RootOfUnityQ

RootOfUnityQ[a]

yields True if a is a root of unity, and yields False otherwise.

Details

  • An algebraic number a is a root of unity if an=1 for some integer n.

Examples

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Basic Examples  (1)

Scope  (5)

Radical expressions:

Root objects:

AlgebraicNumber objects:

Transcendental objects:

RootOfUnityQ threads automatically over lists:

Properties & Relations  (4)

Roots of unity are solutions of for some integer n:

All roots of unity are algebraic integers that lie on the unit circle:

Not all algebraic numbers on the unit circle are roots of unity:

The minimal polynomial of a root of unity is a cyclotomic polynomial or one of its factor:

Roots of cyclotomic polynomials are roots of unity:

Use NumberFieldRootsOfUnity to find all roots of unity in a number field:

Possible Issues  (1)

Approximate numbers will always return False:

Use RootApproximant to get an exact number:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_rootofunityq, author="Wolfram Research", title="{RootOfUnityQ}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/RootOfUnityQ.html}", note=[Accessed: 26-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_rootofunityq, organization={Wolfram Research}, title={RootOfUnityQ}, year={2007}, url={https://reference.wolfram.com/language/ref/RootOfUnityQ.html}, note=[Accessed: 26-April-2025 ]}