Mostrar código-fonte de Ajuda:Formula


==TeX==

[[MediaWiki]] uses '''[[en:TeX|TeX]] markup''' for mathematical formulae. It generates either [[en:PNG|PNG]] images or simple [[en:HTML|HTML]] markup, depending on [[Help:Preferences#Rendering_math|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 [[en:MathML|MathML]] in many cases.

Math markup goes inside ''<nowiki><math> ... </math></nowiki>''. The [[help:edit toolbar|edit toolbar]] has a button for this.

MediaWiki templates, variables and parameters cannot be used within math tags, see [[Template talk:Demo of attempt to use parameters within TeX]].

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. The [[Help:User_style#CSS_selectors|css selector]] of the images is img.tex.

In the case of a non-white page background, the white background of the formula effectively highlights it, which can be an advantage or a disadvantage.

One may want to avoid using TeX markup as part of a line of regular text, as the formulae don't align properly and the font size, as said, usually does not match.

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

Discussion, bug reports and feature requests should go to the [[Mailing_list#Wikitech|Wikitech-l mailing list]].  These can also be filed on [http://bugzilla.wikipedia.org Mediazilla] under ''MediaWiki extensions''.

==General==

Spaces and newlines are ignored. Apart from function and operator names, as is customary in mathematics for variables, letters are in italics; digits are not. For other text, to avoid being rendered in italics like variables, use <code>\mbox</code>: <code><nowiki><math>\mbox{abc}</math></nowiki></code> gives <math>\mbox{abc}</math> 

Line breaks help keep the wikitext clear, for instance, a line break after each term or matrix row.

== Functions, symbols, special characters ==

For producing special characters without math tags, see [[Help:Special characters]].

Comparison:
*<tt>&amp;alpha;</tt> gives &alpha;, <tt><nowiki><math>\alpha</math></nowiki></tt> gives <math>\alpha</math> ("<tt>&amp;</tt>" and "<tt>;</tt>" vs. "<tt>\</tt>", in this case the same code word "<tt>alpha</tt>"
*<tt>&amp;radic;2</tt> gives &radic;2, <tt><nowiki><math>\sqrt{2}</math></nowiki></tt> gives <math>\sqrt{2}</math> (the same difference as above, but also another code word, "<tt>radic</tt>" vs. "<tt>sqrt</tt>"; in TeX braces)
*<tt>&amp;radic;(1-<nowiki>''e''</nowiki>&amp;sup2;)</tt> gives &radic;(1-''e''&sup2;), <tt><nowiki><math>\sqrt{1-e^2}</math></nowiki></tt> gives <math>\sqrt{1-e^2}</math> (parentheses vs. braces, "<tt><nowiki>''e''</nowiki></tt>" vs. "<tt>e</tt>", "<tt>&amp;sup2;</tt>" vs. "<tt>^2</tt>")

{| border="1"
|-
! Feature
! Syntax
! How it looks [[w:Rendering (computer graphics)|render]]ed
|-
| Accents/Diacritics
| \acute{a} \quad \grave{a} \quad \breve{a} \quad \check{a} \quad \tilde{a}
| <math>\acute{a} \quad \grave{a} \quad \breve{a} \quad \check{a} \quad \tilde{a}</math>
|-
| Std. functions (good)
| \sin x + \ln y +\operatorname{sgn} z<br/>
\sin a \ \cos b \ \tan c \ \cot d \ \sec e \ \csc f<br/>
\sinh g \ \cosh h \ \tanh i \ \coth j<br/>
\arcsin k \ \arccos l \ \arctan m<br/>
\lim n \ \limsup o \ \liminf p<br/>
\min q \ \max r \ \inf s \ \sup t<br/>
\exp u \ \lg v \ \log w<br/>
\ker x \ \deg x \gcd x \Pr x \ \det x \hom x \ \arg x \dim x
| <math>\sin x + \ln y +\operatorname{sgn} z</math><br/>
<math>\sin a \ \cos b \ \tan c \ \cot d \ \sec e \ \csc f</math><br/>
<math>\sinh g \ \cosh h \ \tanh i \ \coth j</math><br/>
<math>\arcsin k \ \arccos l \ \arctan m</math><br/>
<math>\lim n \ \limsup o \ \liminf p</math><br/>
<math>\min q \ \max r \ \inf s \ \sup t</math><br/>
<math>\exp u \ \lg v \ \log w</math><br/>
<math>\ker x \ \deg x \gcd x \Pr x \ \det x \hom x \ \arg x \dim x</math>
|-
| Std. functions (wrong)
| sin x + ln y + sgn z
| <math>sin x + ln y + sgn z\,\!</math>
|-
| Modular arithmetic
| s_k \equiv 0 \pmod{m}<br/>
a \bmod b
| <math>s_k \equiv 0 \pmod{m}</math><br/>
<math>a \bmod b\,\!</math>
|-
| Derivatives
| \nabla \; \partial x \; dx \; \dot x \; \ddot y
| <math>\nabla \; \partial x \; dx \; \dot x \; \ddot y</math>
|-
| rowspan="2" | Sets<br/>
(Square symbols may not work for some wikis)
| \forall \; \exists \; \empty \; \emptyset \; \varnothing \in \ni \not\in \notin<br/>
\subset \subseteq \supset \supseteq \cap \bigcap \cup \bigcup \biguplus
| <math>\forall \; \exists \; \empty \; \emptyset \; \varnothing \in \ni \not\in \notin</math><br/>
<math>\subset \subseteq \supset \supseteq \cap \bigcap \cup \bigcup \biguplus</math>
|-
| \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup
| <math>\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup</math>
|-
| Logic
| p \land \wedge \; \bigwedge \; \bar{q} \to p\ lor \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus
| <math>p \land \wedge \; \bigwedge \; \bar{q} \to p \lor \vee \; \bigvee \; \lnot \; \neg q \; \setminus \; \smallsetminus</math>
|-
| rowspan="2" | Root
| \sqrt{2}\approx 1.4
| <math>\sqrt{2}\approx 1.4</math>
|-
| \sqrt[n]{x}
| <math>\sqrt[n]{x}</math>
|-
| Relations
| \sim \; \approx \; \simeq \; \cong \; \le \; < \; \ll \; \gg \; \ge \; > \; \equiv \; \not\equiv \; \ne \; \propto \; \pm \; \mp
| <math>\sim \; \approx \; \simeq \; \cong \; \le \; < \; \ll \; \gg \; \ge \; > \; \equiv \; \not\equiv \; \ne \; \propto \; \pm \; \mp</math>
|-
| Geometric
| \Diamond \; \Box \; \triangle \; \angle \; \perp \; \mid \; \nmid \; <nowiki>\|</nowiki> \; 45^\circ
| <math>\Diamond \; \Box \; \triangle \; \angle \; \perp \; \mid \; \nmid \; \| \; 45^\circ</math>
|-
| rowspan="3" | Arrows<br/>
(Harpoons may not work for some wikis)
| \leftarrow \; \gets \; \rightarrow \; \to \; \leftrightarrow<br/>
\longleftarrow \; \longrightarrow<br/>
\mapsto \; \longmapsto \; \hookrightarrow \; \hookleftarrow<br/>
\nearrow \; \searrow \; \swarrow \; \nwarrow<br/>
\uparrow \; \downarrow \; \updownarrow
| <math>\leftarrow \; \gets \; \rightarrow \; \to \; \leftrightarrow</math><br/>
<math>\longleftarrow \; \longrightarrow</math><br/>
<math>\mapsto \; \longmapsto \; \hookrightarrow \; \hookleftarrow</math><br/>
<math>\nearrow \; \searrow \; \swarrow \; \nwarrow</math><br/>
<math>\uparrow \; \downarrow \; \updownarrow</math>
|-
| \rightharpoonup \; \rightharpoondown \; \leftharpoonup \; \leftharpoondown \; \upharpoonleft \; \upharpoonright \; \downharpoonleft \; \downharpoonright
| <math>\rightharpoonup \; \rightharpoondown \; \leftharpoonup \; \leftharpoondown \; \upharpoonleft \; \upharpoonright \; \downharpoonleft \; \downharpoonright</math>
|-
| \Leftarrow \; \Rightarrow \; \Leftrightarrow<br/>
\Longleftarrow \; \Longrightarrow \; \Longleftrightarrow (or \iff)<br/>
\Uparrow \; \Downarrow \; \Updownarrow
| <math>\Leftarrow \; \Rightarrow \; \Leftrightarrow</math><br/>
<math>\Longleftarrow \; \Longrightarrow \; \Longleftrightarrow (or \iff)</math><br/>
<math>\Uparrow \; \Downarrow \; \Updownarrow</math>
|-
| Special
| \eth \; \S \; \P \; \% \; \dagger \; \ddagger \; \star \; * \; \ldots<br/>
\smile \frown \wr \oplus \bigoplus \otimes \bigotimes<br/>
\times \cdot \circ \bullet \bigodot \triangleleft \triangleright \infty \bot \top \vdash \vDash \Vdash \models \lVert \rVert<br/>
\imath \; \hbar \; \ell \; \mho \; \Finv \; \Re \; \Im \; \wp \; \complement \quad \diamondsuit \; \heartsuit \; \clubsuit \; \spadesuit \; \Game \quad \flat \; \natural \; \sharp
| <math>\eth \; \S \; \P \; \% \; \dagger \; \ddagger \; \star \; * \; \ldots</math><br/>
<math>\smile \frown \wr \oplus \bigoplus \otimes \bigotimes</math><br/>
<math>\times \cdot \circ \bullet \bigodot \triangleleft \triangleright \infty \bot \top \vdash \vDash \Vdash \models \lVert \rVert</math><br/>
<math>\imath \; \hbar \; \ell \; \mho \; \Finv \; \Re \; \Im \; \wp \; \complement \quad \diamondsuit \; \heartsuit \; \clubsuit \; \spadesuit \; \Game \quad \flat \; \natural \; \sharp</math>
|-
| Lowercase \mathcal has some extras
| \mathcal {45abcdenpqstuvwx}
| <math>\mathcal {45abcdenpqstuvwx}</math>
|}

== Subscripts, superscripts, integrals == 
<table border="1">

<tr>
<th>Feature</th>
<th>Syntax</th>
<th colspan="2">How it looks rendered</th>
</tr>

<tr>
<th></th>
<th></th>
<th>HTML</th>
<th>PNG</th>
</tr>

<tr>
<td>Superscript</td>
<td>a^2</td>
<td><math>a^2</math></td>
<td><math>a^2 \,\!</math></td>
</tr>

<tr>
<td>Subscript</td>
<td>a_2</td>
<td><math>a_2</math></td>
<td><math>a_2 \,\!</math></td>
</tr>

<tr>
<td rowspan="2">Grouping</td>
<td>a^{2+2}</td>
<td><math>a^{2+2}</math></td>
<td><math>a^{2+2}\,\!</math></td>
</tr>

<tr>
<td>a_{i,j}</td>
<td><math>a_{i,j}</math></td>
<td><math>a_{i,j}\,\!</math></td>
</tr>

<tr>
<td>Combining sub & super</td>
<td>x_2^3</td>
<td colspan="2"><math>x_2^3</math></td>
</tr>

<tr>
<td>Preceding sub & super</td>
<td>{}_1^2\!X_3^4</td>
<td colspan="2"><math>{}_1^2\!X_3^4</math></td>
</tr>

<tr>
<td>Derivative (good)</td>
<td>x', y<nowiki>''</nowiki></td>
<td><math>x', y''</math></td>
<td><math>x', y''\,\!</math></td>
</tr>

<tr>
<td>Derivative (wrong in HTML)</td>
<td>x^\prime, y^{\prime\prime}</td>
<td><math>x^\prime, y^{\prime\prime}</math></td>
<td><math>x^\prime, y^{\prime\prime}\,\!</math></td>
</tr>

<tr>
<td>Derivative (wrong in PNG)</td>
<td>x\prime, y\prime\prime</td>
<td><math>x\prime, y\prime\prime</math></td>
<td><math>x\prime, y\prime\prime\,\!</math></td>
</tr>

<tr>
<td>Derivative dots</td>
<td>\dot{x}, \ddot{x}</td>
<td colspan="2"><math>\dot{x}, \ddot{x}</math></td>
</tr>

<tr>
<td>Underlines, overlines, vectors</td>
<td>\hat a \ \bar b \ \vec c  \ \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} \ \overline{g h i} \ \underline{j k l}</td>
<td colspan="2"><math>\hat a \ \bar b \ \vec c  \ \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} \ \overline{g h i} \ \underline{j k l}</math></td>
</tr>

<tr>
<td>Overbraces</td>
<td>
\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}
</td>
<td colspan="2">
<math>\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}</math>
</td>
</tr>

<tr>
<td>Underbraces</td>
<td>
\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}
</td>
<td colspan="2">
<math>\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}</math>
</td>
</tr>

<tr>
<td>Sum</td>
<td>\sum_{k=1}^N k^2</td>
<td colspan="2"><math>\sum_{k=1}^N k^2</math></td>
</tr>

<tr>
<td>Product</td>
<td>\prod_{i=1}^N x_i</td>
<td colspan="2"><math>\prod_{i=1}^N x_i</math></td>
</tr>

<tr>
<td>Coproduct</td>
<td>\coprod_{i=1}^N x_i</td>
<td colspan="2"><math>\coprod_{i=1}^N x_i</math></td>
</tr>

<tr>
<td>Limit</td>
<td>\lim_{n \to \infty}x_n</td>
<td colspan="2"><math>\lim_{n \to \infty}x_n</math></td>
</tr>

<tr>
<td>Integral</td>
<td>\int_{-N}^{N} e^x\, dx</td>
<td colspan="2"><math>\int_{-N}^{N} e^x\, dx</math></td>
</tr>

<tr>
<td>Double integral</td>
<td>\iint_{D}^{W} \, dx\,dy</td>
<td colspan="2"><math>\iint_{D}^{W} \, dx\,dy</math></td>
</tr>

<tr>
<td>Triple integral</td>
<td>\iiint_{E}^{V} \, dx\,dy\,dz</td>
<td colspan="2"><math>\iiint_{E}^{V} \, dx\,dy\,dz</math></td>
</tr>

<tr>
<td>Quadruple integral</td>
<td>\iiiint_{F}^{U} \, dx\,dy\,dz\,dt</td>
<td colspan="2"><math>\iiiint_{F}^{U} \, dx\,dy\,dz\,dt</math></td>
</tr>

<tr>
<td>Path integral</td>
<td>\oint_{C} x^3\, dx + 4y^2\, dy</td>
<td colspan="2"><math>\oint_{C} x^3\, dx + 4y^2\, dy</math></td>
</tr>

<tr>
<td>Intersections</td>
<td>\bigcap_1^{n} p</td>
<td colspan="2"><math>\bigcap_1^{n} p</math></td>
</tr>

<tr>
<td>Unions</td>
<td>\bigcup_1^{k} p</td>
<td colspan="2"><math>\bigcup_1^{k} p</math></td>
</tr>
</table>

== Fractions, matrices, multilines == 
<table border="1">

<tr>
<th>Feature</th>
<th>Syntax</th>
<th>How it looks rendered</th>
</tr>

<tr>
<td>Fractions</td>
<td>\frac{2}{4} or {2 \over 4}</td>
<td><math>\frac{2}{4}</math></td>
</tr>

<tr>
<td>Binomial coefficients</td>
<td>{n \choose k}</td>
<td><math>{n \choose k}</math></td>
</tr>

<tr>
<td>Small Fractions</td>
<td>\begin{matrix} \frac{2}{4} \end{matrix}</td>
<td><math>\begin{matrix} \frac{2}{4} \end{matrix}</math></td>
</tr>

<tr>
<td rowspan="6">Matrices</td>
<td>\begin{matrix} x & y \\ z & v \end{matrix}</td>
<td><math>\begin{matrix} x & y \\ z & v
\end{matrix}</math></td>
</tr>

<tr>
<td>\begin{vmatrix} x & y \\ z & v \end{vmatrix}</td>
<td><math>\begin{vmatrix} x & y \\ z & v
\end{vmatrix}</math></td>
</tr>

<tr>
<td>\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}</td>
<td><math>\begin{Vmatrix} x & y \\ z & v
\end{Vmatrix}</math></td>
</tr>

<tr>
<td>\begin{bmatrix} 0 & \cdots & 0 \\ \vdots &
\ddots & \vdots \\ 0 & \cdots &
0\end{bmatrix}</td>
<td><math>\begin{bmatrix} 0 & \cdots & 0 \\ \vdots
& \ddots & \vdots \\ 0 & \cdots &
0\end{bmatrix} </math></td>
</tr>

<tr>
<td>\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}</td>
<td><math>\begin{Bmatrix} x & y \\ z & v
\end{Bmatrix}</math></td>
</tr>

<tr>
<td>\begin{pmatrix} x & y \\ z & v \end{pmatrix}</td>
<td><math>\begin{pmatrix} x & y \\ z & v
\end{pmatrix}</math></td>
</tr>

<tr>
<td>Case distinctions</td>
<td>f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}</td>
<td><math>f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} </math></td>
</tr>

<tr>
<td>Multiline equations</td>
<td>\begin{matrix}f(n+1) & = & (n+1)^2 \\ \ &
= & n^2 + 2n + 1 \end{matrix}</td>
<td><math>\begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix}</math></td>
</tr>

<tr>
<td>Alternative multiline equations (using tables)</td>
<td><pre>
<nowiki>
{|
|-
|&lt;math&gt;f(n+1)&lt;/math&gt;
|&lt;math&gt;=(n+1)^2&lt;/math&gt;
|-
|
|&lt;math&gt;=n^2 + 2n + 1&lt;/math&gt;
|}
</nowiki>
</pre>
</td>
<td>
{|
|-
|<math>f(n+1) \,\!</math>
|<math>=(n+1)^2 \,\!</math>
|-
|
|<math>=n^2 + 2n + 1 \,\!</math>
|}
</td>
</tr>

</table>

== Fonts == 

<table border="1">

<tr>
<th>Feature</th>
<th>Syntax</th>
<th colspan="2">How it looks rendered</th>
</tr>

<tr>
<td>[[en:Greek alphabet|Greek alphabet]]<br/>(Note the lack of omicron; note also that several upper case Greek letters are rendered identically to the corresponding Roman ones)</td>
<td>
\Alpha\ \Beta\ \Gamma\ \Delta\ \Epsilon\ \Zeta\ \Eta\ \Theta\ \Iota\ \Kappa\ \Lambda\ \Mu\ \Nu\ \Xi\ \Pi\ \Rho\ \Sigma\ \Tau\ \Upsilon\ \Phi\ \Chi\ \Psi\ \Omega<br/><br/>
\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega<br/><br/>
\varepsilon\ \digamma\ \vartheta\ \varkappa\ \varpi\ \varrho\ \varsigma\ \varphi
</td>
<td colspan="2">
<math>\Alpha\ \Beta\ \Gamma\ \Delta\ \Epsilon\ \Zeta\ \Eta\ \Theta\ \Iota\ \Kappa\ \Lambda\ \Mu\ \Nu\ \Xi\ \Pi\ \Rho\ \Sigma\ \Tau\ \Upsilon\ \Phi\ \Chi\ \Psi\ \Omega</math><br/><br/>
<math>\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega</math><br/><br/>
<math>\varepsilon\ \digamma\ \vartheta\ \varkappa\ \varpi\ \varrho\ \varsigma\ \varphi</math>
</td>
</tr>

<tr>
<td>[[en:Blackboard bold|blackboard bold]]</td>
<td>\mathbb{N}\ \mathbb{Z}\ \mathbb{Q}\ \mathbb{R}\ \mathbb{C}</td>
<td colspan="2"><math>\mathbb{N}\ \mathbb{Z}\ \mathbb{Q}\ \mathbb{R}\ \mathbb{C}</math></td>
</tr>

<tr>
<td>[[en:boldface|boldface]] (vectors)</td>
<td>\mathbf{x}\cdot\mathbf{y} = 0</td>
<td colspan="2"><math>\mathbf{x}\cdot\mathbf{y} = 0</math></td>
</tr>

<tr>
<td>boldface (greek)</td>
<td>\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}</td>
<td colspan="2"><math>\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}</math></td>
</tr>

<tr>
<td>italics</td>
<td>\mathit{ABCDE abcde 1234}</td>
<td colspan="2"><math>\mathit{ABCDE abcde 1234}\,\!</math></td>
</tr>

<tr>
<td>[[en:Roman typeface|Roman typeface]]</td>
<td>\mathrm{ABCDE abcde 1234}</td>
<td colspan="2"><math>\mathrm{ABCDE abcde 1234}\,\!</math></td>
</tr>

<tr>
<td>[[en:Fraktur (typeface)|Fraktur typeface]]</td>
<td>\mathfrak{ABCDE abcde 1234}</td>
<td colspan="2"><math>\mathfrak{ABCDE abcde 1234}</math></td>
</tr>

<tr>
<td>Calligraphy/Script</td>
<td>\mathcal{ABCDE abcde 1234}</td>
<td colspan="2"><math>\mathcal{ABCDE abcde 1234}</math></td>
</tr>

<tr>
<td>[[en:Hebrew alphabet|Hebrew]]</td>
<td>\aleph \beth \gimel \daleth</td>
<td colspan="2"><math>\aleph\ \beth\ \gimel\ \daleth</math></td>
</tr>

<tr>
<td>non-italicised characters</td>
<td>\mbox{abc}</td>
<td><math>\mbox{abc}</math></td>
<td><math>\mbox{abc} \,\!</math></td>
</tr>

<tr>
<td>mixed italics (bad)</td>
<td>\mbox{if} n \mbox{is even}</td>
<td><math>\mbox{if} n \mbox{is even}</math></td>
<td><math>\mbox{if} n \mbox{is even} \,\!</math></td>
</tr>

<tr>
<td>mixed italics (good)</td>
<td>\mbox{if }n\mbox{ is even}</td>
<td><math>\mbox{if }n\mbox{ is even}</math></td>
<td><math>\mbox{if }n\mbox{ is even} \,\!</math></td>
</tr>

</table>

== Parenthesizing big expressions, brackets, bars == 
<table border="1">

<tr>
<th>Feature</th>
<th>Syntax</th>
<th>How it looks rendered</th>
</tr>

<tr>
<td>Not good</td>
<td>( \frac{1}{2} )</td>
<td><math>( \frac{1}{2} )</math></td>
</tr>

<tr>
<td>Better</td>
<td>\left ( \frac{1}{2} \right )</td>
<td><math>\left ( \frac{1}{2} \right )</math></td>
</tr>

</table>

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

<table border="1">

<tr>
<th>Feature</th>
<th>Syntax</th>
<th>How it looks rendered</th>
</tr>

<tr>
<td>Parentheses</td>
<td>\left ( \frac{a}{b} \right )</td>
<td><math>\left ( \frac{a}{b} \right )</math></td>
</tr>

<tr>
<td>Brackets</td>
<td>\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack</td>
<td><math>\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack</math></td>
</tr>

<tr>
<td>Braces</td>
<td>\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace</td>
<td><math>\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace</math></td>
</tr>

<tr>
<td>Angle brackets</td>
<td>\left \langle \frac{a}{b} \right \rangle</td>
<td><math>\left \langle \frac{a}{b} \right \rangle</math></td>
</tr>

<tr>
<td>Bars and double bars</td>
<td>\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|</td>
<td><math>\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|</math></td>
</tr>

<tr>
<td>Floor and ceiling functions:</td>
<td>\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil</td>
<td><math>\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil</math></td>
</tr>

<tr>
<td>Slashes and backslashes</td>
<td>\left / \frac{a}{b} \right \backslash</td>
<td><math>\left / \frac{a}{b} \right \backslash</math></td>
</tr>

<tr>
<td>Up, down and up-down arrows</td>
<td>\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow</td>
<td><math>\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow</math></td>
</tr>

<tr>
<td>
Delimiters can be mixed,<br/>as long as \left and \right match
</td>
<td>
\left [ 0,1 \right )<br/>\left \langle \psi \right |
</td>
<td>
<math>\left [ 0,1 \right )</math><br/><math>\left \langle \psi \right |</math>
</td>
</tr>

<tr>
<td>Use \left. and \right. if you don't<br/>want a delimiter to appear:</td>
<td>\left . \frac{A}{B} \right \} \to X</td>
<td><math>\left . \frac{A}{B} \right \} \to X</math></td>
</tr>

<tr>
<td rowspan="5">Size of the delimiters</td>
<td>\big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]</td>
<td colspan="2">
<math>\big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]</math>
</td>
</tr>
<tr>
<td>\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle</td>
<td colspan="2">
<math>\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle</math>
</td>
</tr>
<tr>
<td>\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big|</td>
<td colspan="2"><math>\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big|</math></td>
</tr>
<tr>
<td>\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil</td>
<td colspan="2">
<math>\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil</math>
</td>
</tr>
<tr>
<td>\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow</td>
<td colspan="2">
<math>\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow</math>
</td>
</tr>

</table>

== Spacing ==
Note that TeX handles most spacing automatically, but you may sometimes want manual control. 
<table border="1">

<tr>
<th>Feature</th>
<th>Syntax</th>
<th>How it looks rendered</th>
</tr>

<tr>
<td>double quad space</td>
<td>a \qquad b</td>
<td><math>a \qquad b</math></td>
</tr>

<tr>
<td>quad space</td>
<td>a \quad b</td>
<td><math>a \quad b</math></td>
</tr>

<tr>
<td>text space</td>
<td>a\ b</td>
<td><math>a\ b</math></td>
</tr>

<tr>
<td>text space without PNG conversion</td>
<td>a \mbox{ } b</td>
<td><math>a \mbox{ } b</math></td>
</tr>

<tr>
<td>large space</td>
<td>a\;b</td>
<td><math>a\;b</math></td>
</tr>

<tr>
<td>medium space</td>
<td>a\&gt;b</td>
<td>[not supported]</td>
</tr>

<tr>
<td>small space</td>
<td>a\,b</td>
<td><math>a\,b</math></td>
</tr>

<tr>
<td>no space</td>
<td>ab</td>
<td><math>ab\,</math></td>
</tr>

<tr>
<td>negative space</td>
<td>a\!b</td>
<td><math>a\!b</math></td>
</tr>

</table>

== Align with normal text flow ==
Due to the default css

<pre>img.tex { vertical-align: middle; }</pre>

an inline expression like <math>\int_{-N}^{N} e^x\, dx</math> should look good.

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

== Forced PNG rendering ==

To force the formula to render as PNG, add <tt>\,</tt> (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 [[help:Preferences|preferences]]).

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

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:

<table border="1">

<tr>
<th>Syntax</th>
<th>How it looks rendered</th>
</tr>

<tr>
<td>a^{c+2}</td>
<td><math>a^{c+2}</math></td>
</tr>

<tr>
<td>a^{c+2} \,</td>
<td><math>a^{c+2} \,</math></td>
</tr>

<tr>
<td>a^{\,\!c+2}</td>
<td><math>a^{\,\!c+2}</math> </td>
</tr>

<tr>
<td>a^{b^{c+2}}</td>
<td><math>a^{b^{c+2}}</math> (WRONG with option "HTML if possible or else PNG"!)</td>
</tr>

<tr>
<td>a^{b^{c+2}} \,</td>
<td><math>a^{b^{c+2}} \,</math> (WRONG with option "HTML if possible or else PNG"!)</td>
</tr>

<tr>
<td>a^{b^{c+2}}\approx 5</td>
<td><math>a^{b^{c+2}}\approx 5</math> (due to "<math>\approx</math>" correctly displayed, no code "\,\!" needed)</td>
</tr>

<tr>
<td>a^{b^{\,\!c+2}}</td>
<td><math>a^{b^{\,\!c+2}}</math></td>
</tr>

<tr>
<td>\int_{-N}^{N} e^x\, dx</td>
<td><math>\int_{-N}^{N} e^x\, dx</math></td>
</tr>

<tr>
<td>\int_{-N}^{N} e^x\, dx \,</td>
<td><math>\int_{-N}^{N} e^x\, dx \,</math></td>
</tr>

<tr>
<td>\int_{-N}^{N} e^x\, dx \,\!</td>
<td><math>\int_{-N}^{N} e^x\, dx \,\!</math></td>
</tr>

</table>


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:

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

* [http://meta.wikimedia.org/wiki/Help:Editing General help] for editing a Wiki page
* How to [http://meta.wikimedia.org/wiki/Help:Formula enter equations] for a Wiki page
* Sample TeX equations
== Examples ==

<center>
===Quadratic Polynomial===
 <math>x_1 = a^2 + b^2 + c^2</math>
 
 <nowiki><math>x_1 = a^2 + b^2 + c^2 </math></nowiki>

===Quadratic Formula===

 <math>x_{1,55}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
 
 <nowiki><math>x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math></nowiki>

===Parentheses and fractions===

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

===Tall Parentheses and fractions ===

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

===Force Rendering===

 <math>4-2x = 9-3x \!</math>
 
 <nowiki><math>4-2x = 9-3x \!</math></nowiki>

===Force Rendering===

 <math>-2x+3x = 9-4 \!</math>
 
 <nowiki><math>-2x+3x = 9-4 \!</math></nowiki>

===Integrals===

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

===Summation===

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

=== Differential Equation ===

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

===Example===

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

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

===Integral Equation===

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

===Example===
 <math>\int_0^\infty x^\alpha \sin(x)\,dx = 2^\alpha \sqrt{\pi}\, \frac{\Gamma(\frac{\alpha}{2}+1)}{\Gamma(\frac{1}{2}-\frac{\alpha}{2})}\,</math>
  
 <nowiki><math>\int_0^\infty x^\alpha \sin(x)\,dx = 2^\alpha \sqrt{\pi}\,</nowiki>
 <nowiki>\frac{\Gamma(\frac{\alpha}{2}+1)}{\Gamma(\frac{1}{2}-\frac{\alpha}{2})}\,</math></nowiki>

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

===Example===
 <math>f(x) = {a_0\over 2} + \sum_{n=1}^\infty a_n\cos\left({2n\pi x \over T}\right) + b_n\sin\left({2n\pi x\over T}\right)\,</math>
 
 <nowiki><math>f(x) = {a_0\over 2} + \sum_{n=1}^\infty a_n\cos\left({2n\pi x \over T}\right) +</nowiki>
 <nowiki>b_n\sin\left({2n\pi x\over T}\right)\,</math></nowiki>

===Continuation and cases===
 <math>f(x) = \begin{cases}1 & -1 \le x < 0\\
 \frac{1}{2} & x = 0\\x&0<x\le 1\end{cases}</math>
 
 <nowiki>f(x) = \begin{cases}1 & -1 \le x < 0\\</nowiki>
 <nowiki>\frac{1}{2} & x = 0\\x&0<x\le 1\end{cases}</nowiki>

===Example===
 <math>\Gamma(z) = \int_0^\infty e^{-t} t^{z-1} \,dt\,</math>
 
 <nowiki><math>\Gamma(z) = \int_0^\infty e^{-t} t^{z-1} \,dt\,</math></nowiki>

===Example===
 <math>J_p(z) = \sum_{k=0}^\infty \frac{(-1)^k\left(\frac{z}{2}\right)^{2k+p}}{k!\Gamma(k+p+1)}\,</math>
 
 <nowiki><math>J_p(z) = \sum_{k=0}^\infty</nowiki>
 <nowiki>\frac{(-1)^k\left(\frac{z}{2}\right)^{2k+p}}{k!\Gamma(k+p+1)}\,</math></nowiki>
===Example===
 <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>
 
 <nowiki> <math>{}_pF_q(a_1,...,a_p;c_1,...,c_q;z) = \sum_{n=0}^\infty</nowiki>
 <nowiki>\frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}\frac{z^n}{n!}\,</math></nowiki>

===Gamma Function===

 <math>\Gamma(n+1) = n \Gamma(n),  \; n>0</math>
 
 <nowiki><math>\Gamma(n+1) = n \Gamma(n),  \; n>0</math></nowiki>

===Example===
 <nowiki><math>\int_0^1 \frac{1}{\sqrt{-\ln x}} dx\,</math></nowiki>
 
 <math>\int_0^1 \frac{1}{\sqrt{-\ln x}} dx\,</math>

===Example===
 <math>\int_0^\infty e^{-st}t^{x-1}\,dt,\,\,\,s>0\,</math>
 
 <nowiki><math>\int_0^\infty e^{-st}t^{x-1}\,dt,\,\,\,s>0\,</math></nowiki>

===Example===
 <math>B(u) = \sum_{k=0}^N {P_k}{N! \over k!(N - k)!}{u^k}(1 - u)^{N-k}\,</math>
 
 <nowiki><math>B(u) = \sum_{k=0}^N {P_k}{N! \over k!(N - k)!}{u^k}(1 - </nowiki>
 <nowiki>u)^{N-k}\,</math></nowiki>

===Example===
 <math>u(x,y) = \frac{1}{\sqrt{2\pi}}\int_0^\infty f(\xi)\left[g(|x+\xi|,y)+g(|x-\xi|,y)\right]\,d\xi\,</math>
 
 <nowiki><math>u(x,y) = \frac{1}{\sqrt{2\pi}}\int_0^\infty </nowiki>
 <nowiki>f(\xi)\left[g(|x+\xi|,y)+g(|x-\xi|,y)\right]\,d\xi\,</math></nowiki>

</center>

==See also==
*[[w:Wikipedia:How_to_write_a_Wikipedia_article_on_Mathematics#Typesetting_of_mathematical_formulas|Typesetting of mathematical formulas]]
* Proposed [[GNU LilyPond support]]
*[[w:en:Table of mathematical symbols]]
*[[Wikipedia:Wikipedia talk:WikiProject Mathematics/Archive10#blahtex: a LaTeX to MathML converter|blahtex: a LaTeX to MathML converter for Wikipedia]] or [[Blahtex]]

== External Links ==
* A LaTeX tutorial.  http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/
* A [[en:Portable Document Format|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/~mimi/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


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