$\LaTeX$ 語法筆記

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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

\[\LaTeX % 大小寫須正確\] 
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\LaTeX % 大小寫須正確

$\textstyle$
$$\displaystyle$$
%comment
\[\grave apple % 標重音\] 
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\grave apple % 標重音
\[{\bf AB} % 粗體 boldface\] 
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{\bf AB} % 粗體 boldface
\[\bar{A}\] 
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\bar{A}
\[{ a+b \brace c+d }\] 
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{ a+b \brace c+d }
\[\overline{AB}\] 
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\overline{AB}
\[\vec{v}\] 
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\vec{v}
\[\frac{b}{a}\] 
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\frac{b}{a}
% 或
{b \over a}
\[\dfrac{b}{a}\] 
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\dfrac{b}{a}  % d for \displaystyle
\tfrac{b}{a}  % t for \textstyle
\[90^\circ\] 
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90^\circ
\[e^{\theta i}\] 
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e^{\theta i}
\[S_{n}\] 
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S_{n}
\[\lim\limits_{n\to \infty}\] 
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\lim\limits_{n\to \infty}
\[\sum\limits_{x = 0}^k{x^2}\] 
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\sum\limits_{x = 0}^k{x^2}
\[\bigcup\limits_{i = 1}^{\infty}{U_i}\] 
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\bigcup\limits_{i = 1}^{\infty}{U_i}
\[\bigcap\limits_{i = 1}^{\infty}{U_i}\] 
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\bigcap\limits_{i = 1}^{\infty}{U_i}
\[\mathop{\vcenter{\huge\times}}_\limits{i=1}^n{U_i}\] 
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\mathop{\vcenter{\huge\times}}_\limits{i=1}^n{U_i}
\[\int_a^b x^2 \mathrm{d} x\] 
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\int_a^b x^2  \mathrm{d} x
\[\sqrt[n]{1+x+x^2+x^3+\dots+x^n}\] 
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\sqrt[n]{1+x+x^2+x^3+\dots+x^n}
% 或
\root n \of {1+x+x^2+x^3+\dots+x^n}
\[A \implies B\] 
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A \implies B
\[A \impliedby B\] 
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A \impliedby B
\[A \iff B\] 
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A \iff B
\[f: A \to B\] 
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f: A \to B
\[A \leftarrow B\] 
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A \leftarrow B
\[\xrightarrow{中文亦可}\ \xleftarrow{中文亦可}\] 
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\xrightarrow{中文亦可}\ \xleftarrow{中文亦可}
\[a\,\overset{?}{=}\,b\] 
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a\,\overset{?}{=}\,b
\[\forall x \in X, \exists x \in b\] 
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\forall x \in X, \exists x \in b

\(\not\in, \not\gt, \not\lt, \not=\)

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\not\in, \not\gt, \not\lt, \not=   % 利用 \not 組合表示否定
\[a_{1}, a_{2}, \ldots, a_{n}\] 
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a_{1}, a_{2}, \ldots, a_{n}
\[a_{1} + a_{2} + \cdots + a_{n}\] 
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a_{1} + a_{2} + \cdots + a_{n}
\[\begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n}? a_{21} & a_{22} & \cdots & a_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ a_{m1} & \cdots & \cdots & a_{mn} \end{pmatrix}\] 
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\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
\[\left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right.\] 
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\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.

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

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

% 或

\pmatrix{A\B}
\[\begin{bmatrix}A\\B\end{bmatrix}\] 
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\begin{bmatrix}
  A\B
\end{bmatrix}
\[\begin{vmatrix}A\\B\end{vmatrix}\] 
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\begin{vmatrix}
  A\B
\end{vmatrix}
\[\begin{Vmatrix}A\\B\end{Vmatrix}\] 
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\begin{Vmatrix}
  A\B
\end{Vmatrix}
\[\begin{bmatrix} a & b \\ c & d \end{bmatrix}\] 
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\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

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

\[\style{background-color:#eeeeee}{\frac{x+1}{y+2}}\] 
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\style{background-color:#eeeeee}{\frac{x+1}{y+2}}  % 直接以 CSS 改變 style
\[f(x) = a{\color{red}{x}} + b\] 
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f(x) = a{\color{red}{x}} + b
% 或
f(x) = a{\color{#ff0000}{x}} + b
\[\require{color} \colorbox{#eeeeee}{Color Box}\] 
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\require{color}
\colorbox{#eeeeee}{Color Box}
\[{\cal ABCDE12345abcde}\] 
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{\cal ABCDE12345abced} % callgraphic mode
\[\fbox{boxed text}\] 
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\fbox{boxed text}      % in textstyle
\[\boxed{boxed\ text}\] 
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\boxed{boxed\ text}    % in displaystyle

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

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\text{text $E=mc^2$}
\[{\frak ABCDE12345abcde}\] 
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{\frak ABCDE12345abcde}
\[{\it abefg12345}\ abcdefg12345\] 
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{\it abefg12345}\ abcdefg12345   % italic

\(\min\limits_{n}\)

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\min\limits_{n}

Automatic Sizing

\[\{x \mid x\gt 1\}\text{ 與 }\{x | x\gt 1\}\] 
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\{x \mid x\gt 1\}     % 請用 \mid 寫 Set 才好看
\[\left( \dfrac{x^2}{y^3} \right)\] 
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\left(\dfrac{x^2}{y^3}\right)
\[\left\{ \dfrac{1}{2} \right\}\] 
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\left\{ \dfrac{1}{2} \right\}
\[f(x) = \left\{ \begin{array}{r} x + by = c \\ dx + ey = f \end{array} \right.\] 
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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 
}
\[z = \overbrace{ \underbrace{x}_\text{real} + i \underbrace{y}_\text{imaginary} }^\text{complex number}\] 
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z = \overbrace{
    \underbrace{x}_\text{real} + i
    \underbrace{y}_\text{imaginary}
}^\text{complex number}

Alignment

\[\begin{aligned} f(x) &= ax + by + cz + d \\ &= 2x + 3y + 5z + 1 \end{aligned}\] 
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\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
}
\[\begin{cases}n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases}\] 
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\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}
}
\[\begin{pmatrix} aaa & bbb \\ cc & dd \end{pmatrix}\] 
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\begin{pmatrix}
 aaa & bbb \
 cc & dd
\end{pmatrix}
\[\begin{matrix} xxxxxx & xxxxxx & xxxxxx \cr ab & \hfil ab & ab\hfil \cr \end{matrix}\] 
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\begin{matrix}
  xxxxxx & xxxxxx & xxxxxx \cr
  ab & \hfil ab & ab\hfil \cr    % 以 \hfil 自動填空
\end{matrix}
\[\begin{array}{rrrrrr|r} & x_1 & x_2 & s_1 & s_2 & s_3 & \\ \hline s_1 & 0 & 1 & 1 & 0 & 0 & 8 \\ s_2 & 1 & -1 & 0 & 1 & 0 & 4 \\ s_3 & 1 & 1 & 0 & 0 & 1 & 12 \\ \hline & -1 & -1 & 0 & 0 & 0 & 0 \end{array}\] 
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\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

\[\overset{上組合技}{\implies} 或\underset{下組合技}{\impliedby}\] 
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\overset{上組合技}{\implies} 或 \underset{下組合技}{\impliedby}
\[\require{extpfeil} x\xtofrom[f^{-1}]{f} y\] 
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\require{extpfeil}
x \xtofrom[f^{-1}]{f} y
\[\require{mhchem} x \xrightleftharpoons[f^{-1}]{f} y\] 
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\require{mhchem}
x \xrightleftharpoons[f^{-1}]{f} y
\[\require{ams} \begin{equation} \tag{1}\label{eq:eq_1} E = mc^2 \end{equation}\] 
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\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}
\[reference\ equation\eqref{eq:eq_1}\] 
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reference\ equation\eqref{eq:eq_1}
\[\begin{equation*} E = mc^2 \end{equation*}\] 
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\begin{equation*}
  E = mc^2
\end{equation*}
% 不加入 Auto Number，但在 HackMD 上沒差別。
\[\def \kton{\sum\limits_{k=0}^{n}} \begin{aligned} (1+\frac{1}{n})^n &= \kton \binom{n}{k}1^{n-k}(\frac{1}{n})^{k}\\ &= \kton \binom{n}{k} \frac{1}{n^{k}}\\ &= \kton \frac{n!}{k!(n-k)!}\times\frac{1}{n^k}\\ &= \kton \frac{1}{k!} \frac{\overbrace{n(n-1)(n-2)\ldots(n-k+1)}^{共\ k\ 項}}{n^k}\\ &= \kton \frac{1}{k!} (\frac{n}{n}\frac{n-1}{n}\cdots\frac{n-k+1}{n}) \end{aligned}\] 
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% 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}
\[\DeclareMathOperator {\total}{總計} \total_a^b(x)\] 
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\DeclareMathOperator {\total}{總計}
\total_a^b(x)
% 自訂 Operator，命名限 [a-z|A-Z]，不可含數字。

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.

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

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\mathxxx{argument}

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

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

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tags: LaTeX