gives the roots of unity for the field 
generated by the algebraic number 
.
NumberFieldRootsOfUnity
gives the roots of unity for the field 
generated by the algebraic number 
.
Details
- NumberFieldRootsOfUnity gives a list of all algebraic numbers
in the field 
for which 
for some 
. - NumberFieldRootsOfUnity returns any
other than 
as AlgebraicNumber objects in the field 
.
Examples
open all close allBasic Examples (2)
Scope (4)
NumberFieldRootsOfUnity[Sqrt[-3]]Root objects:
NumberFieldRootsOfUnity[Root[9 - 2 #1 ^ 2 + #1 ^ 4&, 1]]AlgebraicNumber objects:
NumberFieldRootsOfUnity[AlgebraicNumber[Root[# ^ 4 - # ^ 2 + 1&, 1], {1, 2, 3, 1}]]NumberFieldRootsOfUnity automatically threads over lists:
NumberFieldRootsOfUnity[{Sqrt[2], I 2 ^ (1 / 3)}]Properties & Relations (2)
A list of roots of unity in the field 
:
roots = NumberFieldRootsOfUnity[1 + I Sqrt[3]]Roots of unity are also algebraic integers and units:
AlgebraicIntegerQ[roots]AlgebraicUnitQ[roots]
AlgebraicNumberNorm[roots]Use RootReduce to get canonical complex expressions:
NumberFieldRootsOfUnity[I + 2 ^ (1 / 3)]RootReduce[%]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