wedge_product()

Matrix * Matrix::wedge_product ( int p, int q, const FreeModule * F )

static

Definition at line 1272 of file matrix.cpp.

{
  const FreeModule *Fp = F->exterior(p);
  const FreeModule *Fq = F->exterior(q);
  const FreeModule *Fn = F->exterior(p + q);
  const FreeModule *G = Fp->tensor(Fq);
  const Ring *R = F->get_ring();
 
  MatrixConstructor mat(Fn, G, nullptr);
 
  if (p < 0 || q < 0 || p + q > F->rank()) return mat.to_matrix();
 
  if (p == 0 || q == 0)
    {
      for (int i = 0; i < G->rank(); i++) mat.set_entry(i, i, R->one());
      return mat.to_matrix();
    }
 
  Subsets C(F->rank(), p + q);
  Subset a(p, 0);
  Subset b(q, 0);
  Subset c(p + q, 0);
  int col = 0;
 
  for (int i = 0; i < Fp->rank(); i++)
    {
      C.decode(i, a);
      for (int j = 0; j < Fq->rank(); j++)
        {
          C.decode(j, b);
          int sgn = Subsets::concatenateSubsets(a, b, c);
          if (sgn == 0)
            {
              col++;
              continue;
            }
          ring_elem r = R->from_long(sgn);
          int row = static_cast<int>(C.encode(c));
          mat.set_entry(row, col++, r);
        }
    }
  return mat.to_matrix();
}

References Subsets::concatenateSubsets(), Subsets::decode(), Subsets::encode(), FreeModule::exterior(), FreeModule, Ring::from_long(), G, FreeModule::get_ring(), Matrix(), MatrixConstructor, Ring::one(), p, FreeModule::rank(), MatrixConstructor::set_entry(), FreeModule::tensor(), MatrixConstructor::to_matrix(), and wedge_product().

Referenced by wedge_product().