koszul() [2/2]

Matrix * Matrix::koszul

(

int

p

)

const

Definition at line 1087 of file matrix.cpp.

{
  if (n_rows() != 1)
    {
      ERROR("expected a matrix with one row");
      return nullptr;
    }
 
  FreeModule *F = cols()->exterior(p - 1);
  FreeModule *G = cols()->exterior(p);
  const Ring *R = get_ring();
  MatrixConstructor mat(F, G, degree_shift());
  if (p <= 0 || p > n_cols()) return mat.to_matrix();
 
  Subsets C(n_cols(), p);
  Subset a(p, 0);
  for (int c = 0; c < G->rank(); c++)
    {
      C.decode(c, a);
      int negate = ((p % 2) != 0);
      for (int r = p - 1; r >= 0; r--)
        {
          negate = !negate;
          size_t x = C.encodeBoundary(r, a);
          ring_elem f = elem(0, static_cast<int>(a[r]));
          if (negate) R->negate_to(f);
 
          mat.set_entry(static_cast<int>(x), c, f);
        }
    }
  return mat.to_matrix();
}

References cols(), Subsets::decode(), degree_shift(), elem(), Subsets::encodeBoundary(), ERROR, FreeModule, G, get_ring(), koszul(), Matrix(), MatrixConstructor, n_cols(), n_rows(), Ring::negate_to(), p, MatrixConstructor::set_entry(), MatrixConstructor::to_matrix(), and x.

Referenced by IM2_Matrix_koszul(), koszul(), and koszul().