def test_t_2_action(self):
es4 = eisenstein_series_degree2(4, 10)
es6 = eisenstein_series_degree2(6, 10)
F10 = rankin_cohen_pair_sym(2, es4, es6)
ev2 = -24 * (1 + 2 ** 8)
prec5 = PrecisionDeg2(5)
self.assertTrue(
all([F10.hecke_operator(2, t) == ev2 * F10[t] for t in prec5]))
def test_vector_vald_klingen_hecke_pol(self):
es4 = eisenstein_series_degree2(4, 5)
es6 = eisenstein_series_degree2(6, 5)
F10 = rankin_cohen_pair_sym(2, es4, es6)
pl = F10.euler_factor_of_spinor_l(2)
x = pl.parent().gens()[0]
f = 1 + 24 * x + 2048 * x ** 2
self.assertTrue(f * f.subs({x: 2 ** 8 * x}) == pl)
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_det_is_divisible_x35_fifth():
prec = 18
x35 = x35_with_prec(prec)
f187 = ModFormQexpLevel1.load_from(os.path.join(data_dir,
"gens_even_det.sobj"))
es4 = eisenstein_series_degree2(4, prec)
es6 = eisenstein_series_degree2(6, prec)
g = (x35 ** 5) * (es4 ** 3 - es6 ** 2)
assert f187 * g[(16, 5, 10)] == g * f187[(16, 5, 10)]
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 check_det_with_prec(prec):
es4 = eisenstein_series_degree2(4, prec)
es6 = eisenstein_series_degree2(6, prec)
x35 = x35_with_prec(prec)
f = (es4**3 - es6**2) * x35**6
t = f._none_zero_tpl()
d = calculator.forms_dict(prec)
# Constructions of the first 11 generators.
cs = list(sorted(calculator._const_vecs, key=lambda x: x.weight()))[:11]
wt = sum(c.weight() for c in cs) + (10 * 11)//2
mat = [d[c].forms for c in cs]
det = det_deg2(mat, wt=wt)
assert f[t] * det == det[t] * f
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_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 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_es4_eigenvalues(self):
es4 = eisenstein_series_degree2(4, 25)
d = {2: 45, 3: 280, 4: 1549, 5: 3276, 9: 69049, 25: 10256401}
for k, v in d.iteritems():
self.assertTrue(es4.hecke_eigenvalue(k) == v)
# -*- coding: utf-8 -*-
from degree2.scalar_valued_smfs import eisenstein_series_degree2, QexpLevel1,\
x10_with_prec, x12_with_prec, x35_with_prec, ModFormQexpLevel1
from degree2.basic_operation import PrecisionDeg2
import unittest
from sage.all import FiniteField, ZZ, QQ, PolynomialRing
import operator
global_prec = 8
# global_prec = [(10, 5, 10), (9, 0, 8)]
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)
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_es6(self):
es6 = eisenstein_series_degree2(6, global_prec)
self.assertTrue(self.sub_dct(es6) == fc_dct6)
def test_es4(self):
es4 = eisenstein_series_degree2(4, global_prec)
self.assertTrue(self.sub_dct(es4) == fc_dct4)
