def test_x5_mul(self): x5 = x5__with_prec(5) x10 = x10_with_prec(4) es4 = eisenstein_series_degree2(4, 5) self.assertEqual(x10, x5 ** 2) self.assertEqual(x10 * x5, x5 ** 3) self.assertEqual(x5 * es4, es4 * x5) self.assertEqual((x5 + x5 * es4) * x5, x10 + x10 * es4)
def test_vector_valued_rankin_cohen(self): prec = 5 M4_10 = vvld_smfs(4, 10, prec) f4_10 = M4_10.basis()[0] f4_15 = vvld_smfs(4, 15, prec).basis()[0] e4 = eisenstein_series_degree2(4, prec) g4_15 = vector_valued_rankin_cohen(e4, f4_10) t = ((1, 1, 1), 0) self.assertEqual(f4_15 * g4_15[t], g4_15 * f4_15[t]) es4, es6, _, _, _ = degree2_modular_forms_ring_level1_gens(5) f = es6 x5 = x5__with_prec(5) f_even_sym2 = rankin_cohen_pair_sym(2, f, x5) f_odd_sym2 = vector_valued_rankin_cohen(es4 * x5, f_even_sym2) a = f_odd_sym2[(1, 0, 2)].vec[1] g_sym2_21 = vvld_smfs(2, 21, 4).basis()[0] b = g_sym2_21[(1, 0, 2)].vec[1] self.assertEqual(f_odd_sym2 * b, g_sym2_21 * a)
def test_x5(self): d = load_from_data_dir("x5_fc_dct.sobj", "eigen_forms") self.assertEqual(d, x5__with_prec(10).fc_dct)
def calc_form(self, prec): es4, es6, x10, x12, x35 = degree2_modular_forms_ring_level1_gens(prec) x5 = x5__with_prec(prec) d = {4: es4, 6: es6, 10: x10, 12: x12, 5: x5, 35: x35} return self._calc_from_gens_dict(d)