RootOfUnityQ
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RootOfUnityQ
Examples
open allclose allBasic Examples (1)Summary of the most common use cases

https://wolfram.com/xid/0v5zw1r0qshy7-zdrcn


https://wolfram.com/xid/0v5zw1r0qshy7-ezux9n

Scope (5)Survey of the scope of standard use cases

https://wolfram.com/xid/0v5zw1r0qshy7-ftwumt

Root objects:

https://wolfram.com/xid/0v5zw1r0qshy7-uuo64p

AlgebraicNumber objects:

https://wolfram.com/xid/0v5zw1r0qshy7-jz69lg


https://wolfram.com/xid/0v5zw1r0qshy7-mk81wz

RootOfUnityQ threads automatically over lists:

https://wolfram.com/xid/0v5zw1r0qshy7-v8wun2

Properties & Relations (4)Properties of the function, and connections to other functions
Roots of unity are solutions of for some integer n:

https://wolfram.com/xid/0v5zw1r0qshy7-57v67s

https://wolfram.com/xid/0v5zw1r0qshy7-7vw1cj

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

https://wolfram.com/xid/0v5zw1r0qshy7-zjlipo


https://wolfram.com/xid/0v5zw1r0qshy7-c36xrn

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

https://wolfram.com/xid/0v5zw1r0qshy7-ypm


https://wolfram.com/xid/0v5zw1r0qshy7-m6b

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

https://wolfram.com/xid/0v5zw1r0qshy7-0mxkoy

https://wolfram.com/xid/0v5zw1r0qshy7-ixr85k


https://wolfram.com/xid/0v5zw1r0qshy7-6i073w

Roots of cyclotomic polynomials are roots of unity:

https://wolfram.com/xid/0v5zw1r0qshy7-fmhqim


https://wolfram.com/xid/0v5zw1r0qshy7-fhx8f2

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

https://wolfram.com/xid/0v5zw1r0qshy7-4a3egw


https://wolfram.com/xid/0v5zw1r0qshy7-ptssnu

Possible Issues (1)Common pitfalls and unexpected behavior
Approximate numbers will always return False:

https://wolfram.com/xid/0v5zw1r0qshy7-g46gtl

Use RootApproximant to get an exact number:

https://wolfram.com/xid/0v5zw1r0qshy7-b3x3b4


https://wolfram.com/xid/0v5zw1r0qshy7-iz5src

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.
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.
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
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: 04-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: 04-April-2025
]}