initialize_weyl()

bool WeylAlgebra::initialize_weyl ( M2_arrayint derivs, M2_arrayint comms, int homog_var )

private

Definition at line 10 of file weylalg.cpp.

{
  if (homog_var >= nvars_)
    {
      ERROR("Weyl algebra homogenizing variable out of range");
      return false;
    }
  if (homog_var < 0) _homog_var = -1;
  if (derivs->len != comms->len)
    {
      ERROR("Weyl algebra: expected arrays of the same length");
      return false;
    }
  for (unsigned int i = 0; i < derivs->len; i++)
    {
      if (derivs->array[i] < 0 || derivs->array[i] >= nvars_)
        {
          ERROR("Weyl algebra: variable out of range");
          return false;
        }
      if (comms->array[i] < 0 || comms->array[i] >= nvars_)
        {
          ERROR("Weyl algebra: variable out of range");
          return false;
        }
    }
 
  this->_nderivatives = derivs->len;
  this->_homogeneous_weyl_algebra = (homog_var >= 0);
  this->_homog_var = homog_var;
 
  this->_derivative = newarray_atomic(int, _nderivatives);
  this->_commutative = newarray_atomic(int, _nderivatives);
  for (int i = 0; i < _nderivatives; i++)
    {
      this->_derivative[i] = derivs->array[i];
      this->_commutative[i] = comms->array[i];
    }
 
  // Now set whether this ring is graded.  This will be the case iff
  // deg(x_i) + deg(D_i) = 2 deg(h), for every i.
 
  if (_homog_var < 0)
    {
      bool isgraded = true;
      auto D = degree_monoid();
      monomial degxD = D->make_one();
      for (int j = 0; j < _nderivatives; j++)
        {
          const_monomial degx = M_->degree_of_var(_commutative[j]);
          const_monomial degD = M_->degree_of_var(_derivative[j]);
          D->mult(degx, degD, degxD);
          if (not D->is_one(degxD))
            {
              isgraded = false;
              break;
            }
        }
      this->setIsGraded(isgraded);
    }
  else
    {
      this->setIsGraded(true);
      auto D = degree_monoid();
      const_monomial degh = M_->degree_of_var(_homog_var);
      monomial deg2h = D->make_one();
      monomial degxD = D->make_one();
      D->mult(degh, degh, deg2h);
 
      for (int j = 0; j < _nderivatives; j++)
        {
          const_monomial degx = M_->degree_of_var(_commutative[j]);
          const_monomial degD = M_->degree_of_var(_derivative[j]);
          D->mult(degx, degD, degxD);
          if (D->compare(deg2h, degxD) != EQ)
            {
              ERROR("Weyl algebra: failed to create homogeneous Weyl algebra");
              return false;
            }
        }
    }
 
  // Now initialize the tables
  initialize1();
  return true;
}

References _commutative, _derivative, _homog_var, _homogeneous_weyl_algebra, _nderivatives, Ring::degree_monoid(), EQ, ERROR, initialize1(), PolynomialRing::M_, monomial, newarray_atomic, PolynomialRing::nvars_, and PolynomialRing::setIsGraded().