NumberFieldRootsOfUnity

NumberFieldRootsOfUnity[a]

gives the roots of unity for the field generated by the algebraic number a.

Details

Examples

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Basic Examples  (2)

Scope  (4)

Radical expressions:

Root objects:

AlgebraicNumber objects:

NumberFieldRootsOfUnity automatically threads over lists:

Properties & Relations  (2)

A list of roots of unity in the field :

Roots of unity are also algebraic integers and units:

And they all have norm :

Use RootReduce to get canonical complex expressions:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_numberfieldrootsofunity, author="Wolfram Research", title="{NumberFieldRootsOfUnity}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/NumberFieldRootsOfUnity.html}", note=[Accessed: 22-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_numberfieldrootsofunity, organization={Wolfram Research}, title={NumberFieldRootsOfUnity}, year={2007}, url={https://reference.wolfram.com/language/ref/NumberFieldRootsOfUnity.html}, note=[Accessed: 22-February-2025 ]}