gbvector_replace_2by2_ZZ()

void GBRing::gbvector_replace_2by2_ZZ	(	const FreeModule *	F,
		const FreeModule *	Fsyz,
		gbvector *&	f,
		gbvector *&	fsyz,
		gbvector *&	g,
		gbvector *&	gsyz )

Definition at line 1114 of file gbring.cpp.

{
  // ASSUMPTIONS: coefficient ring is ZZ
  //  lead monomial of f and g are the same (with possibly different coeffs)
  // If u * leadcoeff(f) + v * leadcoeff(g) = gd is the gcd,
  // then:
  //  g <-- u * f + v * g
  //  f <-- c * f - d * g, where c = leadcoeff(g)//gd, d = leadcoeff(f)//gd
  mpz_t u, v, gd;
  mpz_init(u);
  mpz_init(v);
  mpz_init(gd);
  mpz_gcdext(gd, u, v, f->coeff.get_mpz(), g->coeff.get_mpz());
 
  gbvector *new_g = nullptr;
  gbvector *g2 = nullptr;
  gbvector *new_gsyz = nullptr;
  gbvector *gsyz2 = nullptr;
 
  if (mpz_sgn(v) != 0)
    {
      g2 = gbvector_mult_by_coeff(g, ring_elem(v));
      gsyz2 = gbvector_mult_by_coeff(gsyz, ring_elem(v));
    }
  if (mpz_sgn(u) != 0)
    {
      new_g = gbvector_mult_by_coeff(f, ring_elem(u));
      new_gsyz = gbvector_mult_by_coeff(fsyz, ring_elem(u));
    }
 
  gbvector_add_to(F, new_g, g2);
  gbvector_add_to(Fsyz, new_gsyz, gsyz2);
 
  mpz_fdiv_q(u, g->coeff.get_mpz(), gd);
  mpz_fdiv_q(v, f->coeff.get_mpz(), gd);
  mpz_neg(v, v);
 
  gbvector *new_f = gbvector_mult_by_coeff(f, ring_elem(u));
  gbvector *new_fsyz = gbvector_mult_by_coeff(fsyz, ring_elem(u));
  gbvector *f2 = gbvector_mult_by_coeff(g, ring_elem(v));
  gbvector *fsyz2 = gbvector_mult_by_coeff(gsyz, ring_elem(v));
 
  gbvector_add_to(F, new_f, f2);
  gbvector_add_to(Fsyz, new_fsyz, fsyz2);
 
  f = new_f;
  fsyz = new_fsyz;
  g = new_g;
  gsyz = new_gsyz;
 
  mpz_clear(u);
  mpz_clear(v);
  mpz_clear(gd);
}

References gbvector::coeff, gbvector_add_to(), gbvector_mult_by_coeff(), and ring_elem::get_mpz().