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Mathematica > Mathematics and Algorithms > Number Theory > Algebraic Number Theory >

Built-in Mathematica Symbol

RootOfUnityQ

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

Radical expressions:

Root objects:

Transcendental objects:

RootOfUnityQ threads automatically over lists:

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:

Approximate numbers will always return False:

Use RootApproximant to get an exact number: