exterior()

FreeModule * FreeModule::exterior

(

int

p

)

const

Definition at line 296 of file freemod.cpp.

{
  FreeModule *result;
  if (pp == 0)
    return R->make_FreeModule(1);
  else
    result = new_free();
 
  int rk = rank();
  if (pp > rk || pp < 0) return result;
 
  size_t p = static_cast<size_t>(pp);
 
  Subset a(p, 0);
  for (size_t i = 0; i < p; i++) a[i] = i;
 
  auto D = R->degree_monoid();
  monomial deg = D->make_one();
  do
    {
      D->one(deg);
 
      for (size_t r = 0; r < p; r++)
        D->mult(deg, degree(static_cast<int>(a[r])), deg);
 
      result->append(deg);
    }
  while (Subsets::increment(rk, a));
 
  D->remove(deg);
 
  if (schreyer != nullptr) result->schreyer = schreyer->exterior(pp);
  return result;
}

References degree(), FreeModule(), Subsets::increment(), monomial, new_free(), p, R, rank(), result(), and schreyer.

Referenced by IM2_FreeModule_exterior(), and Matrix::wedge_product().