fiz elleta more cases

["管理员" <c2976501934@qq.com>]

static int
is_special_lattice(GEN w1, GEN w2)
{
  if (!is_real_t(w2)) return 0;
  return gdvd(gmul2n(real_i(w1),1),w2);
}

GEN
elleta(GEN om, long prec)
{
  pari_sp av = avma;
  GEN y1, y2, E2, pi;
  ellred_t T;

  if (!check_periods(om, &T))
  {
    pari_err_TYPE("elleta",om);
    return NULL;/*LCOV_EXCL_LINE*/
  }
  if (T.type == t_PER_ELL) return ellR_eta(om, prec);

  compute_periods(&T, NULL, prec);
  prec = T.prec;
  pi = mppi(prec);
  E2 = cxEk(T.Tau, 2, prec); /* E_2(Tau) */
  if (signe(T.c))
  {
    GEN u = gdiv(T.w2, T.W2);
    /* E2 := u^2 E2 + 6iuc/pi = E_2(tau) */
    E2 = gadd(gmul(gsqr(u), E2), mulcxI(gdiv(gmul(mului(6,T.c), u), pi)));
  }
  y2 = gdiv(gmul(E2, sqrr(pi)), gmulsg(3, T.w2));
  y1 = gsub(gmul(T.tau,y2), PiI2div(T.w2, prec));
  if (is_special_lattice(w2,w1)) y1 = real_i(y1);
  if (is_special_lattice(w1,w2)) y2 = real_i(y2);
  if (T.swap) swap(y1,y2);
  return gc_GEN(av, mkvec2(y1,y2));
}

/* test cases: elleta([3,3/2+I]), elleta([3,3/2-I]), elleta([3,3/2+10*I]), elleta([3,3/2-10*I]), elleta([3,2+10*I]), elleta([3,2-10*I]) */