koszul_monomials()

Matrix * Matrix::koszul_monomials ( int nskew, const Matrix * rows, const Matrix * cols )

static

Definition at line 1162 of file matrix.cpp.

{
  // First check rings: r,c,'this' should be row vectors.
  // and the ring should be a polynomial ring
  const FreeModule *F = r->cols();
 
  const PolynomialRing *P = F->get_ring()->cast_to_PolynomialRing();
  if (P == nullptr)
    {
      ERROR("expected polynomial ring");
      return nullptr;
    }
  const MonomialIdeal *A = makemonideal(r);
 
  const Ring *K = P->getCoefficients();
  const Monoid *M = P->getMonoid();
 
  MatrixConstructor mat(F, c->cols(), nullptr);
 
  int nvars = M->n_vars();
  int *skew_list = newarray_atomic(int, nskew);
  for (int j = 0; j < nskew; j++) skew_list[j] = j;
  SkewMultiplication skew(nvars, nskew, skew_list);
  int ncols = c->n_cols();
 
  exponents_t aexp = newarray_atomic(int, nvars);
  exponents_t bexp = newarray_atomic(int, nvars);
  exponents_t result_exp = newarray_atomic(int, nvars);
  monomial m = M->make_one();
  VECTOR(Bag *) divisors;
  for (int i = 0; i < ncols; i++)
    {
      if (c->elem(i) == nullptr) continue;
      const_monomial a = P->lead_flat_monomial(c->elem(i)->coeff);
      M->to_expvector(a, aexp);
      divisors.clear();
      A->find_all_divisors(aexp, divisors);
      for (int j = 0; j < divisors.size(); j++)
        {
          int rownum = divisors[j]->basis_elem();
          const_monomial b = P->lead_flat_monomial(r->elem(rownum)->coeff);
          M->to_expvector(b, bexp);
          exponents::divide(nvars, aexp, bexp, result_exp);
          int sign = skew.mult_sign(result_exp, bexp);
          if (sign != 0)
            {
              M->from_expvector(result_exp, m);
              ring_elem s = (sign > 0 ? K->one() : K->minus_one());
              ring_elem f = P->make_flat_term(s, m);
              mat.set_entry(rownum, i, f);
            }
        }
    }
  freemem(aexp);
  freemem(bexp);
  freemem(result_exp);
  return mat.to_matrix();
}

References Ring::cast_to_PolynomialRing(), cols(), ExponentVector< int, true >::divide(), elem(), ERROR, MonomialIdeal::find_all_divisors(), freemem(), FreeModule, Monoid::from_expvector(), FreeModule::get_ring(), PolynomialRing::getCoefficients(), PolynomialRing::getMonoid(), koszul_monomials(), PolynomialRing::lead_flat_monomial(), PolynomialRing::make_flat_term(), Monoid::make_one(), makemonideal(), Matrix(), MatrixConstructor, Ring::minus_one(), monomial, SkewMultiplication::mult_sign(), n_cols(), Monoid::n_vars(), newarray_atomic, Ring::one(), s, MatrixConstructor::set_entry(), Monoid::to_expvector(), MatrixConstructor::to_matrix(), and VECTOR.

Referenced by koszul_monomials().