ann()

ring_elem PolyRingQuotient::ann ( const ring_elem a, const ring_elem b ) const

protected

Definition at line 319 of file polyquotient.cpp.

{
  MatrixConstructor mata(make_FreeModule(1), 1);
  mata.set_entry(0, 0, a);
  Matrix *ma = mata.to_matrix();  // {a}
 
  GBComputation *G = make_gb(b);
 
  const Matrix *mrem, *mquot;
  G->matrix_lift(ma, &mrem, &mquot);
  // if (M2_gbTrace >= 2)
  //   {
  //     emit("ann a=");
  //     dringelem(this, a);
  //     emit(" b=");
  //     dringelem(this, b);
  //     emit_line("----------");
  //     emit_line(" G->get_gb is ");
  //     dmatrix(G->get_gb());
  //     emit_line(" G ->get_change()");
  //     dmatrix(G->get_change());
  //     emit_line("----------");
  //     emit_line(" mrem is ");
  //     dmatrix(mrem);
  //     emit_line(" mquot is ");
  //     dmatrix(mquot);
  //     emit_line("---------------");
  //     emit_line("-- gb(b): -----");
  //     G->show();
  //     emit_line("---------------");
  //   }
  if (mquot->n_cols() == 0 || !mrem->is_zero())
    {
      // We have just determined that a/b does not exist.
      // So b is not a unit in this ring.
      set_non_unit(b);
      return from_long(0);
    }
  ring_elem answer = mquot->elem(0,0); // possibly off by a scalar?
  ring_elem a1 = mult (answer, b);
  if (not is_equal(a1, a))
    {
      // so answer * b == a1,
      // and a1 * c == a.  Check this?
      // so (answer * c) * b == a
 
      // emit("a1=");
      // dringelem(this, a1);
      // emit_line("");
      ring_elem c = divide(a, a1);
      if (not is_equal(mult(a1, c), a))
        {
          set_non_unit(b);
          return from_long(0);
        }
      answer = mult(c, answer);
    }
  return answer;
}

References divide(), Matrix::elem(), from_long(), G, RingMap::is_equal(), Matrix::is_zero(), Ring::make_FreeModule(), make_gb(), Matrix, mult(), Matrix::n_cols(), MatrixConstructor::set_entry(), Ring::set_non_unit(), and MatrixConstructor::to_matrix().

Referenced by divide(), and invert().