polcyclofactors

Function: polcyclofactors
Section: polynomials
C-Name: polcyclofactors
Prototype: G
Help: polcyclofactors(f): returns a vector of polynomials, whose product is
 the product of distinct cyclotomic polynomials dividing f.
Doc: returns a vector of polynomials, whose product is the product of
 distinct cyclotomic polynomials dividing $f$.
 \bprog
 ? f = x^10+5*x^8-x^7+8*x^6-4*x^5+8*x^4-3*x^3+7*x^2+3;
 ? v = polcyclofactors(f)
 %2 = [x^2 + 1, x^2 + x + 1, x^4 - x^3 + x^2 - x + 1]
 ? apply(poliscycloprod, v)
 %3 = [1, 1, 1]
 ? apply(poliscyclo, v)
 %4 = [4, 3, 10]
 @eprog\noindent In general, the polynomials are products of cyclotomic
 polynomials and not themselves irreducible:
 \bprog
 ? g = x^8+2*x^7+6*x^6+9*x^5+12*x^4+11*x^3+10*x^2+6*x+3;
 ? polcyclofactors(g)
 %2 = [x^6 + 2*x^5 + 3*x^4 + 3*x^3 + 3*x^2 + 2*x + 1]
 ? factor(%[1])
 %3 =
 [            x^2 + x + 1 1]

 [x^4 + x^3 + x^2 + x + 1 1]
 @eprog