> For the complete documentation index, see [llms.txt](https://overleaf-pro.ayaka.space/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://overleaf-pro.ayaka.space/latex/zh-cn/shu-xue/07-operators.md).

# 运算符

数学模式中的字符通常以斜体显示，但有时某些函数名需要不同的格式，这可以通过使用 LaTeX 中定义的运算符来实现。

## 引言

三角函数、对数及其他函数可以通过一些特殊命令写入文档，如下例所示：

```latex
数学运算符示例：
\[
    \sin(a + b) = \sin a \cos b + \cos a \sin b
.\]
```

[在 Overleaf 中打开此示例](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=Mathematical+operators+example\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cbegin%7Bdocument%7D%0AExamples+of+mathematical+operators%3A%0A%5C%5B%0A++++%5Csin%28a+%2B+b%29+%3D+%5Csin+a+%5Ccos+b+%2B+%5Ccos+a+%5Csin+b%0A.%5C%5D%0A%5Cend%7Bdocument%7D)

此示例生成以下输出：

![Newsincos.png](/files/c2d915966222a12b173ed4ae86cd8b2bbc85819b)

这些命令会以直立（罗马）体而不是斜体显示函数名称。

## 不同上下文中的运算符

某些运算符可以接受以特殊方式处理的参数，例如极限。

```latex
\documentclass{article}
\usepackage{amsmath}
\begin{document}
极限记号测试
\[
    \lim_{h \to 0 } \frac{f(x+h)-f(x)}{h}
.\]
这个运算符在与……一起使用时会发生变化
文本 \( \lim_{h \to 0} (x-h) \)。
\end{document}
```

[在 Overleaf 中打开此示例](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=Mathematical+operators+example\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamsmath%7D%0A%5Cbegin%7Bdocument%7D%0ATesting+notation+for+limits%0A%5C%5B%0A++++%5Clim_%7Bh+%5Cto+0+%7D+%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D%0A.%5C%5D%0AThis+operator+changes+when+used+alongside+%0Atext+%5C%28+%5Clim_%7Bh+%5Cto+0%7D+%28x-h%29+%5C%29.%0A%5Cend%7Bdocument%7D)

此示例生成以下输出：

![OperatorsEx2.png](/files/58277cf1102f1f256674567e69baaaf69458cf78)

该宏包 `amsmath` 该宏需要 `\to`；如果没有这个宏包， `\rightarrow` 必须使用。

注意极限声明可以包含下标。参见 [参考指南](#reference-guide) 以获取可用运算符的完整列表。

某些语言可能会添加或更改一些命令，请查看 [主页](/latex/zh-cn/readme.md) 以获取特定语言的文章。

## 定义你自己的运算符

如果你需要添加一个自定义运算符以直立体而不是斜体显示，请使用 `\DeclareMathOperator`

```latex
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\arctg}{arctg}
\begin{document}
反正切的用户自定义运算符：
\[
    \arctg \frac{\pi}{3} = \sqrt{3}
.\]
\end{document}
```

[在 Overleaf 中打开此示例](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=Example+defining+an+operator\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamsmath%7D%0A%5CDeclareMathOperator%7B%5Carctg%7D%7Barctg%7D%0A%5Cbegin%7Bdocument%7D%0AUser-defined+operator+for+arctangent%3A%0A%5C%5B%0A++++%5Carctg+%5Cfrac%7B%5Cpi%7D%7B3%7D+%3D+%5Csqrt%7B3%7D%0A.%5C%5D%0A%5Cend%7Bdocument%7D)

此示例生成以下输出：

![OperatorsEx3.png](/files/80bc6c58b35ae39771a15521237f6d75a18d66a0)

命令 `\DeclareMathOperator` 接受两个参数，第一个是新运算符的名称，第二个是要显示的文本。要使该命令生效，你必须导入宏包 **amsmath** 在导言区中使用

```latex
\usepackage{amsmath}
```

如果你需要定义的运算符使用下标，该命令可以稍作修改，例如 `\lim` 运算符，在这种情况下请使用 `\DeclareMathOperator*`.

## 参考指南

**数学运算符完整列表**

| 运算符       | 显示为         |
| --------- | ----------- |
| `\cos`    | $$\cos$$    |
| `\csc`    | $$\csc$$    |
| `\exp`    | $$\exp$$    |
| `\ker`    | $$\ker$$    |
| `\limsup` | $$\limsup$$ |
| `\min`    | $$\min$$    |
| `\sinh`   | $$\sinh$$   |
| `\arcsin` | $$\arcsin$$ |
| `\cosh`   | $$\cosh$$   |
| `\deg`    | $$\deg$$    |
| `\gcd`    | $$\gcd$$    |
| `\lg`     | $$\lg$$     |
| `\ln`     | $$\ln$$     |
| `\Pr`     | $$\Pr$$     |
| `\sup`    | $$\sup$$    |
| `\arctan` | $$\arctan$$ |
| `\cot`    | $$\cot$$    |
| `\det`    | $$\det$$    |
| `\hom`    | $$\hom$$    |
| `\lim`    | $$\lim$$    |
| `\log`    | $$\log$$    |
| `\sec`    | $$\sec$$    |
| `\tan`    | $$\tan$$    |
| `\arg`    | $$\arg$$    |
| `\coth`   | $$\coth$$   |
| `\dim`    | $$\dim$$    |
| `\liminf` | $$\liminf$$ |
| `\max`    | $$\max$$    |
| `\sin`    | $$\sin$$    |
| `\tanh`   | $$\tanh$$   |

## 进一步阅读

更多信息请参见

* [数学表达式](/latex/zh-cn/shu-xue/01-mathematical-expressions.md)
* [下标和上标](/latex/zh-cn/shu-xue/02-subscripts-and-superscripts.md)
* [分数和二项式](/latex/zh-cn/shu-xue/05-fractions-and-binomials.md)
* [数学模式中的间距](/latex/zh-cn/shu-xue/08-spacing-in-math-mode.md)
* [积分、求和与极限](/latex/zh-cn/shu-xue/09-integrals-sums-and-limits.md)
* [数学模式中的显示样式](/latex/zh-cn/shu-xue/10-display-style-in-math-mode.md)
* [LaTeX2ε 不那么简短的介绍](http://www.ctan.org/tex-archive/info/lshort/)


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