{%hackmd sMV2zv-CTsuIqnpb0hZLmA %} <style> .markdown-body pre { background-color: #1e1e1e !important; border: 1px solid #555 !important; color: #dfdfdf; } </style> --- title: "$\\LaTeX$ 語法筆記" path: "LaTeX 語法筆記" --- :::info 此頁歡迎共筆。 ::: <img src="https://rintaroutw.github.io/fsg/test/Flag_of_the_Republic_of_China.svg" width="300" height="200"></img> {%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`
Last changed by  
 
愚千慮
50367

Read more

HackMD 筆記

HackMD 筆記 Book Graphviz digraph { graph [bgcolor=transparent]; node[fontcolor="#888888";color="#888888"]; edge [color="#888800"]; a->b; a->c;

1/25/2024
HackMD Custom Header and Style

學海無涯，思境無維；數乃六藝，理之始也。或有一得足矣

8/24/2023
Dark Theme

8/24/2023
Heron's Formula

{%hackmd @RintarouTW/About %} $$ \cases{ b^2=h^2+d^2\ a^2=h^2+(c-d)^2 }\ a^2-b^2=c^2-2cd\ d=\frac{b^2+c^2-a^2}{2c} $$

10/17/2021
Read more from 愚千慮
Published on HackMD