syzygy()

void PolyRingQuotient::syzygy ( const ring_elem a, const ring_elem b, ring_elem & x, ring_elem & y ) const

virtual

Implements Ring.

Definition at line 381 of file polyquotient.cpp.

{
  MatrixConstructor mat(make_FreeModule(1), 2);
  mat.set_entry(0, 0, a);
  mat.set_entry(0, 1, b);
  Matrix *m = mat.to_matrix();  // {a,b}
  M2_arrayint weights = M2_makearrayint(n_vars());
  for (int i = 0; i < n_vars(); i++) weights->array[i] = 1;
  GBComputation *G = GBComputation::choose_gb(m,
                                              true,  // collect syz
                                              -1,    // keep all rows
                                              weights,
                                              false,
                                              -1,
                                              0,
                                              0,
                                              0 // TBB numThreads
                                              /* , max_reduction_count */
                                              );
  G->set_stop_conditions(false,
                         nullptr,
                         -1,
                         1,  // syzygy limit
                         -1,
                         -1,
                         -1,
                         false,
                         nullptr);
  G->start_computation();
  const Matrix *s = G->get_syzygies();
 
  // Now extract the two pieces of info
  x = s->elem(0, 0);
  y = s->elem(1, 0);
  ring_elem c = preferred_associate(x);
  ring_elem x1 = mult(c, x);
  ring_elem y1 = mult(c, y);
  x = x1;
  y = y1;
}

References GBComputation::choose_gb(), G, M2_makearrayint(), Ring::make_FreeModule(), Matrix, mult(), PolynomialRing::n_vars(), preferred_associate(), s, MatrixConstructor::set_entry(), MatrixConstructor::to_matrix(), and x.