Help:數學

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數學

meta:Help:Formula

數學符宜入<math> ... </math>

常符

\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˙
\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
s_k \equiv 0 \pmod{m} sk0(modm)
a\,\bmod\,b amodb
\nabla \, \partial x \, \mathrm{d}x \, \dot x \, \ddot y\, \mathrm{d}y/\mathrm{d}x\, \frac{\mathrm{d}y}{\mathrm{d}x}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2} xdxx˙y¨dy/dxdydx2yx1x2
\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
+ \oplus \bigoplus \pm \mp - +±
\times \otimes \bigotimes \cdot \circ \bullet \bigodot ×
\star * / \div \frac{1}{2} */÷12


\land (or \and) \wedge \bigwedge \bar{q} \to p q¯p
\lor \vee \bigvee \lnot \neg q \And ¬¬q&
\sqrt{x} \sqrt[n]{x} xxn
\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
\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ 45
\leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \nrightarrow \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow
\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \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
\And \eth \S \P \% \dagger \ddagger \ldots \cdots &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
\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 \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\varcoppa\Digamma\Koppa\koppa\Sampi\sampi\Stigma\stigma\varstigma ϘϙϙϜϞϟϠϡϚϛϛ

上標、下標、積分等

功能 語法 效果
上標 a^2 a2
下標 a_2 a2
多文 a^{2+2} a2+2
a_{i,j} ai,j
上下兼用 x_2^3 x23
前置上下標 {}_1^2\!X_3^4 12X34
導數
HTML
x' x
導數
PNG
x^\prime x
導數
錯誤
x\prime x
導數點 \dot{x} x˙
\ddot{y} y¨
向量 \vec{c} c
\overleftarrow{a b} ab
\overrightarrow{c d} cd
\widehat{e f g} efg^
上弧

Template:按

\overset{\frown} {AB} AB
上劃線 \overline{h i j} hij
下劃線 \underline{k l m} klm_
上括號 \overbrace{1+2+\cdots+100} 1+2++100
\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix} 50501+2++100
下括號 \underbrace{a+b+\cdots+z} a+b++z
\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix} a+b++z26
求和 \sum_{k=1}^N k^2 k=1Nk2
\begin{matrix} \sum_{k=1}^N k^2 \end{matrix} k=1Nk2
求積 \prod_{i=1}^N x_i i=1Nxi
\begin{matrix} \prod_{i=1}^N x_i \end{matrix} i=1Nxi
上積 \coprod_{i=1}^N x_i i=1Nxi
\begin{matrix} \coprod_{i=1}^N x_i \end{matrix} i=1Nxi
極限 \lim_{n \to \infty}x_n limnxn
\begin{matrix} \lim_{n \to \infty}x_n \end{matrix} limnxn
積分 \int_{-N}^{N} e^x\, \mathrm{d}x NNexdx
\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix} NNexdx
雙重積分 \iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y DWdxdy
三重積分 \iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z EVdxdydz
四重積分 \iiiint_{F}^{U} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z\,\mathrm{d}t FUdxdydzdt
曲綫曲面積分 \oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y Cx3dx+4y2dy
交集 \bigcap_1^{n} p 1np
並集 \bigcup_1^{k} p 1kp

分數矩陣並多行列式

分數 \frac{2}{4}=0.5 24=0.5
小型分數 \tfrac{2}{4} = 0.5 24=0.5
大型分數(嵌套) \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a 2c+2d+24=a
大型分數(不嵌套) \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a 24=0.52c+2d+24=a
二項式系數 \dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} (nr)=(nnr)=Cnr=Cnnr
小型二項式系數 \tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} (nr)=(nnr)=Cnr=Cnnr
大型二項式系數 \binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} (nr)=(nnr)=Cnr=Cnnr
矩陣
\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)
條件定義
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
多行等式、同餘式
\begin{align}
f(x) & = (m+n)^2 \\
& = m^2+2mn+n^2 \\
\end{align}
f(x)=(m+n)2=m2+2mn+n2
begin{align}
3^{6n+3}+4^{6n+3} 
& \equiv (3^3)^{2n+1}+(4^3)^{2n+1}\\  
& \equiv 27^{2n+1}+64^{2n+1}\\  
& \equiv 27^{2n+1}+(-27)^{2n+1}\\ 
& \equiv 27^{2n+1}-27^{2n+1}\\
& \equiv 0 \pmod{91}\\
\end{align}
36n+3+46n+3(33)2n+1+(43)2n+1272n+1+642n+1272n+1+(27)2n+1272n+1272n+10(mod91)
\begin{alignat}{3}
f(x) & = (m-n)^2 \\
f(x) & = (-m+n)^2 \\
& = m^2-2mn+n^2 \\
\end{alignat}
f(x)=(mn)2f(x)=(m+n)2=m22mn+n2
多行等式(左對齊)
\begin{array}{lcl}
z        & = & a \\
f(x,y,z) & = & x + y + z 
\end{array}
z=af(x,y,z)=x+y+z
多行等式(右對齊)
\begin{array}{lcr}
z        & = & a \\
f(x,y,z) & = & x + y + z    
\end{array}
z=af(x,y,z)=x+y+z
長公式換行

<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=0anxn=a0+a1x+a2x2+

方程組
\begin{cases}
3x + 5y +  z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
{3x+5y+z7x2y+4z6x+3y+2z
數組
\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}
abS001011101110

字體

希蠟文

斜小寫希蠟文者,可置方程也。

正體希臘字母
特徵 語法 效果 註釋/外部鏈接
大寫字母
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta ABΓΔEZHΘ
Α Β Γ Δ Ε Ζ Η Θ
\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi IKΛMNΞOΠ
Ι Κ Λ Μ Ν Ξ Ο Π
\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega PΣTΥΦXΨΩ
Ρ Σ Τ Υ Φ Χ Ψ Ω
小寫字母
\alpha \beta \gamma \delta \epsilon \zeta \eta \theta αβγδϵζηθ
\iota \kappa \lambda \mu \nu \xi \omicron \pi ικλμνξoπ
\rho \sigma \tau \upsilon \phi \chi \psi \omega ρστυϕχψω
異體字母
\Epsilon\epsilon\varepsilon Eϵε
\Theta\theta\vartheta Θθϑ
\Kappa\kappa\varkappa Kκϰ
\Pi\pi\varpi Ππϖ
\Rho\rho\varrho Pρϱ
\Sigma\sigma\varsigma Σσς
\Phi\phi\varphi Φϕφ
已停用字母
\digamma ϝ
Ϝ[1]
粗體希臘字母
特徵 語法 效果
大寫字母
\boldsymbol{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} ABΓΔEZHΘ
\boldsymbol{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi} IKΛMNΞ𝑶Π
\boldsymbol{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega} PΣTΥΦXΨΩ
小寫字母
\boldsymbol{\alpha \beta \gamma \delta \epsilon \zeta \eta \theta} αβγδϵζηθ
\boldsymbol{\iota \kappa \lambda \mu \nu \xi \omicron \pi} ικλμνξ𝒐π
\boldsymbol{\rho \sigma \tau \upsilon \phi \chi \psi \omega} ρστυϕχψω
異體字母
\boldsymbol{\Epsilon\epsilon\varepsilon} Eϵε
\boldsymbol{\Theta\theta\vartheta} Θθϑ
\boldsymbol{\Kappa\kappa\varkappa} Kκϰ
\boldsymbol{\Pi\pi\varpi} Ππϖ
\boldsymbol{\Rho\rho\varrho} Pρϱ
\boldsymbol{\Sigma\sigma\varsigma} Σσς
\boldsymbol{\Phi\phi\varphi} Φϕφ
已停用字母
\boldsymbol{\digamma} ϝ

黑板粗體

\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
𝔸𝔹𝔻𝔼𝔽𝔾𝕀𝕁𝕂𝕃𝕄𝕆𝕊𝕋𝕌𝕍𝕎𝕏𝕐

黑板粗體(Blackboard bold)表示數學、物理學中之向量並集合之符。


正粗體

\mathbf{012…abc…ABC…}
𝟎 𝟏 𝟐 𝟑 𝟒 𝟓 𝟔 𝟕 𝟖 𝟗
𝐚 𝐛 𝐜 𝐝 𝐞 𝐟 𝐠 𝐡 𝐢 𝐣 𝐤 𝐥 𝐦 𝐧 𝐨 𝐩 𝐪 𝐫 𝐬 𝐭 𝐮 𝐯 𝐰 𝐱 𝐲 𝐳
𝐀 𝐁 𝐂 𝐃 𝐄 𝐅 𝐆 𝐇 𝐈 𝐉 𝐊 𝐋 𝐌 𝐍 𝐎 𝐏 𝐐 𝐑 𝐒 𝐓 𝐔 𝐕 𝐖 𝐗 𝐘 𝐙
備註
花括號{},只用拉丁字母並數字,非用希臘字母\alpha等。

斜粗體

\boldsymbol{012…abc…ABC…\alpha \beta \gamma…}
0 1 2 3 4 5 6 7 8 9
𝒂 𝒃 𝒄 𝒅 𝒆 𝒇 𝒈 𝒉 𝒊 𝒋 𝒌 𝒍 𝒎 𝒏 𝒐 𝒑 𝒒 𝒓 𝒔 𝒕 𝒖 𝒗 𝒘 𝒙 𝒚 𝒛
𝑨 𝑩 𝑪 𝑫 𝑬 𝑭 𝑮 𝑯 𝑰 𝑱 𝑲 𝑳 𝑴 𝑵 𝑶 𝑷 𝑸 𝑹 𝑺 𝑻 𝑼 𝑽 𝑾 𝑿 𝒀 𝒁
α β γ δ ϵ ζ η θ ι κ λ μ ν ξ 𝒐 π ρ σ τ υ ϕ χ ψ ω
\boldsymbol{}可粗合符。
\mathit{0123456789}
0123456789
\mathrm{012…abc…ABC…}\mbox{}\operatorname{}
0123456789 
ABCDEFGHIJKLMNOPQRSTUVWXYZ 
abcdefghijklmnopqrstuvwxyz 
羅馬體可用數字拉丁字母
\mathfrak{012…abc…ABC…}
0 1 2 3 4 5 6 7 8 9
𝔞 𝔟 𝔠 𝔡 𝔢 𝔣 𝔤 𝔥 𝔦 𝔧 𝔨 𝔩 𝔪 𝔫 𝔬 𝔭 𝔮 𝔯 𝔰 𝔱 𝔲 𝔳 𝔴 𝔵 𝔶 𝔷
𝔄 𝔅  𝔇 𝔈 𝔉 𝔊   𝔍 𝔎 𝔏 𝔐 𝔑 𝔒 𝔓 𝔔  𝔖 𝔗 𝔘 𝔙 𝔚 𝔛 𝔜 
哥特體可用數字並拉丁字母。
\mathcal{ABC…}
𝒜𝒞𝒟𝒢𝒥𝒦𝒩𝒪𝒫𝒮𝒯𝒰𝒱𝒲𝒳𝒴𝒵
手寫體效大寫拉丁字母。
\aleph\beth\gimel\daleth
功能 語法 顯示
短括號 ( \frac{1}{2} ) (12)
長括號 \left( \frac{1}{2} \right) (12)

可用 \left\right ,示異號:

功能 語法 顯示
圓括號,小括號 \left( \frac{a}{b} \right) (ab)
方括號,中括號 \left[ \frac{a}{b} \right] [ab]
花括號,大括號 \left\{ \frac{a}{b} \right\} {ab}
角括號 \left \langle \frac{a}{b} \right \rangle ab
單豎線,絕對值 \left| \frac{a}{b} \right| |ab|
雙豎線,範 \left \| \frac{a}{b} \right \| ab
取整函數 \left \lfloor \frac{a}{b} \right \rfloor ab
取頂函數 \left \lceil \frac{c}{d} \right \rceil cd
斜線與反斜線 \left / \frac{a}{b} \right \backslash /ab\
上下箭頭 \left \uparrow \frac{a}{b} \right \downarrow ab
\left \Uparrow \frac{a}{b} \right \Downarrow ab
\left \updownarrow \frac{a}{b} \right \Updownarrow ab
混合括號 \left [ 0,1 \right )
\left \langle \psi \right |
[0,1)
ψ|
單左括號 \left \{ \frac{a}{b} \right . {ab
單右括號 \left . \frac{a}{b} \right \} ab}

備註:

  • 可用 \big, \Big, \bigg, \Bigg 制大小
\Bigg ( \bigg [ \Big \{ \big \langle \left | \| \frac{a}{b} \| \right | \big \rangle \Big \} \bigg ] \Bigg )

 示︰

([{|x|}])
2個quad空格 \alpha\qquad\beta αβ 2m 
quad空格 \alpha\quad\beta αβ m 
大空格 \alpha\ \beta α β m3
中等空格 \alpha\;\beta αβ 2m7
小空格 \alpha\,\beta αβ m6
沒有空格 \alpha\beta αβ  0 
緊貼 \alpha\!\beta αβ m6
  • 字色︰-{}-{\color{色調}表達式}
  • 背色︰-{}-{\pagecolor{色調}表達式}
Colors supported
Apricot Aquamarine Bittersweet Black
Blue BlueGreen BlueViolet BrickRed
Brown BurntOrange CadetBlue CarnationPink
Cerulean CornflowerBlue Cyan Dandelion
DarkOrchid Emerald ForestGreen Fuchsia
Goldenrod Gray Green GreenYellow
JungleGreen Lavender LimeGreen Magenta
Mahogany Maroon Melon MidnightBlue
Mulberry NavyBlue OliveGreen Orange
OrangeRed Orchid Peach Periwinkle
PineGreen Plum ProcessBlue Purple
RawSienna Red RedOrange RedViolet
Rhodamine RoyalBlue RoyalPurple RubineRed
Salmon SeaGreen Sepia SkyBlue
SpringGreen Tan TealBlue Thistle
Turquoise Violet VioletRed White
WildStrawberry Yellow YellowGreen YellowOrange

註︰首字母必大寫,如\color{OliveGreen}

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

用PNG

2x=1 \,
2x=1
以PNG圖出。

君亦可用 \,\!,亦能強用PNG圖。

閱讀更多:Help:Displaying a formula#Forced PNG rendering

分類:幫助文檔

  1. 念作WawDigamma