NumberFieldNormRepresentatives

NumberFieldNormRepresentatives[a,m]

gives a list of representatives of classes of algebraic integers of norm +/-m in the field generated by the algebraic number a.

Details

  • Algebraic integers are considered to be in the same class if their quotient is a unit in the field .
  • All elements of the number field with norm +/-m can be obtained from the representatives by multiplication by units in the field.

Examples

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Basic Examples  (1)

Find the representatives of classes of algebraic integers of norm in :

Scope  (4)

Radical expressions:

Root objects:

AlgebraicNumber objects:

NumberFieldNormRepresentatives automatically threads over lists:

Properties & Relations  (5)

Representatives of norm in :

The number has norm :

It can be represented in terms of the representative by multiplying by a unit:

Obtain all elements of norm in by multiplying representatives with units:

Elements generated by :

Elements generated by :

FindInstance gives all Gaussian integers of norm :

Check the result:

Find an instance of a quadratic equation :

Find the representatives of classes of algebraic integers of norm in :

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_numberfieldnormrepresentatives, author="Wolfram Research", title="{NumberFieldNormRepresentatives}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/NumberFieldNormRepresentatives.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_numberfieldnormrepresentatives, organization={Wolfram Research}, title={NumberFieldNormRepresentatives}, year={2007}, url={https://reference.wolfram.com/language/ref/NumberFieldNormRepresentatives.html}, note=[Accessed: 21-December-2024 ]}