Extension:Math/Syntax/de

Category:Outdated pages/de

Die Math Erweiterung verwendet eine Teilmenge der TeX Auszeichnungssprache, einschließlich einiger Erweiterungen von LaTeX und AMS-LaTeX, um mathematische Formeln anzuzeigen. Sie generiert entweder SVG, MathML oder verwendet MathJax zur Darstellung von mathematischen Inhalten auf der Client-Seite, abhängig von Benutzerpräferenzen und der Komplexität des Ausdrucks.

MathML und MathJax sollen in Zukunft vermehrt verwendet werden, während die SVG-Bilder veraltet sein werden.

Genauer gesagt filtert MediaWiki das Markup durch Texvc, das wiederum die Befehle an TeX für das eigentliche rendering weitergibt. Daher wird nur ein begrenzter Teil der vollständigen TeX-Sprache unterstützt; siehe unten für Details.

Allgemeine Syntax

Traditionell werden mathematische Ausdrücke innerhalb des XML-style tag math: <math>...</math> geschrieben.

As with all XML-style tags, one can use the 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 {{!}}.

In TeX werden, wie in HTML, zusätzliche Leerzeichen und Zeilenumbrüche ignoriert.

Rendering

Der Alternativtext der Bilder, der sehbehinderten und anderen Lesern angezeigt wird, die die Bilder nicht sehen können, und der auch verwendet wird, wenn der Text ausgewählt und kopiert wird, entspricht dem TeX-Code, der das Bild erzeugt hat.

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 one of the following: \text, \mbox, \mathrm. For example, <math>\text{abc}</math>abc. Es können auch neue Funktionsnamen mit \operatorname{...} erstellt werden.

Sonderzeichen

Die folgenden Symbole sind reservierte Zeichen, die entweder eine besondere Bedeutung in LaTeX haben oder nicht in allen Schriftarten verfügbar sind.

# $ % ^ & _ { } ~ \

Einige davon können mit einem vorangestellten Backslash eingegeben werden:

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

Andere haben besondere Namen:

<math> \hat{} \quad \tilde{} \quad \backslash </math>^~

TeX und 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 about special characters).

TeX Syntax (forcing PNG) TeX Rendering HTML-Syntax HTML Rendering
<math>\alpha</math> α {{math|<var>&alpha;</var>}} α
<math> f(x) = x^2\,</math> f(x)=x2 {{math|''f''(<var>x</var>) {{=}} <var>x</var><sup>2</sup>}} f(x) = x2
<math>\sqrt{2}</math> 2 {{math|{{radical|2}}}} 2
<math>\sqrt{1-e^2}</math> 1e2 {{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
&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;
&Gamma; &Delta; &Theta; &Lambda; &Xi; &Pi;
&Sigma; &Phi; &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
Γ Δ Θ Λ Ξ Π
Σ Φ Ψ Ω
&int; &sum; &prod; &radic; &minus; &plusmn; &infty;
&asymp; &prop; {{=}} &equiv; &ne; &le; &ge; 
&times; &sdot; &divide; &part; &prime; &Prime;
&nabla; &permil; &deg; &there4; &Oslash; &oslash;
&isin; &notin; 
&cap; &cup; &sub; &sup; &sube; &supe;
&not; &and; &or; &exist; &forall; 
&rArr; &hArr; &rarr; &harr; &uarr; 
&alefsym; - &ndash; &mdash; 
∫ ∑ ∏ √ − ± ∞
≈ ∝ = ≡ ≠ ≤ ≥
× ⋅ ÷ ∂ ′ ″
∇ ‰ ° ∴ Ø ø
∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇
¬ ∧ ∨ ∃ ∀
⇒ ⇔ → ↔ ↑
ℵ - – —

Sowohl HTML als auch TeX haben in bestimmten Situationen Vorteile.

Vorteile von HTML

  1. Formeln in HTML verhalten sich eher wie normaler Text.
  1. The formulas 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.
  1. Formulae typeset with HTML code will be accessible to client-side script links (a.k.a. scriptlets).
  1. 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.
  1. 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.
  1. Formulae using HTML code will render as sharp as possible no matter what device is used to render them.

Vorteile von TeX

  1. TeX is semantically more precise than HTML.
    1. In TeX, "<math>x</math>" means "mathematical variable x", whereas in HTML "x" is generic and somewhat ambiguous.
    1. 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.
  1. One consequence of point 1 is that TeX code can be transformed into HTML, but not vice-versa (unless your wikitext follows the style of point 1.2).

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.

  1. 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 readers graphic device.
  1. TeX is the preferred text formatting language of most professional mathematicians, scientists, and engineers writing in English. It is easier to persuade them to contribute if they can write in TeX.
  1. 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.
  1. 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 ).
  2. 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 editors intentions on a different browser.
  1. 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.
  1. 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.

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).

Funktionen, Symbole, Sonderzeichen

Accents/diacritics

\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a} a´a`a^a~a˘
\check{a} \bar{a} \ddot{a} \dot{a} aˇa¯a¨a˙

Standard functions

\sin a \cos b \tan c sinacosbtanc
\sec d \csc e \cot f secdcscecotf
\arcsin h \arccos i \arctan j arcsinharccosiarctanj
\sinh k \cosh l \tanh m \coth n sinhkcoshltanhmcothn
\operatorname{sh}o\,\operatorname{ch}p\,\operatorname{th}q shochpthq
\operatorname{arsinh}r\,\operatorname{arcosh}s\,\operatorname{artanh}t arsinhrarcoshsartanht
\lim u \limsup v \liminf w \min x \max y limulim supvlim infwminxmaxy
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g infzsupaexpblnclgdlogelog10fkerg
\deg h \gcd i \Pr j \det k \hom l \arg m \dim n deghgcdiPrjdetkhomlargmdimn

Moduloarithmetik

s_k \equiv 0 \pmod{m} sk0(modm)
a\,\bmod\,b amodb

Ableitungen

\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2} xdxx˙y¨dy/dxdydx2yx1x2

Mengen

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

Operatoren

+ \oplus \bigoplus \pm \mp - +±
\times \otimes \bigotimes \cdot \circ \bullet \bigodot ×
\star * / \div \frac{1}{2} */÷12

Logik

\land (or \and) \wedge \bigwedge \bar{q} \to p q¯p
\lor \vee \bigvee \lnot \neg q \And ¬¬q&

Root

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

Relationen

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

Geometric

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

Pfeile

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

Special

\And \eth \S \P \% \dagger \ddagger \ldots \cdots \colon &ð§%:
\smile \frown \wr \triangleleft \triangleright \infty \bot \top
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar ı
\ell \mho \Finv \Re \Im \wp \complement
\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp

Unsorted (new stuff)

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

Größere Ausdrücke

Subscripts, superscripts, integrals

FeatureSyntaxHow it looks rendered
Hochgestellta^2a2
Tiefgestellta_2a2
Groupinga^{2+2}a2+2
a_{i,j}ai,j
Combining sub & super without and with horizontal separationx_2^3x23
{x_2}^3x23
Super super10^{10^{8}}10108
Preceding and/or Additional sub & super _nP_knPk
\sideset{_1^2}{_3^4}\prod_a^b3412ab
{}_1^2\!\Omega_3^412Ω34
Stacking \overset{\alpha}{\omega}ωα
\underset{\alpha}{\omega}ωα
\overset{\alpha}{\underset{\gamma}{\omega}}ωγα
\stackrel{\alpha}{\omega}ωα
Ableitungenx', y'', f', f''x,y,f,f
x^\prime, y^{\prime\prime}x,y
Derivative dots\dot{x}, \ddot{x}x˙,x¨
Underlines, overlines, vectors\hat a \ \bar b \ \vec ca^ b¯ c
\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}ab cd def^
\overline{g h i} \ \underline{j k l}ghi jkl_
\not 1 \ \cancel{123}1 123
Pfeile A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} CAn+μ1BTn±i1C
Overbraces\overbrace{ 1+2+\cdots+100 }^{\text{sum}\,=\,5050}1+2++100sum=5050
Underbraces\underbrace{ a+b+\cdots+z }_{26\text{ terms}}a+b++z26 terms
Summe\sum_{k=1}^N k^2k=1Nk2
Sum (force \textstyle)\textstyle \sum_{k=1}^N k^2 k=1Nk2
Produkt\prod_{i=1}^N x_ii=1Nxi
Produkt (force \textstyle)\textstyle \prod_{i=1}^N x_ii=1Nxi
Koprodukt\coprod_{i=1}^N x_ii=1Nxi
Koprodukt (force \textstyle)\textstyle \coprod_{i=1}^N x_ii=1Nxi
Grenzwert\lim_{n \to \infty}x_nlimnxn
Grenzwert (force \textstyle)\textstyle \lim_{n \to \infty}x_nlimnxn
Integral\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx13e3/xx2dx
Integral (alternate limits style)\int_{1}^{3}\frac{e^3/x}{x^2}\, dx13e3/xx2dx
Integral (force \textstyle)\textstyle \int\limits_{-N}^{N} e^x\, dxNNexdx
Integral (force \textstyle, alternate limits style)\textstyle \int_{-N}^{N} e^x\, dxNNexdx
Doppelintegral\iint\limits_D \, dx\,dyDdxdy
Dreifachintegral\iiint\limits_E \, dx\,dy\,dzEdxdydz
Vierfachintegral\iiiint\limits_F \, dx\,dy\,dz\,dtFdxdydzdt
Linien- oder Wegintegral\int_C x^3\, dx + 4y^2\, dyCx3dx+4y2dy
Closed line or path integral\oint_C x^3\, dx + 4y^2\, dyCx3dx+4y2dy
Durchschnitte\bigcap_1^n p1np
Vereinigungen\bigcup_1^k p1kp

Fractions, matrices, multilines

Feature Syntax How it looks rendered
Brüche \frac{1}{2}=0.5 12=0.5
Small ("text style") fractions \tfrac{1}{2} = 0.5 12=0.5
Large ("display style") fractions \dfrac{k}{k-1} = 0.5 kk1=0.5
Mixture of large and small fractions \dfrac{ \tfrac{1}{2}[1-(\tfrac{1}{2})^n] }{ 1-\tfrac{1}{2} } = s_n 12[1(12)n]112=sn
Kettenbrüche (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
2c+2d+12=a2c+2d+12=a
Binomialkoeffizienten \binom{n}{k} (nk)
Small ("text style") binomial coefficients \tbinom{n}{k} (nk)
Large ("display style") binomial coefficients \dbinom{n}{k} (nk)
Matrizen
\begin{matrix}
x & y \\
z & v 
\end{matrix}
xyzv
\begin{vmatrix}
x & y \\
z & v 
\end{vmatrix}
|xyzv|
\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}
xyzv
\begin{bmatrix}
0      & \cdots & 0      \\
\vdots & \ddots & \vdots \\ 
0      & \cdots & 0
\end{bmatrix}
[0000]
\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}
{xyzv}
\begin{pmatrix}
x & y \\
z & v 
\end{pmatrix}
(xyzv)
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
(abcd)
Arrays
\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0
\end{array}
abS001011101110
Fälle
f(n) = 
\begin{cases} 
n/2,  & \mbox{if }n\mbox{ is even} \\
3n+1, & \mbox{if }n\mbox{ is odd} 
\end{cases}
f(n)={n/2,if n is even3n+1,if n is odd
Gleichungssystem
\begin{cases}
3x + 5y +  z &= 1 \\
7x - 2y + 4z &= 2 \\
-6x + 3y + 2z &= 3
\end{cases}
{3x+5y+z=17x2y+4z=26x+3y+2z=3
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>
f(x)=n=0anxn =a0+a1x+a2x2+
Multiline equations
\begin{align}
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2
\end{align}
f(x)=(a+b)2=a2+2ab+b2
\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2
\end{alignat}
f(x)=(ab)2=a22ab+b2
Multiline equations with aligment specified (left, center, right)
\begin{array}{lcl}
z        & = & a \\
f(x,y,z) & = & x + y + z  
\end{array}
z=af(x,y,z)=x+y+z
\begin{array}{lcr}
z        & = & a \\
f(x,y,z) & = & x + y + z     
\end{array}
z=af(x,y,z)=x+y+z

Parenthesizing big expressions, brackets, bars

FeatureSyntaxHow it looks rendered
Schlecht ( \frac{1}{2} ) (12)
Gut \left ( \frac{1}{2} \right ) (12)

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

Feature Syntax How it looks rendered
Runde Klammern \left ( \frac{a}{b} \right ) (ab)
Eckige Klammern \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack [ab][ab]
Geschweifte Klammern (note the backslash before the braces in the code) \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace {ab}{ab}
Angle brackets \left \langle \frac{a}{b} \right \rangle ab
Bars and double bars (note: "bars" provide the absolute value function) \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \| |ab|cd
Floor and ceiling functions: \left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil abcd
Slashes and backslashes \left / \frac{a}{b} \right \backslash /ab\
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 ababab
Delimiters can be mixed, as long as \left and \right are both used \left [ 0,1 \right )
\left \langle \psi \right |
[0,1)
ψ|
Use \left. or \right. if you don't want a delimiter to appear: \left . \frac{A}{B} \right \} \to X AB}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 ////\\\\

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.

Griechisches Alphabet
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta ABΓΔEZ
\Eta \Theta \Iota \Kappa \Lambda \Mu HΘIKΛM
\Nu \Xi \Omicron \Pi \Rho \Sigma \Tau NΞOΠPΣT
\Upsilon \Phi \Chi \Psi \Omega ΥΦXΨΩ
\alpha \beta \gamma \delta \epsilon \zeta αβγδϵζ
\eta \theta \iota \kappa \lambda \mu ηθικλμ
\nu \xi \omicron \pi \rho \sigma \tau νξoπρστ
\upsilon \phi \chi \psi \omega υϕχψω
\varepsilon \digamma \vartheta \varkappa εϝϑϰ
\varpi \varrho \varsigma \varphi ϖϱςφ
Blackboard Bold/Scripts
\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G} 𝔸𝔹𝔻𝔼𝔽𝔾
\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} 𝕀𝕁𝕂𝕃𝕄
\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} 𝕆𝕊𝕋
\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z} 𝕌𝕍𝕎𝕏𝕐
\C \N \Q \R \Z
boldface (vectors)
\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G} 𝐀𝐁𝐂𝐃𝐄𝐅𝐆
\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M} 𝐇𝐈𝐉𝐊𝐋𝐌
\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T} 𝐍𝐎𝐏𝐐𝐑𝐒𝐓
\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z} 𝐔𝐕𝐖𝐗𝐘𝐙
\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g} 𝐚𝐛𝐜𝐝𝐞𝐟𝐠
\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m} 𝐡𝐢𝐣𝐤𝐥𝐦
\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t} 𝐧𝐨𝐩𝐪𝐫𝐬𝐭
\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z} 𝐮𝐯𝐰𝐱𝐲𝐳
\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4} 𝟎𝟏𝟐𝟑𝟒
\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9} 𝟓𝟔𝟕𝟖𝟗
Boldface (greek)
\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta} ABΓΔEZ
\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu} HΘIKΛM
\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Omicron} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau} NΞOΠPΣT
\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega} ΥΦXΨΩ
\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta} αβγδϵζ
\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu} ηθικλμ
\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\omicron} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau} νξoπρστ
\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega} υϕχψω
\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa} εϝϑϰ
\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi} ϖϱςφ
Kursiv
\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G} ABCDEFG
\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M} HIJKLM
\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T} NOPQRST
\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z} UVWXYZ
\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g} abcdefg
\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m} hijklm
\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t} nopqrst
\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z} uvwxyz
\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4} 01234
\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9} 56789
Roman typeface
\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G} ABCDEFG
\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M} HIJKLM
\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T} NOPQRST
\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z} UVWXYZ
\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g} abcdefg
\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m} hijklm
\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t} nopqrst
\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z} uvwxyz
\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4} 01234
\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9} 56789
Fraktur typeface
\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G} 𝔄𝔅𝔇𝔈𝔉𝔊
\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M} 𝔍𝔎𝔏𝔐
\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T} 𝔑𝔒𝔓𝔔𝔖𝔗
\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z} 𝔘𝔙𝔚𝔛𝔜
\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g} 𝔞𝔟𝔠𝔡𝔢𝔣𝔤
\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m} 𝔥𝔦𝔧𝔨𝔩𝔪
\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t} 𝔫𝔬𝔭𝔮𝔯𝔰𝔱
\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z} 𝔲𝔳𝔴𝔵𝔶𝔷
\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4} 01234
\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9} 56789
Calligraphy/Script
\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G} 𝒜𝒞𝒟𝒢
\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} 𝒥𝒦
\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} 𝒩𝒪𝒫𝒬𝒮𝒯
\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z} 𝒰𝒱𝒲𝒳𝒴𝒵
Hebräisch
\aleph \beth \gimel \daleth
Feature Syntax How it looks rendered
non-italicised characters \mbox{abc} abc
mixed italics (bad) \mbox{if} n \mbox{is even} ifnis even
mixed italics (good) \mbox{if }n\mbox{ is even} if n is even
mixed italics (more legible: ~ is a non-breaking space, while "\ " forces a space) \mbox{if}~n\ \mbox{is even} ifn is even

Farbe

Gleichungen können Farben benutzen:

  • {\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}
    x2+2x1
  • x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}
    x1,2=b±b24ac2a

See here for all named colors (archived) 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.

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

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

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

Empty horizontal or vertical spacing

The phantom commands create empty horizontal and/or vertical space the same height and/or width of the argument.

Feature Syntax How it looks rendered
Empty horizontal and vertical spacing \Gamma^{\phantom{i}j}_{i\phantom{j}k} Γijkij
Empty vertical spacing -e\sqrt{\vphantom{p'}p},\; -e'\sqrt{p'},\; \ldots epp,ep,
Empty horizontal spacing \int u^2\,du=\underline{\hphantom{(2/3)u^3+C}} u2du=(2/3)u3+C_

Alignment with normal text flow

Due to the default CSS

img.tex { vertical-align: middle; }

an inline expression like NNexdx 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.

Chemie

There are two ways to render chemical sum formulae as used in chemical equations:

  • <math chem>
  • <chem>

<chem>X</chem> is short for <math chem>\ce{X}</math>.

(where X is a chemical sum formula)

Technically, <math chem> is a math tag with the extension mhchem enabled, according to the mathjax documentation.

Note, that the commands \cee and \cf are disabled, because they are marked as deprecated in the mhchem LaTeX package documentation.

If the formula reaches a certain "complexity", spaces might be ignored (<chem>A + B</chem> might be rendered as if it were <chem>A+B</chem> with a positive charge).

In that case, write <chem>A{} + B</chem> (and not <chem>{A} + {B}</chem> as was previously suggested).

This will allow auto-cleaning of formulae once the bug will be fixed and/or a newer mhchem version will be used.

Siehe Beispiele unten.

Beispiele

Chemie

Formula Rendered as
<chem>C6H5-CHO</chem> CA6HA5CHO
<chem>\mathit{A} ->[\ce{+H2O}] \mathit{B}</chem> A+HA2OB
<math chem>A \ce{->[\ce{+H2O}]} B</math> A+HA2OB
<chem>SO4^2- + Ba^2+ -> BaSO4 v</chem> SOA4A2+BaA2+BaSOA4
<chem>H2NCO2- + H2O <=> NH4+ + CO3^2-</chem> HA2NCOA2A+HA2ONHA4A++COA3A2
<chem>H2O</chem> HA2O
<chem>Sb2O3</chem> SbA2OA3
<chem>H+</chem> HA+
<chem>CrO4^2-</chem> CrOA4A2
<chem>AgCl2-</chem> AgClA2A
<chem>[AgCl2]-</chem> [AgClA2]A
<chem>Y^{99}+</chem> YA99+
<chem>Y^{99+}</chem> YA99+
<chem>H2_{(aq)}</chem> HA2A(aq)
<chem>NO3-</chem> NOA3A
<chem>(NH4)2S</chem> (NHA4)A2S

Maths using <math>

Quadratic Polynomial

Rendered Formula
ax2+bx+c=0 <math>ax^2 + bx + c = 0</math>

Quadratic Polynomial (Force PNG Rendering)

Rendered Formula
ax2+bx+c=0 <math>ax^2 + bx + c = 0\,</math>

Quadratic Formula

Rendered Formula
x=b±b24ac2a <math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

Hohe Klammern und Brüche

Rendered Formula
2=((3x)×23x) <math>2 = \left(\frac{\left(3-x\right) \times 2}{3-x}\right)</math>

Recurrence

Rendered Formula
Snew=Sold(5T)22 <math>S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}</math>

Integrale

Rendered Formula
axasf(y)dyds=axf(y)(xy)dy <math>\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy</math>

Summation

Rendered Formula
m=1n=1m2n3m(m3n+n3m) <math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}</math>

Differentialgleichung

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

Komplexe Zahlen

Rendered Formula
|z¯|=|z|,|(z¯)n|=|z|n,arg(zn)=narg(z) <math>|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)</math>

Grenzwerte

Rendered Formula
limzz0f(z)=f(z0) <math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math>

Integralgleichung

Rendered Formula
ϕn(κ)=14π2κ20sin(κR)κRR[R2Dn(R)R]dR <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>

Numeric value with parameter

Rendered Formula
ϕn(κ)=0.033Cn2κ11/3,1L0κ1l0 <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

Rendered Formula
f(x)={11x<012x=01x2otherwise <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

Rendered Formula
pFq(a1,,ap;c1,,cq;z)=n=0(a1)n(ap)n(c1)n(cq)nznn! <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

Rendered Formula
ab ab <math> \frac {a}{b}\ \tfrac {a}{b} </math>

Bug reports

Bug reports and feature requests should be reported on Phabricator with the tag Math.

Siehe auch

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