Help:Formula

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MediaWiki uses a subset of AMS-LaTeX markup, a superset of LaTeX markup which is in turn a superset of TeX markup, for mathematical formulae. It generates PNG images by default. Alternatively, the MathJax renderer can be selected in the user preferences: this uses a combination of HTML and CSS to display the equation.

Although, in all cases mentioned, TeX is generated by compilation, and not by an interpreter program, there is one essential difference between, e.g., Knuth's TeX or Lamport's LaTeX and the present implementation: whereas in the first two cases the compiler typically generates an all-in-one printable output, which has the quality of a whole book with all chapters, sections and subsections, and where no line is "special", in the present case one has, typically, a mixture of TeX images (more precisely: PNG images) for the equations, embedded into usual text, and with short TeX elements usually replaced by HTML parts. As a consequence, in many cases TeX-elements, e.g. vector symbols, "stick out" below (or above) the text line. This "sticking out" is not  the case in the above-mentioned original products, and the HTML-substitutes for small TeX additions to the text are often insufficient in quality for many readers. In spite of these shortcomings, the present product characterized by "many embedded PNG-images" should be preferred for small texts, where the equations do not dominate.

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

To have math rendered in a particular MediaWiki installation, one has to set $wgUseTeX = true; in LocalSettings.php.

Contents

Basics

Math markup goes inside Template:Tag.

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 for more information.

LaTeX commands

LaTeX commands are case-sensitive, and take one of the following two formats:

  • They start with a backslash \ and then have a name consisting of letters only. Command names are terminated by a space, a number or any other "non-letter".
  • They consist of a backslash \ and exactly one non-letter.

Some commands need an argument, which has to be given between curly braces { } after the command name. Some commands support optional parameters, which are added after the command name in square brackets []. The general syntax is:

\commandname[option1,option2,...]{argument1}{argument2}...

Special characters

The following symbols are reserved characters that either have a special meaning under LaTeX or are unavailable in all the fonts. If you enter them directly in your text, they will normally not render, but rather do things you did not intend.

# $ % ^ & _ { } ~ \

These characters can be entered by adding a prefix backslash:

\# \$ \% \textasciicircum{} \& \_ \{ \} \~{} \textbackslash{}

The other symbols and many more can be rendered with special commands in mathematical formulae or as accents.

The backslash character \ can not be entered by adding another backslash in front of it (\\); this sequence is used for line breaking. For introducing a backslash in math mode, you can use \backslash instead.

The command \~ produces a tilde which is placed over the next letter. For example \~n gives ñ. To produce just the character ~, use \~{} which places a ~ over an empty box. Alternatively \sim produces a large centred ~ which may be more appropriate in some situations, but may not render properly in simple expressions which are converted to HTML.

Similarly, the command \^ produces a hat over the next character, for example \^{o} produces ô. If you need in text to display the ^ symbol you have to use \textasciicircum.

Spaces

"Whitespace" characters, such as blank or tab, are treated uniformly as "space" by LaTeX. Several consecutive whitespace characters are treated as one "space". See below for commands that produces spaces of different size.

LaTeX environments

Environments in LaTeX have a role that is quite similar to commands, but they usually have effect on a wider part of formula. Their syntax is:

 \begin{environmentname}
   text to be influenced
 \end{environmentname}

Environments supported by Wikipedia include matrix, align, etc. See below.

Rendering

By default, the PNG images are rendered black on white, with a transparent background. On darker backgrounds, the characters may show white edges. To remove these, match the PNG background color with the background color of the page using \pagecolor. However, black text on a dark background is hard to read and should be avoided altogether where possible.

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); a work-around is described in the "Alignment with normal text flow" section below. 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 whose alt text is "Square root of pi". This should not be confused with the title attribute that produces popup text when the hovering over the PNG image, for example <math title="pi">\pi</math> generates an image whose popup text is "pi".

Apart from function and operator names, as is customary in mathematics, variables and 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, \text{abc} gives .

Latex does not have full support for Unicode characters and not all characters render. Most Latin characters with accents render correctly. However some do not, in particular those that include multiple diacritics (e.g. with Latin letters used in Vietnamese) or that cannot be precomposed into a single character (such as the uppercase Latin letter W with ring), or that use other diacritics (like the ogonek or the double grave accent, used in Central European languages like Polish, or the horn attached above some vowels in Vietnamese), or other modified letter forms (used in IPA notations, or African languages, or in medieval texts), some digram ligatures (like IJ in Dutch), or Latin letters borrowed from Greek, or small capitals, as well as superscripts and subscript letters. For example \text{ð} or \mbox{ð}, and \text{þ} or \mbox{þ} (used in Icelandic) will give errors.

TeX vs HTML

{{#invoke:main|main}} Before using TeX markup for producing special characters, it should be noted that, as this comparison table shows, sometimes similar results can be achieved in HTML, with Template:Math or Template:Bigmath (also see: Help:Special characters).

TeX syntax TeX rendering HTML syntax HTML rendering
\alpha\,\! {{math|<VAR>&alpha;</VAR>}} α
f(x) = x^2\,\! {{math|''f''(<var>x</var>) {{=}} <var>x</var><sup>2</sup>}} f(x) = x2
\sqrt{2} {{math|{{radical|2}}}} Template:Radical
\sqrt{1-e^2} {{math|{{radical|1 &minus; ''e''<sup>2</sup>}}}} Template:Radical
\sqrt{1-z^3} {{bigmath|{{radical|1 &minus; ''z''<sup>3</sup>}}}} Template:Bigmath

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
&alpha; &beta; &gamma; &delta; &epsilon; &zeta;
&eta; &theta; &iota; &kappa; &lambda; &mu; &nu;
&xi; &omicron; &pi; &rho; &sigma; &sigmaf;
&tau; &upsilon; &phi; &chi; &psi; &omega;

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

&Gamma; &Delta; &Theta; &Lambda; &Xi; &Pi;
&Sigma; &Phi; &Psi; &Omega;

Γ Δ Θ Λ Ξ Π
Σ Φ Ψ Ω

&int; &sum; &prod; &radic; &minus; &plusmn; &infin;
&asymp; &prop; = &equiv; &ne; &le; &ge;
&times; &middot; &sdot; &divide; &part; &prime; &Prime;
&nabla; &permil; &deg; &there4; &empty;

∫ ∑ ∏ √ − ± ∞
≈ ∝ = ≡ ≠ ≤ ≥
× · ⋅ ÷ ∂ ′ ″
∇ ‰ ° ∴ ∅

&isin; &notin; &cap; &cup; &sub; &sup; &sube; &supe;
&not; &and; &or; &exist; &forall;
&rArr; &hArr; &rarr; &harr; &uarr; &darr;
&alefsym; - &ndash; &mdash;

∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇
¬ ∧ ∨ ∃ ∀
⇒ ⇔ → ↔ ↑ ↓
ℵ - – —

The project has settled on using 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 copied-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.
  7. Unlike generated bitmaps, HTML is not sensitive to dots per inch variances between viewing platforms.

Pros of TeX

  1. TeX is semantically more precise than HTML.
    1. In TeX, "x" means "mathematical variable ", 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 is available to logged in users as an preferences opt-in).
  2. One consequence of point 1 is that TeX code can be transformed into HTML, but not vice-versa.[1] This means that on the server side we can always transform a formula, based on its complexity and location within the text, user preferences, type of browser, etc. Therefore, where possible, all the benefits of HTML can be retained, together with the benefits of TeX. It is true that the current situation is not ideal, but that is not a good reason to drop information/contents. It is more a reason to help improve the situation.
  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 ‘  ’ and ‘  ’).
  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.[2]
  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), copying and pasting from a TeX PNG image in Wikipedia into simple text will return the LaTeX source.
^ unless your wikitext follows the style of point 1.2
^ 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 hereafter, for an example).

Using MathJax

The MathJax renderer, selectable through My Preferences - Appearance - Math, uses a very different system to the standard texvc renderer. Rather than rendering a static image on the server side a combination of JavaScript, HTML and CSS is used to locally construct the formula. This allows high-quality typesetting, and other problems such as font sizes not matching your browser settings or wrong baselines are fixed as well. MathJax may also reduce the download time of images but entails a small delay as the JavaScript interpreter runs to render the formulas. (After the small delay, the vertical dimension of the displayed page tends to update asynchronously—math content usually becomes taller—which can cause a disorienting jump in the document view position in some user agents; speedy mouse-wheelers might wish to check into this as part of their usability evaluation.)

Alternatively to the preferences option, MathJax can also be selected using the mathJax user script. It is the basis for the global option, and hence more experimental but also more up to date. Bug reports are taken care of at the script's talk page.

The quality of font rendering is dependent on your browser and operating system. Speed and appearance can be improved by installing the STIX fonts; for installation details see the MathJax font help page. Further information is also available at this page.

Formatting using TeX

Functions, symbols, special characters

Accents/diacritics

\dot{a}, \ddot{a}, \acute{a}, \grave{a}
\check{a}, \breve{a}, \tilde{a}, \bar{a}
\hat{a}, \widehat{a}, \vec{a}

Standard numerical functions

\exp_a b = a^b, \exp b = e^b, 10^m
\ln c, \lg d = \log e, \log_{10} f
\sin a, \cos b, \tan c, \cot d, \sec e, \csc f
\arcsin h, \arccos i, \arctan j
\sinh k, \cosh l, \tanh m, \coth n
\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n
\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q
\sgn r, \left\vert s \right\vert
\min(x,y), \max(x,y)

Bounds

\min x, \max y, \inf s, \sup t
\lim u, \liminf v, \limsup w
\dim p, \deg q, \det m, \ker\phi

Projections

\Pr j, \hom l, \lVert z \rVert, \arg z

Differentials and derivatives

dt, \operatorname{d}\!t, \partial t, \nabla\psi
dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y
\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y

Letter-like symbols or constants

\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar
\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS

Modular arithmetic

s_k \equiv 0 \pmod{m}
a\,\bmod\,b
\gcd(m, n), \operatorname{lcm}(m, n)
\mid, \nmid, \shortmid, \nshortmid

Radicals

\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2}

Operators

+, -, \pm, \mp, \dotplus
\times, \div, \divideontimes, /, \backslash
\cdot, * \ast, \star, \circ, \bullet
\boxplus, \boxminus, \boxtimes, \boxdot
\oplus, \ominus, \otimes, \oslash, \odot
\circleddash, \circledcirc, \circledast
\bigoplus, \bigotimes, \bigodot

Sets

\{ \}, \O \empty \emptyset, \varnothing
\in, \notin \not\in, \ni, \not\ni
\cap, \Cap, \sqcap, \bigcap
\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus
\setminus, \smallsetminus, \times
\subset, \Subset, \sqsubset
\supset, \Supset, \sqsupset
\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq
\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq
\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq
\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq

Relations

=, \ne, \neq, \equiv, \not\equiv
\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, :=
\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong
\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto
<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot
>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot
\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq
\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq
\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless
\leqslant, \nleqslant, \eqslantless
\geqslant, \ngeqslant, \eqslantgtr
\lesssim, \lnsim, \lessapprox, \lnapprox
\gtrsim, \gnsim, \gtrapprox, \gnapprox
\prec, \nprec, \preceq, \npreceq, \precneqq
\succ, \nsucc, \succeq, \nsucceq, \succneqq
\preccurlyeq, \curlyeqprec
\succcurlyeq, \curlyeqsucc
\precsim, \precnsim, \precapprox, \precnapprox
\succsim, \succnsim, \succapprox, \succnapprox

Geometric

\parallel, \nparallel, \shortparallel, \nshortparallel
\perp, \angle, \sphericalangle, \measuredangle, 45^\circ
\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar
\bigcirc, \triangle \bigtriangleup, \bigtriangledown
\vartriangle, \triangledown
\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright

Logic

\forall, \exists, \nexists
\therefore, \because, \And
\or \lor \vee, \curlyvee, \bigvee
\and \land \wedge, \curlywedge, \bigwedge
\bar{q}, \bar{abc}, \overline{q}, \overline{abc},

\lnot \neg, \not\operatorname{R}, \bot, \top


\vdash \dashv, \vDash, \Vdash, \models
\Vvdash \nvdash \nVdash \nvDash \nVDash
\ulcorner \urcorner \llcorner \lrcorner

Arrows

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

Special

\amalg \P \S \% \dagger \ddagger \ldots \cdots
\smile \frown \wr \triangleleft \triangleright
\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp

Unsorted (new stuff)

\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes
\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq
\intercal \barwedge \veebar \doublebarwedge \between \pitchfork
\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright
\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq

For a little more semantics on these symbols, see the brief TeX Cookbook.

Larger expressions

Subscripts, superscripts, integrals

Feature Syntax How it looks rendered
Superscript a^2
Subscript a_2
Grouping 10^{30} a^{2+2}
a_{i,j} b_{f'}
Combining sub & super without and with horizontal separation x_2^3
{x_2}^3
Super super 10^{10^{8}}
Preceding and/or additional sub & super \sideset{_1^2}{_3^4}\prod_a^b
{}_1^2\!\Omega_3^4
Stacking \overset{\alpha}{\omega}
\underset{\alpha}{\omega}
\overset{\alpha}{\underset{\gamma}{\omega}}
\stackrel{\alpha}{\omega}
Derivatives x', y'', f', f''
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}
Arc (workaround) \overset{\frown} {AB}
Arrows 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
Sum in a fraction (default \textstyle) \frac{\sum_{k=1}^N k^2}{a}
Sum in a fraction (force \displaystyle) \frac{\displaystyle \sum_{k=1}^N k^2}{a}
Sum in a fraction (alternative limits style) \frac{\sum\limits^{^N}_{k=1} k^2}{a}
Product \prod_{i=1}^N x_i
Product (force \textstyle) \textstyle \prod_{i=1}^N x_i
Coproduct \coprod_{i=1}^N x_i
Coproduct (force \textstyle) \textstyle \coprod_{i=1}^N x_i
Limit \lim_{n \to \infty}x_n
Limit (force \textstyle) \textstyle \lim_{n \to \infty}x_n
Integral \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx
Integral (alternative limits style) \int_{1}^{3}\frac{e^3/x}{x^2}\, dx
Integral (force \textstyle) \textstyle \int\limits_{-N}^{N} e^x\, dx
Integral (force \textstyle, alternative limits style) \textstyle \int_{-N}^{N} e^x\, dx
Double integral \iint\limits_D \, dx\,dy
Triple integral \iiint\limits_E \, dx\,dy\,dz
Quadruple integral \iiiint\limits_F \, dx\,dy\,dz\,dt
Line or path integral \int_{(x,y)\in C} x^3\, dx + 4y^2\, dy
Closed line or path integral \oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy
Intersections \bigcap_{i=_1}^n E_i
Unions \bigcup_{i=_1}^n E_i

Fractions, matrices, multilines

Feature Syntax How it looks rendered
Fractions \frac{2}{4}=0.5 or {2 \over 4}=0.5
Small fractions \tfrac{2}{4} = 0.5
Large (normal) fractions \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a
Large (nested) fractions \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
Cancellations in fractions
Note does not work with MathJax
\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}
Binomial coefficients \binom{n}{k}
Small binomial coefficients \tbinom{n}{k}
Large (normal) binomial coefficients \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)
Case distinctions
f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}
Multiline equations
\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}
Multiline equations (must define number of columns used ({lcr}) (should not be used unless needed)
\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}
Breaking up a long expression so that it wraps when necessary, at the expense of destroying correct spacing
f(x) =
\sum_{n=0}^\infty a_n x^n =
a_0+a_1x+a_2x^2+\cdots
Simultaneous equations
\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
Arrays
\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}

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 \quad
\left \Vert \frac{c}{d} \right \|
Floor and ceiling functions: \left \lfloor \frac{a}{b} \right \rfloor \quad
\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
do not want a delimiter to appear
\left . \frac{A}{B} \right \} \to X
Size of the delimiters (add "l" or "r" to indicate the side for proper spacing) ( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]
\{ \bigl\{ \Bigl\{ \biggl\{ \Biggl\{ \dots
\Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle
\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big| |
\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots
\Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \ceil
\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots
\Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow
\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots
\Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow
/ \big/ \Big/ \bigg/ \Bigg/ \dots
\Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash

Equation numbering

The templates {{NumBlk}} and {{EquationRef}} can be used to number equations. The template {{EquationNote}} can be used to refer to a numbered equation from surrounding text. For example, the following syntax:

{{NumBlk|:|<math>x^2 + y^2 + z^2 = 1 \,</math>|{{EquationRef|1}}}}

produces the following result (note the equation number in the right margin):

Template:NumBlk

Later on, the text can refer to this equation by its number using syntax like this:

As seen in equation ({{EquationNote|1}}), blah blah blah...

The result looks like this:

As seen in equation (Template:EquationNote), blah blah blah...

Note that the equation number produced by {{EquationNote}} is a link that the user can click to go immediately to the cited equation.

Alphabets and typefaces

{{#invoke:see also|seealso}} Texvc cannot render arbitrary Unicode characters. Those it can handle can be entered by the expressions below. For others, such as Cyrillic, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas.

Greek alphabet
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta
\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho
\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega
\alpha \beta \gamma \delta \epsilon \zeta \eta \theta
\iota \kappa \lambda \mu \nu \xi \pi \rho
\sigma \tau \upsilon \phi \chi \psi \omega
\varepsilon \digamma \varkappa \varpi
\varrho \varsigma \vartheta \varphi
Hebrew symbols
\aleph \beth \gimel \daleth
Blackboard bold/scripts
\mathbb{ABCDEFGHI}
\mathbb{JKLMNOPQR}
\mathbb{STUVWXYZ}
Boldface
\mathbf{ABCDEFGHI}
\mathbf{JKLMNOPQR}
\mathbf{STUVWXYZ}
\mathbf{abcdefghijklm}
\mathbf{nopqrstuvwxyz}
\mathbf{0123456789}
Boldface (Greek)
\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta}
\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho}
\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}
\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta}
\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho}
\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega}
\boldsymbol{\varepsilon\digamma\varkappa\varpi}
\boldsymbol{\varrho\varsigma\vartheta\varphi}
Italics (default for Latin alphabet)
\mathit{0123456789}
Greek italics (default for lowercase Greek)
\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta}
\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho}
\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}
Roman typeface
\mathrm{ABCDEFGHI}
\mathrm{JKLMNOPQR}
\mathrm{STUVWXYZ}
\mathrm{abcdefghijklm}
\mathrm{nopqrstuvwxyz}
\mathrm{0123456789}
Sans serif
\mathsf{ABCDEFGHI}
\mathsf{JKLMNOPQR}
\mathsf{STUVWXYZ}
\mathsf{abcdefghijklm}
\mathsf{nopqrstuvwxyz}
\mathsf{0123456789}
Sans serif Greek (capital only)
\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}
\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}
\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}
Calligraphy/script
\mathcal{ABCDEFGHI}
\mathcal{JKLMNOPQR}
\mathcal{STUVWXYZ}
Fraktur typeface
\mathfrak{ABCDEFGHI}
\mathfrak{JKLMNOPQR}
\mathfrak{STUVWXYZ}
\mathfrak{abcdefghijklm}
\mathfrak{nopqrstuvwxyz}
\mathfrak{0123456789}
Small scriptstyle text
{\scriptstyle\text{abcdefghijklm}}

Mixed text faces

Feature Syntax How it looks rendered
Italicised characters (spaces are ignored) x y z
Non-italicised characters \text{x y z}
Mixed italics (bad) \text{if} n \text{is even}
Mixed italics (good) \text{if }n\text{ is even}
Mixed italics (alternative: ~ or "\ " forces a space) \text{if}~n\ \text{is even}

Color

Equations can use color with the \color command. The default Texvc renderer and the MathJax renderers have different syntaxes to support both use {\color{Blue}{text}}. For example

There are several alternate notations styles

Some color names are predeclared according to the following table, you can use them directly for the rendering of formulas (or for declaring the intended color of the page background).

Colors supported