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数学表記

最終更新日時: 2025年08月25日 12:57

TODOs
Section titled “TODOs”
  • nothing

xyz \([^[:space:]]+\) \([^[:space:]]+\) \(.*)

\1
記号入力記号入力記号入力
α\alpha \alpha A\Alpha \Alpha
β\beta \beta B\Beta \Beta
γ\gamma \gamma Γ\Gamma \Gamma
δ\delta \delta Δ\Delta \Delta
ϵ\epsilon \epsilon E\Epsilon \Epsilon
ε\varepsilon \varepsilon
ζ\zeta \zeta Z\Zeta \Xeta
η\eta \eta H\Eta \Eta
θ\theta \theta Θ\Theta \Theta
ϑ\vartheta \vartheta
ι\iota \iota I\Iota \Iota
κ\kappa \kappa K\Kappa \Kappa
λ\lambda \lambda Λ\Lambda \Lambda
ν\nu \nu N\Nu \Nu
μ\mu \mu M\Mu \Mu
ξ\xi \xi Ξ\Xi \Xi
ο\omicron \omicron O\Omicron \Omicron
π\pi \pi Π\Pi \Pi
ϖ\varpi \varpi
ρ\rho \rho P\Rho \Rho
ϱ\varrho \varrho
σ\sigma \sigma Σ\Sigma \Sigma
ς\varsigma \varsigma
τ\tau \tau T\Tau \Tau
υ\upsilon \upsilon Υ\Upsilon \Upsilon
ϕ\phi \phi Φ\Phi \Phi
φ\varphi \varphi
χ\chi \chi X\Chi \Chi
ψ\psi \psi Ψ\Psi \Psi
ω\omega \omega Ω\Omega \Omega
℧\mho \mho
∏\prod \prod Σ\Sigma \Sigma
∇\nabla \nabla
∂\partial \partial
ℜ\Re \Re ℑ\Im \Im
⟨\langle \langle ⟩\rangle \rangle
∀\forall \forall ∃\exists \exists
ℵ\aleph \aleph
ℶ\beth \beth
ℸ\daleth \daleth
ℷ\gimel \gimel
∁\complement \complement
ℓ\ell \ell
ð\eth \eth
ℏ\hbar \hbar ℏ\hslash \hslash
℘\wp \wp
∨\vee \vee
∈\in \in
⊃\supset \supset
∪\cup \cup
∅\emptyset \emptyset ∞\infty \infty
ı\imath \imath ȷ\jmath \jmath
̸\not \not ∖\setminus \setminus$
×\times \times ⋅\cdot \cdot
¬\neg \neg
′\prime \prime
min⁡\min \min max⁡\max \max
sin⁡\sin \sin cos⁡\cos \cos tan⁡\tan \tan
arcsin⁡\arcsin \arcsin arccos⁡\arccos \arccos arctan⁡\arctan \arctan
exp⁡\exp \exp log⁡\log \log ln⁡\ln \ln
≡\equiv \equiv ≒\fallingdotseq \fallingdotseq ≠\neq \neq
∼\sim \sim ≃\simeq \simeq ≈\approx \approx

矢印

Section titled “矢印”
記号入力記号入力記号入力
→\rightarrow \rightarrow ←\leftarrow \leftarrow ↔\leftrightarrow \leftrightarrow
⇒\Rightarrow \Rightarrow ⇐\Leftarrow \Leftarrow ⇔\Leftrightarrow \Leftrightarrow
↑\uparrow \uparrow ↓\downarrow \downarrow
↦\mapsto \mapsto

長い矢印

Section titled “長い矢印”
記号入力
⟶\longrightarrow \longrightarrow
⟵\longleftarrow \longleftarrow
⟷\longleftrightarrow \longleftrightarrow
⟸\Longleftarrow \Longleftarrow
⟹\Longrightarrow \Longrightarrow
⟺\Longleftrightarrow \Longleftrightarrow
⟼\longmapsto \longmapsto

ベクトル表記

Section titled “ベクトル表記”

\vec{a}はベクトルにならない。普通にただの矢印なしアルファベットになる（a⃗\vec{a})

a\mathbf{a}
$$
\mathbf{a}
$$
a\bm{a}
$$
\bm{a}
$$
a⇀\overrightharpoon{a}
$$
\overrightharpoon{a}
$$
a→\overrightarrow{a}
$$
\overrightarrow{a}
$$

絶対値/ノルム

Section titled “絶対値/ノルム”

\left \rightで囲むと縦方向にいっぱいになる

∣x∣|x|
$$
|x|
$$
∣x∣\lvert x \rvert
$$
\lvert x \rvert
$$
∣x∣\mid x \mid
$$
\mid x \mid
$$
∥x∥\|x\|
$$
\|x\|
$$
∣ab∣|\frac{a}{b}|
$$
|\frac{a}{b}|
$$
∣ab∣\left|\frac{a}{b}\right|
$$
\left|\frac{a}{b}\right|
$$

カッコ

Section titled “カッコ”

\left \rightで囲むと縦方向にいっぱいになる

(ab)(\frac{a}{b})
$$
(\frac{a}{b})
$$
(ab)\left(\frac{a}{b}\right)
$$
\left(\frac{a}{b}\right)
$$
[ab]\left[\frac{a}{b}\right]
$$
\left[\frac{a}{b}\right]
$$
<ab>\left<\frac{a}{b}\right>
$$
\left<\frac{a}{b}\right>
$$
{ab}\left\{\frac{a}{b}\right\}
$$
\left\{\frac{a}{b}\right\}
$$

中カッコだけはmathの文法の囲い記号と分けるためにエスケープする

積分

Section titled “積分”
∫f(x)dx\int f(x) dx
$$
\int f(x) dx
$$
∫f(x) dx\int f(x) \, dx
$$
\int f(x) \, dx
$$

ちょっとだけ間が空く

∫−∞+∞f(x)dx\int_{- \infty}^{+ \infty} f(x) dx
$$
\int_{- \infty}^{+ \infty} f(x) dx
$$
∬−∞+∞f(x)dxdy\iint_{- \infty}^{+ \infty} f(x) dx dy
$$
\iint_{- \infty}^{+ \infty} f(x) dx dy
$$
∮Cf(z)dz\oint_{C} f(z) dz
$$
\oint_{C} f(z) dz
$$

偏微分

Section titled “偏微分”
∂f∂x\frac{\partial f}{\partial x}
$$
\frac{\partial f}{\partial x}
$$

コメント

Section titled “コメント”
(−1)×(−1)⏞先に計算+1÷2⏞先に計算−5=−72 \overbrace{(-1)\times(-1)}^{\text{先に計算}}+ \overbrace{1\div2}^{\text{先に計算}}-5= -\frac{7}{2}
$$
    \overbrace{(-1)\times(-1)}^{\text{先に計算}}+
    \overbrace{1\div2}^{\text{先に計算}}-5=
    -\frac{7}{2}
$$

cases

Section titled “cases”

本来は場合分けの記述に使う

{x+y=13x+2y=0 \begin{cases} x+y &= 1 \\ 3x+2y & = 0\\ \end{cases}
$$
    \begin{cases}
    x+y &= 1 \\
    3x+2y & = 0\\
    \end{cases}
$$

ベクトル/行列

Section titled “ベクトル/行列”
v→= (vxvyvz)\overrightarrow{v}= \ \begin{pmatrix} v_{x}\\ v_{y}\\ v_{z} \end{pmatrix}
$$
\overrightarrow{v}=
\
\begin{pmatrix}
v_{x}\\
v_{y}\\
v_{z}
\end{pmatrix}
$$
v→= [vxvyvz]\overrightarrow{v}= \ \begin{bmatrix} v_{x}\\ v_{y}\\ v_{z} \end{bmatrix}
$$
\overrightarrow{v}=
\
\begin{bmatrix}
v_{x}\\
v_{y}\\
v_{z}
\end{bmatrix}
$$

align*　その１

Section titled “align*　その１”

式を列挙

{x=ayy=bzzz=c\left\{ \begin{aligned} x &= a\\ yy &= b\\ zzz &= c \end{aligned} \right.
$$
\left\{
\begin{align*}
  x &= a\\
 yy &= b\\
zzz &= c
\end{align*}
\right.
$$

align*　その２

Section titled “align*　その２”
{x=ayy=bzzz=c\left\{ \begin{aligned} & x &= a\\ & yy &= b\\ & zzz &= c \end{aligned} \right.
$$
\left\{
\begin{align*}
  & x   &= a\\
  & yy  &= b\\
  & zzz &= c
\end{align*}
\right.
$$

align*　その３

Section titled “align*　その３”

偶数個目の&はスペースを入れることを利用

{x=ayy=bzzz=c\left\{ \begin{aligned} & x &= &&a\\ & yy &= &&b\\ & zzz &= &&c \end{aligned} \right.
$$
\left\{
\begin{align*}
  & x   &= &&a\\
  & yy  &= &&b\\
  & zzz &= &&c
\end{align*}
\right.
$$

align

Section titled “align”

式に番号付き列挙

{x=ayy=bzzz=c\left\{ \begin{align} x &= a &\\ yy &= b &\\ zzz &= c & \end{align} \right.
$$
\left\{
\begin{align}
  x &= a &\\
  yy &= b &\\
  zzz &= c &
\end{align}
\right.
$$

align + tag

Section titled “align + tag”

式番号を指定して列挙

{x=ay=bz=c\left\{ \begin{align} x &= a & \tag{12} \\ y &= b & \tag{23} \\ z &= c & \tag{33} \\ \end{align} \right.
$$
\left\{
\begin{align}
  x &= a & \tag{12} \\
  y &= b & \tag{23} \\
  z &= c & \tag{33} \\
\end{align}
\right.
$$

equation+aligned

Section titled “equation+aligned”

複数の式でも、まとめて一つの式として番号付け

{x=ay=bz=c\begin{equation} \left\{ \begin{aligned} x &= a\\ y &= b\\ z &= c \end{aligned} \right. \end{equation}
$$
\begin{equation}
\left\{
\begin{aligned}
  x &= a\\
  y &= b\\
  z &= c
\end{aligned}
\right.
\end{equation}
$$

式に番号付き列挙

{x=ay=bz=c\left\{ \begin{align} x &= a &\\ y &= b &\\ z &= c & \end{align} \right.
$$
\left\{
\begin{align}
  x &= a &\\
  y &= b &\\
  z &= c &
\end{align}
\right.
$$

align + tag

Section titled “align + tag”

式番号を指定して列挙

{x=ay=bz=c\left\{ \begin{align} x &= a & \tag{12} \\ y &= b & \tag{23} \\ z &= c & \tag{33} \\ \end{align} \right.
$$
\left\{
\begin{align}
  x &= a & \tag{12} \\
  y &= b & \tag{23} \\
  z &= c & \tag{33} \\
\end{align}
\right.
$$

equation+aligned

Section titled “equation+aligned”

複数の式でも、まとめて一つの式として番号付け

{x=ay=bz=c\begin{equation} \left\{ \begin{aligned} x &= a\\ y &= b\\ z &= c \end{aligned} \right. \end{equation}
$$
\begin{equation}
\left\{
\begin{aligned}
  x &= a\\
  y &= b\\
  z &= c
\end{aligned}
\right.
\end{equation}
$$

カッコ

Section titled “カッコ”
分数には小さい
Section titled “分数には小さい”
(1x+1y)( \frac{1}{x} + \frac{1}{y} )
$$
(
\frac{1}{x} + \frac{1}{y}
t)
$$
全体を覆う
Section titled “全体を覆う”
(1x+1y)\left( \frac{1}{x} + \frac{1}{y} \right)
$$
\left(
\frac{1}{x} + \frac{1}{y}
\right)
$$

定義(\gdef)

Section titled “定義(\gdef)”

同じブロックでないと定義は使えない

dx,ddx,dfdx,dnfdxn \gdef\dd{\mathrm{d}} \gdef\d#1{\frac{\dd}{\dd #1}} \gdef\dv#1#2{\frac{\dd #2}{\dd #1}} \gdef\ndv#1#2#3{\frac{\dd^{#3} #2}{\dd #1^{#3}}} \dd x, \d{x}, \dv{x}{f}, \ndv{x}{f}{n}
$$
    \gdef\dd{\mathrm{d}}
    \gdef\d#1{\frac{\dd}{\dd #1}}
    \gdef\dv#1#2{\frac{\dd #2}{\dd #1}}
    \gdef\ndv#1#2#3{\frac{\dd^{#3} #2}{\dd #1^{#3}}}


    \dd x, \d{x}, \dv{x}{f}, \ndv{x}{f}{n}
$$

rei

Section titled “rei”

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