def f21_sym6(prec):
'''One of the generator with the determinant weight 21 given by
van Dorp.
'''
Q = _sym6_od_Q(21, (4, 6, 10))
phi4 = eisenstein_series_degree2(4, prec)
phi6 = eisenstein_series_degree2(6, prec)
x10 = x10_with_prec(prec)
forms = _rankin_cohen_bracket_func(Q)([phi4, phi6, x10])
return SWMFE(forms, 21, prec)
def assert_degree_2(self, k):
es = eisenstein_series_degree2(k, prec=10)
es1 = sess(weight=k, degree=2)
self.assertTrue(
all(es[(n, r, m)] == es1.fourier_coefficient(matrix([[n, ZZ(r) / ZZ(2)],
[ZZ(r) / ZZ(2), m]]))
for n, r, m in es.prec))
def f17_sym6(prec):
'''One of the generator with the determinant weight 17 given by
van Dorp.
'''
Q = _sym6_od_Q(17, (5, 5, 6))
phi6 = eisenstein_series_degree2(6, prec + 1)
return rankin_cohen_triple_x5(Q, phi6, prec)
def f15_sym6(prec):
'''One of the generator with the determinant weight 15 given by
van Dorp.
'''
Q = _sym6_od_Q(15, (5, 5, 4))
phi4 = eisenstein_series_degree2(4, prec + 1)
return rankin_cohen_triple_x5(Q, phi4, prec)
def test_det(self):
prec = 10
l = [eisenstein_series_degree2(k, prec) for k in [4, 6, 10, 12]]
m = [[a.wt * a for a in l],
[a.differentiate_wrt_tau() for a in l],
[a.differentiate_wrt_w() for a in l],
[a.differentiate_wrt_z() for a in l]]
d = det_deg2(m, wt=35)
d = d * d[(2, -1, 3)] ** (-1)
self.assertEqual(d, x35_with_prec(prec))
def test_interpolate(self):
prec = 15
es4 = eisenstein_series_degree2(4, prec)
x35 = x35_with_prec(prec)
f = es4.differentiate_wrt_tau()
self.assertEqual(calc_forms(lambda fs: fs[0] ** 2, [es4], prec, wt=8),
es4 ** 2)
self.assertEqual(calc_forms(lambda fs: fs[0] * fs[1],
[es4, x35], prec, wt=39), es4 * x35)
self.assertEqual(calc_forms(lambda fs: fs[0] ** 2,
[f], prec, autom=False), f ** 2)
# -*- coding: utf-8; mode: sage -*-
from sage.all import QQ
from degree2.all import (
rankin_cohen_pair_sym, eisenstein_series_degree2,
x10_with_prec, x12_with_prec, x35_with_prec,
rankin_cohen_pair_det2_sym,
rankin_cohen_triple_det_sym4)
from degree2.interpolate import det_deg2
prec_ev = 7
phi4 = eisenstein_series_degree2(4, prec_ev)
phi6 = eisenstein_series_degree2(6, prec_ev)
x10 = x10_with_prec(prec_ev)
x12 = x12_with_prec(prec_ev)
x35 = x35_with_prec(prec_ev)
f1 = rankin_cohen_pair_sym(4, phi4, phi4)
f2 = rankin_cohen_pair_sym(4, phi4, phi6)
f3 = rankin_cohen_pair_det2_sym(4, phi4, phi6)
f4 = rankin_cohen_pair_sym(4, phi4, x10)
f5 = rankin_cohen_pair_sym(4, phi6, x10)
x70 = det_deg2([f.forms for f in [f1, f2, f3, f4, f5]],
wt=sum([f.wt for f in [f1, f2, f3, f4, f5]]) + 10)
y70 = x70 * QQ(-19945421021123916595200000)**(-1)
assert y70 == x35**2
f15 = f15_sym6(prec_od)
f17 = f17_sym6(prec_od)
f19 = f19_sym6(prec_od)
f21 = f21_sym6(prec_od)
f23 = f23_sym6(prec_od)
# The rank of A_{Sym(6)}^{1}(Gamma_2) is equal to 7.
# Therefore we need other two vector valued Siegel modular forms.
# We construct two modular forms f17_1 and f17_2 by
# Siegel modualr forms of weight det^12 Sym(6) and
# Rankin-Cohen type differential operator defined by Dorp
# (i.e. function vector_valued_rankin_cohen).
es4 = eisenstein_series_degree2(4, prec_od)
es6 = eisenstein_series_degree2(6, prec_od)
x35 = x35_with_prec(prec_od)
f12 = rankin_cohen_pair_det2_sym(6, es4, es6)
h12 = rankin_cohen_pair_sym(6, es4, es4**2)
f17_1 = vector_valued_rankin_cohen(es4, f12)
# f12_prect2 is {phi4, phi6}_{det^2 Sym(6)}.
# The prec of f12_prect2 is larger than other forms.
f12_prect2 = rankin_cohen_pair_det2_sym(
6,
eisenstein_series_degree2(4, prec_od*2),
eisenstein_series_degree2(6, prec_od*2))
def _g12():
def assert_pullback_m_2(self, k, A1, prec=3):
f0 = eisenstein_pullback_coeff(k, A1, tpl_to_half_int_mat((0, 0, 0)))
f = eisenstein_series_degree2(k, prec=5) * f0
for t in PrecisionDeg2(prec):
self.assertEqual(f[t],
eisenstein_pullback_coeff(k, A1, tpl_to_half_int_mat(t)))
