rawGCDRingElement()

const RingElement * rawGCDRingElement	(	const RingElement *	f,
		const RingElement *	g,
		const RingElement *	mipo,
		M2_bool	inExtension )

Polynomial GCD and factorization interface routines via Factory and MPSolve

Definition at line 488 of file factory.cpp.

{
  const RingElement *ret = nullptr;
  const PolynomialRing *P = f->get_ring()->cast_to_PolynomialRing();
  const PolynomialRing *P2 = g->get_ring()->cast_to_PolynomialRing();
  if (P == nullptr)
    {
      if (f->get_ring()->cast_to_Tower() != nullptr) return towerGCD(f, g);
      // else we really do have an error:
      ERROR("expected polynomial ring");
      return nullptr;
    }
  if (P != P2)
    {
      ERROR("encountered different rings");
      return nullptr;
    }
  {
    struct enter_factory foo(P);
    if (foo.mode == modeError)
      {
        algebraicElement_M2 = nullptr;
        return nullptr;
      }
    if (foo.mode == modeGF)
      {
        assert(!inExtension);
        set_GF_minimal_poly(P);
      }
    if (inExtension)
      {
        CanonicalForm minp = convertToFactory(*mipo, false);
        algebraicElement_Fac = rootOf(minp, 'a');
      }
    CanonicalForm p = convertToFactory(*f, inExtension);
    CanonicalForm q = convertToFactory(*g, inExtension);
    CanonicalForm h = gcd(p, q);
    if (inExtension)
      {
        assert(foo.mode != modeGF);
        algebraicElement_M2 = RingElement::make_raw(
            P, P->var(P->n_vars() - 1));  // the algebraic generator is always
                                          // the last variable in M2, the first
                                          // one in factory
      }
    ret = convertToM2(P, h);
    if (error())
      {
        algebraicElement_M2 = nullptr;
        return nullptr;
      }
  }
  if (ret->is_zero()) return ret;
  ring_elem a = P->getNumeratorRing()->preferred_associate_divisor(
      ret->get_value());  // an element in the coeff ring
  ring_elem b = P->getCoefficients()->invert(a);
  ring_elem r = ret->get_value();
  P->mult_coeff_to(b, r);
  algebraicElement_M2 = nullptr;
  return RingElement::make_raw(P, r);
}

References algebraicElement_Fac, algebraicElement_M2, Ring::cast_to_PolynomialRing(), Ring::cast_to_Tower(), convertToFactory(), convertToM2(), ERROR, error(), RingElement::get_ring(), RingElement::get_value(), PolynomialRing::getCoefficients(), PolynomialRing::getNumeratorRing(), Ring::invert(), RingElement::is_zero(), RingElement::make_raw(), enter_factory::mode, modeError, modeGF, PolynomialRing::mult_coeff_to(), p, PolyRing::preferred_associate_divisor(), and towerGCD().

Referenced by LocalRing::lift_up(), FractionField::lower_content(), LocalRing::lower_content(), FractionField::simplify(), and LocalRing::simplify().