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🔥 📝 Fixed #148 Add English language support.

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---
title: Mathematical Formula Rendering
description: The theme supports mathematical formula rendering schemes for two different plugins, mathjs and katex
keywords: "math,formula"
date: 2025-01-29T20:50:02+08:00
lastmod: 2025-01-29T20:50:02+08:00
categories:
- ThirdParty
- Mathematical formulas
tags:
- Mathematical formulas
- mathjax
- katex
url: "demo/math-formula.html"
math: mathjax
---
This theme supports two different schemes, `mathjax` and `katex`, and supports rendering mathematical formulas. You can choose according to your own needs.
<!--more-->
In the following example, [MathJax](https://www.mathjax.org/) will be used Plan to showcase rendering effects.
{{< note info >}}
- Create a new article using the `hugo new` command;
- You can globally enable data formula rendering. Please configure the parameter `math: katex` or `math: mathjax` in the article front parameters;
- Or configure the parameter to the header of the page where mathematical formulas need to be displayed.
> reducing unnecessary resource loading consumption
{{< /note >}}
**Attention:** Use [Supported TeX Features](https://docs.mathjax.org/en/latest/input/tex/index.html) Online reference materials.
## Example
### Insider formula
Quadratic formula:$ Ax ^ 2+bx+c=0 $(supports using ` \ $...)\$` Format of inline formulas
Quadratic formula (line break display formula) $$ax ^ 2+bx+c=0$$
The more complex formula is as follows:$ \lim^{x \to \infty}_{y \to 0}{\frac{x}{y}}$
Other inline formulas display ( _score_ _expression_ ): \(\frac{1}{2}\) (Supports inline formula effects in `\(...\)` format)
### Repeated scores
$$
\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} \equiv 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }
$$
### Sum mark
$$
\left(\sum_{k=1}^n a_k b_k \right)^2 \leq \left(\sum_{k=1}^n a_k^2 \right) \left(\sum_{k=1}^n b_k^2 \right)
$$
### Sum of geometric series
I have divided the next two examples into several lines so that they perform better on mobile phones. That's why they contain '\ display style'. Alternatively, truncation can be performed using syntax similar to '\ showlines {x=a+b \ \ y=b+c}', as detailed in: [mathjax-issues2312](https://github.com/mathjax/MathJax/issues/2312)
$$
\displaystyle\sum_{i=1}^{k+1}i
$$
$$
\displaystyle= \left(\sum_{i=1}^ {k}i \right) +(k+1)
$$
$$
\displaystyle= \frac{k(k+1)}{2}+k+1
$$
$$
\displaystyle= \frac{k(k+1)+2(k+1)}{2}
$$
$$
\displaystyle= \frac{(k+1)(k+2)}{2}
$$
$$
\displaystyle= \frac{(k+1)((k+1)+1)}{2}
$$
### Riding symbols
$$
\displaystyle 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
$$
$$
\displaystyle \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\displaystyle\text{ for }\lvert q\rvert < 1.
$$
### Random number formula
These are some linear mathematics:$ k_{n+1} = n^2 + k_n^2 - k_{n-1} $ ， Then there are more texts.
### Greek alphabet
$$
\displaylines{\Gamma\ \Delta\ \Theta\ \Lambda\ \Xi\ \Pi\ \Sigma\ \Upsilon\ \Phi\ \Psi\ \Omega
\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \\\\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi \ \omicron\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega\ \varepsilon\ \vartheta\ \varpi\ \varrho\ \varsigma\ \varphi}
$$
### Arrow
$$
\gets\ \to\ \leftarrow\ \rightarrow\ \uparrow\ \Uparrow\ \downarrow\ \Downarrow\ \updownarrow\ \Updownarrow
$$
$$
\displaylines{\Leftarrow\ \Rightarrow\ \leftrightarrow\ \Leftrightarrow\ \mapsto\ \hookleftarrow
\leftharpoonup\ \leftharpoondown\ \\\\\ \rightleftharpoons\ \longleftarrow\ \Longleftarrow\ \longrightarrow}
$$
$$
\Longrightarrow\ \longleftrightarrow\ \Longleftrightarrow\ \longmapsto\ \hookrightarrow\ \rightharpoonup
$$
$$
\rightharpoondown\ \leadsto\ \nearrow\ \searrow\ \swarrow\ \nwarrow
$$
## Symbols
$$
\surd\ \barwedge\ \veebar\ \odot\ \oplus\ \otimes\ \oslash\ \circledcirc\ \boxdot\ \bigtriangleup
$$
$$
\bigtriangledown\ \dagger\ \diamond\ \star\ \triangleleft\ \triangleright\ \angle\ \infty\ \prime\ \triangle
$$
### Calculus
$$
\int u \frac{dv}{dx}\,dx=uv-\int \frac{du} {dx}v \, dx
$$
$$
f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x}
$$
$$
\oint \vec{F} \cdot d\vec{s}=0
$$
### Lorenz equation
$$
\begin{aligned} \dot{x} & = \sigma(y-x) \\\\ \dot{y} & = \rho x - y - xz \\\\ \dot{z} & = -\beta z + xy \end{aligned}
$$
### Cross product
This is feasible in KaTeX, but the separation of fractions is not very good in this environment.
$$
\mathbf {V}_1 \times \mathbf {V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\\\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix}
$$
Here is a solution: use additional classes of the "mfrac" class (no difference in the case of MathJax) to make the score smaller:
$$
\mathbf {V}_1 \times \mathbf {V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\\\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix}
$$
## Emphasize
$$
\hat{x}\ \vec{x}\ \ddot{x}
$$
### Elastic parentheses
$$
\left(\frac{x^2}{y^3}\right)
$$
### Scope of evaluation
$$
\left. \frac{x^3}{3}\right|_0^1
$$
### Diagnostic criteria
$$
f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\\\ 3n+1, & \text{if } n\text{ is odd} \end{cases}
$$
### Maxwell's equations system
$$
\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\\\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
$$
## Statistics
Fixed phrases:$$ \frac{n!}{k!(n-k)!} = {^n}C_k{n \choose k}$$
### Score in Score
$$
\frac{\frac{1}{x}+\frac{1}{y}}{y-z}
$$
### Nth root
$$
\sqrt[n]{1+x+x^2+x^3+\ldots}
$$
### Matrix
$$
\begin{pmatrix} a_{11} & a_{12} & a_{13}\\\\ a_{21} & a_{22} & a_{23}\\\\ a_{31} & a_{32} & a_{33} \end{pmatrix}
\begin{bmatrix} 0 & \cdots & 0 \\\\ \vdots & \ddots & \vdots \\\\ 0 & \cdots & 0 \end{bmatrix}
$$
## Punctuation marks
$$
f(x) = \sqrt{1+x} \quad (x \ge -1)
f(x) \sim x^2 \quad (x\to\infty)
$$
Now use punctuation marks:
$$
f(x) = \sqrt{1+x}, \quad x \ge -1
f(x) \sim x^2, \quad x\to\infty
$$

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---
title: "数学公式渲染"
description: "主题支持mathjs和katex两种不同插件的数学公式渲染方案。"
keywords: "math,formula"
date: 2022-09-11T10:16:02+08:00
lastmod: 2024-12-12T18:48:32+08:00
categories:
- 第三方引入
- 数学公式
tags:
- 数学公式
- mathjax
- katex
url: "demo/math-formula.html"
math: mathjax
---
本主题支持 `mathjax` 和 `katex` 两种不的方案支持数学公式的渲染，可根据自已的需求进行选择。
<!--more-->
接下的示例中，将使用 [MathJax](https://www.mathjax.org/) 方案来展示渲染效果。
{{< note info >}}
- 使用 `hugo new` 命令创建一篇新的文章
- 可以全局启用数据公式渲染，请在项目配置参数 `math: katex` 或 `math: mathjax`
- 或是将该参数配置到需要显示数学公式的页面头部（减少不必要的资源加载消耗）
{{< /note >}}
**注意：** 使用[支持的TeX功能](https://docs.mathjax.org/en/latest/input/tex/index.html)的联机参考资料。
## 例子
### 内行公式
二次公式： $ax^2 + bx + c = 0$ （支持用`\$....\$`格式的行内公式）
二次公式（换行显示公式） $$ax^2 + bx + c = 0$$
更加复杂公式是这样的: $\lim^{x \to \infty}_{y \to 0}{\frac{x}{y}}$
其它内联公式显示（分数表达 ）：\(\frac{1}{2}\)（支持用`\(...\)`格式的行内公式效果）
### 重复的分数
$$
\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} \equiv 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }
$$
### 总和记号
$$
\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
$$
### 几何级数之和
我把接下来的两个例子分成了几行，这样它在手机上表现得更好。这就是为什么它们包含 `\displaystyle`。或者可使用类似 `\displaylines{x = a + b \\\ y = b + c}` 语法进行截断，具体信息可见：[mathjax-issues2312](https://github.com/mathjax/MathJax/issues/2312)
$$
\displaystyle\sum_{i=1}^{k+1}i
$$
$$
\displaystyle= \left(\sum_{i=1}^{k}i\right) +(k+1)
$$
$$
\displaystyle= \frac{k(k+1)}{2}+k+1
$$
$$
\displaystyle= \frac{k(k+1)+2(k+1)}{2}
$$
$$
\displaystyle= \frac{(k+1)(k+2)}{2}
$$
$$
\displaystyle= \frac{(k+1)((k+1)+1)}{2}
$$
### 乘记号
$$
\displaystyle 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
$$
$$
\displaystyle \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\displaystyle\text{ for }\lvert q\rvert < 1.
$$
### 随文数式
这是一些线性数学: $ k_{n+1} = n^2 + k_n^2 - k_{n-1} $ ， 然后是更多的文本。
### 希腊字母
$$
\displaylines{\Gamma\ \Delta\ \Theta\ \Lambda\ \Xi\ \Pi\ \Sigma\ \Upsilon\ \Phi\ \Psi\ \Omega
\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \\\\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi \ \omicron\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega\ \varepsilon\ \vartheta\ \varpi\ \varrho\ \varsigma\ \varphi}
$$
### 箭头
$$
\gets\ \to\ \leftarrow\ \rightarrow\ \uparrow\ \Uparrow\ \downarrow\ \Downarrow\ \updownarrow\ \Updownarrow
$$
$$
\displaylines{\Leftarrow\ \Rightarrow\ \leftrightarrow\ \Leftrightarrow\ \mapsto\ \hookleftarrow
\leftharpoonup\ \leftharpoondown\ \\\\\ \rightleftharpoons\ \longleftarrow\ \Longleftarrow\ \longrightarrow}
$$
$$
\Longrightarrow\ \longleftrightarrow\ \Longleftrightarrow\ \longmapsto\ \hookrightarrow\ \rightharpoonup
$$
$$
\rightharpoondown\ \leadsto\ \nearrow\ \searrow\ \swarrow\ \nwarrow
$$
## 符号
$$
\surd\ \barwedge\ \veebar\ \odot\ \oplus\ \otimes\ \oslash\ \circledcirc\ \boxdot\ \bigtriangleup
$$
$$
\bigtriangledown\ \dagger\ \diamond\ \star\ \triangleleft\ \triangleright\ \angle\ \infty\ \prime\ \triangle
$$
### 微积分学
$$
\int u \frac{dv}{dx}\,dx=uv-\int \frac{du}{dx}v\,dx
$$
$$
f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x}
$$
$$
\oint \vec{F} \cdot d\vec{s}=0
$$
### 洛伦茨方程
$$
\begin{aligned} \dot{x} & = \sigma(y-x) \\\\ \dot{y} & = \rho x - y - xz \\\\ \dot{z} & = -\beta z + xy \end{aligned}
$$
### 交叉乘积
这在KaTeX中是可行的，但在这种环境中馏分的分离不是很好。
$$
\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\\\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix}
$$
这里有一个解决方案:使用“mfrac”类(在MathJax情况下没有区别)的额外类使分数更小:
$$
\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\\\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix}
$$
## 强调
$$
\hat{x}\ \vec{x}\ \ddot{x}
$$
### 有弹性的括号
$$
\left(\frac{x^2}{y^3}\right)
$$
### 评估范围
$$
\left.\frac{x^3}{3}\right|_0^1
$$
### 诊断标准
$$
f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\\\ 3n+1, & \text{if } n\text{ is odd} \end{cases}
$$
### 麦克斯韦方程组
$$
\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\\\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
$$
## 统计学
固定词组：$$\frac{n!}{k!(n-k)!} = {^n}C_k{n \choose k}$$
### 分数在分数
$$
\frac{\frac{1}{x}+\frac{1}{y}}{y-z}
$$
### ｎ次方根
$$
\sqrt[n]{1+x+x^2+x^3+\ldots}
$$
### 矩阵
$$
\begin{pmatrix} a_{11} & a_{12} & a_{13}\\\\ a_{21} & a_{22} & a_{23}\\\\ a_{31} & a_{32} & a_{33} \end{pmatrix}
\begin{bmatrix} 0 & \cdots & 0 \\\\ \vdots & \ddots & \vdots \\\\ 0 & \cdots & 0 \end{bmatrix}
$$
## 标点符号
$$
f(x) = \sqrt{1+x} \quad (x \ge -1)
f(x) \sim x^2 \quad (x\to\infty)
$$
现在用标点符号:
$$
f(x) = \sqrt{1+x}, \quad x \ge -1
f(x) \sim x^2, \quad x\to\infty
$$