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AlgebraicNumberDenominator[a]

给出使得 n a 为代数整数的最小正整数 n.

范例  
基本范例  
范围  
应用  
属性和关系  
可能存在的问题  
参见
技术笔记
相关指南
历史
按以下格式引用：

AlgebraicNumberDenominator

AlgebraicNumberDenominator[a]

给出使得 n a 为代数整数的最小正整数 n.

范例

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基本范例  (1)

计算简单代数数的分母：

Wolfram Language code: AlgebraicNumberDenominator[1 / Sqrt[3]]
Wolfram Language code: AlgebraicNumberDenominator[(1 + Sqrt[5]) / 2]

范围  (3)

根表达式：

Wolfram Language code: AlgebraicNumberDenominator[1 / Sqrt[Sqrt[2] + 3]]
Wolfram Language code: AlgebraicNumberDenominator[(1 + 3I) ^ (-1 / 3)]

Root 和 AlgebraicNumber 对象：

Wolfram Language code: AlgebraicNumberDenominator[Root[5 - 6#1 + 3#1 ^ 3 &, 1]]
Wolfram Language code: AlgebraicNumberDenominator[AlgebraicNumber[Sqrt[2], {1 / 5, 1}]]

AlgebraicNumberDenominator 自动线性作用于列表：

Wolfram Language code: AlgebraicNumberDenominator[{Sqrt[2], 1 / Sqrt[2], 1 / 3}]

应用  (1)

以代数整数 α 和一个整数 n 的商 α/n 的形式表示 1/(1+)：

Wolfram Language code: n = AlgebraicNumberDenominator[1 / (1 + Sqrt[3])]
Wolfram Language code: α = n ToNumberField[1 / (1 + Sqrt[3]), Sqrt[3]]
Wolfram Language code: AlgebraicIntegerQ[α]

属性和关系  (2)

对一个代数整数 n 而言，其分母为 1：

Wolfram Language code: AlgebraicNumberDenominator[Sqrt[2]]

将一个代数数和其分母相乘得到一个代数整数：

Wolfram Language code: α = 1 / Sqrt[1 + I];
Wolfram Language code: AlgebraicIntegerQ[α]
Wolfram Language code: AlgebraicIntegerQ[AlgebraicNumberDenominator[α]α]

可能存在的问题  (1)

参数必须是一个代数数：

Wolfram Language code: AlgebraicNumberDenominator[Pi]
Wolfram Language code: Element[Pi, Algebraics]
Wolfram Research (2007)，AlgebraicNumberDenominator，Wolfram 语言函数，https://reference.wolfram.com/language/ref/AlgebraicNumberDenominator.html.

文本

Wolfram Research (2007)，AlgebraicNumberDenominator，Wolfram 语言函数，https://reference.wolfram.com/language/ref/AlgebraicNumberDenominator.html.

CMS

Wolfram 语言. 2007. "AlgebraicNumberDenominator." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/AlgebraicNumberDenominator.html.

APA

Wolfram 语言. (2007). AlgebraicNumberDenominator. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/AlgebraicNumberDenominator.html 年

BibTeX

@misc{reference.wolfram_2026_algebraicnumberdenominator, author="Wolfram Research", title="{AlgebraicNumberDenominator}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/AlgebraicNumberDenominator.html}", note=[Accessed: 15-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_algebraicnumberdenominator, organization={Wolfram Research}, title={AlgebraicNumberDenominator}, year={2007}, url={https://reference.wolfram.com/language/ref/AlgebraicNumberDenominator.html}, note=[Accessed: 15-August-2026]}