Help:Displaying a formula

From Eugene Neighbors

{{#if:|Other languages:}} Template:H-langs:

{{#if:|Other languages:}} Template:H-langs: {{#if: Help||}}}} MediaWiki uses a subset of TeX markup, including some extensions from LaTeX and AMSLaTeX, for mathematical formulae. It generates either PNG images or simple HTML markup, depending on user preferences and the complexity of the expression. In the future, as more browsers are smarter, it will be able to generate enhanced HTML or even MathML in many cases. (See blahtex for information about current work on adding MathML support.)

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

To have math rendered, you have to set $wgUseTeX = true; in LocalSettings.php.

[edit] Syntax

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

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

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

[edit] Rendering

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

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

Apart from function and operator names, as is customary in mathematics for variables, letters are in italics; digits are not. For other text, (like variable labels) to avoid being rendered in italics like variables, use \mbox or \mathrm. For example, <math>\mbox{abc}</math> gives <math>\mbox{abc}</math>.

[edit] TeX vs HTML

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

The codes on the left produce the symbols on the right, but the latter can also be put directly in the wikitext.

α β γ δ ε ζ
η θ ι κ λ μ ν
ξ ο π ρ  σ ς
τ υ φ χ ψ ω
Γ Δ Θ Λ Ξ Π
Σ Φ Ψ Ω

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

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

[edit] Pros of HTML

1. In-line HTML formulae always align properly with the rest of the HTML text.
2. The formula's background, font size and face match the rest of HTML contents and the appearance respects CSS and browser settings.
3. Pages using HTML will load faster.

[edit] Pros of TeX

1. TeX is semantically superior to HTML. In TeX, "<math>x</math>" means "mathematical variable <math>x</math>", whereas in HTML "x" could mean anything. Information has been irrevocably lost.
2. TeX has been specifically designed for typesetting formulae, so input is easier and more natural, and output is more aesthetically pleasing.
3. One consequence of point 1 is that TeX can be transformed into HTML, but not vice-versa. This means that on the server side we can always transform a formula, based on its complexity and location within the text, user preferences, type of browser, etc. Therefore, where possible, all the benefits of HTML can be retained, together with the benefits of TeX. It's true that the current situation is not ideal, but that's not a good reason to drop information/contents. It's more a reason to help improve the situation.
4. Another consequence of point 1 is that TeX can be converted to MathML for browsers which support it, thus keeping its semantics and allowing it to be renderred vectorally.
5. When writing in TeX, editors need not worry about whether this or that version of this or that browser supports this or that HTML entity. The burden of these decisions is put on the server. This doesn't hold for HTML formulae, which can easily end up being rendered wrongly or differently from the editor's intentions on a different browser.
6. 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.

[edit] Functions, symbols, special characters

[edit] Subscripts, superscripts, integrals

[edit] Fractions, matrices, multilines

\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)

 a&b\\ c&d

f(n) = 
\begin{cases} 
  n/2,  & \mbox{if }n\mbox{ is even} \\
  3n+1, & \mbox{if }n\mbox{ is odd} 
\end{cases}

 n/2,  & \mbox{if }n\mbox{ is even} \\ 
 3n+1, & \mbox{if }n\mbox{ is odd} 

\begin{align}
 f(x) & = (a+b)^2 \\
      & = a^2+2ab+b^2 \\
\end{align}

f(x) & = (a+b)^2 \\
     & = a^2+2ab+b^2 \\

\begin{alignat}{2}
 f(x) & = (a-b)^2 \\
      & = a^2-2ab+b^2 \\
\end{alignat}

f(x) & = (a-b)^2 \\
     & = a^2-2ab+b^2 \\

\begin{array}{lcl}
  z        & = & a \\
  f(x,y,z) & = & x + y + z  
\end{array}

 z        & = & a \\
 f(x,y,z) & = & x + y + z  

\begin{array}{lcr}
  z        & = & a \\
  f(x,y,z) & = & x + y + z     
\end{array}

 z        & = & a \\
 f(x,y,z) & = & x + y + z     

<math>f(x) \,\!</math>
<math>= \sum_{n=0}^\infty a_n x^n </math>
<math>= a_0+a_1x+a_2x^2+\cdots</math>

\begin{cases}
    3x + 5y +  z \\
    7x - 2y + 4z \\
   -6x + 3y + 2z 
\end{cases}

\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}

[edit] Alphabets and typefaces

[edit] Parenthesizing big expressions, brackets, bars

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

[edit] Spacing

Note that TeX handles most spacing automatically, but you may sometimes want manual control.

[edit] Align 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 <font style="vertical-align:-100%;"><math>...</math></font> and play with the vertical-align argument until you get it right; however, how it looks may depend on the browser and the browser settings.

Also note that if you rely on this workaround, if/when the rendering on the server gets fixed in future releases, as a result of this extra manual offset your formulae will suddenly be aligned incorrectly. So use it sparingly, if at all.

[edit] Forced PNG rendering

To force the formula to render as PNG, add \, (small space) at the end of the formula (where it is not rendered). This will force PNG if the user is in "HTML if simple" mode, but not for "HTML if possible" mode (math rendering settings in preferences).

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

This could be useful to keep the rendering of formulae in a proof consistent, for example, or to fix formulae that render incorrectly in HTML (at one time, a^{2+2} rendered with an extra underscore), or to demonstrate how something is rendered when it would normally show up as HTML (as in the examples above).

For instance:

This has been tested with most of the formulae on this page, and seems to work perfectly.

You might want to include a comment in the HTML so people don't "correct" the formula by removing it:

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

[edit] Color

Equations can use color:

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

  <math>{\color{Blue}x^2}+{\color{Brown}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>

See here for all named colours 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.

[edit] Examples

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<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>

 <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>

[edit] 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.

[edit] See also

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

[edit] External links

• A LaTeX tutorial. http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/
• A PDF document introducing TeX -- see page 39 onwards for a good introduction to the maths side of things: http://www.ctan.org/tex-archive/info/gentle/gentle.pdf
• A PDF document introducing LaTeX -- skip to page 59 for the math section. See page 72 for a complete reference list of symbols included in LaTeX and AMS-LaTeX. http://www.ctan.org/tex-archive/info/lshort/english/lshort.pdf
• TeX reference card: http://www.csit.fsu.edu/docs/tex/tex-refcard-letter.pdf
• http://www.ams.org/tex/amslatex.html
• A set of public domain fixed-size math symbol bitmaps: http://us.metamath.org/symbols/symbols.html
• MathML - A product of the W3C Math working group, is a low-level specification for describing mathematics as a basis for machine to machine communication. http://www.w3.org/Math/

be:Вікіпэдыя:TeX de:Hilfe:TeX en:Meta:Help:Formula es:Wikipedia:Usando TeX fr:Wikipédia:Formules TeX ia:Wikipedia:Formulas mathematic it:Wikipedia:Formule matematiche TeX ja:m:ヘルプ:数式の書き方 nl:Wikipedia:TeX in Wikipedia ru:Википедия:Формулы sv:Wikipedia:Användarhandledning för TeX uk:Довідка:Математичні формули та спецсимволи zh:Wikipedia:数学公式

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[edit] Links to other help pages

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[edit] Links to other help pages

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Meta | Wikinews | Wikipedia | Wikiquote | Wiktionary | commons: | mw: | b: | s:

Versions of this help page (for other languages see below)

Meta | Wikinews | {{#if:|{{#if:Wikipedia|Wikipedia|w:Help:Displaying_a_formula#}}|{{#if:Wikipedia|Wikipedia|w:Help:Displaying_a_formula}}}}http://en.wikipedia.org{{#if:|/wiki/Help:Displaying_a_formula#|/wiki/Help:Displaying_a_formula}} | Wikiquote | Wiktionary

Links to this page from Meta (int) Meta (ext) Wikipedia MediaWiki

Reading

Go | Search | Stop words | URL | Namespace | Page name | Section

Backlinks | Link | Piped link | Interwiki link | Redirect | Category | Image page

Logging in and preferences

Logging in | Preferences | User style

Editing

Advanced editing | Editing FAQ | Editing toolbar | Export | Import

Editing tips and tricks | Editing shortcuts

Tracking changes

Recent changes (enhanced) | Related changes | Watching pages | Diff

Page history | Edit summary | User contributions | Minor edit | Patrolled edit

Style & formatting

Wikitext examples | Wikitext reference | Reference card

HTML in wikitext | HTML elements

List | Table | Sorting

Special input and output

Inputbox | Special characters | Displaying a formula | Images and other uploaded files | EasyTimeline

Advanced functioning

Template | Advanced templates | Parser function | ParserFunctions | Parameter default | Variable | Magic word | System message | Substitution

Array | Calculation

Page management

Starting a new page | Renaming (moving) a page | Maintenance | Merging and moving pages | Protecting pages

Resolving disputes | Deleting a page

Special pages

Talk page | Testing | Sandbox

Lists of resources

Lists of Categories | Copyrights | Infobox

Redirect | Reference Desk | Shortcuts | Stub types

Other languages: Template:H-langs:Formula }}