# AlgebraicNumberNorm

gives the norm of the algebraic number a.

# Details and Options

• The norm of a is defined to be the product of the roots of its minimal polynomial.
• AlgebraicNumberNorm[a,Extension->θ] finds the norm of a over the field .

# Examples

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## Basic Examples(1)

Norms of algebraic numbers:

## Scope(4)

Integers and rational numbers:

Radical expressions:

Root and AlgebraicNumber objects:

AlgebraicNumberNorm automatically threads over lists:

Norm of over :

## Applications(1)

is irreducible in :

Since AlgebraicNumberNorm is multiplicative, having a prime norm implies the original number is prime:

## Properties & Relations(3)

AlgebraicNumberNorm is multiplicative:

Units in a number field have norm :

Compute the smallest field that includes , i.e. :

Compute the norm in that field:

## Neat Examples(1)

Plot of norms of elements in :

Wolfram Research (2007), AlgebraicNumberNorm, Wolfram Language function, https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html.

#### Text

Wolfram Research (2007), AlgebraicNumberNorm, Wolfram Language function, https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html.

#### CMS

Wolfram Language. 2007. "AlgebraicNumberNorm." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html.

#### APA

Wolfram Language. (2007). AlgebraicNumberNorm. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html

#### BibTeX

@misc{reference.wolfram_2024_algebraicnumbernorm, author="Wolfram Research", title="{AlgebraicNumberNorm}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html}", note=[Accessed: 27-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_algebraicnumbernorm, organization={Wolfram Research}, title={AlgebraicNumberNorm}, year={2007}, url={https://reference.wolfram.com/language/ref/AlgebraicNumberNorm.html}, note=[Accessed: 27-May-2024 ]}