Wiki Math

From Liki

This is a mirror of http://meta.wikimedia.org/wiki/Help:Formula and thus will not be open for editing. Please note that where you find error messages, our wiki software does not have the corresponding commands available.

Template:H:h MediaWiki uses a subset of TeX markup, including some extensions from LaTeX and AMSLaTeX, 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. (See blahtex for information about current work on adding MathML support.)

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.

To have math rendered, you have to enable it in LocalSettings.php.

Syntax

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

Similarly 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. See Template:Tim.

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 most of these shortcomings have been addressed by Maynard Handley, but have not been released 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. For other text, (like variable labels) to avoid being rendered in italics like variables, use \mbox or \mathrm. For example, <math>\mbox{abc}</math> gives abc.

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;	α
<math>\sqrt{2}</math>		&radic;2	√2
<math>\sqrt{1-e^2}</math>		&radic;(1&minus;''e''&sup2;)	√(1−e²)

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, font size and face match the rest of HTML contents and the appearance respects CSS and browser settings.
3. Pages using HTML will load faster.

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. TeX has been specifically designed for typesetting formulae, so input is easier and more natural, and output is more aesthetically pleasing.
3. One consequence of point 1 is that TeX can be transformed into HTML, but not vice-versa. 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's true that the current situation is not ideal, but that's not a good reason to drop information/contents. It's more a reason to help improve the situation.
4. Another consequence of point 1 is that TeX can be converted to MathML for browsers which support it, thus keeping its semantics and allowing it to be renderred vectorally.
5. 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 server. This doesn't hold for HTML formulae, which can easily end up being rendered wrongly or differently from the editor's intentions on a different browser.

Functions, symbols, special characters

Accents/Diacritics
\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}
\check{a} \bar{a} \ddot{a} \dot{a}
Standard functions
\sin a \cos b \tan c
\sec d \csc e \cot f
\arcsin h \arccos i \arctan j
\sinh k \cosh l \tanh m \coth n
\operatorname{sh}o \operatorname{ch}p \operatorname{th}q
\operatorname{argsh}r \operatorname{argch}s \operatorname{argth}t
\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
\deg h \gcd i \Pr j \det k \hom l \arg m \dim n
Modular arithmetic
s_k \equiv 0 \pmod{m} a \bmod b
Derivatives
\nabla \partial x dx \dot x \ddot y
Sets
\forall \exists \empty \emptyset \varnothing
\in \ni \not \in \notin \subset \subseteq \supset \supseteq
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup
Operators
+ \oplus \bigoplus \pm \mp -
\times \otimes \bigotimes \cdot \circ \bullet \bigodot
\star * / \div \frac{1}{2}
Logic
\land \wedge \bigwedge \bar{q} \to p
\lor \vee \bigvee \lnot \neg q \And
Root
\sqrt{2} \sqrt[n]{x}
Relations
\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}	Failed to parse (unknown error\overset): \sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}\,\!
\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto
Geometric
\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ
Arrows
\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow
\mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow
\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft
\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow	Failed to parse (unknown error\rightleftharpoons): \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow\,\!
\Longrightarrow \Longleftrightarrow (or \iff) \Uparrow \Downarrow \Updownarrow \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft	Failed to parse (unknown error\leftleftarrows): \Longrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,\!
\leftrightharpoons \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright	Failed to parse (unknown error\leftrightharpoons): \leftrightharpoons \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright\,\!
\curvearrowright \circlearrowright \Rsh \downdownarrows \multimap \leftrightsquigarrow \rightsquigarrow \nLeftarrow \nleftrightarrow \nRightarrow	Failed to parse (unknown error\curvearrowright): \curvearrowright \circlearrowright \Rsh \downdownarrows \multimap \leftrightsquigarrow \rightsquigarrow \nLeftarrow \nleftrightarrow \nRightarrow\,\!
\nLeftrightarrow \longleftrightarrow	Failed to parse (unknown error\nLeftrightarrow): \nLeftrightarrow \longleftrightarrow\,\!
Special
\eth \S \P \% \dagger \ddagger \ldots \cdots
\smile \frown \wr \triangleleft \triangleright \infty \bot \top
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar
\ell \mho \Finv \Re \Im \wp \complement \diamondsuit
\heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp
Unsorted (new stuff)
\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown	Failed to parse (unknown error\vartriangle): \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown
\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge	Failed to parse (unknown error\blacksquare): \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge
\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes	Failed to parse (unknown error\veebar): \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes
\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant	Failed to parse (unknown error\rightthreetimes): \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant
\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq	Failed to parse (unknown error\eqslantless): \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq
\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft	Failed to parse (unknown error\fallingdotseq): \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft
\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot	Failed to parse (unknown error\Vvdash): \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot
\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq	Failed to parse (unknown error\ggg): \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq
\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork	Failed to parse (unknown error\Supset): \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork
\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq	Failed to parse (unknown error\varpropto): \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq
\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid	Failed to parse (unknown error\lvertneqq): \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid
\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr	Failed to parse (unknown error\nvdash): \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr
\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq	Failed to parse (unknown error\ngeqslant): \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq
\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq	Failed to parse (unknown error\succnsim): \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq
\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq	Failed to parse (unknown error\nsupseteqq): \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq
\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus	Failed to parse (unknown error\jmath): \jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus\,\!
\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq	Failed to parse (unknown error\oslash): \oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq\,\!
\dashv \asymp \doteq \parallel	Failed to parse (unknown error\dashv): \dashv \asymp \doteq \parallel\,\!

Subscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
		HTML	PNG
Superscript	a^2	a2
Subscript	a_2	a2
Grouping	a^{2+2}	a2 + 2
	a_{i,j}	ai,j
Combining sub & super	x_2^3
Preceding and/or Additional sub & super	\sideset{_1^2}{_3^4}\prod_a^b	Failed to parse (unknown error\sideset): \sideset{_1^2}{_3^4}\prod_a^b
	{}_1^2\!\Omega_3^4
Stacking	\overset{\alpha}{\omega}	Failed to parse (unknown error\overset): \overset{\alpha}{\omega}
	\underset{\alpha}{\omega}	Failed to parse (unknown error\underset): \underset{\alpha}{\omega}
	\overset{\alpha}{\underset{\gamma}{\omega}}	Failed to parse (unknown error\overset): \overset{\alpha}{\underset{\gamma}{\omega}}
	\stackrel{\alpha}{\omega}	Failed to parse (unknown error\stackrel): \stackrel{\alpha}{\omega}
Derivative (forced PNG)	x', y, f', f\!
Derivative (f in italics may overlap primes in HTML)	x', y, f', f	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}
Arrows	A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C	Failed to parse (unknown error\xleftarrow): A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
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	Failed to parse (unknown error\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	Failed to parse (unknown error\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	Failed to parse (unknown error\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	Failed to parse (unknown error\textstyle): \textstyle \lim_{n \to \infty}x_n
Integral	\int_{-N}^{N} e^x\, dx
Integral (force \textstyle)	\textstyle \int_{-N}^{N} e^x\, dx	Failed to parse (unknown error\textstyle): \textstyle \int_{-N}^{N} e^x\, dx
Double integral	\iint_{D}^{W} \, dx\,dy
Triple integral	\iiint_{E}^{V} \, dx\,dy\,dz
Quadruple integral	\iiiint_{F}^{U} \, dx\,dy\,dz\,dt
Path integral	\oint_{C} x^3\, dx + 4y^2\, dy
Intersections	\bigcap_1^{n} p
Unions	\bigcup_1^{k} p

Fractions, matrices, multilines

Feature	Syntax	How it looks rendered
Fractions	\frac{2}{4}=0.5
Small Fractions	\tfrac{2}{4} = 0.5	Failed to parse (unknown error\tfrac): \tfrac{2}{4} = 0.5
Large (normal) Fractions	\dfrac{2}{4} = 0.5	Failed to parse (unknown error\dfrac): \dfrac{2}{4} = 0.5
Large (nested) Fractions	\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
Binomial coefficients	\binom{n}{k}	Failed to parse (PNG conversion failed; check for correct installation of latex, dvips, gs, and convert): \binom{n}{k}
Small Binomial coefficients	\tbinom{n}{k}	Failed to parse (unknown error\tbinom): \tbinom{n}{k}
Large (normal) Binomial coefficients	\dbinom{n}{k}	Failed to parse (unknown error\dbinom): \dbinom{n}{k}
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}
	\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)	Failed to parse (unknown error\bigl): \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)
Case distinctions	f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}
Multiline equations	\begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align}	Failed to parse (unknown error\begin): \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align}
	\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat}	Failed to parse (unknown error\begin): \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat}
Multiline equations (must define number of colums used ({lcr}) (should not be used unless needed)	\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}	Failed to parse (unknown error\begin): \begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}
Multiline equations (more)	\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}	Failed to parse (unknown error\begin): \begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}
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}

Alphabets and typefaces

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}	abc
mixed italics (bad)	\mbox{if} n \mbox{is even}	ifnis even
mixed italics (good)	\mbox{if }n\mbox{ is even}	if n is even
mixed italics (more legible: ~ is a non-breaking space, while "\ " forces a space)	\mbox{if}~n\ \mbox{is even}

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 ) \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( ... \Bigg] \bigg] \Big] \big]
	\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle
	\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big|
	\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil
	\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow
	\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow
	\big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash

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	a b
large space	a\;b
medium space	a\>b	[not supported]
small space	a\,b
no space	ab
small negative space	a\!b

Align 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 <font style="vertical-align:-100%;"><math>...</math></font> 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}	ac + 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.-->

Color

Equations can use color:

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

  Failed to parse (unknown error\color): {\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}

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

  Failed to parse (unknown error\color): x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}

See here for all named colours supported by LaTeX.

Note that color should not be used as the only way to identify something because color blind people may not be able to distinguish between the two colors. See en:Wikipedia:Manual of Style#Formatting issues.

Examples

ax2 + bx + c = 0

<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_{new} = S_{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 & 0 < x\le 1
 \end{cases}
 </math>

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

Bug reports

Discussions, bug reports and feature requests should go to the Wikitech-l mailing list. These can also be filed on Mediazilla under MediaWiki extensions.

See also

• Typesetting of mathematical formulas
• Proposed m:GNU LilyPond support
• Table of mathematical symbols
• m:Blahtex, or blahtex: a LaTeX to MathML converter for Wikipedia
• General help for editing a Wiki page
• Mimetex alternative for an another way to display mathematics using Mimetex.cgi

External links

• A LaTeX tutorial. http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/
• A PDF document introducing TeX -- see page 39 onwards for a good introduction to the maths side of things: http://www.ctan.org/tex-archive/info/gentle/gentle.pdf
• A PDF document introducing LaTeX -- skip to page 59 for the math section. See page 72 for a complete reference list of symbols included in LaTeX and AMS-LaTeX. http://www.ctan.org/tex-archive/info/lshort/english/lshort.pdf
• TeX reference card: http://www.csit.fsu.edu/docs/tex/tex-refcard-letter.pdf
• http://www.ams.org/tex/amslatex.html
• A set of public domain fixed-size math symbol bitmaps: http://us.metamath.org/symbols/symbols.html
• 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. http://www.w3.org/Math/

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