> 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-tw/shu-xue/07-operators.md).

# 運算子

數學模式中的字元通常會以斜體顯示，但有時某些函數名稱需要不同的格式；這可以透過使用 LaTeX 中定義的運算子來完成。

## 簡介

三角函數、對數及其他函數可以透過一些特殊指令寫入文件中，如下列範例所示：

```latex
數學運算子的範例：
\[
    \sin(a + b) = \sin a \cos b + \cos a \sin b
.\]
```

[在 Overleaf 中開啟此範例](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)

此範例會產生以下輸出：

![Newsincos.png](/files/6c96f27bf850caffe7a99acccfb1bfb20878ce85)

這些指令會以正體（羅馬）文字而非斜體輸出函數名稱。

## 不同情境中的運算子

某些運算子可以接受以特殊方式處理的參數，例如極限。

```latex
\documentclass{article}
\usepackage{amsmath}
\begin{document}
極限定記號測試
\[
    \lim_{h \to 0 } \frac{f(x+h)-f(x)}{h}
.\]
當此運算子與
文字 \( \lim_{h \to 0} (x-h) \) 一起使用時會改變。
\end{document}
```

[在 Overleaf 中開啟此範例](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)

此範例會產生以下輸出：

![OperatorsEx2.png](/files/d3f73af46ab9a56f77fdcae9e7dee581565974fe)

套件 `amsmath` 是巨集所需的 `\to`；若沒有此套件，則必須使用 `\rightarrow` 。

請注意，極限定義可以包含下標。請參閱 [參考指南](#reference-guide) 以取得可用運算子的完整清單。

某些語言可能會新增或變更某些指令，請查看 [主頁](/latex/zh-tw/readme.md) 以查看特定語言的文章。

## 定義您自己的運算子

如果您需要新增一個個人化運算子，使其以羅馬字體而非斜體顯示，請使用 `\DeclareMathOperator`

```latex
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\arctg}{arctg}
\begin{document}
反正切的使用者自訂運算子：
\[
    \arctg \frac{\pi}{3} = \sqrt{3}
.\]
\end{document}
```

[在 Overleaf 中開啟此範例](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)

此範例會產生以下輸出：

![OperatorsEx3.png](/files/443522e7c7c900f9707d7b1b11300228c07eb780)

指令 `\DeclareMathOperator` 需要兩個參數，第一個是新運算子的名稱，第二個是要顯示的文字。要使此指令運作，您必須在導言區匯入套件 **amsmath** 並使用

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

如果您定義的運算子需要使用下標，則可稍微修改此指令，例如 `\lim` 運算子，在此情況下請使用 `\DeclareMathOperator*`.

## 參考指南

**數學運算子的完整清單**

| 運算子       | 顯示為         |
| --------- | ----------- |
| `\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`   | $$\tanh$$   |

## 延伸閱讀

更多資訊請參見

* [數學表達式](/latex/zh-tw/shu-xue/01-mathematical-expressions.md)
* [下標與上標](/latex/zh-tw/shu-xue/02-subscripts-and-superscripts.md)
* [分數與二項式係數](/latex/zh-tw/shu-xue/05-fractions-and-binomials.md)
* [數學模式中的間距](/latex/zh-tw/shu-xue/08-spacing-in-math-mode.md)
* [積分、加總與極限](/latex/zh-tw/shu-xue/09-integrals-sums-and-limits.md)
* [數學模式中的顯示樣式](/latex/zh-tw/shu-xue/10-display-style-in-math-mode.md)
* [LaTeX2ε 的不算太短的入門介紹](http://www.ctan.org/tex-archive/info/lshort/)


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