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_divide_vector_valued(self): prec = 6 x10 = x10_with_prec(prec + 1) es4 = eisenstein_series_degree2(4, prec + 1) es6 = eisenstein_series_degree2(6, prec + 1) f = rankin_cohen_pair_sym(2, es4, es6) g = f * x10 self.assertEqual(f._down_prec(prec), g.divide(x10, prec, parallel=True))
def test_eisenstein(self): prec = 10 es4, es6, es10, es12 = [eisenstein_series_degree2(k, prec) for k in [4, 6, 10, 12]] f10 = es4 * es6 - es10 f12 = 3 ** 2 * 7 ** 2 * es4 ** 3 + 2 * 5 ** 3 * es6 ** 2 - 691 * es12 f10 = f10 * (f10[(1, 1, 1)]) ** (-1) f12 = f12 * (f12[(1, 1, 1)]) ** (-1) self.assertTrue(f10 == x10_with_prec(prec)) self.assertTrue(f12 == x12_with_prec(prec))
def polynomial_to_form(f, prec): es4 = eisenstein_series_degree2(4, prec) es6 = eisenstein_series_degree2(6, prec) x10 = x10_with_prec(prec) x12 = x12_with_prec(prec) x35 = x35_with_prec(prec) gens = [es4, es6, x10, x12, x35] def monom(t): return reduce(operator.mul, [f ** a for f, a in zip(gens, t)]) return sum([a * monom(t) for t, a in f.dict().iteritems()])
def test_division_cusp(self): '''Test the method calc_form of ConstDivision in the case when division by a cusp form. ''' prec = 5 x10 = x10_with_prec(prec) sccs = [SMFC([4, 10]), SMFC([6, 10])] cvc = ConstVectValued(2, sccs, 0, None) cd = ConstDivision([cvc], [1], SMFC([10]), 1) F = cvc.calc_form(prec) G = cd.calc_form(prec) self.assertNotEqual(F, 0) self.assertEqual(G.prec.value, prec) self.assertEqual(G * x10, F)
es4 = eisenstein_series_degree2(4, global_prec) qsres4 = QexpLevel1(es4.fc_dct, global_prec, base_ring=ZZ) ffld = FiniteField(5) ff_es4 = es4.change_ring(ffld) ff_qsres4 = qsres4.change_ring(ffld) es6 = eisenstein_series_degree2(6, global_prec) qsres6 = QexpLevel1(es6.fc_dct, global_prec, base_ring=ZZ) ff_es6 = es6.change_ring(ffld) ff_qsres6 = qsres6.change_ring(ffld) x10 = x10_with_prec(global_prec) qsrx10 = QexpLevel1(x10.fc_dct, global_prec, base_ring=ZZ, is_cuspidal=True) ff_x10 = x10.change_ring(ffld) ff_qsrx10 = qsrx10.change_ring(ffld) dzx10 = x10.differentiate_wrt_z() ff_dzx10 = dzx10.change_ring(ffld) x12 = x12_with_prec(global_prec) qsrx12 = QexpLevel1(x12.fc_dct, global_prec, is_cuspidal=True, base_ring=ZZ) dzx12 = x12.differentiate_wrt_z()
def testdivide(self): prec = 10 x10 = x10_with_prec(prec + 1) es4 = eisenstein_series_degree2(4, prec + 1) self.assertEqual((es4 * x10).divide(x10, prec), es4) self.assertEqual((x10 * x10).divide(x10, prec), x10)
def test_x10(self): x10 = x10_with_prec(global_prec) self.assertTrue(self.sub_dct(x10) == fc_dct10)