KaTeXで数式を書く

改行

$$
\begin{aligned} 
  x^2 - (a + b)x + ab = 0 \\
  (x - a) (x - b) = 0 \\
  x = a, b
\end{aligned}
$$

$$\begin{aligned} x^2 - (a + b)x + ab = 0 \\ (x - a) (x - b) = 0 \\ x = a, b \end{aligned}$$

揃える

$$
\begin{aligned} 
  x^2 - (a + b)x + ab &= 0 \\
  (x - a) (x - b) &= 0 \\
  x &= a, b
\end{aligned}
$$

$$\begin{aligned} x^2 - (a + b)x + ab &= 0 \\ (x - a) (x - b) &= 0 \\ x &= a, b \end{aligned}$$

空白

$$
\begin{aligned} 
  x^2 - (a + b)x + ab &= 0 \\
  (x - a) (x - b) &= 0 \\
  x &= a, \qquad\quad b
\end{aligned}
$$

$$\begin{aligned} x^2 - (a + b)x + ab &= 0 \\ (x - a) (x - b) &= 0 \\ x &= a, \qquad\quad b \end{aligned}$$

添字

x^{2} -> $x^{2}$

x^{2+i} -> $x^{2+i}$

x_{i} -> $x_{i}$

x_{i-1} -> $x_{i-1}$

x^{2}_{i} -> $x^{2}_{i}$

x_{i}^{2} -> $x_{i}^{2}$

{x_{i}}^{2} -> ${x_{i}}^{2}$

{x^{2}}_{i} -> ${x^{2}}_{i}$

x^{y^{2}} -> $x^{y^{2}}$

x^{y_{2}} -> $x^{y_{2}}$

x_{y_{i}} -> $x_{y_{i}}$

x_{y^{2}} -> $x_{y^{2}}$

x^{\prime} -> $x^{\prime}$

{}^{\forall}x -> ${}^{\forall}x$

{}^{\exists}x -> ${}^{\exists}x$

{}_{n}C_{r} -> ${}_{n}C_{r}$

分数

\frac{1}{2} ->

$$\frac{1}{2}$$

y = \frac{1}{x+1} ->

$$y = \frac{1}{x+1}$$

根号記号

\sqrt[1]{2} ->

$$\sqrt[1]{2}$$

L = \int_{b}^{a} \sqrt{ \left( \frac{dx}{dt} \right)^{2} + \left( \frac{dy}{dt} \right)^{2} } dt ->

$$L = \int_{b}^{a} \sqrt{ \left( \frac{dx}{dt} \right)^{2} + \left( \frac{dy}{dt} \right)^{2} } dt$$

シグマ記号

\sum -> $\sum$

\sum^{n}_{k=1}(a_{k}+b_{k}) = \sum^{n}_{k=1}a_{k} + \sum^{n}_{k=1}b_{k} ->

$$\sum^{n}_{k=1}(a_{k}+b_{k}) = \sum^{n}_{k=1}a_{k} + \sum^{n}_{k=1}b_{k}$$

積分記号

\int -> $\int$

\int^{b}_{a}f(x)dx = \int^{c}_{a}f(x)dx + \int^{b}_{c}f(x)dx ->

$$\int^{b}_{a}f(x)dx = \int^{c}_{a}f(x)dx + \int^{b}_{c}f(x)dx$$

省略記号

\ldots -> $\ldots$

\vdots -> $\vdots$

\cdots -> $\cdots$

\ddots -> $\ddots$

\left( \begin{array}{rrcr}
1      & 2        & \cdots & n      \\
2      & 4        & \cdots & 2n     \\
\vdots & \vdots   & \ddots & \vdots \\
m      & m\cdot 2 & \cdots & m\cdot n 
\end{array} \right) \;\;\; (n , m = 0, 1, 2, \ldots)

->

$\left( \begin{array}{rrcr} 1 & 2 & \cdots & n \\ 2 & 4 & \cdots & 2n \\ \vdots & \vdots & \ddots & \vdots \\ m & m\cdot 2 & \cdots & m\cdot n \end{array} \right) \;\;\; (n , m = 0, 1, 2, \ldots)$

文字修飾記号

\vec{x} -> $\vec{x}$

\hat{x} -> $\hat{x}$

\dot{x} -> $\dot{x}$

\acute{x} -> $\acute{x}$

\check{x} -> $\check{x}$

\bar{x} -> $\bar{x}$

\tilde{x} -> $\tilde{x}$

\ddot{x} -> $\ddot{x}$

\grave{x} -> $\grave{x}$

\breve{x} -> $\breve{x}$

\vec{a} + \vec{b} + \vec{c} + \vec{d} + \vec{e} + \vec{f} -> $\vec{a} + \vec{b} + \vec{c} + \vec{d} + \vec{e} + \vec{f}$

上線

\overline{A} \cup \overline{B} = \overline{A \cap B} -> $\overline{A} \cup \overline{B} = \overline{A \cap B}$

否定記号

a \neq b -> $a \neq b$

その他の数学記号

\log -> $\log$

\sin -> $\sin$

\cos -> $\cos$

\tan -> $\tan$

\max -> $\max$

\min -> $\min$

\gcd -> $\gcd$

\det -> $\det$

\exp -> $\exp$

\ln -> $\ln$

\pm -> $\pm$

\mp -> $\mp$

\times -> $\times$

\div -> $\div$

\ast -> $\ast$

\star -> $\star$

\circ -> $\circ$

\bullet -> $\bullet$

\cdot -> $\cdot$

\bigcirc -> $\bigcirc$

\setminus -> $\setminus$

\wr -> $\wr$

\in -> $\in$

\ni -> $\ni$

\cap -> $\cap$

\cup -> $\cup$

\vee -> $\vee$

\wedge -> $\wedge$

\subset -> $\subset$

\subseteq -> $\subseteq$

\supset -> $\supset$

\supseteq -> $\supseteq$

\oplus -> $\oplus$

\ominus -> $\ominus$

\otimes -> $\otimes$

\oslash -> $\oslash$

\leq -> $\leq$

\geq -> $\geq$

\ll -> $\ll$

\gg -> $\gg$

\neq -> $\neq$

\equiv -> $\equiv$

\sim -> $\sim$

\cong -> $\cong$

\propto -> $\propto$

\approx -> $\approx$

\parallel -> $\parallel$

\perp -> $\perp$

\emptyset -> $\emptyset$

\angle -> $\angle$

\langle -> $\langle$

\rangle -> $\rangle$

\lfloor -> $\lfloor$

\rfloor -> $\rfloor$

\lceil -> $\lceil$

\rceil -> $\rceil$

\infty -> $\infty$

\partial -> $\partial$

\prime -> $\prime$

\ell -> $\ell$

\imath -> $\imath$

\jmath -> $\jmath$

\surd -> $\surd$

\nabla -> $\nabla$

\forall -> $\forall$

\exists -> $\exists$

\neg -> $\neg$

\backslash -> $\backslash$

\prod -> $\prod$

\coprod -> $\coprod$

\dagger -> $\dagger$

\ddagger -> $\ddagger$

\aleph -> $\aleph$

\sharp -> $\sharp$

\flat -> $\flat$

\natural -> $\natural$

\triangleleft -> $\triangleleft$

\triangleright -> $\triangleright$

\bigtriangleup -> $\bigtriangleup$

\bigtriangledown -> $\bigtriangledown$

\triangle -> $\triangle$

\Box -> $\Box$

\Diamond -> $\Diamond$

\diamond -> $\diamond$

\clubsuit -> $\clubsuit$

\diamondsuit -> $\diamondsuit$

\heartsuit -> $\heartsuit$

\spadesuit -> $\spadesuit$

矢印記号

\leftarrow -> $\leftarrow$

\longleftarrow -> $\longleftarrow$

\uparrow -> $\uparrow$

\Leftarrow -> $\Leftarrow$

\Longleftarrow -> $\Longleftarrow$

\Uparrow -> $\Uparrow$

\rightarrow -> $\rightarrow$

\longrightarrow -> $\longrightarrow$

\downarrow -> $\downarrow$

\Rightarrow -> $\Rightarrow$

\Longrightarrow -> $\Longrightarrow$

\Downarrow -> $\Downarrow$

\leftrightarrow -> $\leftrightarrow$

\longleftrightarrow -> $\longleftrightarrow$

\updownarrow -> $\updownarrow$

\Leftrightarrow -> $\Leftrightarrow$

\Longleftrightarrow -> $\Longleftrightarrow$

\Updownarrow -> $\Updownarrow$

\mapsto -> $\mapsto$

\longmapsto -> $\longmapsto$

\nearrow -> $\nearrow$

\hookleftarrow -> $\hookleftarrow$

\hookrightarrow -> $\hookrightarrow$

\searrow -> $\searrow$

\leftharpoonup -> $\leftharpoonup$

\rightharpoonup -> $\rightharpoonup$

\swarrow -> $\swarrow$

\leftharpoondown -> $\leftharpoondown$

\rightharpoondown -> $\rightharpoondown$

\nwarrow -> $\nwarrow$

\rightleftharpoons -> $\rightleftharpoons$

基本的な数学記号

\int -> $\int$ ->

$$\int$$

\int_{0}^{\infty} -> $\int_{0}^{\infty}$ ->

$$\int_{0}^{\infty}$$

\sum -> $\sum$ ->

$$\sum$$

\sum_{n = 1}^{\infty} -> $\sum_{n = 1}^{\infty}$ ->

$$\sum_{n = 1}^{\infty}$$

\lim -> $\lim$ ->

$$\lim$$

\lim_{n \to -\infty} -> $\lim_{n \to -\infty}$ ->

$$\lim_{n \to -\infty}$$

数式モードでの空白制御

a\;b -> $a\;b$

a\:b -> $a\:b$

a\,b -> $a\,b$

a\!b -> $a\!b$

\int\int_{G}f(x,y)dxdy ->

$\int\int_{G}f(x,y)dxdy$

\int\!\!\!\int_{G}f(\,x,\,y\,)\;\,dx\:dy ->

$\int\!\!\!\int_{G}f(\,x,\,y\,)\;\,dx\:dy$

ギリシャ文字

\Gamma -> $\Gamma$

\Delta -> $\Delta$

\Theta -> $\Theta$

\Lambda -> $\Lambda$

\Xi -> $\Xi$

\Pi -> $\Pi$

\Sigma -> $\Sigma$

\Upsilon -> $\Upsilon$

\Phi -> $\Phi$

\Psi -> $\Psi$

\Omega -> $\Omega$

\alpha -> $\alpha$

\beta -> $\beta$

\gamma -> $\gamma$

\delta -> $\delta$

\epsilon -> $\epsilon$

\varepsilon -> $\varepsilon$

\zeta -> $\zeta$

\eta -> $\eta$

\theta -> $\theta$

\vartheta -> $\vartheta$

\iota -> $\iota$

\kappa -> $\kappa$

\lambda -> $\lambda$

\mu -> $\mu$

\nu -> $\nu$

\xi -> $\xi$

\pi -> $\pi$

\varpi -> $\varpi$

\rho -> $\rho$

\varrho -> $\varrho$

\sigma -> $\sigma$

\varsigma -> $\varsigma$

\tau -> $\tau$

\upsilon -> $\upsilon$

\phi -> $\phi$

\varphi -> $\varphi$

\chi -> $\chi$

\psi -> $\psi$

\omega -> $\omega$

大きさの変化する括弧，矢印記号

( \frac{x}{z} )^{2} + \left( \frac{y}{z} \right)^{2} = 1 ->

$$( \frac{x}{z} )^{2} + \left( \frac{y}{z} \right)^{2} = 1$$

f(x) = \left\{ \frac{( x + 1 )( x + 2 )}{x}\right\} ->

$$f(x) = \left\{ \frac{( x + 1 )( x + 2 )}{x}\right\}$$

行列を書く

\left( \begin{array}{rr}
a & b \\ c & d
\end{array} \right) \left( \begin{array}{r}
x \\ y
\end{array} \right) = 0 \; \Longleftrightarrow \; \left\{
\begin{array}{rrrrr}
ax & + & by & = & 0 \\
cx & + & dy & = & 0
\end{array} \right.

->

$$\left( \begin{array}{rr} a & b \\ c & d \end{array} \right) \left( \begin{array}{r} x \\ y \end{array} \right) = 0 \; \Longleftrightarrow \; \left\{ \begin{array}{rrrrr} ax & + & by & = & 0 \\ cx & + & dy & = & 0 \end{array} \right.$$