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---
title: "$\\LaTeX$ 語法筆記"
path: "LaTeX 語法筆記"
---

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{%hackmd @RintarouTW/About %}

> HackMD 是透過 MathJax 支援 $\LaTeX$ ，雖未支援所有語法，對多數人應已足夠，一起把 Web 上醜死的公式換成美美的吧～

# $\LaTeX$ 語法筆記

$$
\LaTeX % 大小寫須正確
$$

\LaTeX % 大小寫須正確

$\textstyle$
$$\displaystyle$$
%comment

$$
\grave apple % 標重音
$$

\grave apple % 標重音

$$
{\bf AB} % 粗體 boldface
$$

{\bf AB} % 粗體 boldface

$$
\bar{A}
$$

\bar{A}

$$
{ a+b \brace c+d }
$$

{ a+b \brace c+d }

$$
\overline{AB}
$$

\overline{AB}

$$
\vec{v}
$$

\vec{v}

$$
\frac{b}{a}
$$

\frac{b}{a}
% 或
{b \over a}

$$
\dfrac{b}{a}
$$

\dfrac{b}{a}  % d for \displaystyle
\tfrac{b}{a}  % t for \textstyle

$$
90^\circ
$$

90^\circ

$$
e^{\theta i}
$$

e^{\theta i}

$$
S_{n}
$$

S_{n}

$$
\lim\limits_{n\to \infty}
$$

\lim\limits_{n\to \infty}

$$
\sum\limits_{x = 0}^k{x^2}
$$

\sum\limits_{x = 0}^k{x^2}

$$
\bigcup\limits_{i = 1}^{\infty}{U_i}
$$

\bigcup\limits_{i = 1}^{\infty}{U_i}

$$
\bigcap\limits_{i = 1}^{\infty}{U_i}
$$

\bigcap\limits_{i = 1}^{\infty}{U_i}

$$
\mathop{\vcenter{\huge\times}}_\limits{i=1}^n{U_i}
$$

\mathop{\vcenter{\huge\times}}_\limits{i=1}^n{U_i}

$$
\int_a^b x^2 \mathrm{d} x
$$

\int_a^b x^2  \mathrm{d} x

$$
\sqrt[n]{1+x+x^2+x^3+\dots+x^n}
$$

\sqrt[n]{1+x+x^2+x^3+\dots+x^n}
% 或
\root n \of {1+x+x^2+x^3+\dots+x^n}

$$
A \implies B
$$

A \implies B

$$
A \impliedby B
$$

A \impliedby B

$$
A \iff B
$$

A \iff B

$$
f: A \to B
$$

f: A \to B

$$
A \leftarrow B
$$

A \leftarrow B

$$
\xrightarrow{中文亦可}\ \xleftarrow{中文亦可}
$$

\xrightarrow{中文亦可}\ \xleftarrow{中文亦可}

$$
a\,\overset{?}{=}\,b
$$

a\,\overset{?}{=}\,b

$$
\forall x \in X, \exists x \in b
$$

\forall x \in X, \exists x \in b

$$
\not\in, \not\gt, \not\lt, \not=
$$

\not\in, \not\gt, \not\lt, \not=   % 利用 \not 組合表示否定

$$
\vert a \vert, \Vert a \Vert
$$

\vert a \vert, \Vert a \Vert % absolute value and norm

$$
a_{1}, a_{2}, \ldots, a_{n}
$$

a_{1}, a_{2}, \ldots, a_{n}

$$
a_{1} + a_{2} + \cdots + a_{n}
$$

a_{1} + a_{2} + \cdots + a_{n}

$$
\begin{pmatrix}
a_{11} & a_{12} & \cdots & a_{1n}\\
a_{21} & a_{22} & \cdots & a_{2n}\\
\vdots & \vdots & \ddots & \vdots\\
a_{m1} & \cdots & \cdots & a_{mn}
\end{pmatrix}
$$

\begin{pmatrix}
  a_{11} & a_{12} & \cdots & a_{1n}\\
  a_{21} & a_{22} & \cdots & a_{2n}\\
  \vdots & \vdots & \ddots & \vdots\\
  a_{m1} & \cdots & \cdots & a_{mn}
\end{pmatrix}

% ldots: low dots
% cdots: center dots
% ddots: diagonal dots
% vdots: vertical dots

$$
\left\{
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \\
a_2x+b_2y+c_2z=d_2 \\
a_3x+b_3y+c_3z=d_3
\end{array}
\right.
$$

\left\{ 
  \begin{array}{c}
    a_1x+b_1y+c_1z=d_1 \\ 
    a_2x+b_2y+c_2z=d_2 \\ 
    a_3x+b_3y+c_3z=d_3
  \end{array}
\right.

$$
\begin{align*}
a + b = 0 \\
a + b + c = 1
\end{align*}
$$

\begin{align*}  # align equations using equal sign
    a + b = 0 \\ # switch line
    a + b + c = 1
\end{align*}

# Operator/Relation

$A\times B$ = A\times B
$a\cdot b$ = a\cdot b
$\div$ = \div
$\pmod n$ = \pmod n
$\pm$ = \pm (plus and minus)
$\partial$ = \partial
$\oplus$ = \oplus
$\&$= \\&
$\gt$ = \gt (greater than)
$\lt$ = \lt (less than)
$\ge$ = \ge (greater or equal)
$\le$ = \le (less or equal)
$\lhd$ = \lhd (normal subgroup)
$\unlhd$ = \unlhd
$\ne$ = \ne (not equal)
$\approx$ = \approx (approximate to)
$\sim$ = \sim (similar)
$\cong$ = \cong (congruent)
$\equiv$ = \equiv (equivalent)
$\ll$ = \ll, much less than
$\gg$ = \gg, much greater than
$\nless$ = \nless, not less than
$\ngtr$ = \ngtr, not greater than
$\cap$ = \cap, 像帽子, intersection
$\cup$ = \cup, 像杯子, union
$\subset$ = \subset, or implied
$\supset$ = \superset, or implies
$\subseteq$ = \subseteq
$\supseteq$ = \supseteq
$\land$ = \land (logical and); \wedge (wedge product)
$\lor$ = \lor (logical or)

[List of Logic Symbols](https://en.wikipedia.org/wiki/List_of_logic_symbols)

# Function

$\binom{a}{b}$ = \binom{a}{b}

>Binomial : $\frac{C!}{n!(n-k)!}, where\ (n+k) = constant$
或 \binom a b
或 { a \choose b }
\tbinom a b (t for \textstyle)
\dbinom a b (d for \displaystyle)

$\cos{\theta}$ = \cos{\theta}
$\sin{\theta}$ = \sin{\theta}
$\log_{b}{x}$ = \log_{b}{x}
$\ln{x}$ = \ln{x}
$\lceil x \rceil$ = \lceil x \rceil
$\lfloor x \rfloor$ = \lfloor x \rfloor

# Matrix

$$
\begin{pmatrix}A\\B\end{pmatrix}
$$

\begin{pmatrix}
  A\\B                % \\ 為 newline(換行)
\end{pmatrix}

% 或

\pmatrix{A\\B}

$$
\begin{bmatrix}A\\B\end{bmatrix}
$$

\begin{bmatrix}
  A\\B
\end{bmatrix}

$$
\begin{vmatrix}A\\B\end{vmatrix}
$$

\begin{vmatrix}
  A\\B
\end{vmatrix}

$$
\begin{Vmatrix}A\\B\end{Vmatrix}
$$

\begin{Vmatrix}
  A\\B
\end{Vmatrix}

$$
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix}
$$

\begin{bmatrix}
  a & b \\
  c & d 
\end{bmatrix}

# Greek
$\alpha$ = \alpha
$\beta$ = \beta
$\Delta$ = \Delta, $\delta$ = \delta
$\epsilon$ = \epsilon, $\varepsilon$ = \varepsilon
$\gamma$ = \gamma
$\theta$ = \theta
$\sigma$ = \sigma
$\pi$ = \pi
$\mu$ = \mu
$\lambda$ = \lambda
$\omega$ = \omega
$\phi$ = \phi
$\varphi$ = \varphi
$\rho$ = \rho

## Blod of Greek
### Default size:
$$
\alpha \quad \beta \quad \gamma
$$

\alpha \quad \beta \quad \gamma

### Using `\boldsymbol{}`
$$
\boldsymbol{\alpha \quad \beta \quad \gamma}
$$

\boldsymbol{\alpha \quad \beta \quad \gamma}

### Using `pmb{}`
$$
\pmb{\alpha \quad \beta \quad \gamma}
$$

\pmb{\alpha \quad \beta \quad \gamma}

###### reference: [How to represent bold greek letters in $\LaTeX$?](https://www.physicsread.com/latex-bold-greek-letters/)

# Misc
$\angle$ = \angle
$\triangle$ = \triangle
$\square$ = \square
$\quad (space)$ = \quad (space)
$\propto$ = \propto (propotional to)

$\because$ = \because
$\therefore$ = \therefore
$\mathbb{Z}$ = \mathbb{Z}
$\mathbb{P}$ = \mathbb{P}
$\mathbb{R}$ = \mathbb{R}
$\mathbb{C}$ = \mathbb{C}
$\Im$ = \Im (Imaginary Space)
$\Re$ = \Re (Real Space)

$\emptyset$ = \emptyset
$\varnothing$ = \varnothing (以此表示空集合較好看)
$\in$ = \in
$\not\in$ = \not\in
$\langle S\rangle$ = \langel S\rangle (generator)
$\chi$ = \chi
$\circlearrowleft$ = \circlearrowleft
$\circlearrowright$ = \circlearrowright
$\curvearrowleft$ = \curvearrowleft
$\curvearrowright$ = \curvearrowright
$\hbar$ = \hbar (Planck's Constant)

https://oeis.org/wiki/List_of_LaTeX_mathematical_symbols#Set_and.2For_logic_notation

# Format

## Style

$$
\style{background-color:#eeeeee}{\frac{x+1}{y+2}}
$$

\style{background-color:#eeeeee}{\frac{x+1}{y+2}}  % 直接以 CSS 改變 style

$$
f(x) = a{\color{red}{x}} + b
$$

f(x) = a{\color{red}{x}} + b
% 或
f(x) = a{\color{#ff0000}{x}} + b

$$
\require{color}
\colorbox{#eeeeee}{Color Box}
$$

\require{color}
\colorbox{#eeeeee}{Color Box}

$$
{\cal ABCDE12345abcde}
$$

{\cal ABCDE12345abced} % callgraphic mode

$$
\fbox{boxed text}
$$

\fbox{boxed text}      % in textstyle

$$
\boxed{boxed\ text}
$$

\boxed{boxed\ text}    % in displaystyle

$$
\text{text $E=mc^2$}
$$

\text{text $E=mc^2$}

$$
{\frak ABCDE12345abcde}
$$

{\frak ABCDE12345abcde}

$$
{\it abefg12345}\ abcdefg12345
$$

{\it abefg12345}\ abcdefg12345   % italic

$$
\min\limits_{n}
$$

\min\limits_{n}

If you want to represent bold greek letters.
[link for Blod of Greek](#Blod-of-Greek)

## Automatic Sizing

$$
\{x \mid x\gt 1\}\text{ 與 }\{x | x\gt 1\}
$$

\{x \mid x\gt 1\}     % 請用 \mid 寫 Set 才好看

$$
\left( \dfrac{x^2}{y^3} \right)
$$

\left(\dfrac{x^2}{y^3}\right)

$$
\left\{ \dfrac{1}{2} \right\}
$$

\left\{ \dfrac{1}{2} \right\}

$$
f(x) = \left\{
\begin{array}{r}
x + by = c \\
dx + ey = f
\end{array}
\right.
$$

f(x) = \left\{
\begin{array}{r}
   x + by = c \\
  dx + ey = f 
\end{array}
\right.

% {r} for right alignment within array
% {l} for left alignment within array
% 或

\array{
   x + by = c \\
  dx + ey = f 
}

$$
z = \overbrace{
\underbrace{x}_\text{real} + i
\underbrace{y}_\text{imaginary}
}^\text{complex number}
$$

z = \overbrace{
    \underbrace{x}_\text{real} + i
    \underbrace{y}_\text{imaginary}
}^\text{complex number}

## Alignment

$$
\begin{aligned}
f(x) &= ax + by + cz + d \\
&= 2x + 3y + 5z + 1
\end{aligned}
$$

\begin{aligned}
f(x) &= ax + by + cz + d \\
     &= 2x + 3y + 5z + 1
\end{aligned}

% 或

\begin{align}
f(x) &= ax + by + cz + d \\
     &= 2x + 3y + 5z + 1
\end{align}

% 或

\eqalign{
f(x) &= ax + by + cz + d \\
     &= 2x + 3y + 5z + 1
}

$$
\begin{align}
a_{1} + b_{1} &= c_{1} \\
a_{2} + b_{2} &= c_{2} \\
&\vdots \\
a_{10} + b_{10} &= c_{10}
\end{align}
$$

\begin{align}
    a_{1} + b_{1} &= c_{1} \\
    a_{2} + b_{2} &= c_{2} \\
    &\vdots  \\
    a_{10} + b_{10} &= c_{10}
\end{align}

$$
\begin{cases}n/2, & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd}
\end{cases}
$$

\begin{cases}
  n/2, & \text{if $n$ is even} \\
  3n+1, & \text{if $n$ is odd}
\end{cases}

% 或

\cases{
  n/2, & \text{if $n$ is even} \\
  3n+1, & \text{if $n$ is odd}
}

$$
\begin{pmatrix}
aaa & bbb \\
cc & dd
\end{pmatrix}
$$

\begin{pmatrix}
 aaa & bbb \\
 cc & dd
\end{pmatrix}

$$
\begin{matrix}
xxxxxx & xxxxxx & xxxxxx \cr
ab & \hfil ab & ab\hfil \cr
\end{matrix}
$$

\begin{matrix}
  xxxxxx & xxxxxx & xxxxxx \cr
  ab & \hfil ab & ab\hfil \cr    % 以 \hfil 自動填空
\end{matrix}

$$
\begin{array}{rrrrrr|r}
& x_1 & x_2 & s_1 & s_2 & s_3 & \\ \hline
s_1 & 0 & 1 & 1 & 0 & 0 & 8 \\
s_2 & 1 & -1 & 0 & 1 & 0 & 4 \\
s_3 & 1 & 1 & 0 & 0 & 1 & 12 \\ \hline
& -1 & -1 & 0 & 0 & 0 & 0
\end{array}
$$

\begin{array}{rrrrrr|r}
       & x_1 & x_2 & s_1 & s_2 & s_3 &    \\ \hline
   s_1 &   0 &   1 &   1 &   0 &   0 &  8 \\
   s_2 &   1 &  -1 &   0 &   1 &   0 &  4 \\
   s_3 &   1 &   1 &   0 &   0 &   1 & 12 \\ \hline
       &  -1 &  -1 &   0 &   0 &   0 &  0
\end{array}

# Advanced

$$
\overset{上組合技}{\implies} 或\underset{下組合技}{\impliedby}
$$

\overset{上組合技}{\implies} 或 \underset{下組合技}{\impliedby}

$$
\require{extpfeil}
x\xtofrom[f^{-1}]{f} y
$$

\require{extpfeil}
x \xtofrom[f^{-1}]{f} y

$$
\require{mhchem}
x \xrightleftharpoons[f^{-1}]{f} y
$$

\require{mhchem}
x \xrightleftharpoons[f^{-1}]{f} y

$$
\require{ams}
\begin{equation}
\tag{1}\label{eq:eq_1} E = mc^2
\end{equation}
$$

\require{ams}
\begin{equation}
   \tag{1}\label{eq:eq_1} E = mc^2 
\end{equation}
% MathJax 照理說已支援 Auto Number，但 HackMD 不支援。
% 只能手動自己加 \tag{1}\label{eq:equation_name}

$$
reference\ equation\eqref{eq:eq_1}
$$

reference\ equation\eqref{eq:eq_1}

$$
\begin{equation*}
E = mc^2
\end{equation*}
$$

\begin{equation*}
  E = mc^2
\end{equation*}
% 不加入 Auto Number，但在 HackMD 上沒差別。

$$
\def \kton{\sum\limits_{k=0}^{n}}
\begin{aligned}
(1+\frac{1}{n})^n &= \kton \binom{n}{k}1^{n-k}(\frac{1}{n})^{k}\\
&= \kton \binom{n}{k} \frac{1}{n^{k}}\\
&= \kton \frac{n!}{k!(n-k)!}\times\frac{1}{n^k}\\
&= \kton \frac{1}{k!} \frac{\overbrace{n(n-1)(n-2)\ldots(n-k+1)}^{共\ k\ 項}}{n^k}\\
&= \kton \frac{1}{k!} (\frac{n}{n}\frac{n-1}{n}\cdots\frac{n-k+1}{n})
\end{aligned}
$$

% 若命令又長又重複，可用 \def 自訂

\def \kton{\sum\limits_{k=0}^{n}}
\begin{aligned}
  (1+\frac{1}{n})^n &= \kton \binom{n}{k}1^{n-k}(\frac{1}{n})^{k}\\
  &= \kton \binom{n}{k} \frac{1}{n^{k}}\\
  &= \kton \frac{n!}{k!(n-k)!}\times\frac{1}{n^k}\\
  &= \kton \frac{1}{k!} \frac{\overbrace{n(n-1)(n-2)\ldots(n-k+1)}^{共\ k\ 項}}{n^k}\\
  &= \kton \frac{1}{k!} (\frac{n}{n}\frac{n-1}{n}\cdots\frac{n-k+1}{n})
\end{aligned}

$$
\DeclareMathOperator {\total}{總計}
\total_a^b(x)
$$

\DeclareMathOperator {\total}{總計}
\total_a^b(x)
% 自訂 Operator，命名限 [a-z|A-Z]，不可含數字。

$$
x_{ij} = A_{i}X_{j} + b_{i} ~~~~~~~~~~~~~~~ i=1 \ldots m; ~~ j = 1 \ldots n
$$

% 加入多個空格在數學公式後面
x_{ij} = A_{i}X_{j} + b_{i} ~~~~~~~~~~~~~~~ i=1 \ldots m; ~~ j = 1 \ldots n

## 微調字體、字距

### Font

$$
\mathbb{ABCDE12345abcde}
$$

\mathbb - Used to turn on blackboard-bold for uppercase letters and lowercase 'k'.

$$
\mathbf{ABCDE12345abcde}
$$

\mathbf - Used to turn on boldface for uppercase and lowercase letters and digits.

$$
\mathit{ABCDE12345abcde}
$$

\mathit - forces the math italic mode.

$$
\mathcal{ABCDE12345abcde}
$$

\mathcal - Used to turn on calligraphic font for uppercase letters and digits.

$$
\mathfrak{ABCDE12345abcde}
$$

\mathfrak - turn on fraktur font for uppercase and lowercase letters and digits (and a few other characters).

$$
\mathrm{ABCDE12345abcde}
$$

\mathrm - Used to turn on roman typestyle for uppercase and lowercase letters.

$$
\mathscr{ABCDE12345abcde}
$$

\mathscr - Used to turn on script typestyle for uppercase letters. If lowercase script letters are not available, then they are typeset in a roman typestyle.

$$
\mathsf{ABCDE12345abcde}
$$

\mathsf - Used to turn on sans serif typestyle for uppercase and lowercase letters and digits; also affects uppercase greek.

$$
\mathtt{ABCDE12345abcde}
$$

\mathtt - Used to turn on typewriter typestyle for uppercase and lowercase letters and digits.

$$
\oldstyle{ABCDE12345abcde}
$$

\oldstyle - Used to turn on oldstyle font.

If you want to represent bold greek letters.
[link for Blod of Greek](#Blod-of-Greek)

### Operator (Class Assignment)

\mathord - forces the argument to be treated in the 'ordinary' class.
\mathrel - forces the argument to be treated in the 'relation' class.
\mathinner - forces the argument to appear 'inside' other formulas, and should be surrounded by additional space in certain circumstances.
\mathbin - Used to give the correct spacing to make an object into a binary operator.
\mathstrut - Used to achieve more uniform appearance in adjacent formulas as an invisible box whose width is zero.
\mathpunct
\mathopen
\mathclose
\mathop

\mathxxx{argument}

\mathchoice - provides content that is dependent on the current style (display, text, script, or scriptscript).

\mathchoice{D}{T}{S}{SS}

# More
* https://en.wikibooks.org/wiki/LaTeX/Mathematics
* https://en.wikibooks.org/wiki/LaTeX/Advanced_Mathematics#Custom_operators
* https://en.wikibooks.org/wiki/LaTeX/Mathematics#Adding_text_to_equations
* [MathJax Tutorial](https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference)
* https://tex.stackexchange.com/
* [手寫辨認查詢](http://detexify.kirelabs.org/classify.html)
* [MathJax Commands](http://docs.mathjax.org/en/latest/input/tex/macros/index.html)
* [LaTeX Arrows](https://www.sascha-frank.com/Arrow/latex-arrows.html)
* https://en.wikipedia.org/wiki/List_of_logic_symbols
* [$\LaTeX$ for Twitch Chat](https://rintaroutw.github.io/LaTeX4TwitchChat/)

###### tags: `LaTeX`