long ComputeDegree(const ZZ_pX& h, const ZZ_pXModulus& F)
// f = F.f is assumed to be an "equal degree" polynomial
// h = X^p mod f
// the common degree of the irreducible factors of f is computed
{
if (F.n == 1 || IsX(h)) return 1;
FacVec fvec;
FactorInt(fvec, F.n);
return RecComputeDegree(fvec.length()-1, h, F, fvec);
}
void BuildIrred(ZZ_pEX& f, long n)
{
if (n <= 0)
LogicError("BuildIrred: n must be positive");
if (NTL_OVERFLOW(n, 1, 0)) ResourceError("overflow in BuildIrred");
if (n == 1) {
SetX(f);
return;
}
FacVec fvec;
FactorInt(fvec, n);
RecBuildIrred(f, fvec.length()-1, fvec);
}
long DetIrredTest(const ZZ_pEX& f)
{
if (deg(f) <= 0) return 0;
if (deg(f) == 1) return 1;
ZZ_pEXModulus F;
build(F, f);
ZZ_pEX h;
FrobeniusMap(h, F);
ZZ_pEX s;
PowerCompose(s, h, F.n, F);
if (!IsX(s)) return 0;
FacVec fvec;
FactorInt(fvec, F.n);
return RecIrredTest(fvec.length()-1, h, F, fvec);
}