Yardım:Matematiksel formüller

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MediaWiki yazılımı matematiksel ifadelerin biçimlendirilmesinde LaTeX ve AMSLaTeX yazılımlarını içeren TeX yazılımını kullanmaktadır. Bazı matematiksel formüller kişisel tercihlere bağlı olarak PNG, bazıları ise HTML olarak gözükebilir. Şablon:Türkçe değil


Kodlama

Matematiksel kodlar <math> ... </math> kodları arasına yazılır. Math markup goes inside <math> ... </math>. The edit toolbar has a button for this.


Tex kodları doğru yazılmadıkları zaman hata uyarısı verirler. Bu nedenle kodları doğru yazdığınızdan emin olmalısınız.


Sunum

It should be pointed out that most of these shortcomings have been addressed by Maynard Handley, but have not been released 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 abc.

TeX ve HTML

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

TeX kodlaması TeX çıktısı HTML kodlaması HTML çıktısı
<math>\alpha\,</math> α &alpha; α
<math>\sqrt{2}</math> 2 &radic;2 √2
<math>\sqrt{1-e^2}</math> 1−e2 &radic;<span style="text-decoration: overline;">1&minus;''e''&sup2;</div> √1−e²


as follows.

HTML'nin avantajları

  1. HTML ile yazılan formüller her zaman yazının bütünü gibi durur.
  2. HTML ile yazılan formüllerde, sayfanın arka planı, font türü, internet sunucusunun ayarları aktif olarak çalışır.
  3. HTML kullanarak yazılan formüller sayfa açılım hızını arttırır.


TeX kullanımının avantajları

  1. Tex kalite bakımından HTML'den ileri bir yazılımdır.
  2. Tex yazılımında "<math>x</math>" kodlaması matematiksel değişken anlamına gelir. Fakat HTML'de "x" kodlaması herhangi bir anlama gelebilir. Bu yüzden bilgiler daha kolay kaybolabilir.
  3. TeX yazılımı özellikle formül yazımı için tasarlanmıştır. Bu nedenle daha kolay ve daha işlevseldir.
  4. 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.
  5. Diğer önemli husus TeX MathML kodlamasına, bu kodlamayı destekleyen sunucular tarafından çevirlebilmektedir.
  6. TeX komutlarını kullanırken sunucu desteğine ya da diğer teknik desteklere ihtiyaç duymazsınız. Bu kodlamanın işlevselliğini serverler sağlamaktadır. Bu nedenle her türlü sunucuda, rahatlıkla yazıp kullanabileceğiniz bir kodlama türüdür.

Fonksiyonlar, semboller, özel karakterler

Aksanlar/Vurgular

\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˙

Standart fonksiyonlar

\sin a \cos b \tan c sin⁡acos⁡btan⁡c
\sec d \csc e \cot f sec⁡dcsc⁡ecot⁡f
\arcsin h \arccos i \arctan j arcsin⁡harccos⁡iarctan⁡j
\sinh k \cosh l \tanh m \coth n sinh⁡kcosh⁡ltanh⁡mcoth⁡n
\operatorname{sh}o \operatorname{ch}p \operatorname{th}q sh⁡och⁡pth⁡q
\operatorname{argsh}r \operatorname{argch}s \operatorname{argth}t argsh⁡rargch⁡sargth⁡t
\lim u \limsup v \liminf w \min x \max y lim⁡ulim sup⁡vlim inf⁡wmin⁡xmax⁡y
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g inf⁡zsup⁡aexp⁡bln⁡clg⁡dlog⁡elog10fker⁡g
\deg h \gcd i \Pr j \det k \hom l \arg m \dim n deg⁡hgcd⁡iPr⁡jdet⁡khom⁡larg⁡mdim⁡n

Modüler aritmatik

s_k \equiv 0 \pmod{m} a \bmod b sk≡0(modm)amodb

Türevsel karakterler

\nabla \partial x dx \dot x \ddot y ∇∂xdxx˙y¨

Kümeler

\forall \exists \empty \emptyset \varnothing ∀∃∅∅∅
\in \ni \not \in \notin \subset \subseteq \supset \supseteq ∈∋∉∉⊂⊆⊃⊇
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus ∩⋂∪⋃⨄∖∖
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup ⊏⊑⊐⊒⊓⊔⨆

Operatör işaretler

+ \oplus \bigoplus \pm \mp - +⊕⨁±∓−
\times \otimes \bigotimes \cdot \circ \bullet \bigodot ×⊗⨂⋅∘∙⨀
\star * / \div \frac{1}{2} ⋆*/÷12

Mantıksal ifadeler

\land \wedge \bigwedge \bar{q} \to p ∧∧⋀q¯→p
\lor \vee \bigvee \lnot \neg q \And ∨∨⋁¬¬q&

Kök alma

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

Eşitlik/Denklik/Benzerlik işaretleri

\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=} ∼≈≃≅=˙=def
\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto ≤<≪≫≥>≡≢≠or≠∝

Geometrik

\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ ◊◻△∠⊥∣∤‖45∘

Oklar/Bildiri ifadeleri

\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow ←←→→↛↔⟵⟶
\mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow ↦⟼↪↩↗↘↙↖
\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft ↑↓↕⇀⇁↼↽↿
\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow ↾⇃⇂⇌⇐⇒⇔⟸
\Longrightarrow \Longleftrightarrow (or \iff) \Uparrow \Downarrow \Updownarrow \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft ⟹⟺⇑⇓⇕⇇⇆⇚↢↫
\leftrightharpoons \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright ⇋↶↺↰⇈⇉⇄⇛↣↬
\curvearrowright \circlearrowright \Rsh \downdownarrows \multimap \leftrightsquigarrow \rightsquigarrow \nLeftarrow \nleftrightarrow \nRightarrow ↷↻↱⇊⊸↭⇝⇍↮⇏
\nLeftrightarrow \longleftrightarrow ⇎⟷

Özel

\eth \S \P \% \dagger \ddagger \ldots \cdots ð§%†‡…⋯
\smile \frown \wr \triangleleft \triangleright \infty \bot \top ⌣⌢≀◃▹∞⊥⊤
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar ⊢⊨⊩⊨‖‖ıℏ
\ell \mho \Finv \Re \Im \wp \complement \diamondsuit ℓ℧Ⅎℜℑ℘∁♢
\heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp ♡♣♠⅁♭♮♯

Unsorted (new stuff)

\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown △▽◊Ⓢ∡∄𝕜‵▴▾
\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 \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot ⊪≏≎≧⩾⪖≳⪆≂⋗
\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq ⋙≷⋛⪌≖≗≜∼≈⫆
\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \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 ⊬⊮⋪⋬⊈⊈⊊⫋⫋≯
\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 ⊣≍≐∥

Üslü ifadeler, toplam-çarpım sembolleri, türev, integral

Feature Syntax How it looks rendered
HTML PNG
Superscript a^2 a2 a2
Subscript a_2 a2 a2
Grouping a^{2+2} a2+2 a2+2
a_{i,j} ai,j ai,j
Combining sub & super x_2^3 x23
Preceding and/or Additional sub & super \sideset{_1^2}{_3^4}\prod_a^b ∏3412ab
{}_1^2\!\Omega_3^4 12Ω34
Stacking \overset{\alpha}{\omega} ωα
\underset{\alpha}{\omega} ωα
\overset{\alpha}{\underset{\gamma}{\omega}} ωγα
\stackrel{\alpha}{\omega} ωα
Derivative (forced PNG) x', y, f', f\!   x′,y″,f′,f″
Derivative (f in italics may overlap primes in HTML) x', y, f', f x′,y″,f′,f″ x′,y″,f′,f″
Derivative (HTML-yanlış) x^\prime, y^{\prime\prime} x′,y′′ x′,y′′
Derivative (PNG-yanlış) x\prime, y\prime\prime x′,y′′ x′,y′′
Derivative dots \dot{x}, \ddot{x} x˙,x¨
Underlines, overlines, vectors \hat a \ \bar b \ \vec c a^ 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_
Arrows A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C A←n+μ−1B→Tn±i−1C
Overbraces \overbrace{ 1+2+\cdots+100 }^{5050} 1+2+⋯+100⏞5050
Underbraces \underbrace{ a+b+\cdots+z }_{26} a+b+⋯+z⏟26
Sum \sum_{k=1}^N k^2 ∑k=1Nk2
Sum (force \textstyle) \textstyle \sum_{k=1}^N k^2 ∑k=1Nk2
Product \prod_{i=1}^N x_i ∏i=1Nxi
Product (force \textstyle) \textstyle \prod_{i=1}^N x_i ∏i=1Nxi
Coproduct \coprod_{i=1}^N x_i ∐i=1Nxi
Coproduct (force \textstyle) \textstyle \coprod_{i=1}^N x_i ∐i=1Nxi
Limit \lim_{n \to \infty}x_n limn→∞xn
Limit (force \textstyle) \textstyle \lim_{n \to \infty}x_n limn→∞xn
Integral \int_{-N}^{N} e^x\, dx ∫−NNexdx
İntegral (force \textstyle) \textstyle \int_{-N}^{N} e^x\, dx ∫−NNexdx
Çift katlı integral \iint_{D}^{W} \, dx\,dy ∬DWdxdy
Üç katlı integral \iiint_{E}^{V} \, dx\,dy\,dz ∭EVdxdydz
Dört katlı integral \iiiint_{F}^{U} \, dx\,dy\,dz\,dt ⨌FUdxdydzdt
Path integral \oint_{C} x^3\, dx + 4y^2\, dy ∮Cx3dx+4y2dy
Intersections \bigcap_1^{n} p ⋂1np
Unions \bigcup_1^{k} p ⋃1kp

Fractions, matrices, multilines

Feature Syntax How it looks rendered
Fractions \frac{2}{4}=0.5 24=0.5
Small Fractions \tfrac{2}{4} = 0.5 24=0.5
Large (normal) Fractions \dfrac{2}{4} = 0.5 24=0.5
Large (nestled) Fractions \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a 2c+2d+24=a
Binomial coefficients \binom{n}{k} (nk)
Small Binomial coefficients \tbinom{n}{k} (nk)
Large (normal) Binomial coefficients \dbinom{n}{k} (nk)
Matrices 
\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}
 [0⋯0⋮⋱⋮0⋯0] 
\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)
Case distinctions 
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
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)=(a−b)2=a2−2ab+b2
Multiline equations (must define number of colums used ({lcr}) (should not be used unless needed) 
\begin{array}{lcl}
  z        & = & a \\
  f(x,y,z) & = & x + y + z  
\end{array}
 z=af(x,y,z)=x+y+z
Multiline equations (more) 
\begin{array}{lcr}
  z        & = & a \\
  f(x,y,z) & = & x + y + z     
\end{array}
 z=af(x,y,z)=x+y+z
Breaking up a long expression so that it wraps when necessary 

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

f(x)=∑n=0∞anxn=a0+a1x+a2x2+⋯

Simultaneous equations 
\begin{cases}
    3x + 5y +  z \\
    7x - 2y + 4z \\
   -6x + 3y + 2z 
\end{cases}
 {3x+5y+z7x−2y+4z−6x+3y+2z

Alphabets and typefaces

Greek alphabet
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta ABΓΔEZ
\Eta \Theta \Iota \Kappa \Lambda \Mu HΘIKΛM
\Nu \Xi \Pi \Rho \Sigma \Tau NΞΠPΣT
\Upsilon \Phi \Chi \Psi \Omega ΥΦXΨΩ
\alpha \beta \gamma \delta \epsilon \zeta αβγδϵζ
\eta \theta \iota \kappa \lambda \mu ηθικλμ
\nu \xi \pi \rho \sigma \tau νξπρστ
\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} 𝔸𝔹ℂ𝔻𝔼𝔽𝔾
\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} ℍ𝕀𝕁𝕂𝕃𝕄
\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} ℕ𝕆ℙℚℝ𝕊𝕋
\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z} 𝕌𝕍𝕎𝕏𝕐ℤ
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{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau} NΞΠPΣT
\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{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau} νξπρστ
\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
Italics
\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} 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{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} 𝒜ℬ𝒞𝒟ℰℱ𝒢
\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} ℋℐ𝒥𝒦ℒℳ
\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} 𝒩𝒪𝒫𝒬ℛ𝒮𝒯
\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z} 𝒰𝒱𝒲𝒳𝒴𝒵
Hebrew
\aleph \beth \gimel \daleth ℵℶℷℸ
Feature Syntax How it looks rendered
non-italicised characters \mbox{abc} abc abc
mixed italics (bad) \mbox{if} n \mbox{is even} ifnis even ifnis even
mixed italics (good) \mbox{if }n\mbox{ is even} if n 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 ifn is even

Parenthesizing big expressions, brackets, bars

Feature Syntax How it looks rendered
Bad ( \frac{1}{2} ) (12)
Good \left ( \frac{1}{2} \right ) (12)

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

Feature Syntax How it looks rendered
Parentheses \left ( \frac{a}{b} \right ) (ab)
Brackets \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack [ab][ab]
Braces \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 \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 ⌊ab⌋⌈cd⌉
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 ↑ab↓⇑ab⇓↕ab⇕

Delimiters can be mixed,
as long as \left and \right match

\left [ 0,1 \right )
\left \langle \psi \right |

[0,1)
⟨ψ|

Use \left. and \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( ... \Bigg] \bigg] \Big] \big]

((((...]]]]

\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle

{{{{...⟩⟩⟩⟩

\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big| ‖‖‖‖...||||
\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil

⌊⌊⌊⌊...⌉⌉⌉⌉

\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow

↑↑↑↑...⇓⇓⇓⇓

\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow

↕↕↕↕...⇕⇕⇕⇕

\big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash

////...\\\\

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

Align with normal text flow

Due to the default css 

img.tex { vertical-align: middle; }

an inline expression like ∫−NNexdx=2sinh⁡N 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.

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:

Syntax How it looks rendered
a^{c+2} ac+2
a^{c+2} \, ac+2
a^{\,\!c+2} ac+2
a^{b^{c+2}} abc+2 (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}} \, abc+2 (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}}\approx 5 abc+2≈5 (due to "≈" correctly displayed, no code "\,\!" needed)
a^{b^{\,\!c+2}} abc+2
\int_{-N}^{N} e^x\, dx ∫−NNexdx


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.-->

Color

Equations can use color:

  • {\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}
    x2+2x−1
  • x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}
    x1,2=−b±b2−4ac2a

See here for all named colours supported by LaTeX.

Note that color should not be used as the only way to identify something because color blind people may not be able to distinguish between the two colors. See en:Wikipedia:Manual of Style#Formatting issues.

Examples

Quadratic Polynomial

ax2+bx+c=0

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

Quadratic Polynomial (Force PNG Rendering)

ax2+bx+c=0

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

Quadratic Formula

x=−b±b2−4ac2a

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

Tall Parentheses and Fractions

2=((3−x)×23−x)

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

Snew=Sold+(5−T)22

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

Integrals

∫ax∫asf(y)dyds=∫axf(y)(x−y)dy

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

Summation

∑m=1∞∑n=1∞m2n3m(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>

Differential Equation

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>

Complex numbers

|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>

Limits

limz→z0f(z)=f(z0)

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

Integral Equation

ϕn(κ)=14π2κ2∫0∞sin⁡(κR)κR∂∂R[R2∂Dn(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>

Example

ϕn(κ)=0.033Cn2κ−11/3,1L0≪κ≪1l0

<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

f(x)={1−1≤x<012x=01−x20<x≤1

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

Prefixed subscript

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\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}
 \frac{z^n}{n!}</math>

Bug reports

Discussions, bug reports and feature requests should go to the Wikitech-l mailing list. These can also be filed on Mediazilla under MediaWiki extensions.

See also

"https://tr.wiki.beta.math.wmflabs.org/w/index.php?title=Yardım:Matematiksel_formüller&oldid=606" sayfasından alınmıştır