{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## 1 Markdown 中使用LaTex基础语法" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "LaTeX 公式有两种，一种是用在正文中的，一种是单独显示的。\n", "\n", "正文中的公式如下: \n", "\n", "$\\$...\\\n", "\n", "单独一行显示的时候使用如下命令：\n", "\n", "$\\$\\$...\\$\\\n", "\n", "其中， \\$符号中间包含的三个点表格的是LaTex的公式命令。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**举个例子如下：**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "行内公式$ f(x) = \\sum_{i=0}^{N} \\int_{a}^{b} g(t,i) \\text{d}t $行内公式\n", "\n", "下面是单独一行显示：\n", "\n", " $$f(x) = \\sum_{i=0}^{N} \\int_{a}^{b} g(t,i) \\text{d}t \\tag{a}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "编辑上述公式的代码如下：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "行内公式$ f(x) = \\sum_{i=0}^{N} \\int_{a}^{b} g(t,i) \\text{d}t $行内公式\n", "\n", "下面是单独一行显示：\n", "\n", " $$f(x) = \\sum_{i=0}^{N} \\int_{a}^{b} g(t,i) \\text{d}t \\tag{a}$$\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2 常用数学表达命令" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 指数和下标" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "指数和下标可以用 ^ 和 _ 后加相应字符来实现。比如：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "LaTex命令| 显示结果 | LaTex命令| 显示结果 | LaTex命令| 显示结果 \n", "- |- | - | - | - | -\n", "a_{1} |$a_{1}$| x^{2} |$x^{2}$| \\sum_{i=1}^{N} |$\\sum_{i=1}^{N} $" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2 平方根和n次方根" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "平方根的输入命令为 \\sqrt ， n次方根的命令为 \\sqrt[n]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "LaTex命令| 显示结果 | LaTex命令| 显示结果 | LaTex命令| 显示结果 \n", "- |- | - | - | - | -\n", "\\sqrt{x} |$\\sqrt{x}$| \\sqrt[3]{4} |$\\sqrt[3]{4}$| \\sqrt{x^2+y^2} |$ \\sqrt{x^2+y^2} $" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\\sqrt{x^{2}+\\sqrt{y}} \\tag{2-1}$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\sqrt{x^{2}+\\sqrt{y}} \\tag{2-1}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.3 上下水平线" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "命令 \\overline 和 \\underline 在表达式的上、下方画出水平线。比如：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "LaTex命令| 显示结果 | LaTex命令| 显示结果 \n", "- |- | - | - | - | -\n", "\\overline{x+y} |$ \\overline{x+y} $| \\underline{x+y} |$ \\underline{x+y} $" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.4 上下大括号" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "命令 \\overbrace 和 \\underbrace 在表达式上、下方画出一个水平的大括号。比如：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\underbrace{1+2+3+\\cdots+100}_{100}\n", "\\tag{2-2}\n", "$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\underbrace{1+2+3+\\cdots+100}_{100}\n", "\\tag{2-2}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.5 向量" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "向量通常是上方有小箭头的变量表示。这可以由 \\vec 得到。 在定义从 A 到 B 的向量时，命令 \\overrightarrow 和 \\overleftarrow 非常有用。比如：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "LaTex命令| 显示结果 | LaTex命令| 显示结果 \n", "- |- | - | - | - | -\n", "\\vec a |$ \\vec a $| \\overrightarrow{AB} |$ \\overrightarrow{AB} $" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.6 其他" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "其他，比如 分数可以用 \\frac 命令， 求和可以用 \\sum 命令， 乘积运算可以用 \\prod 生成， 积分可以用 \\int 命令。部分示例如下：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "\n", "LaTex命令| 显示结果 | LaTex命令| 显示结果 | LaTex命令| 显示结果 \n", "- |- | - | - | - | -\n", "\\sum |$\\sum$| \\int |$\\int$| \\sum_{i=1}^{N} |$\\sum_{i=1}^{N} $\n", "\\int_{a}^{b} |$\\int_{a}^{b}$| \\prod |$\\prod$| \\iint |$\\iint $\n", "\\prod_{i=1}^{N} |$\\prod_{i=1}^{N}$| \\iint_{a}^{b} |$\\iint_{a}^{b}$| \\bigcup |$\\bigcup $\n", "\\bigcap |$\\bigcap$| \\bigcup_{i=1}^{N} |$\\bigcup_{i=1}^{N}$| \\bigcap_{i=1}^{N} |$\\bigcap_{i=1}^{N} $\n", "\\sqrt[3]{2} |$\\sqrt[3]{2}$| \\sqrt{3} |$\\sqrt{3}$| x_{3} |$ x_{3} $\n", "\\lim_{x \\to 0} |$\\lim_{x \\to 0}$| \\frac{1}{2} |$\\frac{1}{2}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3 矩阵编辑" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "生成矩阵使用的命令如下：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\\begin{matrix}\n", "...\n", "\\end{matrix}$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "其中 … 表示的是 LaTeX 的矩阵命令，矩阵命令中每一行以 \\ 结束，矩阵的元素之间用 & 来分隔开。举例如下：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\begin{matrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{matrix} \\tag{3-1}\n", "$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{matrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{matrix} \\tag{3-1}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "上述矩阵显示的不是很美观，可以给矩阵加上括号，加括号的方式有多种。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1 带括号的矩阵 \\left \\right" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\left \\{\n", "\\begin{matrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{matrix} \n", "\\right \\} \\tag{3-2}\n", "$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\left \\{\n", "\\begin{matrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{matrix} \n", "\\right \\} \\tag{3-2}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "或者：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\left [\n", "\\begin{matrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{matrix} \n", "\\right ] \\tag{3-3}\n", "$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\left [\n", "\\begin{matrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{matrix} \n", "\\right ] \\tag{3-3}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2 带括号的矩阵 \\bmatrix \\Bmatrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\begin{bmatrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{bmatrix} \n", " \\tag{3-4}\n", "$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{bmatrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{bmatrix} \n", " \\tag{3-4}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "或者：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\begin{Bmatrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{Bmatrix} \n", " \\tag{3-5}\n", "$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{Bmatrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{Bmatrix} \n", " \\tag{3-5}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.3 带括号的矩阵 \\vmatrix \\Vmatrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\begin{vmatrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{vmatrix} \n", " \\tag{3-6}\n", "$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{vmatrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{vmatrix} \n", " \\tag{3-6}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "或者：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\begin{Vmatrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{Vmatrix} \n", " \\tag{3-7}\n", "$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{Vmatrix}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{Vmatrix} \n", " \\tag{3-7}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.4 带省略号的矩阵" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "如果矩阵元素太多，可以用 \\cdots$\\cdots$\\ddots$\\ddots$\\vdots$\\vdots$等省略符号来定义矩阵。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\begin{bmatrix}\n", "1 & 2 & \\cdots & 4 \\\\\n", "7 & 6 & \\cdots & 5 \\\\\n", "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n", "8 & 9 & \\cdots & 10\n", "\\end{bmatrix} \\tag{3-8}\n", "$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{bmatrix}\n", "1 & 2 & \\cdots & 4 \\\\\n", "7 & 6 & \\cdots & 5 \\\\\n", "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n", "8 & 9 & \\cdots & 10\n", "\\end{bmatrix} \\tag{3-8}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.5 带参数的矩阵" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "写增广矩阵，可能需要最右边一列单独考虑。可以用array命令来处理：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "$$\n", "\\left [\n", "\\begin{array}{cc|c}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{array}\n", "\\right ]\n", " \\tag{3-9}\n", "$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\left [\n", "\\begin{array}{cc|c}\n", "1 & 2 & 3 \\\\\n", "4 & 5 & 6 \\\\\n", "7 & 8 & 9\n", "\\end{array}\n", "\\right ]\n", " \\tag{3-9}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.6 行内矩阵" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "可以使用 \\big( 和 \\big) 来定义行间矩阵。Demo如下：\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "这是行内矩阵的Demo：\n", "$\\big( \n", " \\begin{smallmatrix}\n", " 1 & 2 & 3 \\\\\n", " 4 & 5 & 6 \\\\\n", " 7 & 8 & 9\n", " \\end{smallmatrix}\n", " \\big)$后面还有……\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "这是行内矩阵的Demo：\n", "$\\big( \n", " \\begin{smallmatrix}\n", " 1 & 2 & 3 \\\\\n", " 4 & 5 & 6 \\\\\n", " 7 & 8 & 9\n", " \\end{smallmatrix}\n", " \\big)$后面还有……" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "或者：" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "这是行内矩阵的Demo：\n", "$ \n", " \\begin{bmatrix}\n", " 1 & 2 & 3 \\\\\n", " 4 & 5 & 6 \\\\\n", " 7 & 8 & 9\n", " \\end{bmatrix} \n", "$后面还有……\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "这是行内矩阵的Demo：\n", "$ \n", " \\begin{bmatrix}\n", " 1 & 2 & 3 \\\\\n", " 4 & 5 & 6 \\\\\n", " 7 & 8 & 9\n", " \\end{bmatrix} \n", "$后面还有……" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## LaTex 常用数学符号整理" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表1 数学模式重音符号 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ \\hat{a} $| \\hat{a} |$ \\check{a} $| \\check{a} |$ \\tilde{a} $| \\tilde{a}\n", "$ \\grave{a} $|\\grave{a} |$\\dot{a}$| \\dot{a} |$\\ddot{a}$| \\ddot{a}\n", "$ \\bar{a} $|\\bar{a} |$\\vec{a}$| \\vec{a} |$\\widehat{A}$| \\widehat{A}\n", "$ \\acute{a} $|\\acute{a} |$\\breve{a}$| \\breve{a} |$\\widetilde{A}$| \\widetilde{A}\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表2 希腊字母 ** \n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | - | - | -\n", "$ \\alpha $| \\alpha |$ \\theta $| \\theta |$ o $| o |$ \\upsilon $| \\upsilon\n", "$ \\beta $| \\beta |$ \\vartheta $| \\vartheta |$ \\pi $| \\pi |$ \\phi $| \\phi\n", "$ \\gamma $| \\gamma |$ \\iota $| \\iota |$ \\varpi $| \\varpi |$ \\varphi $| \\varphi\n", "$ \\delta $| \\delta |$ \\kappa $| \\kappa |$ \\rho $| \\rho |$ \\chi $| \\chi\n", "$ \\epsilon $| \\epsilon |$ \\lambda $| \\lambda |$ \\varrho $| \\varrho |$ \\psi $| \\psi\n", "$ \\varepsilon $| \\varepsilon |$ \\mu $| \\mu |$ \\sigma $| \\sigma |$ \\omega $| \\omega\n", "$ \\zeta $| \\zeta |$ \\nu $| \\nu |$ \\varsigma $| \\varsigma |$ \\mathcal{O} $| \\mathcal{O}\n", "$ \\eta $| \\eta |$ \\xi $| \\xi |$ \\tau $| \\tau \n", "$ \\Gamma $| \\Gamma |$ \\Lambda $| \\Lambda |$ \\Sigma $| \\sigma |$ \\Psi $| \\Psi\n", "$ \\Delta $| \\Delta |$ \\Xi $| \\Xi |$ \\Upsilon $| \\Upsilon |$ \\Omega $| \\Omega\n", "$ \\Theta $| \\Theta |$ \\Pi $| \\Pi |$ \\Phi $| \\Phi \n", "\n", " \n", "** Tips: **\n", " \n", "如果使用大写的希腊字母，把命令的首字母变成大写即可，例如 \\Gamma 输出的是$\\Gamma$。\n", " \n", "如果使用斜体大写希腊字母，再在大写希腊字母的LaTeX命令前加上var，例如 \\varGamma 生成$\\varGamma$。\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表3 二元关系 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ < $| < |$ > $| > |$ = $| =\n", "$ \\le $|\\leq 或 \\le |$\\ge $| \\geq 或 \\ge |$\\equiv$| \\equiv\n", "$ \\ll $|\\ll |$\\gg $| \\gg |$\\doteq$| \\doteq\n", "$ \\prec $|\\prec |$\\succ $| \\succ |$\\sim$| \\sim\n", "$ \\preceq $|\\preceq |$\\succeq $| \\succeq |$\\simeq$| \\simeq\n", "$ \\subset $|\\subset |$\\supset $| \\supset |$\\approx$| \\approx\n", "$ \\subseteq $|\\subseteq |$\\supseteq $| \\supseteq |$\\cong$| \\cong\n", "$ \\sqsubset $|\\sqsubset |$\\sqsupset $| \\sqsupset |$\\Join$| \\Join\n", "$ \\sqsubseteq $|\\sqsubseteq |$\\sqsupseteq $| \\sqsupseteq |$\\bowtie$| \\bowtie\n", "$ \\in $|\\in |$\\ni $| \\ni 或 \\owns |$\\propto$| \\propto\n", "$ \\vdash $|\\vdash |$\\dashv $| \\dashv |$\\models$| \\models\n", "$ \\mid $|\\mid |$\\parallel $| \\parallel |$\\perp$| \\perp\n", "$ \\smile $|\\smile |$\\frown $| \\frown |$\\asymp$| \\asymp\n", "$ : $| : |$\\notin $| \\notin |$\\neq$| \\neq 或 \\ne\n", "\n", "\n", "\n", " \n", "** Tips: **\n", "\n", " \n", "\n", "可以在上述符号的相应命令前加上 \\not 命令，得到其否定形式。\n", " \n", "\n", "例如： \\not\\subset 生成$ \\not\\subset$\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表4 二元运算符 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ + $| + |$ - $| - \n", "$ \\pm $|\\pm |$\\mp $| \\mp |$\\triangleleft$| \\triangleleft\n", "$ \\cdot $|\\cdot |$\\div $| \\div |$\\triangleright$| \\triangleright\n", "$ \\times $|\\times |$\\setminus $| \\setminus |$\\star$| \\star\n", "$ \\cup $|\\cup |$\\cap $| \\cap |$\\ast$| \\ast\n", "$ \\sqcup $|\\sqcup |$\\sqcap $| \\sqcap |$\\circ$| \\circ\n", "$ \\vee $|\\vee 或 \\lor |$\\wedge $| \\wedge 或 \\land |$\\bullet$| \\bullet\n", "$ \\oplus $|\\oplus |$\\ominus $| \\ominus |$\\diamond$| \\diamond\n", "$ \\odot $|\\odot |$\\oslash $| \\oslash |$\\uplus$| \\uplus\n", "$ \\otimes $|\\otimes |$\\bigcirc $| \\bigcirc |$\\amalg$| \\amalg\n", "$ \\bigtriangleup $|\\bigtriangleup |$\\bigtriangledown $| \\bigtriangledown |$\\dagger$| \\dagger\n", "$ \\lhd $|\\ldh |$\\rhd $| \\rhd |$\\ddagger$| \\ddagger\n", "$ \\unlhd $|\\unldh |$\\unrhd $| \\unrhd |$\\wr$| \\wr" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表5 \"大\"运算符 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ \\sum $|\\sum |$\\bigcup $| \\bigcup |$\\bigvee$| \\bigvee\n", "$ \\prod $|\\prod |$\\bigcap $| \\bigcap |$\\bigwedge$| \\bigwedge\n", "$ \\coprod $|\\coprod |$\\bigsqcup $| \\bigsqcup |$\\biguplus$| \\biguplus\n", "$ \\int $|\\int |$\\oint $| \\oint |$\\bigodot$| \\bigodot\n", "$ \\bigoplus $|\\bigoplus |$\\bigotimes $| \\bigotimes \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表6 箭头 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令\n", "- |- | - | - \n", "$ \\leftarrow $|\\leftarrow 或 \\gets |$\\longleftarrow $| \\longleftarrow \n", "$ \\rightarrow $|\\rightarrow 或 \\to |$\\longrightarrow $| \\longrightarrow \n", "$ \\leftrightarrow $|\\leftrightarrow |$\\longleftrightarrow $| \\longleftrightarrow \n", "$ \\Leftarrow $|\\Leftarrow |$\\Longleftarrow $| \\Longleftarrow \n", "$ \\Rightarrow $|\\Rightarrow |$\\Longrightarrow $| \\Longrightarrow \n", "$ \\Leftrightarrow $|\\Leftrightarrow |$\\Longleftrightarrow $| \\Longleftrightarrow \n", "$ \\mapsto $|\\mapsto |$\\longmapsto $| \\longmapsto \n", "$ \\hookleftarrow $|\\hookleftarrow |$\\hookrightarrow $| \\hookrightarrow \n", "$ \\leftharpoonup $|\\leftharpoonup |$\\rightharpoonup $| \\rightharpoonup \n", "$ \\leftharpoondown $|\\leftharpoondown |$\\rightharpoondown $| \\rightharpoondown \n", "$ \\rightleftharpoons $|\\rightleftharpoons |$\\iff $| \\iff \n", "$ \\uparrow $|\\uparrow |$\\downarrow $| \\downarrow \n", "$ \\updownarrow $|\\updownarrow |$\\Uparrow $| \\Uparrow \n", "$ \\Downarrow $|\\Downarrow |$\\Updownarrow $| \\Updownarrow \n", "$ \\nearrow $|\\nearrow |$\\searrow $| \\searrow \n", "$ \\swarrow $|\\swarrow |$\\nwarrow $| \\nwarrow \n", "$ \\leadsto $|\\leadsto " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表7 定界符 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ ( $| ( |$ ) $| ) |$\\uparrow$| \\uparrow\n", "$ [ $| [ 或 \\lbrack |$ ] $| ] 或 \\rbrack |$\\downarrow$| \\downarrow\n", "$ \\{ $| \\{ 或 \\lbrace |$ \\} $| \\} 或 \\rbrace |$\\updownarrow$| \\updownarrow\n", "$ \\langle $| \\langle |$ \\rangle $| \\rangle |$ \\vert $| \\vert\n", "$ \\lfloor $| \\lfloor |$ \\rfloor $| \\rfloor |$ \\lceil $| \\lceil\n", "$ / $| / |$ \\backslash $| \\backslash |$ \\Updownarrow $| \\Updownarrow\n", "$ \\Uparrow $| \\Uparrow |$ \\Downarrow $| \\Downarrow |$ \\Vert $| \\Vert\n", "$ \\rceil $| \\rceil" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ " **表8 大定界符 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ \\lgroup $| \\lgroup |$ \\rgroup $| \\rgroup |$\\lmoustache$| \\lmoustache\n", "$ \\arrowvert $| \\arrowvert |$ \\Arrowvert $| \\Arrowvert |$\\bracevert$| \\bracevert\n", "$ \\rmoustache $| \\rmoustache" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表9 其他字符 ** \n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | - | - | -\n", "$ \\dots $| \\dots |$ \\cdots $| \\cdots |$ \\vdots $| \\vdots |$ \\ddots $| \\ddtos\n", "$ \\hbar $| \\hbar |$ \\imath $| \\imath |$ \\jmath $| \\jmath |$ \\ell $| \\ell\n", "$ \\Re $| \\Re |$ \\Im $| \\Im |$ \\aleph $| \\aleph |$ \\wp $| \\wp\n", "$ \\forall $| \\forall |$ \\exists $| \\exists |$ \\mho $| \\mho |$ \\partial $| \\partial\n", "$ ' $| ' |$ \\prime $| \\prime |$ \\emptyset $| \\emptyset |$ \\infty $| \\infty\n", "$ \\nabla $| \\nabla |$ \\triangle $| \\triangle |$ \\Box $| \\Box |$ \\Diamond $| \\Diamond\n", "$ \\bot $| \\bot |$ \\top $| \\top |$ \\angle $| \\angle |$ \\surd $| \\surd\n", "$ \\diamondsuit $| \\diamondsuit |$ \\heartsuit $| \\heartsuit |$ \\clubsuit $| \\clubsuit |$ \\spadesuit $| \\spadesuit\n", "$ \\neg $| \\neg 或 \\lnot |$ \\flat $| \\flat |$ \\natural $| \\natural |$ \\sharp $| \\sharp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表10 非数学符号 ** \n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | - | - | -\n", "$ \\dagger $| \\dagger |$ \\S $| \\S |$\\copyright$| \\copyright |$ \\textregistered $| \\textregistered\n", "$ \\ddagger $| \\ddagger |$ \\P $| \\P |$ \\pounds $| \\pounds |$ \\% $| \\%" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表11 AMS 定界符 ** \n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | - | - | -\n", "$ \\ulcorner $| \\ulcorner |$ \\urcorner $| \\urcorner |$\\llcorner$| \\llcorner |$ \\lrcorner $| \\llcorner\n", "$ \\lvert $| \\lvert |$ \\rvert $| \\rvert |$ \\lVert $| \\lVert |$ \\rVert $| \\rVert" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表12 AMS 希腊和希伯来字母 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ \\digamma $| \\digamma |$ \\varkappa $| \\varkappa |$\\beth$| \\beth\n", "$ \\gimel $| \\gimel |$ \\daleth $| \\daleth" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表13 AMS 二元关系 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ \\lessdot $| \\lessdot |$ \\gtrdot $| \\gtrdot |$\\doteqdot$| \\doteqdot\n", "$ \\leqslant $| \\leqslant |$ \\geqslant $| \\geqslant |$\\risingdotseq$| \\risingdotseq\n", "$ \\eqslantless $| \\eqslantless |$ \\eqslantgtr $| \\eqslantgtr |$\\fallingdotseq$| \\fallingdotseq\n", "$ \\leqq $| \\leqq |$ \\geqq $| \\geqq |$\\eqcirc$| \\eqcirc\n", "$ \\lll $| \\lll 或 \\llless |$ \\ggg $| \\ggg |$\\circeq$| \\circeq\n", "$ \\lesssim $| \\lesssim |$ \\gtrsim $| \\gtrsim |$\\triangleq$| \\triangleq\n", "$ \\lessapprox $| \\lessapprox |$ \\gtrapprox $| \\gtrapprox |$\\bumpeq$| \\bumpeq\n", "$ \\lessgtr $| \\lessgtr |$ \\gtrless $| \\gtrless |$\\Bumpeq$| \\Bumpeq\n", "$ \\lesseqgtr $| \\lesseqgtr |$ \\gtreqless $| \\gtreqless |$\\thicksim$| \\thicksim\n", "$ \\lesseqqgtr $| \\lesseqqgtr |$ \\gtreqqless $| \\gtreqqless |$\\thickapprox$| \\thickapprox\n", "$ \\preccurlyeq $| \\preccurlyeq |$ \\succcurlyeq $| \\succcurlyeq |$\\approxeq$| \\approxeq\n", "$ \\curlyeqprec $| \\curlyeqprec |$ \\curlyeqsucc $| \\curlyeqsucc |$\\backsim$| \\backsim\n", "$ \\precsim $| \\precsim |$ \\succsim $| \\succsim |$\\backsimeq$| \\backsimeq\n", "$ \\precapprox $| \\precapprox |$ \\succapprox $| \\succapprox |$\\vDash$| \\vDash\n", "$ \\subseteqq $| \\subseteqq |$ \\supseteqq $| \\supseteqq |$\\Vdash$| \\Vdash\n", "$ \\shortparallel $| \\shortparallel |$ \\Supset $| \\Supset |$\\Vvdash$| \\Vvdash\n", "$ \\blacktriangleleft $| \\blacktriangleleft |$ \\sqsupset $| \\sqsupset |$\\backepsilon$| \\backepsilon\n", "$ \\vartriangleright $| \\vartriangleright |$ \\because $| \\because |$\\varpropto$| \\varpropto\n", "$ \\blacktriangleright $| \\blacktriangleright |$ \\Subset $| \\Subset |$\\between$| \\between\n", "$ \\trianglerighteq $| \\trianglerighteq |$ \\smallfrown $| \\smallfrown |$\\pitchfork$| \\pitchfork\n", "$ \\vartriangleleft $| \\vartriangleleft |$ \\shortmid $| \\shortmid |$\\smallsmile$| \\smallsmile\n", "$ \\trianglelefteq $| \\trianglelefteq |$ \\therefore $| \\therefore |$\\sqsubset$| \\sqsubset\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表14 AMS 箭头 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ \\dashleftarrow $| \\dashleftarrow |$ \\leftleftarrows $| \\leftleftarrows |$\\leftrightarrows$| \\leftrightarrows\n", "$ \\dashrightarrow $| \\dashrightarrow |$ \\rightrightarrows $| \\rightrightarrows |$\\rightleftarrows$| \\rightleftarrows\n", "$ \\Lleftarrow $| \\Lleftarrow |$ \\twoheadleftarrow $| \\twoheadleftarrow |$\\leftarrowtail$| \\leftarrowtail\n", "$ \\Rrightarrow $| \\Rrightarrow |$ \\twoheadrightarrow $| \\twoheadrightarrow |$\\rightarrowtail$| \\rightarrowtail\n", "$ \\leftrightharpoons $| \\leftrightharpoons |$ \\Lsh $| \\Lsh |$\\looparrowleft$| \\looparrowleft\n", "$ \\rightleftharpoons $| \\rightleftharpoons |$ \\Rsh $| \\Rsh |$\\looparrowright$| \\looparrowright\n", "$ \\curvearrowleft $| \\curvearrowleft |$ \\circlearrowleft $| \\circlearrowleft |$\\upuparrows$| \\upuparrows\n", "$ \\curvearrowright $| \\curvearrowright |$ \\circlearrowright $| \\circlearrowright |$\\downdownarrows$| \\downdownarrows\n", "$ \\upharpoonleft $| \\upharpoonleft |$ \\rightsquigarrow $| \\rightsquigarrow |$\\multimap$| \\multimap\n", "$ \\upharpoonright $| \\upharpoonright |$ \\leftrightsquigarrow $| \\leftrightsquigarrow \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表15 AMS 二元否定关系符和箭头 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | - | - | -\n", "$ \\nless $| \\nless |$ \\lneq $| \\lneq |$ \\nleq $| \\nleq |$\\varsubsetneqq$| \\varsubsetneqq\n", "$ \\ngtr $| \\ngtr |$ \\gneq $| \\gneq |$ \\ngeq $| \\ngeq |$\\varsubsetneqq$| \\varsubsetneqq\n", "$ \\nleqslant $| \\nleqslant |$ \\lneqq $| \\lneqq |$ \\nmid $| \\nmid |$\\nsubseteqq$| \\nsubseteqq\n", "$ \\ngeqslant $| \\nngeqslantgtr |$ \\gneqq $| \\gneqq |$ \\nparallel $| \\nparallel |$\\nsupseteqq$| \\nsupseteqq\n", "$ \\lvertneqq $| \\lvertneqq |$ \\nleqq $| \\nleqq |$ \\lnsim $| \\lnsim |$\\nshortmid$| \\nshortmid\n", "$ \\gvertneqq $| \\gvertneqq |$ \\ngeqq $| \\ngeqq |$ \\gnsim $| \\gnsim |$\\nshortparallel$| \\nshortparallel\n", "$ \\lnapprox $| \\lnapprox |$ \\nsim $| \\nsim |$ \\lnapprox $| \\lnapprox |$\\nprec$| \\nprec\n", "$ \\gnapprox $| \\gnapprox |$ \\ncong $| \\ncong |$ \\gnapprox $| \\gnapprox |$\\nsucc$| \\nsucc\n", "$ \\npreceq $| \\npreceq |$ \\nvdash $| \\nvdash |$ \\nVdash $| \\nVdash |$\\precneqq$| \\precneqq\n", "$ \\nsucceq $| \\nsucceq |$ \\nvDash $| \\nvDash |$ \\nVDash $| \\nVDash |$\\succneqq$| \\succneqq\n", "$ \\precnsim $| \\precnsim |$ \\precnapprox $| \\precnapprox |$ \\subsetneq $| \\subsetneq |$\\ntriangleleft$| \\ntriangleleft\n", "$ \\succnsim $| \\succnsim |$ \\succnapprox $| \\succnapprox |$ \\supsetneq $| \\supsetneq |$\\ntriangleright$| \\ntriangleright\n", "$ \\varsubsetneq $| \\varsubsetneq |$ \\nsubseteq $| \\nsubseteq |$ \\subsetneqq $| \\subsetneqq |$\\ntrianglelefteq$| \\ntrianglelefteq\n", "$ \\varsupsetneq $| \\varsupsetneq |$ \\nsupseteq $| \\nsupseteq |$ \\supsetneqq $| \\supsetneqq |$\\ntrianglerighteq$| \\ntrianglerighteq\n", "$ \\nleftarrow $| \\nleftarrow |$ \\nrightarrow $| \\nrightarrow |$ \\nleftrightarrow $| \\nleftrightarrow \n", "$ \\nLeftarrow $| \\nLeftarrow |$ \\nRightarrow $| \\nRightarrow |$ \\nLeftrightarrow $| \\nLeftrightarrow " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表16 AMS 二元运算符 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ \\dotplus $| \\dotplus |$ \\centerdot $| \\centerdot |$\\divideontimes$| \\divideontimes\n", "$ \\ltimes $| \\ltimes |$ \\rtimes $| \\rtimes |$\\smallsetminus$| \\smallsetminus\n", "$ \\doublecup $| \\doublecup |$ \\doublecap $| \\doublecap |$\\doublebarwedge$| \\doublebarwedge\n", "$ \\veebar $| \\veebar |$ \\barwedge $| \\barwedge |$\\circleddash$| \\circleddash\n", "$ \\boxplus $| \\boxplus |$ \\boxminus $| \\boxminus |$\\circledcirc$| \\circledcirc\n", "$ \\boxtimes $| \\boxtimes |$ \\boxdot $| \\boxdot |$\\rightthreetimes$| \\rightthreetimes\n", "$ \\intercal $| \\intercal |$ \\circledast $| \\circledast |$\\leftthreetimes$| \\leftthreetimes\n", "$ \\curlyvee $| \\curlyvee |$ \\curlywedge $| \\curlywedge " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " **表17 AMS 其他符号 ** \n", "\n", "\n", "\n", "符号|LaTex命令 | 符号 | LaTex命令 | 符号 |LaTex命令\n", "- |- | - | - | - | -\n", "$ \\hbar $| \\hbar |$ \\hslash $| \\hslash |$\\Bbbk$| \\Bbbk\n", "$ \\square $| \\square |$ \\blacksquare $| \\blacksquare |$\\circledS$| \\circledS\n", "$ \\vartriangle $| \\vartriangle |$ \\blacktriangle $| \\blacktriangle |$\\complement$| \\complement\n", "$ \\triangledown $| \\triangledown |$ \\blacktriangledown $| \\blacktriangledown |$\\Game$| \\Game\n", "$ \\lozenge $| \\lozenge |$ \\blacklozenge $| \\blacklozenge |$\\bigstar$| \\bigstar\n", "$ \\angle $| \\angle |$ \\measuredangle $| \\measuredangle \n", "$ \\diagup $| \\diagup |$ \\diagdown $| \\diagdown |$\\backprime$| \\backprime\n", "$ \\nexists $| \\nexists |$ \\Finv $| \\Finv |$\\varnothing$| \\varnothing\n", "$ \\eth $| \\eth |$ \\sphericalangle $| \\sphericalangle |$\\mho\$ | \\mho" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**参考文献：**\n", "1. 一份不太简短的 LaTex2e 介绍\n", "1. Markdown 中使用 LaTex， Binean的博客" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 2 }