\prime, y^{\prime\prime} $x^\prime, y^{\prime\prime}$ $x^\prime, y^{\prime\prime}\,\!$ Derivative (wrong in PNG) x\prime, y\prime\prime $x\prime, y\prime\prime$ $x\prime, y\prime\prime\,\!$ Derivative dots \dot{x}, \ddot{x} $\dot{x}, \ddot{x}$ Underlines, overlines, vectors \hat a \ \bar b \ \vec c $\hat a \ \bar b \ \vec c$ \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} $\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}$ \overline{g h i} \ \underline{j k l} $\overline{g h i} \ \underline{j k l}$ Overbraces \overbrace{ 1+2+\cdots+100 }^{5050} $\overbrace{ 1+2+\cdots+100 }^{5050}$ Underbraces \underbrace{ a+b+\cdots+z }_{26} $\underbrace{ a+b+\cdots+z }_{26}$ Sum \sum_{k=1}^N k^2 $\sum_{k=1}^N k^2$ Sum (force \textstyle) \textstyle \sum_{k=1}^N k^2 $\textstyle \sum_{k=1}^N k^2$ Product \prod_{i=1}^N x_i $\prod_{i=1}^N x_i$ Product (force \textstyle) \textstyle \prod_{i=1}^N x_i $\textstyle \prod_{i=1}^N x_i$ Coproduct \coprod_{i=1}^N x_i $\coprod_{i=1}^N x_i$ Coproduct (force \textstyle) \textstyle \coprod_{i=1}^N x_i $\textstyle \coprod_{i=1}^N x_i$ Limit \lim_{n \to \infty}x_n $\lim_{n \to \infty}x_n$ Limit (force \textstyle) \textstyle \lim_{n \to \infty}x_n $\textstyle \lim_{n \to \infty}x_n$ Integral \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx $\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx$ Integral (alternate limits style) \int_{1}^{3}\frac{e^3/x}{x^2}\, dx $\int_{1}^{3}\frac{e^3/x}{x^2}\, dx$ Integral (force \textstyle) \textstyle \int\limits_{-N}^{N} e^x\, dx $\textstyle \int\limits_{-N}^{N} e^x\, dx$ Integral (force \textstyle, alternate limits style) \textstyle \int_{-N}^{N} e^x\, dx $\textstyle \int_{-N}^{N} e^x\, dx$ Double integral \iint\limits_D \, dx\,dy $\iint\limits_D \, dx\,dy$ Triple integral \iiint\limits_E \, dx\,dy\,dz $\iiint\limits_E \, dx\,dy\,dz$ Quadruple integral \iiiint\limits_F \, dx\,dy\,dz\,dt $\iiiint\limits_F \, dx\,dy\,dz\,dt$ Line or path integral \int_C x^3\, dx + 4y^2\, dy $\int_C x^3\, dx + 4y^2\, dy$ Closed line or path integral \oint_C x^3\, dx + 4y^2\, dy $\oint_C x^3\, dx + 4y^2\, dy$ Intersections \bigcap_1^n p $\bigcap_1^n p$ Unions \bigcup_1^k p $\bigcup_1^k p$ Fractions, matrices, multilines Feature Syntax How it looks rendered Fractions \frac{1}{2}=0.5 $\frac{1}{2}=0.5$ Large (nested) Fractions \cfrac{2}{c + \cfrac{2}{d + \cfrac{1}{2}}} = a $\cfrac{2}{c + \cfrac{2}{d + \cfrac{1}{2}}} = a$ Matrices \begin{matrix} x & y \\ z & v \end{matrix} $\begin{matrix} x & y \\ z & v \end{matrix}$ \begin{vmatrix} x & y \\ z & v \end{vmatrix} $\begin{vmatrix} x & y \\ z & v \end{vmatrix}$ \begin{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} $\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix}$ \begin{Bmatrix} x & y \\ z & v \end{Bmatrix} $\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}$ \begin{pmatrix} x & y \\ z & v \end{pmatrix} $\begin{pmatrix} x & y \\ z & v \end{pmatrix}$ Case distinctions f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} $f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}$ 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> $f(x) \,\!$ $= \sum_{n=0}^\infty a_n x^n$ $= a_0 +a_1x+a_2x^2+\cdots$ Simultaneous equations \begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases} $\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}$ Parenthesizing big expressions, brackets, bars Feature Syntax How it looks rendered Bad ( \frac{1}{2} ) $( \frac{1}{2} )$ Good \left ( \frac{1}{2} \right ) $\left ( \frac{1}{2} \right )$ You can use various delimiters with \left and \right: Feature Syntax How it looks rendered Parentheses \left ( \frac{a}{b} \right ) $\left ( \frac{a}{b} \right )$ Brackets \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack $\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack$ Braces \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace $\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace$ Angle brackets \left \langle \frac{a}{b} \right \rangle $\left \langle \frac{a}{b} \right \rangle$ Bars and double bars \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \| $\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|$ Floor and ceiling functions: \left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil $\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil$ Slashes and backslashes \left / \frac{a}{b} \right \backslash $\left / \frac{a}{b} \right \backslash$ 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 $\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow$ Delimiters can be mixed, as long as \left and \right match \left [ 0,1 \right )</code> <br/> <code>\left \langle \psi \right | $\left [ 0,1 \right )$ $\left \langle \psi \right |$ Use \left. and \right. if you don't want a delimiter to appear: \left . \frac{A}{B} \right \} \to X $\left . \frac{A}{B} \right \} \to X$ Size of the delimiters \big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]/<code> $\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]$ <code>\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle $\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle$ \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big| $\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|$ \big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil $\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil$ \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow $\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow$ \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow $\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow$ \big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash $\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash$ 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 $\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \,\!$ \Eta \Theta \Iota \Kappa \Lambda \Mu $\Eta \Theta \Iota \Kappa \Lambda \Mu \,\!$ \Nu \Xi \Pi \Rho \Sigma \Tau $\Nu \Xi \Pi \Rho \Sigma \Tau\,\!$ \Upsilon \Phi \Chi \Psi \Omega $\Upsilon \Phi \Chi \Psi \Omega \,\!$ \alpha \beta \gamma \delta \epsilon \zeta $\alpha \beta \gamma \delta \epsilon \zeta \,\!$ \eta \theta \iota \kappa \lambda \mu $\eta \theta \iota \kappa \lambda \mu \,\!$ \nu \xi \pi \rho \sigma \tau $\nu \xi \pi \rho \sigma \tau \,\!$ \upsilon \phi \chi \psi \omega $\upsilon \phi \chi \psi \omega \,\!$ \varepsilon \digamma \vartheta \varkappa $\varepsilon \digamma \vartheta \varkappa \,\!$ \varpi \varrho \varsigma \varphi $\varpi \varrho \varsigma \varphi\,\!$ Blackboard Bold/Scripts \mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G} $\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G} \,\!$ \mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} $\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} \,\!$ \mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} $\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} \,\!$ \mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z} $\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}\,\!$ boldface (vectors) \mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G} $\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G} \,\!$ \mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M} $\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M} \,\!$ \mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T} $\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T} \,\!$ \mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z} $\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z} \,\!$ \mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g} $\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g} \,\!$ \mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m} $\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m} \,\!$ \mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t} $\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t} \,\!$ \mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z} $\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z} \,\!$ \mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4} $\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4} \,\!$ \mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9} $\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}\,\!$ Boldface (greek) \boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta} $\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta} \,\!$ \boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu} $\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}\,\!$ \boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau} $\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}\,\!$ \boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega} $\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}\,\!$ \boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta} $\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}\,\!$ \boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu} $\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}\,\!$ \boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau} $\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}\,\!$ \boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega} $\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}\,\!$ \boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa} $\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa} \,\!$ \boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi} $\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}\,\!$ Italics \mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G} $\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G} \,\!$ \mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M} $\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M} \,\!$ \mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T} $\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T} \,\!$ \mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z} $\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z} \,\!$ \mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g} $\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g} \,\!$ \mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m} $\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m} \,\!$ \mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t} $\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t} \,\!$ \mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z} $\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z} \,\!$ \mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4} $\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4} \,\!$ \mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9} $\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}\,\!$ Roman typeface \mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G} $\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G} \,\!$ \mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M} $\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M} \,\!$ \mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T} $\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T} \,\!$ \mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z} $\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z} \,\!$ \mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g} $\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}\,\!$ \mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m} $\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m} \,\!$ \mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t} $\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t} \,\!$ \mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z} $\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z} \,\!$ \mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4} $\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4} \,\!$ \mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9} $\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}\,\!$ Fraktur typeface \mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G} $\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G} \,\!$ \mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M} $\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M} \,\!$ \mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T} $\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T} \,\!$ \mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z} $\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z} \,\!$ \mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g} $\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g} \,\!$ \mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m} $\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m} \,\!$ \mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t} $\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t} \,\!$ \mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z} $\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z} \,\!$ \mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4} $\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4} \,\!$ \mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9} $\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}\,\!$ Calligraphy/Script \mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G} $\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G} \,\!$ \mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} $\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} \,\!$ \mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} $\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} \,\!$ \mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z} $\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}\,\!$ Hebrew \aleph \beth \gimel \daleth $\aleph \beth \gimel \daleth\,\!$ Feature Syntax How it looks rendered non-italicised characters \mbox{abc} $\mbox{abc}$ $\mbox{abc} \,\!$ mixed italics (bad) \mbox{if} n \mbox{is even} $\mbox{if} n \mbox{is even}$ $\mbox{if} n \mbox{is even} \,\!$ mixed italics (good) \mbox{if }n\mbox{ is even} $\mbox{if }n\mbox{ is even}$ $\mbox{if }n\mbox{ is even} \,\!$ mixed italics (more legible: ~ is a non-breaking space, while "\ " forces a space) \mbox{if}~n\ \mbox{is even} $\mbox{if}~n\ \mbox{is even}$ $\mbox{if}~n\ \mbox{is even} \,\!$ Color Equations can use color: {\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1} ${\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}$ x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a} $x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}$ 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. Formatting issues 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 $a \qquad b$ quad space a \quad b $a \quad b$ text space a\ b $a\ b$ text space without PNG conversion a \mbox{ } b $a \mbox{ } b$ large space a\;b $a\;b$ medium space a\>b [not supported] small space a\,b $a\,b$ no space ab $ab\,$ small negative space a\!b $a\!b$ 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> $0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots$ 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> ${0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}$ Alignment with normal text flow Due to the default css img.tex { vertical-align: middle; } an inline expression like $\int_{-N}^{N} e^x\, dx$ 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. 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} \, $a^{c+2} \,$ a^{\,\!c+2} $a^{\,\!c+2}$ a^{b^{c+2}} $a^{b^{c+2}}$ (WRONG with option "HTML if possible or else PNG"!) a^{b^{c+2}} \, $a^{b^{c+2}} \,$ (WRONG with option "HTML if possible or else PNG"!) a^{b^{c+2}}\approx 5 $a^{b^{c+2}}\approx 5$ (due to "$\approx$" correctly displayed, no code "\,\!" needed) a^{b^{\,\!c+2}} $a^{b^{\,\!c+2}}$ \int_{-N}^{N} e^x\, dx $\int_{-N}^{N} e^x\, dx$ 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.--> Commutative diagrams To make a commutative diagram, there are three steps: Write the diagram in TeX Convert to SVG Upload the file. 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} 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. 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 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]] Examples A sample conforming diagram is commons:Image:PSU-PU.svg. Examples Quadratic Polynomial $ax^2 + bx + c = 0$ <math>ax^2 + bx + c = 0</math> Quadratic Polynomial (Force PNG Rendering) $ax^2 + bx + c = 0\,\!$ <math>ax^2 + bx + c = 0\,\!</math> Quadratic Formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ <math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math> Tall Parentheses and Fractions $2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)$ <math>2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)</math> $S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}$ <math>S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}</math> Integrals $\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy$ <math>\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy</math> Summation $\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}$ <math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} {3^m\left(m\,3^n+n\,3^m\right)}</math> Differential Equation $u'' + p(x)u' + q(x)u=f(x),\quad x>a$ <math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math> Complex numbers $|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)$ <math>|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)</math> Limits $\lim_{z\rightarrow z_0} f(z)=f(z_0)$ <math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math> Integral Equation $\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR$ <math>\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> Example $\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}$ <math>\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math> Continuation and cases $f(x) = \begin{cases}1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \mbox{otherwise}\end{cases}$ <math> f(x) = \begin{cases} 1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \mbox{otherwise} \end{cases} </math> Prefixed subscript ${}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}\frac{z^n}{n!}$ <math>{}_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> Fraction and small fraction $\frac {a}{b}$   $\tfrac {a}{b}$ <math> \frac {a}{b}\ \tfrac {a}{b} </math> 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.