Beta Wikipedia

Help:MathTest

This page aims to cover a wide range of mathematical expressions and was generated from the documentation of the English Wikipedia [1]. Please refer to phab:T346795 for further information and to Help:MathTestNative for a version of this page that forces the new layout independent of the selected rendering mode.


Formatting using TeX edit

Functions, symbols, special characters edit

Accents/diacritics edit

\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 edit

\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 edit

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

Projections edit

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

Differentials and derivatives edit

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 edit

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

Modular arithmetic edit

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

Radicals edit

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

Operators edit

+, -, \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 edit

\{ \}, \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 edit

=, \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, \nleqq, \lneqq, \lvertneqq  
\ge \geq, \gneq, \geqq, \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 edit

\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 edit

\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 edit

\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 edit

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

Unsorted (new stuff) edit

\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 edit

Subscripts, superscripts, integrals edit

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 edit

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

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

Equation numbering edit

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):

 

 

 

 

 

(1)

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 (1), 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 edit

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}  

Mixed text faces edit

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 edit

Equations can use color:

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


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
       
       
       
       
       
       
       
       
       
       
       
       
       
       
       

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 Wikipedia:Manual of Style (accessibility)#Color.

Formatting issues edit

Spacing edit

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

Feature Syntax How it looks rendered
double quad space a \qquad b  
quad space a \quad b  
text space a\ b  
text space without PNG conversion a \mbox{ } b  
large space a\;b  
medium space a\&gt;b [not supported]
small space a\,b  
tiny space (use for multiplication of factors) ab  
no space (use for multi-letter variables) \mathit{ab}  
small negative space a\!b  

Automatic spacing may be broken in very long expressions (because they produce an overfull hbox in TeX):

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

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

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

Alignment with normal text flow edit

Due to the default CSS 

img.tex { vertical-align: middle; }

an inline expression like   should look good.

If you need to align it otherwise, use style="vertical-align:-100%;">... 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.

Centering edit

We introduce the new attribute display with the two options "inline" and "block".

Inline edit

If the the value of the display attribute is inline the render will render math in inline mode, i.e. there will be no new paragraph for the equation and the operators will be rendered consuming only little vertical space.

Example edit

The sum   converges to 2.

The next line-width is not disturbed by large operators.

The code for the math example reads:

<math display="inline">\sum_{i=0}^\infty 2^{-i}</math>
Technical implementation edit

Technically it will add the command \textstyle will be added to the user input before the tex command is passed to the renderer. The result will be displayed without further by outputting the image or MathMLelement to the page.

Remark edit

The convention https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style_(mathematics)#Using_HTML is really annoying. I'd prefer to use inline math for that, since it helps to differentiate between math and other elements.

Block edit

In block-style the equation is rendered in its own paragraph and the operator are rendered consuming less horizontal space.

Example edit

The equation

 
is used in a joke about mathematicians entering a bar and ordering beer.

It was entered as

<math display="block">\text{geometric series:}\quad \sum_{i=0}^\infty 2^{-i}=2 </math>
Technical implementation edit

Technically it will add the command \displaystyle will be added to the user input, if the user input does not contain the string \displaystyle or \align before the tex command is passed to the renderer. The result will be displayed in a new paragraph. Therefore the style of the MathImage is altered i.e. the style attribute "display:block;margin:auto" is added. For MathML it is ensured that display=inline is replaced by display block which produces a new paragraph

Discussion edit

Fréderic Wang would prefer that displaystyle is always added in depended of the fact if \displaystlye is already in the equation. He remarks that it has to be checked if that works if the equation starts with \begin.

Not specified edit

If nothing is specified the current behavior is preserved. That means all equation are rendered in display style but not using a new paragraph.

Example edit

The sum   converges to 2.

The next line-width is disturbed by large operators.

The code for the math example reads:

<math>\sum_{i=0}^\infty 2^{-i}</math>


The equation

 

is used in a joke about mathematicians entering a bar and ordering beer.

It was entered as

<math>\text{geometric series:}\quad \sum_{i=0}^\infty 2^{-i}=2 </math>

Commutative diagrams edit

To make a commutative diagram, there are three steps:

  1. write the diagram in TeX
  2. convert to SVG
  3. upload the file to Wikimedia Commons

Diagrams in TeX edit

Xy-pic (online manual) is the most powerful and general-purpose diagram package in TeX. Diagrams created using it can be found at Commons: Category:Xy-pic diagrams.

Simpler packages include:

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, dvips]{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{
%%% Diagram goes here %%%
}

$$}}} % end math, end frame
\end{document}

Convert to SVG edit

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

The pdfcrop and pdf2svg utilities are needed for this procedure. You can alternatively use pdf2svg from PDFTron for the last step.

If you do not have pdfTeX (which is unlikely) you can use the following commands to replace the first step (TeX → PDF): 

latex file.tex
dvipdfm file.dvi

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:

Upload the file edit

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

{{Information
|description =
{{en|1= Description [[:en:Link to WP page|topic]]
}}
|source = {{own}}, created as per:
 [[:en:Help:Displaying a formula#Commutative diagrams]];
 source code below.
|date = The Creation Date, like 1999-12-31
|author = [[User:YourUserName|Your Real Name]]
|permission = {{self|PD-self (or other license)
    |author = [[User:YourUserName|Your Real Name]]}}
}}



==TeX source==
<source lang=latex>
% TeX source here
</source>

[[Category:Commutative diagrams]]
[[Category:Xy-pic diagrams]]
[[Category:Images with LaTeX source code]]
Source code
  • Include the source code in the image page, in the Source section of the {{Information}} template, 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.
  • You may optionally make the source code section collapsible, using the {{cot}}/{{cob}} templates.
  • (Don't include it in the Summary section, which is just supposed to be a summary.)
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. (The 1= is necessary if you use nest templates within the description, and harmless otherwise.)
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 [[File:Diagram.svg]]

Examples edit

A sample conforming diagram is commons:Image:PSU-PU.svg.

Unimplemented elements and workarounds edit

\oiint and \oiiint edit

Elements which are not yet implemented are \oiint, a two-fold integral \iint ( ) with a circular curve through the centre of the two integrals, and similarly \oiiint, a circular curve through three integrals. In contrast, \oint ( ) exists for the single dimension (integration over a curved line within a plane or any space with higher dimension).

These elements appear in many contexts: \oiint denotes a surface integral over the closed 2d boundary of a 3d region (which occurs in much of 3d vector calculus and physical applications – like Maxwell's equations), likewise \oiiint denotes integration over the closed 3d boundary (surface volume) of a 4d region, and they would be strong candidates for the next TeX version. As such there are a lot of workarounds in the present version.

\oiint and \oiiint using currently implemented symbols
\oiint looks like:
  •  , which uses \iint along with \subset and \supset (overdrawn after backspacing):
\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset \mathbf D \cdot \mathrm{d}\mathbf A
  •  , which uses \int twice (with some backward kerning) along with \bigcirc (also overdrawn after backpacing) to produce a more consistent circle:
\int\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\cdot\mathrm{d}\mathbf A

\oiiint (should also be preferably more tightly kerned) looks more or less like:

  •   which uses three \int symbols (with more backward kerning) with \subset and \supset (overdrawn after backspacing):
\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\;\cdot\mathrm{d}\mathbf A
  •  , which uses three \int symbols (with more backward kerning) along with \bigcirc (also overdrawn after backspacing):
\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\;\cdot\mathrm{d}\mathbf A

However, since no standardisation exists as yet, any workaround like this (which uses many \! symbols for backspacing) should be avoided, if possible. See below for a possibility using PNG image enforcement.

Note that \iint (the double integral) and \iiint (the triple integral) are still not kerned as they should preferably be, and are currently rendered as if they were successive \int symbols ; this is not a major problem for reading the formulas, even if the integral symbols before the last one do not have bounds, so it's best to avoid backspacing "hacks" as they may be inconsistent with a possible future better implementation of integrals symbols (with more precisely computed kerning positions).

\oiint and \oiiint as PNG images edit

These symbols are available as PNG images which are also integrated into two templates, {{oiint}} and {{oiiint}}, which take care of the formatting around the symbols.

The templates have three parameters:

preintegral
the text or formula immediately before the integral
intsubscpt
the subscript below the integral
integrand
the text or formula immediately after the integral
Examples edit
  • Stokes' theorem: {{oiint | intsubscpt = <math>{\scriptstyle S}</math> | integrand=<math>( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} </math> }}
   
  • Ampère's law + correction: {{oiint | preintegral=<math>\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 </math> | intsubscpt = <math>{\scriptstyle S}</math> | integrand = <math>\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}</math> }}
    
  • Continuity of 4-momentum flux (in general relativity):[1] {{oiiint | preintegral=<math>\bold{P} = </math> | intsubscpt = <math>{\scriptstyle \partial \Omega}</math> | integrand = <math>\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0</math> }}
    

Oriented \oiint and \oiiint as PNG images edit

Some variants of \oiint and \oiiint have arrows on them to indicate the sense of integration, such as a line integral around a closed curve in the clockwise sense, and higher dimensional analogues. These are not implemented in TeX on Wikipedia either, although the template {{intorient}} is available - see link for details.

\overarc edit

\overarc is not yet implemented to display the arc notation. However, there exists a workaround: use \overset{\frown}{AB}, which gives  

Examples of implemented TeX formulas edit

Quadratic polynomial edit

  

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

Quadratic formula edit

  

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

Tall parentheses and fractions edit

  

<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>

Integrals edit

  

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

Matrices and determinants edit

  

<math>\det(\mathsf{A}-\lambda\mathsf{I}) = 0</math>

Summation edit

  

<math>\sum_{i=0}^{n-1} i</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 edit

  

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

Complex numbers edit

  

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

Limits edit

  

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

Integral equation edit

  

<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 edit

  

<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 edit

  

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

Prefixed subscript edit

  

 <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 edit

  

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

Area of a quadrilateral edit

  

<math>S=dD\,\sin\alpha\!</math>

Volume of a sphere-stand edit

  

<math>V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]</math>

Multiple equations edit

    

<math>\begin{align}
u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\
v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v)
\end{align}</math>

See also edit

Test cases from parserTests edit

  • pre-save transform: comment containing math
  • BUG 1887: A ‎<math> with a thumbnail- we don't render math in the parsertests by default, so math is not stripped and turns up as escaped <math> tags.
     
     
  • BUG 1887, part 2: A ‎<math> with a thumbnail- math enabled
     
     
  • Math section safety when disabled  
  • BUG 26380: Add \widetilde support to match \widehat
    •  
    •  
  • BUG 27324: Euro symbol for math
    •  
    •  
    •  
    •  
    •  
  • BUG 27754: Archaic Greek letters for math (may require texlive-lang-greek)
    •  
    •  
    •  
    •  
    •  
    •  
  • BUG 19547: Apostrophe / single quotes in math \text{...}
    •  
    •  
    •  
  • BUG 6722: Spacing fix for functions in math HTML output:
    •  
    •  
    •  
    •  
    •  
    •  
  • BUG 18912: Add \sen function for Spanish sin to math
    •  
    •  
    •  
    •  
    •  
    •  
  • BUG 18912: \operatorname{sen} x gets wrong spacing in math:  
  • BUG 31442: Multiple math accents without braces fails to parse:  
  • BUG 31442: Math accents with math font fail to parse if braces not used: 
  • BUG 31824: Empty math tag returns uniq:
  • BUG 31824: Empty math tag returns uniq:

Additional tests edit

   

External links edit

 
Wikibooks has a book on the topic of: LaTeX
  • A LaTeX tutorial
  • Doob, Michael, A Gentle Introduction to TeX: A Manual for Self-study (PDF). A paper introducing TeX — see page 39 onwards for a good introduction to the maths side of things.
  • Oetiker, Tobias; Partl, Hubert; Hyna, Irene; Schlegl, Elisabeth (December 13, 2009), The Not So Short Introduction to LaTeX 2ε (PDF) (4.27 ed.){{citation}}: CS1 maint: date and year (link). 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.
  1. ^ J. A. Wheeler, C. Misner, K. S. Thorne (1973). Gravitation (2nd ed.). W. H. Freeman & Co. ISBN 0-7167-0344-0.{{cite book}}: CS1 maint: multiple names: authors list (link)
Retrieved from "https://en.wikipedia.beta.wmflabs.org/w/index.php?title=Help:MathTest&oldid=602834"