Help:Displaying a formula

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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.

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 set $wgUseTeX = true; in LocalSettings.php.

Technicals

Syntax

Traditionally, math markup goes inside the XML-style tag math: <math> ... </math>. The old edit toolbar has the button for this, and it is possible to customize the WikiEditor toolbar to add a similar button. The icons are like these: MediaWiki:Math tip and <math>\sqrt{n}</math>.

However, one can also use parser function #tag: {{#tag:math|...}}; this is more versatile: the wikitext at the dots is first expanded before interpreting the result as TeX code. Thus it can contain parameters, variables, parser functions and templates. Note however that with this syntax double braces in the TeX code must have a space in between, to avoid confusion with their use in template calls etc. Also, to produce the character "|" inside the TeX code, use {{!}}.<ref>This requires the wiki to have the Template:! containing "|", as many wikis do, see e.g. also w:Template:!.</ref>

In TeX, as in HTML, extra spaces and newlines are ignored.

Rendering

By default, the PNG images are black on white (not transparent), but since bug 8 was fixed (see rev:59550) these colors can be customized for each formula. The 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 (see bug 32694). The css selector of the images is img.tex.

The alt text of the PNG images, which is displayed to visually impaired and other readers who cannot see the images, and is also used when the text is selected and copied, defaults to the wikitext that produced the image, excluding the <math> and </math>. You can override this by explicitly specifying an alt attribute for the math element. For example, <math alt="Square root of pi">\sqrt{\pi}</math> generates an image <math alt="Square root of pi">\sqrt{\pi}</math> whose alt text is "Square root of pi".

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 \text, \mbox, or \mathrm. You can also define new function names using \operatorname{...}. For example, <math>\text{abc}</math> gives <math>\text{abc}</math>. This does not work for special characters, they are ignored unless the whole <math> expression is rendered in HTML:

• <math>\text {abcdefghijklmnopqrstuvwxyzàáâãäåæçčďèéěêëìíîïňñòóôõöřšť÷øùúůûüýÿž}</math>
• <math>\text {abcdefghijklmnopqrstuvwxyzàáâãäåæçčďèéěêëìíîïňñòóôõöřšť÷øùúůûüýÿž}\,</math>

gives:

• <math>\text {abcdefghijklmnopqrstuvwxyzàáâãäåæçčďèéěêëìíîïňñòóôõöřšť÷øùúůûüýÿž}</math>
• <math>\text {abcdefghijklmnopqrstuvwxyzàáâãäåæçčďèéěêëìíîïňñòóôõöřšť÷øùúůûüýÿž}\,</math>

See bug 798 for details.

Nevertheless, using \mbox instead of \text, more characters are allowed

For example,

• <math>\mbox {abcdefghijklmnopqrstuvwxyzàáâãäåæçčďèéěêëìíîïňñòóôõöřšť÷øùúůûüýÿž}</math>
• <math>\mbox {abcdefghijklmnopqrstuvwxyzàáâãäåæçčèéêëìíîïñòóôõö÷øùúûüýÿ}\,</math>

gives:

• <math>\mbox {abcdefghijklmnopqrstuvwxyzàáâãäåæçčďèéěêëìíîïňñòóôõöřšť÷øùúůûüýÿž}</math>
• <math>\mbox {abcdefghijklmnopqrstuvwxyzàáâãäåæçčďèéěêëìíîïňñòóôõöřšť÷øùúůûüýÿž}\,</math>

But \mbox{ð} and \mbox{þ} will give an error:

• <math>\mbox {ð}</math>
• <math>\mbox {þ}</math>

Using \text{}

• <math>\text {ð}</math>
• <math>\text {þ}</math>

Special characters

The following symbols are reserved characters that either have a special meaning under LaTeX or are unavailable in all the fonts.

# $ % ^ & _ { } ~ \

Some of these can be entered with a backslash in front:

<math>\# \$ \% \_ \{ \}</math> gives <math>\# \$ \% \_ \{ \}</math>

TeX and 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>	<math>\alpha</math>	{{math|<VAR>&alpha;</VAR>}}	α
<math> f(x) = x^2\,</math>	<math> f(x) = x^2\,</math>	{{math|''f''(<var>x</var>) {{=}} <var>x</var><sup>2</sup>}}	f(x) = x2
<math>\sqrt{2}</math>	<math>\sqrt{2}</math>	{{math|{{radical|2}}}}	√2
<math>\sqrt{1-e^2}</math>	<math>\sqrt{1-e^2}</math>	{{math|{{radical|1 &minus; ''e''&sup2;}}}}	√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 ‘=’.

Syntax	Rendering
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
∫ ∑ ∏ √ − ± &infty; ≈ ∝ {{=}} ≡ ≠ ≤ ≥ × · ÷ ∂ ′ ″ ∇ ‰ ° ∴ Ø ø ∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇ ¬ ∧ ∨ ∃ ∀ ⇒ ⇔ → ↔ ↑ ℵ - – —	∫ ∑ ∏ √ − ± ∞ ≈ ∝ = ≡ ≠ ≤ ≥ × · ÷ ∂ ′ ″ ∇ ‰ ° ∴ Ø ø ∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇ ¬ ∧ ∨ ∃ ∀ ⇒ ⇔ → ↔ ↑ ℵ - – —

The project has settled on both HTML and TeX because each has advantages in some situations.

Pros of HTML

1. Formulas in HTML behave more like regular text. In-line HTML formulae always align properly with the rest of the HTML text and, to some degree, can be cut-and-pasted (this is not a problem if TeX is rendered using MathJax, and the alignment should not be a problem for PNG rendering once bug 32694 is fixed).
2. The formula’s background and font size match the rest of HTML contents (this can be fixed on TeX formulas by using the commands \pagecolor and \definecolor) 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 more precise than HTML.
   1. In TeX, "<math>x</math>" means "mathematical variable <math>x</math>", whereas in HTML "x" is generic and somewhat ambiguous.
   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 if no other rendering options are available (such as MathJax, which was requested on bug 31406 for use on Wikimedia wikis and is being implemented on Extension:Math as a new rendering option).
2. One consequence of point 1 is that TeX code 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 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.
3. Another consequence of point 1 is that TeX can be converted to MathML (e.g. by MathJax) for browsers which support it, thus keeping its semantics and allowing the rendering to be better suited for the reader’s graphic device.
4. 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.
5. 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.
6. Once a formula is done correctly in TeX, it will render reliably, whereas the success of HTML formulae is somewhat dependent on browsers or versions of browsers. Another aspect of this dependency is fonts: 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 ’).
7. 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.
8. TeX formulae, by default, render larger and are usually more readable than HTML formulae and are not dependent on client-side browser resources, such as fonts, and so the results are more reliably WYSIWYG.
9. While TeX does not assist you in finding HTML codes or Unicode values (which you can obtain by viewing the HTML source in your browser), cutting and pasting from a TeX PNG in Wikipedia into simple text will return the LaTeX source.

Note: dilHTML

unless your wikitext follows the style of point 1.2

Note: entHTML

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. &ndash; for ‘–’ and &minus; for ‘−’).

In some cases it may be the best choice to use neither TeX nor the html-substitutes, but instead the simple ASCII symbols of a standard keyboard (see below, for an example).

Functions, symbols, special characters

Accents/diacritics

\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}	<math>\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}\,</math>
\check{a} \bar{a} \ddot{a} \dot{a}	<math>\check{a} \bar{a} \ddot{a} \dot{a}</math>

Standard functions

\sin a \cos b \tan c	<math>\sin a \cos b \tan c</math>
\sec d \csc e \cot f	<math>\sec d \csc e \cot f\,</math>
\arcsin h \arccos i \arctan j	<math>\arcsin h \arccos i \arctan j\,</math>
\sinh k \cosh l \tanh m \coth n	<math>\sinh k \cosh l \tanh m \coth n</math>
\operatorname{sh}o\,\operatorname{ch}p\,\operatorname{th}q	<math>\operatorname{sh}o\,\operatorname{ch}p\,\operatorname{th}q</math>
\operatorname{arsinh}r\,\operatorname{arcosh}s\,\operatorname{artanh}t	<math>\operatorname{arsinh}r\,\operatorname{arcosh}s\,\operatorname{artanh}t</math>
\lim u \limsup v \liminf w \min x \max y	<math>\lim u \limsup v \liminf w \min x \max y</math>
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g	<math>\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g</math>
\deg h \gcd i \Pr j \det k \hom l \arg m \dim n	<math>\deg h \gcd i \Pr j \det k \hom l \arg m \dim n</math>

Modular arithmetic

s_k \equiv 0 \pmod{m}	<math>s_k \equiv 0 \pmod{m}\,</math>
a\,\bmod\,b	<math>a\,\bmod\,b\,</math>

Derivatives

\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}

<math>\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2}</math>

Sets

\forall \exists \empty \emptyset \varnothing	<math>\forall \exists \empty \emptyset \varnothing\,</math>
\in \ni \not \in \notin \subset \subseteq \supset \supseteq	<math>\in \ni \not \in \notin \subset \subseteq \supset \supseteq\,</math>
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus	<math>\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus\,</math>
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup	<math>\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup\,</math>

Operators

+ \oplus \bigoplus \pm \mp -	<math>+ \oplus \bigoplus \pm \mp - \,</math>
\times \otimes \bigotimes \cdot \circ \bullet \bigodot	<math>\times \otimes \bigotimes \cdot \circ \bullet \bigodot\,</math>
\star * / \div \frac{1}{2}	<math>\star * / \div \frac{1}{2}\,</math>

Logic

\land (or \and) \wedge \bigwedge \bar{q} \to p	<math>\land \wedge \bigwedge \bar{q} \to p\,</math>
\lor \vee \bigvee \lnot \neg q \And	<math>\lor \vee \bigvee \lnot \neg q \And\,</math>

Root

\sqrt{2} \sqrt[n]{x}

<math>\sqrt{2} \sqrt[n]{x}\,</math>

Relations

\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}	<math>\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}\,</math>
< \le \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto	<math>< \le \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto\,</math>
\lessapprox \lesssim \eqslantless \leqslant \leqq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox	<math> \lessapprox \lesssim \eqslantless \leqslant \leqq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox</math>

Geometric

\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ

45^\circ\,</math>

Arrows

\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \nrightarrow \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow	<math>\leftarrow \rightarrow \nleftarrow \nrightarrow \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow \,</math>
\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow (or \implies) \Longleftrightarrow (or \iff)	<math>\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow </math>
\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow	<math>\uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow </math>
\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons	<math>\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,</math>
\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright	<math>\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright \,</math>
\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft	<math>\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,</math>
\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow	<math>\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \,</math>

Special

\And \eth \S \P \% \dagger \ddagger \ldots \cdots	<math>\And \eth \S \P \% \dagger \ddagger \ldots \cdots\,</math>
\smile \frown \wr \triangleleft \triangleright \infty \bot \top	<math>\smile \frown \wr \triangleleft \triangleright \infty \bot \top\,</math>
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar	<math>\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar\,</math>
\ell \mho \Finv \Re \Im \wp \complement	<math>\ell \mho \Finv \Re \Im \wp \complement\,</math>
\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp	<math>\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp\,</math>

Unsorted (new stuff)

\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown	<math> \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown</math>
\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge	<math> \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge</math>
\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes	<math> \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes</math>
\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant	<math> \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant</math>
\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq	<math> \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq</math>
\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft	<math> \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft</math>
\Vvdash \bumpeq \Bumpeq \eqsim \gtrdot	<math> \Vvdash \bumpeq \Bumpeq \eqsim \gtrdot</math>
\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq	<math> \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq</math>
\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \between \shortparallel \pitchfork	<math> \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \between \shortparallel \pitchfork</math>
\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq	<math> \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq</math>
\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid	<math> \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid</math>
\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr	<math> \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr</math>
\subsetneq	<math>\subsetneq</math>
\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq	<math> \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq</math>
\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq	<math> \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq</math>
\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq	<math> \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq</math>
\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus	<math>\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus\,</math>
\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq	<math>\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq\,</math>
\dashv \asymp \doteq \parallel	<math>\dashv \asymp \doteq \parallel\,</math>
\ulcorner \urcorner \llcorner \lrcorner	<math>\ulcorner \urcorner \llcorner \lrcorner</math>
\Coppa\coppa\varcoppa\Digamma\Koppa\koppa\Sampi\sampi\Stigma\stigma\varstigma	<math>\Coppa\coppa\varcoppa\Digamma\Koppa\koppa\Sampi\sampi\Stigma\stigma\varstigma</math>

Larger expressions

Subscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
Superscript	a^2	<math>a^2</math>
Subscript	a_2	<math>a_2</math>
Grouping	a^{2+2}	<math>a^{2+2}</math>
	a_{i,j}	<math>a_{i,j}</math>
Combining sub & super without and with horizontal separation	x_2^3	<math>x_2^3</math>
	{x_2}^3	<math>{x_2}^3</math>
Super super	10^{10^{8}}	<math>10^{10^{8}}</math>
Preceding and/or Additional sub & super	_nP_k	<math>_nP_k</math>
	\sideset{_1^2}{_3^4}\prod_a^b	<math>\sideset{_1^2}{_3^4}\prod_a^b</math>
	{}_1^2\!\Omega_3^4	<math>{}_1^2\!\Omega_3^4</math>
Stacking	\overset{\alpha}{\omega}	<math>\overset{\alpha}{\omega}</math>
	\underset{\alpha}{\omega}	<math>\underset{\alpha}{\omega}</math>
	\overset{\alpha}{\underset{\gamma}{\omega}}	<math>\overset{\alpha}{\underset{\gamma}{\omega}}</math>
	\stackrel{\alpha}{\omega}	<math>\stackrel{\alpha}{\omega}</math>
Derivatives	x', y'', f', f''	<math>x', y, f', f</math>
	x^\prime, y^{\prime\prime}	<math>x^\prime, y^{\prime\prime}</math>
Derivative dots	\dot{x}, \ddot{x}	<math>\dot{x}, \ddot{x}</math>
Underlines, overlines, vectors	\hat a \ \bar b \ \vec c	<math>\hat a \ \bar b \ \vec c</math>
	\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}	<math>\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}</math>
	\overline{g h i} \ \underline{j k l}	<math>\overline{g h i} \ \underline{j k l}</math>
	\not 1 \ \cancel{123}	<math>\not 1 \ \cancel{123}</math>
Arrows	A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C	<math> A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C</math>
Overbraces	\overbrace{ 1+2+\cdots+100 }^{\text{sum}\,=\,5050}	<math>\overbrace{ 1+2+\cdots+100 }^{\text{sum}\,=\,5050}</math>
Underbraces	\underbrace{ a+b+\cdots+z }_{26\text{ terms}}	<math>\underbrace{ a+b+\cdots+z }_{26\text{ terms}}</math>
Sum	\sum_{k=1}^N k^2	<math>\sum_{k=1}^N k^2</math>
Sum (force \textstyle)	\textstyle \sum_{k=1}^N k^2	<math>\textstyle \sum_{k=1}^N k^2</math>
Product	\prod_{i=1}^N x_i	<math>\prod_{i=1}^N x_i</math>
Product (force \textstyle)	\textstyle \prod_{i=1}^N x_i	<math>\textstyle \prod_{i=1}^N x_i</math>
Coproduct	\coprod_{i=1}^N x_i	<math>\coprod_{i=1}^N x_i</math>
Coproduct (force \textstyle)	\textstyle \coprod_{i=1}^N x_i	<math>\textstyle \coprod_{i=1}^N x_i</math>
Limit	\lim_{n \to \infty}x_n	<math>\lim_{n \to \infty}x_n</math>
Limit (force \textstyle)	\textstyle \lim_{n \to \infty}x_n	<math>\textstyle \lim_{n \to \infty}x_n</math>
Integral	\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx	<math>\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx</math>
Integral (alternate limits style)	\int_{1}^{3}\frac{e^3/x}{x^2}\, dx	<math>\int_{1}^{3}\frac{e^3/x}{x^2}\, dx</math>
Integral (force \textstyle)	\textstyle \int\limits_{-N}^{N} e^x\, dx	<math>\textstyle \int\limits_{-N}^{N} e^x\, dx</math>
Integral (force \textstyle, alternate limits style)	\textstyle \int_{-N}^{N} e^x\, dx	<math>\textstyle \int_{-N}^{N} e^x\, dx</math>
Double integral	\iint\limits_D \, dx\,dy	<math>\iint\limits_D \, dx\,dy</math>
Triple integral	\iiint\limits_E \, dx\,dy\,dz	<math>\iiint\limits_E \, dx\,dy\,dz</math>
Quadruple integral	\iiiint\limits_F \, dx\,dy\,dz\,dt	<math>\iiiint\limits_F \, dx\,dy\,dz\,dt</math>
Line or path integral	\int_C x^3\, dx + 4y^2\, dy	<math>\int_C x^3\, dx + 4y^2\, dy</math>
Closed line or path integral	\oint_C x^3\, dx + 4y^2\, dy	<math>\oint_C x^3\, dx + 4y^2\, dy</math>
Intersections	\bigcap_1^n p	<math>\bigcap_1^n p</math>
Unions	\bigcup_1^k p	<math>\bigcup_1^k p</math>

Fractions, matrices, multilines

Feature	Syntax	How it looks rendered
Fractions	\frac{1}{2}=0.5	<math>\frac{1}{2}=0.5</math>
Small ("text style") fractions	\tfrac{1}{2} = 0.5	<math>\tfrac{1}{2} = 0.5</math>
Large ("display style") fractions	\dfrac{k}{k-1} = 0.5	<math>\dfrac{k}{k-1} = 0.5</math>
Mixture of large and small fractions	\dfrac{ \tfrac{1}{2}[1-(\tfrac{1}{2})^n] }{ 1-\tfrac{1}{2} } = s_n	<math>\dfrac{ \tfrac{1}{2}[1-(\tfrac{1}{2})^n] }{ 1-\tfrac{1}{2} } = s_n</math>
Continued fractions (note the difference in formatting)	\cfrac{2}{ c + \cfrac{2}{ d + \cfrac{1}{2} } } = a \qquad \dfrac{2}{ c + \dfrac{2}{ d + \dfrac{1}{2} } } = a	<math>\cfrac{2}{ c + \cfrac{2}{ d + \cfrac{1}{2} } } = a \qquad \dfrac{2}{ c + \dfrac{2}{ d + \dfrac{1}{2} } } = a</math>
Binomial coefficients	\binom{n}{k}	<math>\binom{n}{k}</math>
Small ("text style") binomial coefficients	\tbinom{n}{k}	<math>\tbinom{n}{k}</math>
Large ("display style") binomial coefficients	\dbinom{n}{k}	<math>\dbinom{n}{k}</math>
Matrices	\begin{matrix} x & y \\ z & v \end{matrix}	<math>\begin{matrix} x & y \\ z & v \end{matrix}</math>
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}	<math>\begin{vmatrix} x & y \\ z & v \end{vmatrix}</math>
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}	<math>\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}</math>
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}	<math>\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} </math>
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}	<math>\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}</math>
	\begin{pmatrix} x & y \\ z & v \end{pmatrix}	<math>\begin{pmatrix} x & y \\ z & v \end{pmatrix}</math>
	\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)	<math> \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) </math>
Arrays	\begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array}	<math> \begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array} </math>
Cases	f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}	<math>f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} </math>
System of equations	\begin{cases} 3x + 5y + z &= 1 \\ 7x - 2y + 4z &= 2 \\ -6x + 3y + 2z &= 3 \end{cases}	<math>\begin{cases} 3x + 5y + z &= 1 \\ 7x - 2y + 4z &= 2 \\ -6x + 3y + 2z &= 3 \end{cases}</math>
Breaking up a long expression so it wraps when necessary	<math>f(x) = \sum_{n=0}^\infty a_n x^n</math> <math>= a_0 + a_1x + a_2x^2 + \cdots</math>	<math>f(x) = \sum_{n=0}^\infty a_n x^n</math> <math>= a_0 + a_1x + a_2x^2 + \cdots</math>
Multiline equations	\begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align}	<math> \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} </math>
	\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat}	<math> \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} </math>
Multiline equations with aligment specified (left, center, right)	\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}	<math>\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}</math>
	\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}	<math>\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}</math>

Parenthesizing big expressions, brackets, bars

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

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

Feature	Syntax	How it looks rendered
Parentheses	\left ( \frac{a}{b} \right )	<math>\left ( \frac{a}{b} \right )</math>
Brackets	\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack	<math>\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack</math>
Braces (note the backslash before the braces in the code)	\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace	<math>\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace</math>
Angle brackets	\left \langle \frac{a}{b} \right \rangle	<math>\left \langle \frac{a}{b} \right \rangle</math>
Bars and double bars (note: "bars" provide the absolute value function)	\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|	\frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|</math>
Floor and ceiling functions:	\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil	<math>\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil</math>
Slashes and backslashes	\left / \frac{a}{b} \right \backslash	<math>\left / \frac{a}{b} \right \backslash</math>
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	<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>
Delimiters can be mixed, as long as \left and \right are both used	\left [ 0,1 \right ) \left \langle \psi \right |	</math>
Use \left. or \right. if you don't want a delimiter to appear:	\left . \frac{A}{B} \right \} \to X	<math>\left . \frac{A}{B} \right \} \to X</math>
Size of the delimiters	\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]	<math>\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]</math>
	\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle	<math>\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle</math>
	\big| \Big| \bigg| \Bigg| \dots \Bigg\| \bigg\| \Big\| \big\|	\Big| \bigg| \Bigg| \dots \Bigg\| \bigg\| \Big\| \big\|</math>
	\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil	<math>\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil</math>
	\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow	<math>\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow</math>
	\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow	<math>\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow</math>
	\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash	<math>\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash</math>

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

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

Color

Equations can use color:

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

  <math>{\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}</math>

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

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

It is also possible to change the background color (since r59550), as in the following example:

Background	Wikicode	Rendering (in PNG)
White	e^{i \pi} + 1 = 0	<math>e^{i \pi} + 1 = 0\,</math>
	\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0	<math>\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0\,</math>
Orange	e^{i \pi} + 1 = 0	<math>e^{i \pi} + 1 = 0\,</math>
	\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0	<math>\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0\,</math>

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. See en:Wikipedia:Manual of Style#Color coding.

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	<math>a \qquad b</math>
quad space	a \quad b	<math>a \quad b</math>
text space	a\ b	<math>a\ b</math>
text space without PNG conversion	a \mbox{ } b	<math>a \mbox{ } b</math>
large space	a\;b	<math>a\;b</math>
medium space	a\>b	[not supported]
small space	a\,b	<math>a\,b</math>
no space	ab	<math>ab\,</math>
small negative space	a\!b	<math>a\!b</math>

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>

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

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

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

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

Alignment with normal text flow

Due to the default css

img.tex { vertical-align: middle; }

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

Commutative diagrams

To make a commutative diagram, there are three steps:

• Write the diagram in TeX
• Convert to SVG
• Upload the file to Wikimedia Commons

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 TUGboat, Volume 17 1996, No. 3):

\documentclass{amsart}
\usepackage[all, ps]{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)

pdflatex and the pdfcrop and pdf2svg utilities are needed for this procedure.

If you do not have these programs, you can also use the commands

latex file.tex
dvipdfm file.dvi

to get a PDF version of your diagram.

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

See also: commons:Commons:First steps/Upload form

See also: en:Help:Contents/Images and media

As the diagram is your own work, upload it to Wikimedia Commons, so that all projects (notably, all languages) can use it without having to copy it to their language's Wiki. (If you've previously uploaded a file to somewhere other than Commons, transwiki it to Commons.)

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

Login to Wikimedia Commons, then upload the file; for the Summary, give a brief description.

Now go to the image page and add a description, including the source code, using this template (using {{Information}}):

{{Information
|Description =
{{en| Description [[:en:Link to WP page|topic]]
}}
|Source = {{own}}

Created as per:

[[:en:meta:Help:Displaying a formula#Commutative diagrams]]; source code below.
|Date = The Creation Date, like 1999-12-31
|Author = [[User:YourUserName|Your Real Name]]
|Permission = Public domain; (or other license) see below. 
}}

== 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

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

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

Quadratic Polynomial (Force PNG Rendering)

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

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

Quadratic Formula

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

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

Tall Parentheses and Fractions

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

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

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

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

Integrals

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

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

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>

<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

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

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

Complex numbers

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

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

Limits

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

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

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>

<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

<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>\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

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

<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

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

 <math>{}_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

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

Future

In the future, once the MathJax option which was added to the Math extension is stable enough, it may be enabled on Wikimedia wikis (per bug 31406) as a better alternative for the PNG rendering of TeX formulas. MathJax is a JavaScript library for inline rendering of mathematical formulae, and can be used to translate LaTeX into MathML for direct interpretation by the browser.

See also

• Comparison between ParserFunctions syntax and TeX syntax
• Typesetting of mathematical formulas
• Proposed m:Music markup
• Table of mathematical symbols
• mw:Extension:Blahtex, or blahtex: a LaTeX to MathML converter for Wikipedia
• General help for editing a Wiki page
• Mimetex alternative for another way to display mathematics using Mimetex.cgi

Notes

<references group=""></references>

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.

Links to other help pages

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