예제 #1
0
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);
}
예제 #2
0
void FactorInt(FacVec& fvec, long n)
{
   if (n <= 1) LogicError("internal error: FactorInt(FacVec,long n) with n<=1");

   if (NTL_OVERFLOW(n, 1, 0))
      ResourceError("internal error: FactorInt(FacVec,long n) with n too large");

   long NumFactors;
   long q;

   fvec.SetLength(2*NextPowerOfTwo(n));

   NumFactors = 0;
   q = 2;

   while (n != 1) {
      if (n%q == 0) {
         fvec[NumFactors].q = q;
         n = n/q;
         fvec[NumFactors].a = 1;
         fvec[NumFactors].val = q;
         while (n%q == 0) {
            n = n/q;
            (fvec[NumFactors].a)++;
            fvec[NumFactors].val *= q;
         }         
         fvec[NumFactors].link = -1;
         NumFactors++;
      }

      q++;
   }

   fvec.SetLength(2*NumFactors-1);

   long lo = 0;
   long hi = NumFactors - 1;

   while (lo < hi) {
      FindMin(fvec, lo, hi);
      FindMin(fvec, lo+1, hi);
      hi++;
      fvec[hi].link = lo;
      fvec[hi].val = fvec[lo].val * fvec[lo+1].val;
      lo += 2;
   }
}
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);
}