LaTeX 数学公式
LaTeX 数学公式
写了这么久 latex 数学公式，一直翻几个文档看有点麻烦，干脆自己做一个文档好了。
目前用的最多的就是这个 LaTeX-Math-Symbols.pdf ，不知道是什么人做的，反正好用就行。
然后我用的编辑器是 Typora 1.14.10 ，好像是 Mathjax v3 ，不过本站目前使用的是 Mathjax v2.7.7。
本站 md 生成器为 "hexo-renderer-pandoc": "^0.5.0"
，参数为 --mathjax ，即 mathjax 负责渲染。
本文只讲怎么使用 latex 书写数学公式，不讲怎么使用 latex 写各种文档，因为我自己不怎么会。
推荐采用以下方式写公式，这是最不容易出问题的写法，不听建议后果自负。
% 行内公式推荐按下面的写法，也就是 $公式$ ，不要有多余空格，并且推荐公式两侧适当加空格
根据 $a^2 + b^2 = c^2$ 我们可以得出……
% 行间公式推荐按下面的风格写，至少我用的 Typora 和 hexo-renderer-pandoc 是完全没问题的
$$
\mathrm{Ans} = \sum_{p=0}^k(-1)^p \sum_A\binom{k + r - 1 - \sum_A n_{A_i}-p}{k-1}
$$上面那段行间公式效果如下 \[ \mathrm{Ans} = \sum_{p=0}^k(-1)^p \sum_A\binom{k + r - 1 - \sum_A n_{A_i}-p}{k-1} \]
当然你写下面这样有时候也是可以的，只不过效果可能会有点区别，不推荐。
$$\mathrm{Ans} = \sum_{p=0}^k(-1)^p \sum_A\binom{k + r - 1 - \sum_A n_{A_i}-p}{k-1}$$效果如下（在 Typora 上会靠左对齐，而且会采用行内公式的效果，不过本站倒是没区别）
\[\mathrm{Ans} = \sum_{p=0}^k(-1)^p \sum_A\binom{k + r - 1 - \sum_A n_{A_i}-p}{k-1}\]
然后如果你需要行内公式和行间公式的效果一样，可以用
\displaystyle 和 \textstyle 来控制
比如行内公式版本的行间公式 \[ \textstyle \mathrm{Ans} = \sum_{p=0}^k(-1)^p \sum_A\binom{k + r - 1 - \sum_A n_{A_i}-p}{k-1} \]
$$
\textstyle \mathrm{Ans} = \sum_{p=0}^k(-1)^p \sum_A\binom{k + r - 1 - \sum_A n_{A_i}-p}{k-1}
$$以及行间公式版本的行内公式 \(\displaystyle \mathrm{Ans} = \sum_{p=0}^k(-1)^p \sum_A\binom{k + r - 1 - \sum_A n_{A_i}-p}{k-1}\)
$\displaystyle \mathrm{Ans} = \sum_{p=0}^k(-1)^p \sum_A\binom{k + r - 1 - \sum_A n_{A_i}-p}{k-1}$至于这段公式是干什么，只是随便找了篇文章 copy 了一个公式而已。
另外感谢可爱大肥鱼（DeepSeek）对编写本文的支持，这么多全靠手打肯定是不可能的。
若不是你突然闯进我生活～我怎会把死守的寂寞放任了～
那么就开始吧～
一、希腊字母和希伯来字母
这个表并不是按希腊字母顺序排序的，稍微有一点点乱。
| \(\alpha\) | \alpha |
\(\kappa\) | \kappa |
\(\psi\) | \psi |
\(\digamma\) | \digamma |
\(\Delta\) | \Delta |
\(\Theta\) | \Theta |
| \(\beta\) | \beta |
\(\lambda\) | \lambda |
\(\rho\) | \rho |
\(\varepsilon\) | \varepsilon |
\(\Gamma\) | \Gamma |
\(\Upsilon\) | \Upsilon |
| \(\chi\) | \chi |
\(\mu\) | \mu |
\(\sigma\) | \sigma |
\(\varkappa\) | \varkappa |
\(\Lambda\) | \Lambda |
\(\Xi\) | \Xi |
| \(\delta\) | \delta |
\(\nu\) | \nu |
\(\tau\) | \tau |
\(\varphi\) | \varphi |
\(\Omega\) | \Omega |
||
| \(\epsilon\) | \epsilon |
\(o\) | o |
\(\theta\) | \theta |
\(\varpi\) | \varpi |
\(\Phi\) | \Phi |
\(\aleph\) | \aleph |
| \(\eta\) | \eta |
\(\omega\) | \omega |
\(\upsilon\) | \upsilon |
\(\varrho\) | \varrho |
\(\Pi\) | \Pi |
\(\beth\) | \beth |
| \(\gamma\) | \gamma |
\(\phi\) | \phi |
\(\xi\) | \xi |
\(\varsigma\) | \varsigma |
\(\Psi\) | \Psi |
\(\daleth\) | \daleth |
| \(\iota\) | \iota |
\(\pi\) | \pi |
\(\zeta\) | \zeta |
\(\vartheta\) | \vartheta |
\(\Sigma\) | \Sigma |
\(\gimel\) | \gimel |
其中 \(o\) 即 Omicron 在标准 LaTeX
里并没有，直接用字母 o 替代就可以了，外观一模一样。
大写希腊字母比如大写的 Alpha 直接用字母 A
就行了，外观一模一样。
注意这个表格里有 \(\phi\) 和 \(\varphi\) 两种风格的写法，也就是印刷体和常用手写体的差异。
二、latex 数学构造（分数、根号等）
| \(\frac{abc}{xyz}\) | \frac{abc}{xyz} |
\(\overline{a b c}\) | \overline{abc} |
\(\overrightarrow{a b c}\) | \overrightarrow{abc} |
| \(f^{\prime}\) | f'或f^{\prime} |
\(\underline{a b c}\) | \underline{abc} |
\(\overleftarrow{abc}\) | \overleftarrow{abc} |
| \(\sqrt{abc}\) | \sqrt{abc} |
\(\widehat{a b c}\) | \widehat{abc} |
\(\overbrace{abc}\) | \overbrace{abc} |
| \(\sqrt[n]{abc}\) | \sqrt[n]{abc} |
无 | \widetilde{abc} |
\(\underbrace{abc}\) | \underbrace{abc} |
其中 \widetilde{abc} 我这里渲染不了，就是在 \(abc\) 上面画一个 \(\sim\) 一样的东西。
小号和大号分数
分数还可以用 \dfrac{abc}{xyz} 来写大号的分数，行内效果为
\(\dfrac{abc}{xyz}\) 。
行间公式和 \frac
在多数情况下是一样的，除了分数套分数，可以看看下面这段对比 \[
\dfrac{abc}{xyz} \quad\frac{abc}{xyz}
\\[6pt]\frac{\dfrac{1}{2}}{3} \quad \frac{\frac{1}{2}}{3}
\\[6pt]\frac{\displaystyle \frac{1}{2}}{3} \quad \frac{\frac{1}{2}}{3}
\] 源码如下
\dfrac{abc}{xyz} \quad\frac{abc}{xyz}
\\[6pt]\frac{\dfrac{1}{2}}{3} \quad \frac{\frac{1}{2}}{3}
\\[6pt]\frac{\displaystyle \frac{1}{2}}{3} \quad \frac{\frac{1}{2}}{3}为文本上下的大括号添加文本
如果你需要在 \(\underbrace{abc}\)
这样的东西大括号下加上文本，可以用下面这样的写法（原理是通过
array 控制对齐） \[
\begin{array}{c}\underbrace{1+2+\cdots+100}\\5050\end{array}
\]
\begin{array}{c}\underbrace{1+2+\cdots+100}\\5050\end{array}或者还有一种兼容性不是很好的写法如下 \[ \underset{5050}{\underbrace{1+2+\cdots+100}} \]
\underset{5050}{\underbrace{1+2+\cdots+100}}反过来也行 \[ \overset{5050}{\overbrace{1+2+\cdots+100}} \]
\overset{5050}{\overbrace{1+2+\cdots+100}}小号和大号组合数
可以使用 \binom 和 \dbinom
书写下面这样的组合数，和大小号分数是一个原理
范德蒙德卷积公式 (Vandermonde’s Identity) \[ \sum_{k=0}^r\binom{n}{k}\binom{m}{r-k}=\binom{n+m}{r} \] 源码如下
\sum_{k=0}^r\binom{n}{k}\binom{m}{r-k}=\binom{n+m}{r}当然你也可以用 array 来写，就是好像在 Mathjax v3 下显示的会非常奇怪，不推荐 \[ \sum_{k=0}^{r} \left(\begin{array}{c} n \\ k \end{array}\right) \left(\begin{array}{c} m \\ r-k \end{array}\right) =\left(\begin{array}{c} n+m \\ r \end{array}\right) \]
\sum_{k=0}^{r}
\left(\begin{array}{c} n \\ k \end{array}\right)
\left(\begin{array}{c} m \\ r-k \end{array}\right)
=\left(\begin{array}{c} n+m \\ r \end{array}\right)不过我用那个 Mathpix Snip
扫出来经常给我这个形式，这个就很尴尬，还有现在有大肥鱼DeepSeek
。
三、分隔符（括号、绝对值等）
| \(|\) | | |
\(\{\) | \{ |
\(\lfloor\) | \lfloor |
\(/\) | / |
\(\Uparrow\) | \Uparrow |
\(\llcorner\) | \llcorner |
| \(\vert\) | \vert |
\(\}\) | \} |
\(\rfloor\) | \rfloor |
\(\backslash\) | \backslash |
\(\uparrow\) | \uparrow |
\(\lrcorner\) | \lrcorner |
| \(\|\) | \| |
\(\langle\) | \langle |
\(\lceil\) | \lceil |
\([\) | [ |
\(\Downarrow\) | \Downarrow |
\(\ulcorner\) | \ulcorner |
| \(\Vert\) | \Vert |
\(\rangle\) | \rangle |
\(\rceil\) | \rceil |
\(]\) | ] |
\(\downarrow\) | \downarrow |
\(\urcorner\) | \urcorner |
可以使用 \left 和 \right
来控制这些东西的，比如 \[
\left\{\frac{123}{456}\right\}
\quad \left\lfloor\frac{123}{456}\right\rfloor
\quad \left[\frac{123}{456}\right]
\quad \left[\frac{123}{456}\right.
\quad \left(\frac{123}{456}\right]
\] 源码如下
\left\{\frac{123}{456}\right\}
\quad \left\lfloor\frac{123}{456}\right\rfloor
\quad \left[\frac{123}{456}\right]
\quad \left[\frac{123}{456}\right.
\quad \left(\frac{123}{456}\right]四、大小可变的符号（求和、积分等）
| \(\sum \displaystyle\sum\) | \sum |
\(\int \displaystyle \int\) | \int |
\(\biguplus \displaystyle\biguplus\) | \biguplus |
\(\bigoplus\displaystyle\bigoplus\) | \bigoplus |
\(\bigvee \displaystyle\bigvee\) | \bigvee |
| \(\prod \displaystyle\prod\) | \prod |
\(\oint \displaystyle\oint\) | \oint |
\(\bigcap \displaystyle\bigcap\) | \bigcap |
\(\bigotimes \displaystyle\bigotimes\) | \bigotimes |
\(\bigwedge \displaystyle\bigwedge\) | \bigwedge |
| \(\coprod \displaystyle\coprod\) | \coprod |
\(\iint \displaystyle \iint\) | \iint |
\(\bigcup\displaystyle\bigcup\) | \bigcup |
\(\bigodot \displaystyle\bigodot\) | \bigodot |
\(\bigsqcup\displaystyle\bigsqcup\) | \bigsqcup |
大小变化取决于行内还是行间公式，不过可以使用
\displaystyle 和 \textstyle 来手动控制。
五、标准函数名称（sin、cos等）
| \(\arccos\) | \arccos |
\(\arcsin\) | \arcsin |
\(\arctan\) | \arctan |
\(\arg\) | \arg |
| \(\cos\) | \cos |
\(\cosh\) | \cosh |
\(\cot\) | \cot |
\(\coth\) | \coth |
| \(\csc\) | \csc |
\(\deg\) | \deg |
\(\det\) | \det |
\(\dim\) | \dim |
| \(\exp\) | \exp |
\(\gcd\) | \gcd |
\(\hom\) | \hom |
\(\inf\) | \inf |
| \(\ker\) | \ker |
\(\lg\) | \lg |
\(\lim\) | \lim |
\(\liminf\) | \liminf |
| \(\limsup\) | \limsup |
\(\ln\) | \ln |
\(\log\) | \log |
\(\max\) | \max |
| \(\min\) | \min |
\(\Pr\) | \Pr |
\(\sec\) | \sec |
\(\sin\) | \sin |
| \(\sinh\) | \sinh |
\(\sup\) | \sup |
\(\tan\) | \tan |
\(\tanh\) | \tanh |
当然你也可以用 \mathrm 来输入这样的字体，比如 \[
\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\\[6pt]\mathrm{abcdefghijklmnopqrstuvwxyz}
\\[6pt]\mathrm{Genshin\ Impact}
\] 源码如下
\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\\[6pt]\mathrm{abcdefghijklmnopqrstuvwxyz}
\\[6pt]\mathrm{Genshin\ Impact}其他字体详见后面的字体章节。
六、二元运算或关系符号
表格1
| \(\ast\) | \ast |
\(\pm\) | \pm |
\(\cap\) | \cap |
\(\lhd\) | \lhd |
| \(\star\) | \star |
\(\mp\) | \mp |
\(\cup\) | \cup |
\(\rhd\) | \rhd |
| \(\cdot\) | \cdot |
\(\amalg\) | \amalg |
\(\uplus\) | \uplus |
\(\triangleleft\) | \triangleleft |
| \(\circ\) | \circ |
\(\odot\) | \odot |
\(\sqcap\) | \sqcap |
\(\triangleright\) | \triangleright |
| \(\bullet\) | \bullet |
\(\ominus\) | \ominus |
\(\sqcup\) | \sqcup |
\(\unlhd\) | \unlhd |
| \(\bigcirc\) | \bigcirc |
\(\oplus\) | \oplus |
\(\wedge\) | \wedge |
\(\unrhd\) | \unrhd |
| \(\diamond\) | \diamond |
\(\oslash\) | \oslash |
\(\vee\) | \vee |
\(\bigtriangledown\) | \bigtriangledown |
| \(\times\) | \times |
\(\otimes\) | \otimes |
\(\dagger\) | \dagger |
\(\bigtriangleup\) | \bigtriangleup |
| \(\div\) | \div |
\(\wr\) | \wr |
\(\ddagger\) | \ddagger |
\(\setminus\) | \setminus |
| \(\centerdot\) | \centerdot |
\(\Box\) | \Box |
\(\barwedge\) | \barwedge |
\(\veebar\) | \veebar |
| \(\circledast\) | \circledast |
\(\boxplus\) | \boxplus |
\(\curlywedge\) | \curlywedge |
\(\curlyvee\) | \curlyvee |
| \(\circledcirc\) | \circledcirc |
\(\boxminus\) | \boxminus |
\(\Cap\) | \Cap |
\(\Cup\) | \Cup |
| \(\circleddash\) | \circleddash |
\(\boxtimes\) | \boxtimes |
\(\bot\) | \bot |
\(\top\) | \top |
| \(\dotplus\) | \dotplus |
\(\boxdot\) | \boxdot |
\(\intercal\) | \intercal |
\(\rightthreetimes\) | \rightthreetimes |
| \(\divideontimes\) | \divideontimes |
\(\square\) | \square |
\(\doublebarwedge\) | \doublebarwedge |
\(\leftthreetimes\) | \leftthreetimes |
表格2
| \(\equiv\) | \equiv |
\(\leq\) | \leq |
\(\geq\) | \geq |
\(\perp\) | \perp |
| \(\cong\) | \cong |
\(\prec\) | \prec |
\(\succ\) | \succ |
\(\mid\) | \mid |
| \(\neq\) | \neq |
\(\preceq\) | \preceq |
\(\succeq\) | \succeq |
\(\parallel\) | \parallel |
| \(\sim\) | \sim |
\(\ll\) | \ll |
\(\gg\) | \gg |
\(\bowtie\) | \bowtie |
| \(\simeq\) | \simeq |
\(\subset\) | \subset |
\(\supset\) | \supset |
\(\Join\) | \Join |
| \(\approx\) | \approx |
\(\subseteq\) | \subseteq |
\(\supseteq\) | \supseteq |
\(\ltimes\) | \ltimes |
| \(\asymp\) | \asymp |
\(\sqsubset\) | \sqsubset |
\(\sqsupset\) | \sqsupset |
\(\rtimes\) | \rtimes |
| \(\doteq\) | \doteq |
\(\sqsubseteq\) | \sqsubseteq |
\(\sqsupseteq\) | \sqsupseteq |
\(\smile\) | \smile |
| \(\propto\) | \propto |
\(\dashv\) | \dashv |
\(\vdash\) | \vdash |
\(\frown\) | \frown |
| \(\models\) | \models |
\(\in\) | \in |
\(\ni\) | \ni |
\(\notin\) | \notin |
表格3
| \(\approxeq\) | \approxeq |
\(\leqq\) | \leqq |
\(\geqq\) | \geqq |
\(\lessgtr\) | \lessgtr |
| \(\thicksim\) | \thicksim |
\(\leqslant\) | \leqslant |
\(\geqslant\) | \geqslant |
\(\lesseqgtr\) | \lesseqgtr |
| \(\backsim\) | \backsim |
\(\lessapprox\) | \lessapprox |
\(\gtrapprox\) | \gtrapprox |
\(\lesseqqgtr\) | \lesseqqgtr |
| \(\backsimeq\) | \backsimeq |
\(\lll\) | \lll |
\(\ggg\) | \ggg |
\(\gtreqqless\) | \gtreqqless |
| \(\triangleq\) | \triangleq |
\(\lessdot\) | \lessdot |
\(\gtrdot\) | \gtrdot |
\(\gtreqless\) | \gtreqless |
| \(\circeq\) | \circeq |
\(\lesssim\) | \lesssim |
\(\gtrsim\) | \gtrsim |
\(\gtrless\) | \gtrless |
| \(\bumpeq\) | \bumpeq |
\(\eqslantless\) | \eqslantless |
\(\eqslantgtr\) | \eqslantgtr |
\(\backepsilon\) | \backepsilon |
| \(\Bumpeq\) | \Bumpeq |
\(\precsim\) | \precsim |
\(\succsim\) | \succsim |
\(\between\) | \between |
| \(\doteqdot\) | \doteqdot |
\(\precapprox\) | \precapprox |
\(\succapprox\) | \succapprox |
\(\pitchfork\) | \pitchfork |
| \(\thickapprox\) | \thickapprox |
\(\Subset\) | \Subset |
\(\Supset\) | \Supset |
\(\shortmid\) | \shortmid |
| \(\fallingdotseq\) | \fallingdotseq |
\(\subseteqq\) | \subseteqq |
\(\supseteqq\) | \supseteqq |
\(\smallfrown\) | \smallfrown |
| \(\risingdotseq\) | \risingdotseq |
\(\sqsubset\) | \sqsubset |
\(\sqsupset\) | \sqsupset |
\(\smallsmile\) | \smallsmile |
| \(\varpropto\) | \varpropto |
\(\preccurlyeq\) | \preccurlyeq |
\(\succcurlyeq\) | \succcurlyeq |
\(\Vdash\) | \Vdash |
| \(\therefore\) | \therefore |
\(\curlyeqprec\) | \curlyeqprec |
\(\curlyeqsucc\) | \curlyeqsucc |
\(\vDash\) | \vDash |
| \(\because\) | \because |
\(\blacktriangleleft\) | \blacktriangleleft |
\(\blacktriangleright\) | \blacktriangleright |
\(\Vvdash\) | \Vvdash |
| \(\eqcirc\) | \eqcirc |
\(\trianglelefteq\) | \trianglelefteq |
\(\trianglerighteq\) | \trianglerighteq |
\(\shortparallel\) | \shortparallel |
| \(\neq\) | \neq |
\(\vartriangleleft\) | \vartriangleleft |
\(\vartriangleright\) | \vartriangleright |
\(\nshortparallel\) | \nshortparallel |
表格4
| \(\ncong\) | \ncong |
\(\nleq\) | \nleq |
\(\ngeq\) | \ngeq |
\(\nsubseteq\) | \nsubseteq |
| \(\nmid\) | \nmid |
\(\nleqq\) | \nleqq |
\(\ngeqq\) | \ngeqq |
\(\nsupseteq\) | \nsupseteq |
| \(\nparallel\) | \nparallel |
\(\nleqslant\) | \nleqslant |
\(\ngeqslant\) | \ngeqslant |
\(\nsubseteqq\) | \nsubseteqq |
| \(\nshortmid\) | \nshortmid |
\(\nless\) | \nless |
\(\ngtr\) | \ngtr |
\(\nsupseteqq\) | \nsupseteqq |
| \(\nshortparallel\) | \nshortparallel |
\(\nprec\) | \nprec |
\(\nsucc\) | \nsucc |
\(\subsetneq\) | \subsetneq |
| \(\nsim\) | \nsim |
\(\npreceq\) | \npreceq |
\(\nsucceq\) | \nsucceq |
\(\supsetneq\) | \supsetneq |
| \(\nVDash\) | \nVDash |
\(\precnapprox\) | \precnapprox |
\(\succnapprox\) | \succnapprox |
\(\subsetneqq\) | \subsetneqq |
| \(\nvDash\) | \nvDash |
\(\precnsim\) | \precnsim |
\(\succnsim\) | \succnsim |
\(\supsetneqq\) | \supsetneqq |
| \(\nvdash\) | \nvdash |
\(\lnapprox\) | \lnapprox |
\(\gnapprox\) | \gnapprox |
\(\varsubsetneq\) | \varsubsetneq |
| \(\ntriangleleft\) | \ntriangleleft |
\(\lneq\) | \lneq |
\(\gneq\) | \gneq |
\(\varsupsetneq\) | \varsupsetneq |
| \(\ntrianglelefteq\) | \ntrianglelefteq |
\(\lneqq\) | \lneqq |
\(\gneqq\) | \gneqq |
\(\varsubsetneqq\) | \varsubsetneqq |
| \(\ntriangleright\) | \ntriangleright |
\(\lnsim\) | \lnsim |
\(\gnsim\) | \gnsim |
\(\varsupsetneqq\) | \varsupsetneqq |
| \(\ntrianglerighteq\) | \ntrianglerighteq |
\(\lvertneqq\) | \lvertneqq |
\(\gvertneqq\) | \gvertneqq |
七、各种箭头
表格1
| \(\leftarrow\) | \leftarrow |
\(\longleftarrow\) | \longleftarrow |
\(\uparrow\) | \uparrow |
\(\Leftarrow\) | \Leftarrow |
| \(\Longleftarrow\) | \Longleftarrow |
\(\Uparrow\) | \Uparrow |
\(\rightarrow\) | \rightarrow |
\(\longrightarrow\) | \longrightarrow |
| \(\downarrow\) | \downarrow |
\(\Rightarrow\) | \Rightarrow |
\(\Longrightarrow\) | \Longrightarrow |
\(\Downarrow\) | \Downarrow |
| \(\leftrightarrow\) | \leftrightarrow |
\(\longleftrightarrow\) | \longleftrightarrow |
\(\updownarrow\) | \updownarrow |
\(\Leftrightarrow\) | \Leftrightarrow |
| \(\Longleftrightarrow\) | \Longleftrightarrow |
\(\Updownarrow\) | \Updownarrow |
\(\mapsto\) | \mapsto |
\(\longmapsto\) | \longmapsto |
| \(\nearrow\) | \nearrow |
\(\hookleftarrow\) | \hookleftarrow |
\(\hookrightarrow\) | \hookrightarrow |
\(\searrow\) | \searrow |
| \(\leftharpoonup\) | \leftharpoonup |
\(\rightharpoonup\) | \rightharpoonup |
\(\swarrow\) | \swarrow |
\(\leftharpoondown\) | \leftharpoondown |
| \(\rightharpoondown\) | \rightharpoondown |
\(\nwarrow\) | \nwarrow |
\(\rightleftharpoons\) | \rightleftharpoons |
\(\leadsto\) | \leadsto |
表格2
| \(\dashrightarrow\) | \dashrightarrow |
\(\dashleftarrow\) | \dashleftarrow |
\(\leftleftarrows\) | \leftleftarrows |
\(\leftrightarrows\) | \leftrightarrows |
| \(\Lleftarrow\) | \Lleftarrow |
\(\twoheadleftarrow\) | \twoheadleftarrow |
\(\leftarrowtail\) | \leftarrowtail |
\(\looparrowleft\) | \looparrowleft |
| \(\leftrightharpoons\) | \leftrightharpoons |
\(\curvearrowleft\) | \curvearrowleft |
\(\circlearrowleft\) | \circlearrowleft |
\(\Lsh\) | \Lsh |
| \(\upuparrows\) | \upuparrows |
\(\upharpoonleft\) | \upharpoonleft |
\(\downharpoonleft\) | \downharpoonleft |
\(\multimap\) | \multimap |
| \(\leftrightsquigarrow\) | \leftrightsquigarrow |
\(\rightrightarrows\) | \rightrightarrows |
\(\rightleftarrows\) | \rightleftarrows |
\(\rightrightarrows\) | \rightrightarrows |
| \(\rightleftarrows\) | \rightleftarrows |
\(\twoheadrightarrow\) | \twoheadrightarrow |
\(\rightarrowtail\) | \rightarrowtail |
\(\looparrowright\) | \looparrowright |
| \(\rightleftharpoons\) | \rightleftharpoons |
\(\curvearrowright\) | \curvearrowright |
\(\circlearrowright\) | \circlearrowright |
\(\Rsh\) | \Rsh |
| \(\downdownarrows\) | \downdownarrows |
\(\upharpoonright\) | \upharpoonright |
\(\downharpoonright\) | \downharpoonright |
\(\rightsquigarrow\) | \rightsquigarrow |
| \(\nleftarrow\) | \nleftarrow |
\(\nrightarrow\) | \nrightarrow |
\(\nLeftarrow\) | \nLeftarrow |
\(\nRightarrow\) | \nRightarrow |
| \(\nleftrightarrow\) | \nleftrightarrow |
\(\nLeftrightarrow\) | \nLeftrightarrow |
八、其他符号（无穷、存在、任意、省略号等）
| \(\infty\) | \infty |
\(\forall\) | \forall |
\(\Bbbk\) | \Bbbk |
\(\wp\) | \wp |
| \(\nabla\) | \nabla |
\(\exists\) | \exists |
\(\bigstar\) | \bigstar |
\(\angle\) | \angle |
| \(\partial\) | \partial |
\(\nexists\) | \nexists |
\(\diagdown\) | \diagdown |
\(\measuredangle\) | \measuredangle |
| \(\eth\) | \eth |
\(\emptyset\) | \emptyset |
\(\diagup\) | \diagup |
\(\sphericalangle\) | \sphericalangle |
| \(\clubsuit\) | \clubsuit |
\(\varnothing\) | \varnothing |
\(\Diamond\) | \Diamond |
\(\complement\) | \complement |
| \(\diamondsuit\) | \diamondsuit |
\(\imath\) | \imath |
\(\Finv\) | \Finv |
\(\triangledown\) | \triangledown |
| \(\heartsuit\) | \heartsuit |
\(\jmath\) | \jmath |
\(\Game\) | \Game |
\(\triangle\) | \triangle |
| \(\spadesuit\) | \spadesuit |
\(\ell\) | \ell |
\(\hbar\) | \hbar |
\(\vartriangle\) | \vartriangle |
| \(\cdots\) | \cdots |
\(\iiiint\) | \iiiint |
\(\hslash\) | \hslash |
\(\blacklozenge\) | \blacklozenge |
| \(\vdots\) | \vdots |
\(\iiint\) | \iiint |
\(\lozenge\) | \lozenge |
\(\blacksquare\) | \blacksquare |
| \(\ldots\) | \ldots |
\(\iint\) | \iint |
\(\mho\) | \mho |
\(\blacktriangle\) | \blacktriangle |
| \(\ddots\) | \ddots |
\(\sharp\) | \sharp |
\(\prime\) | \prime |
无 | \blacktrinagledown |
| \(\Im\) | \Im |
\(\flat\) | \flat |
\(\square\) | \square |
\(\backprime\) | \backprime |
| \(\Re\) | \Re |
\(\natural\) | \natural |
\(\surd\) | \surd |
\(\circledS\) | \circledS |
其中 \blacktrinagledown
我这里渲染不了，是一个黑色的倒三角。
还有个特别的 \(\LaTeX\) 即
\LaTeX ，然而并没有任何用。
九、各种上标或变音符号
| \(\acute{a}\) | \acute{a} |
\(\bar{a}\) | \bar{a} |
\(\acute{\acute{A}}\) | \Acute{\Acute{A}} |
\(\bar{\bar{A}}\) | \Bar{\Bar{A}} |
| \(\breve{a}\) | \breve{a} |
\(\check{a}\) | \check{a} |
\(\breve{\breve{A}}\) | \Breve{\Breve{A}} |
\(\check{\check{A}}\) | \Check{\Check{A}} |
| \(\ddot{a}\) | \ddot{a} |
\(\dot{a}\) | \dot{a} |
\(\ddot{\ddot{A}}\) | \Ddot{\Ddot{A}} |
\(\dot{\dot{A}}\) | \Dot{\Dot{A}} |
| \(\grave{a}\) | \grave{a} |
\(\hat{a}\) | \hat{a} |
\(\grave{\grave{A}}\) | \Grave{\Grave{A}} |
\(\hat{\hat{A}}\) | \Hat{\Hat{A}} |
| \(\tilde{a}\) | \tilde{a} |
\(\vec{a}\) | \vec{a} |
\(\tilde{\tilde{A}}\) | \Tilde{\Tilde{A}} |
\(\vec{\vec{A}}\) | \Vec{\Vec{A}} |
十、非常好用的 array 环境
第一个例子 \[ \left( \begin{array}{cc} 2\tau & 7\phi-\frac5{12} \\ 3\psi & \frac{\pi}8 \end{array} \right) \left( \begin{array}{c} x \\ y \end{array} \right) \ \mbox{and}\ \left[ \begin{array}{cc|r} 3 & 4 & 5 \\ 1 & 3 & 729 \end{array} \right] \] 源码如下
\left( \begin{array}{cc} 2\tau & 7\phi-\frac5{12} \\
3\psi & \frac{\pi}8 \end{array} \right)
\left( \begin{array}{c} x \\ y \end{array} \right)
\ \mbox{and}\ \left[ \begin{array}{cc|r}
3 & 4 & 5 \\ 1 & 3 & 729 \end{array} \right]第二个例子 \[ f(z) = \left\{ \begin{array}{rcl} \overline{\overline{z^2}+\cos z} & \mbox{for} & |z|<3 \\ 0 & \mbox{for} & 3\leq|z|\leq5 \\ \sin\overline{z} & \mbox{for} & |z|>5 \end{array}\right. \] 源码如下
f(z) = \left\{ \begin{array}{rcl}
\overline{\overline{z^2}+\cos z} & \mbox{for}
& |z|<3 \\ 0 & \mbox{for} & 3\leq|z|\leq5 \\
\sin\overline{z} & \mbox{for} & |z|>5
\end{array}\right.其中 \begin{array}{} 后面那个大括号里输入
lrc 分别对应左对齐、右对齐、居中对齐
然后可以用 | 作为分隔符，比如下面这样 \[
\begin{array}{c|l||r}
aaaa & bbbb & cccc
\\ aaa & bbb & ccc
\\ aa & bb & cc
\end{array}
\] 源码如下
\begin{array}{c|l||r}
aaaa & bbbb & cccc
\\ aaa & bbb & ccc
\\ aa & bb & cc
\end{array}十一、字体
花体 Caligraphic letters \[ \mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\[6pt]\mathcal{abcdefghijklmnopqrstuvwxyz} \\[6pt]\mathcal{0123456789} \]
\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\\[6pt]\mathcal{abcdefghijklmnopqrstuvwxyz}
\\[6pt]\mathcal{0123456789}黑板粗体 Mathbb letters（在 mathjax 2.7.7 下对小写字母和数字支持有限，更高版本貌似支持） \[ \mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\[6pt]\mathbb{abcdefghijklmnopqrstuvwxyz} \\[6pt]\mathbb{0123456789} \]
\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\\[6pt]\mathbb{abcdefghijklmnopqrstuvwxyz}
\\[6pt]\mathbb{0123456789}Fraktur哥特体 Mathfrak letters，不支持数字，详见 Fraktur 哥特体 \[ \mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\[6pt]\mathfrak{abcdefghijklmnopqrstuvwxyz} \]
\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\\[6pt]\mathfrak{abcdefghijklmnopqrstuvwxyz}无衬线体 Math Sans serif letters \[ \mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\[6pt]\mathsf{abcdefghijklmnopqrstuvwxyz} \\[6pt]\mathsf{0123456789} \]
\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\\[6pt]\mathsf{abcdefghijklmnopqrstuvwxyz}
\\[6pt]\mathsf{0123456789}粗体 Math bold letters \[ \mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\[6pt]\mathbf{abcdefghijklmnopqrstuvwxyz} \\[6pt]\mathbf{0123456789} \]
\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\\[6pt]\mathsf{abcdefghijklmnopqrstuvwxyz}
\\[6pt]\mathsf{0123456789}十二、字体或大小控制符
仅支持数学公式的控制符（常用的就是前两个） \[ {\displaystyle\int f^{-1}(x-x_a)\,\mathrm{d}x} \\[6pt] {\textstyle \int f^{-1}(x-x_a)\,\mathrm{d}x} \\[6pt] {\scriptstyle\int f^{-1}(x-x_a)\,\mathrm{d}x} \\[6pt] {\scriptscriptstyle\int f^{-1}(x-x_a)\,\mathrm{d}x} \]
{\displaystyle\int f^{-1}(x-x_a)\,\mathrm{d}x}
\\[6pt] {\textstyle \int f^{-1}(x-x_a)\,\mathrm{d}x}
\\[6pt] {\scriptstyle\int f^{-1}(x-x_a)\,\mathrm{d}x}
\\[6pt] {\scriptscriptstyle\int f^{-1}(x-x_a)\,\mathrm{d}x}支持文本的控制符 \[ {\tiny \text{哒哒哒哒哒，好想玩原神 AaBb}} \\[6pt] {\scriptsize \text{哒哒哒哒哒，好想玩原神 AaBb}} \\[6pt] {\small \text{哒哒哒哒哒，好想玩原神 AaBb}} \\[6pt] {\normalsize \text{哒哒哒哒哒，好想玩原神 AaBb}} \\[6pt] {\large \text{哒哒哒哒哒，好想玩原神 AaBb}} \\[6pt] {\Large \text{哒哒哒哒哒，好想玩原神 AaBb}} \\[6pt] {\LARGE \text{哒哒哒哒哒，好想玩原神 AaBb}} \\[6pt] {\huge \text{哒哒哒哒哒，好想玩原神 AaBb}} \\[6pt] {\Huge \text{哒哒哒哒哒，好想玩原神 AaBb}} \]
{\tiny \text{哒哒哒哒哒，好想玩原神 AaBb}}
\\[6pt] {\scriptsize \text{哒哒哒哒哒，好想玩原神 AaBb}}
\\[6pt] {\small \text{哒哒哒哒哒，好想玩原神 AaBb}}
\\[6pt] {\normalsize \text{哒哒哒哒哒，好想玩原神 AaBb}}
\\[6pt] {\large \text{哒哒哒哒哒，好想玩原神 AaBb}}
\\[6pt] {\Large \text{哒哒哒哒哒，好想玩原神 AaBb}}
\\[6pt] {\LARGE \text{哒哒哒哒哒，好想玩原神 AaBb}}
\\[6pt] {\huge \text{哒哒哒哒哒，好想玩原神 AaBb}}
\\[6pt] {\Huge \text{哒哒哒哒哒，好想玩原神 AaBb}}十三、变音符号与特殊符号（文本模式）
Mathjax 对这些符号的兼容性比较差，版本差异也很大，本站不支持的我就标“无”了
| \(\acute{o}\) | \’{o} |
\(\ddot{o}\) | \"{o} |
\(\hat{o}\) | \^{o} |
\(\grave{o}\) | \‘{o} |
| \(\tilde{o}\) | \~{o} |
\(\bar{o}\) | \={o} |
无 | \d s |
\(\dot{o}\) | \.{o} |
| \(\breve{o}\) | \u{o} |
无 | \H{o} |
无 | \t{oo} |
无 | \c{o} |
| 无 | \d{o} |
无 | \r s |
无 | \b{o} |
无 | \AA |
| 无 | \aa |
无 | \ss |
无 | \i |
无 | \j |
| 无 | \H s |
无 | \o |
无 | \t s |
无 | \v s |
| 无 | \O |
无 | \P |
\(\S\) | \S |
无 | \ae |
| 无 | \AE |
无 | \dag |
无 | \ddag |
无 | \copyright |
| 无 | \pounds |
可以查看下面的图
十四、强制空格
多数情况 latex 会自动处理空格，不过我们也可以手动强制空格。
以无空格的 \(xy\) 为例（空格宽度为0）
| \(x\!y\) | \! |
\(x\,y\) | \, |
| \(x\;y\) | \; |
\(x\ y\) | \ |
| \(x\quad y\) | \quad |
\(x \qquad y\) | \qquad |
以上空格宽度分别为 \(-\frac{m}{6},\frac{m}{6},\frac{2m}{7},\frac{m}{3},m,2m\) ，其实看着 ok 就行也不用细算。
十五、颜色
语法如下
% 字体颜色
{\color{颜色}文本文本}
% 背景颜色, 似乎只支持文本模式
{\color{颜色}\colorbox{背景色}{文本文本}}比如说 \[ x=\dfrac{-b\pm\sqrt{\color{Red}b^2-4ac}}{\color{Green}{2a}} \]
x=\dfrac{-b\pm\sqrt{\color{Red}b^2-4ac}}{\color{Green}{2a}}本站的 Mathjax v2.7.7 不支持背景色的写法，我用的 Typora 的 v3 倒是支持的。
而且本站的渲染对于 \color{Red}b^2-4ac 会只渲染字母 \(b\) ，只有像 \color{Green}{2a}
这样框住才行。
因此不是很建议使用带颜色的写法，兼容性可能有点小问题，或者也可以提前写好了放个图片出来。
比如下面这样（这是在latexlive做好的图片，就是导出的图有点清晰过头了，用 PS 缩小了一下）
源码如下
x=\dfrac{-b\pm\sqrt{\color{Red}b^2-4ac}}{\color{White}\colorbox{Green}{2a}}
\\x=\dfrac{-b\pm\sqrt{{\color{Gold}{b^2}}-\colorbox{Gray}{4ac}}}{\color{CornflowerBlue}{2a}}十六、常用排版方式
把公式框起来 \[ \boxed{\sum\limits_{i = 1}^{n} i = \dfrac{n(n - 1)}{2}} \]
\boxed{\sum\limits_{i = 1}^{n} i = \dfrac{n(n - 1)}{2}}对齐等式，通过 & 进行控制 \[
\begin{aligned}
哒哒哒哒哒, 好想玩原神&=我&要玩&原神
\\&=我&必须玩&\text{Genshin Impact}
\\&=原神启动
\end{aligned}
\] 源码如下
\begin{aligned}
哒哒哒哒哒, 好想玩原神&=我&要玩&原神
\\&=我&必须玩&\text{Genshin Impact}
\\&=原神启动
\end{aligned}正常一点的情况 \[ \begin{aligned} \left|\bigcap_{i=1}^k \overline{S_i}\right| &= |U| - \left( \sum_{1\le i\le n}\left|S_i\right|-\sum_{1\le i < j \le n}\left|S_i \cap S_j\right|+\sum_{1\le i < j < k \le n}\left|S_i \cap S_j \cap S_k\right|-\cdots +(-1)^{n-1}\left|\bigcap_{i=1}^n S_i\right|\right) \\[6pt] &= n! - (n-1)!\times\binom{n}{1} + (n-2)!\times\binom{n}{2} - \cdots + (-1)^n \times 0! \times \binom{n}{n}\ \\[6pt] &= n! - \frac{n!}{1!} + \frac{n!}{2!} - \cdots + (-1)^n\frac{n!}{n!} \\[6pt] &= n!\left(1 - \frac{1}{1!} + \frac{1}{2!}-\frac{1}{3!} + \cdots + \frac{(-1)^n}{n!}\right) \end{aligned} \]
源码如下
\begin{aligned}
\left|\bigcap_{i=1}^k \overline{S_i}\right| &= |U| - \left(
\sum_{1\le i\le n}\left|S_i\right|-\sum_{1\le i < j \le n}\left|S_i \cap S_j\right|+\sum_{1\le i < j < k \le n}\left|S_i \cap S_j \cap S_k\right|-\cdots +(-1)^{n-1}\left|\bigcap_{i=1}^n S_i\right|\right)
\\[6pt] &= n! - (n-1)!\times\binom{n}{1} + (n-2)!\times\binom{n}{2} - \cdots + (-1)^n \times 0! \times \binom{n}{n}\
\\[6pt] &= n! - \frac{n!}{1!} + \frac{n!}{2!} - \cdots + (-1)^n\frac{n!}{n!}
\\[6pt] &= n!\left(1 - \frac{1}{1!} + \frac{1}{2!}-\frac{1}{3!} + \cdots + \frac{(-1)^n}{n!}\right)
\end{aligned}
