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CyclotomicFactorIndexes    --    find indexes of cyclotomic factors of a polynomial


Syntax
CyclotomicFactorIndexes(f: RINGELEM): LIST of INT
CyclotomicFactors_BeukersSmyth(f: RINGELEM): RECORD
CyclotomicFactors(f: RINGELEM): RECORD

Description
The function CyclotomicFactorIndexes computes a list of indexes of the cyclotomic factors of the univariate polynomial f; it may contain some false positives (typically 3, 4 and/or 6).

The function CyclotomicFactors_BeukersSmyth produces a factorization of the product of all cyclotomic factors in f; these factors are coprime.

The function CyclotomicFactors computes the cyclotomic factors of the univariate polynomial f; it can be slower than CyclotomicFactorIndexes.

Example
/**/  use QQ[z];
/**/  f := (z^2+1)^2 * (z^4+z^2+1);
/**/  CyclotomicFactorIndexes(f);
[3, 4, 6]
/**/  CyclotomicFactors(f);
record[RemainingFactor:=1, factors := [z^2+z+1, z^2-z+1, z^2+1], multiplicities := [1, 1, 2]]
/**/  CyclotomicFactors_BeukersSmyth(f);
record[RemainingFactor:=1, factors := [z^4+z^2+1, z^2+1], multiplicities := [1, 2]]

See Also