do_ideal()

void hilb_comp::do_ideal ( MonomialIdeal * I )

private

Definition at line 524 of file hilb.cpp.

{
  // This either will multiply to current->h1, or it will recurse down
  // Notice that one, and minus_one are global in this class.
  // LOCAL_deg1, LOCAL_vp are scratch variables defined in this class
  nideal++;
  ring_elem F = R->from_long(1);
  ring_elem G;
  int len = I->size();
  if (len <= 2)
    {
      // len==1: set F to be 1 - t^(deg m), where m = this one element
      // len==2: set F to be 1 - t^(deg m1) - t^(deg m2) + t^(deg lcm(m1,m2))
      M->degree_of_varpower(I->first_elem(), LOCAL_deg1);
      G = R->make_flat_term(minus_one, LOCAL_deg1);
      R->add_to(F, G);
 
      if (len == 2)
        {
          M->degree_of_varpower(I->second_elem(), LOCAL_deg1);
          G = R->make_flat_term(minus_one, LOCAL_deg1);
          R->add_to(F, G);
          varpower::lcm(I->first_elem(), I->second_elem(), LOCAL_vp);
          M->degree_of_varpower(LOCAL_vp.data(), LOCAL_deg1);
          G = R->make_flat_term(one, LOCAL_deg1);
          R->add_to(F, G);
        }
      delete I;
    }
  else
    {
      int npure;
      gc_vector<int> pivot;
      gc_vector<int> pure_a(I->topvar() + 1);
      exponents_t pure = pure_a.data();
      if (!find_pivot(*I, npure, pure, pivot))
        {
          // set F to be product(1-t^(deg x_i^e_i))
          //              - t^(deg pivot) product((1-t^(deg x_i^(e_i - m_i)))
          // where e_i >= 1 is the smallest number s.t. x_i^(e_i) is in I,
          // and m_i = exponent of x_i in pivot element (always < e_i).
          M->degree_of_varpower(pivot.data(), LOCAL_deg1);
          G = R->make_flat_term(one, LOCAL_deg1);
          for (index_varpower i = pivot.data(); i.valid(); ++i)
            if (pure[i.var()] != -1)
              {
                ring_elem H = R->from_long(1);
                D->power(M->degree_of_var(i.var()), pure[i.var()], LOCAL_deg1);
                ring_elem tmp = R->make_flat_term(minus_one, LOCAL_deg1);
                R->add_to(H, tmp);
                R->mult_to(F, H);
                R->remove(H);
 
                H = R->from_long(1);
                D->power(M->degree_of_var(i.var()),
                         pure[i.var()] - i.exponent(),
                         LOCAL_deg1);
                tmp = R->make_flat_term(minus_one, LOCAL_deg1);
                R->add_to(H, tmp);
                R->mult_to(G, H);
                R->remove(H);
              }
          R->subtract_to(F, G);
          delete I;
        }
      else
        {
          // This is the one case in which we recurse down
          R->remove(F);
          recurse(I, pivot.data());
          return;
        }
    }
  R->mult_to(current->h1, F);
  R->remove(F);
  current->i--;
}

References current, D, find_pivot(), MonomialIdeal::first_elem(), G, ExponentList< int, true >::lcm(), LOCAL_deg1, LOCAL_vp, M, minus_one, nideal, one, R, recurse(), MonomialIdeal::second_elem(), MonomialIdeal::size(), and MonomialIdeal::topvar().

Referenced by step().