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title: "

$LaTeX$ 語法筆記"
path: "LaTeX 語法筆記"

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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

$$$$

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

$$LATEX$$

\LaTeX % 大小寫須正確

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

$$\stackrel{`}{a}pple$$

\grave apple % 標重音

$$\mathbf{A}\mathbf{B}$$

{\bf AB} % 粗體 boldface

$$\overline{A}$$

\bar{A}

$$\{\genfrac{}{}{0ex}{}{a+b}{c+d}\}$$

{ a+b \brace c+d }

$$\overline{AB}$$

\overline{AB}

$$\overrightarrow{v}$$

\vec{v}

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

\frac{b}{a}
% 或
{b \over a}

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

\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}

$$\underset{n\to \mathrm{\infty }}{lim}$$

\lim\limits_{n\to \infty}

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

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

$$\bigcup _{i=1}^{\mathrm{\infty }}{U}_i$$

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

$$\bigcap _{i=1}^{\mathrm{\infty }}{U}_i$$

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

$$\underset{i=1}{\overset{n}{\times }}{U}_i$$

\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

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

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

$$A⟹B$$

A \implies B

$$A⟸B$$

A \impliedby B

$$A⟺B$$

A \iff B

$$f:A\to B$$

f: A \to B

$$A\leftarrow B$$

A \leftarrow B

$$\stackrel{\mathrm{中}\mathrm{文}\mathrm{亦}\mathrm{可}}{\to }\stackrel{\mathrm{中}\mathrm{文}\mathrm{亦}\mathrm{可}}{\leftarrow }$$

\xrightarrow{中文亦可}\ \xleftarrow{中文亦可}

$$a\stackrel{?}{=}b$$

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

$$\mathrm{\forall }x\in X,\mathrm{\exists }x\in b$$

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

$$\notin ,\ngtr ,\nless ,\ne$$

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

$$|a|,\Vert a\Vert$$

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

$$a_1,a_2,\dots ,a_n$$

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

$$a_1+a_2+\cdots +a_n$$

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

$$\left(\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{m1}& \cdots & \cdots & a_{mn}\end{array}\right)$$

\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

$$\{\begin{array}{c}{a}_{1}x+b_{1}y+c_{1}z=d_1\\ a_{2}x+b_{2}y+c_{2}z=d_2\\ a_{3}x+b_{3}y+c_{3}z=d_3\end{array}$$

\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.

$$\begin{array}{r}a+b=0\\ a+b+c=1\end{array}$$

\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

$(\mathrm{mod}n)$ = \pmod n

$\pm$ = \pm (plus and minus)

$\partial$ = \partial

$\oplus$ = \oplus

$\mathrm{\&}$= \&

$>$ = \gt (greater than)

$<$ = \lt (less than)

$\ge$ = \ge (greater or equal)

$\le$ = \le (less or equal)

$⊲$ = \lhd (normal subgroup)

$⊴$ = \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

$\wedge$ = \land (logical and); \wedge (wedge product)

$\vee$ = \lor (logical or)

List of Logic Symbols

Function

$(\genfrac{}{}{0ex}{}{a}{b})$ = \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

$$\left(\begin{array}{c}A\\ B\end{array}\right)$$

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

% 或

\pmatrix{A\\B}

$$\left[\begin{array}{c}A\\ B\end{array}\right]$$

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

$$\left|\begin{array}{c}A\\ B\end{array}\right|$$

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

$$\Vert \begin{array}{c}A\\ B\end{array}\Vert$$

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

$$\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$$

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

Greek

$\alpha$ = \alpha

$\beta$ = \beta

$\mathrm{\Delta }$ = \Delta,

$\delta$ = \delta

$ϵ$ = \epsilon,

$\epsilon$ = \varepsilon

$\gamma$ = \gamma

$\theta$ = \theta

$\sigma$ = \sigma

$\pi$ = \pi

$\mu$ = \mu

$\lambda$ = \lambda

$\omega$ = \omega

$\varphi$ = \phi

$\phi$ = \varphi

$\rho$ = \rho

Blod of Greek

Default size:

$$\alpha \beta \gamma$$

\alpha \quad \beta \quad \gamma

Using \boldsymbol{}

$$\text{boldsymbol}\alpha \beta \gamma$$

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

Using pmb{}

$$\alpha \beta \gamma \alpha \beta \gamma$$

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

reference: How to represent bold greek letters in

$LATEX$?

Misc

$\mathrm{\angle }$ = \angle

$\mathrm{△}$ = \triangle

$◻$ = \square

$(space)$ = \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}

$\mathrm{\Im }$ = \Im (Imaginary Space)

$\mathrm{\Re }$ = \Re (Real Space)

$\mathrm{\varnothing }$ = \emptyset

$\varnothing$ = \varnothing (以此表示空集合較好看)

$\in$ = \in

$\notin$ = \not\in

$⟨S⟩$ = \langel S\rangle (generator)

$\chi$ = \chi

$\circlearrowleft$ = \circlearrowleft

$\circlearrowright$ = \circlearrowright

$\curvearrowleft$ = \curvearrowleft

$\curvearrowright$ = \curvearrowright

$\hslash$ = \hbar (Planck's Constant)

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

Format

Style

$$\text{You can't use 'macro parameter character \#' in math mode}$$

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

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

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

$$\text{You can't use 'macro parameter character \#' in math mode}$$

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

$$\mathcal{A}\mathcal{B}\mathcal{C}\mathcal{D}\mathcal{E}\mathcal{12345}\mathcal{a}\mathcal{b}\mathcal{c}\mathcal{d}\mathcal{e}$$

{\cal ABCDE12345abced} % callgraphic mode

$$\boxed{\text{boxed text}}$$

\fbox{boxed text}      % in textstyle

$$\boxed{{\displaystyle boxedtext}}$$

\boxed{boxed\ text}    % in displaystyle

$$\text{text }E=m{c}^2$$

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

$$\mathfrak{A}\mathfrak{B}\mathfrak{C}\mathfrak{D}\mathfrak{E}\mathfrak{12345}\mathfrak{a}\mathfrak{b}\mathfrak{c}\mathfrak{d}\mathfrak{e}$$

{\frak ABCDE12345abcde}

$$\mathit{a}\mathit{b}\mathit{e}\mathit{f}\mathit{g}\mathit{12345}abcdefg12345$$

{\it abefg12345}\ abcdefg12345   % italic

$$\underset{n}{min}$$

\min\limits_{n}

If you want to represent bold greek letters.
link for Blod of Greek

Automatic Sizing

$$\{x\mid x>1\}\text{ 與 }\{x|x>1\}$$

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

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

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

$$\left\{{\displaystyle \frac{1}{2}}\right\}$$

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

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

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 
}

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

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

Alignment

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

\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
}

$$\begin{array}{rl}{a}_1+b_1& =c_1\\ a_2+b_2& =c_2\\ & ⋮\\ a_{10}+b_{10}& =c_{10}\end{array}$$

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

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

\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}
}

$$\left(\begin{array}{cc}aaa& bbb\\ cc& dd\end{array}\right)$$

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

$$\begin{array}{ccc}xxxxxx& xxxxxx& xxxxxx\\ ab& \hfill ab& ab\hfill \end{array}$$

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

$$\begin{array}{rrrrrrr}& x_1& x_2& s_1& s_2& s_3& \\ s_1& 0& 1& 1& 0& 0& 8\\ s_2& 1& -1& 0& 1& 0& 4\\ s_3& 1& 1& 0& 0& 1& 12\\ & -1& -1& 0& 0& 0& 0\end{array}$$

\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

$$\stackrel{\mathrm{上}\mathrm{組}\mathrm{合}\mathrm{技}}{⟹}\mathrm{或}\underset{\mathrm{下}\mathrm{組}\mathrm{合}\mathrm{技}}{⟸}$$

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

$$x\text{xtofrom}[f^{-1}]fy$$

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

$$x\text{xrightleftharpoons}[f^{-1}]fy$$

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

$$\text{Label 'eq:eq\_1' multiply defined}$$

\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}

$$referenceequation\text{(1)}$$

reference\ equation\eqref{eq:eq_1}

$$E=m{c}^2$$

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

$$\begin{array}{rl}(1+\frac{1}{n}{)}^n& =\sum _{k=0}^n(\genfrac{}{}{0ex}{}{n}{k})1^{n-k}(\frac{1}{n}{)}^k\\ & =\sum _{k=0}^n(\genfrac{}{}{0ex}{}{n}{k})\frac{1}{n^k}\\ & =\sum _{k=0}^n\frac{n!}{k!(n-k)!}\times \frac{1}{n^k}\\ & =\sum _{k=0}^n\frac{1}{k!}\frac{\stackrel{\mathrm{共}k\mathrm{項}}{\overbrace{n(n-1)(n-2)\dots (n-k+1)}}}{n^k}\\ & =\sum _{k=0}^n\frac{1}{k!}(\frac{n}{n}\frac{n-1}{n}\cdots \frac{n-k+1}{n})\end{array}$$

% 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}

$${\mathrm{總}\mathrm{計}}_a^b(x)$$

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

$$x_{ij}=A_i{X}_j+b_{i}i=1\dots m;j=1\dots n$$

% 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

$$\mathbb{ABCDE}\mathbb{12345}\mathbb{abcde}$$

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

$$\mathbf{ABCDE}\mathbf{12345}\mathbf{abcde}$$

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

$$\mathit{ABCDE}\mathit{12345}\mathit{abcde}$$

\mathit - forces the math italic mode.

$$\mathcal{ABCDE}\mathcal{12345}\mathcal{abcde}$$

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

$$\mathfrak{ABCDE}\mathfrak{12345}\mathfrak{abcde}$$

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

$$\mathrm{ABCDE}12345\mathrm{abcde}$$

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

$$\mathcal{ABCDE}\mathcal{12345}\mathcal{abcde}$$

\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.

$$\mathsf{ABCDE}\mathsf{12345}\mathsf{abcde}$$

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

$$\mathtt{ABCDE}\mathtt{12345}\mathtt{abcde}$$

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

$$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}\mathrm{E}\mathrm{12345}\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}\mathrm{e}$$

\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