koszul() [1/2]

Matrix * Matrix::koszul ( const Matrix * rows, const Matrix * cols )

static

Definition at line 1225 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) return nullptr;
  const Ring *K = P->getCoefficients();
  const Monoid *M = P->getMonoid();
 
  MatrixConstructor mat(F, c->cols(), nullptr);
 
  int nvars = M->n_vars();
  int nrows = r->n_cols();
  int ncols = c->n_cols();
  const_monomial a, b;
  exponents_t aexp = newarray_atomic(int, nvars);
  exponents_t bexp = newarray_atomic(int, nvars);
  exponents_t result_exp = newarray_atomic(int, nvars);
  for (int i = 0; i < ncols; i++)
    {
      if (c->elem(i) == nullptr) continue;
      a = P->lead_flat_monomial(c->elem(i)->coeff);
      M->to_expvector(a, aexp);
      for (int j = 0; j < nrows; j++)
        {
          if (r->elem(j) == nullptr) continue;
          b = P->lead_flat_monomial(r->elem(j)->coeff);
          M->to_expvector(b, bexp);
          int sign = signdivide(nvars, aexp, bexp, result_exp);
          if (sign != 0)
            {
              monomial m = M->make_one();
              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(j, i, f);
            }
        }
    }
  freemem(aexp);
  freemem(bexp);
  freemem(result_exp);
  return mat.to_matrix();
}

References Ring::cast_to_PolynomialRing(), cols(), elem(), freemem(), FreeModule, Monoid::from_expvector(), FreeModule::get_ring(), PolynomialRing::getCoefficients(), PolynomialRing::getMonoid(), koszul(), PolynomialRing::lead_flat_monomial(), PolynomialRing::make_flat_term(), Monoid::make_one(), Matrix(), MatrixConstructor, Ring::minus_one(), monomial, n_cols(), Monoid::n_vars(), newarray_atomic, Ring::one(), s, MatrixConstructor::set_entry(), signdivide(), Monoid::to_expvector(), and MatrixConstructor::to_matrix().