title: "\(\\LaTeX\) 語法筆記" path: "LaTeX 語法筆記"

學海無涯，思境無維；數乃六藝，理之始也。 或有一得足矣 愚千慮

\[ \require{newcommand} \newcommand{\bmatrix}[1] {\begin{bmatrix}#1\end{bmatrix}} \newcommand{\vmatrix}[1] {\begin{vmatrix}#1\end{vmatrix}} \]

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

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 \(\LaTeX\)?

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

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

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://tex.stackexchange.com/
• 手寫辨認查詢
• MathJax Commands
• LaTeX Arrows
• https://en.wikipedia.org/wiki/List_of_logic_symbols
• \(\LaTeX\) for Twitch Chat

tags: LaTeX