def calcRestrictMatrix_py(D, HermWeight, B_cF, S): """ This is a Python implementation of the C++ `calcMatrix()` function from `algo.cpp`. This is just for testing. See `test_calcMatrix()`. It does also exactly the same as `calcRestrictMatrix_any()`. """ # We also have a Python implementation for calculating the indexset, # but we can test that separately (`test_herm_modform_indexset()`) # and use the fast version here. if calcRestrictMatrix_py_Pure: indexset = herm_modform_indexset_py(D=D, B_cF=B_cF) else: from algo import herm_modform_indexset indexset = herm_modform_indexset(D=D, B_cF=B_cF) indexset_map = dict([(T,i) for (i,T) in enumerate(indexset)]) precDim = calcPrecisionDimension(B_cF=B_cF, S=S) matrixRowCount = precDim matrixColumnCount = len(indexset) M = matrix(ZZ, matrixRowCount, matrixColumnCount) for T in curlF_iter_py(D=D, B_cF=B_cF): reduced = ReducedGL(T=T, D=D) column = indexset_map[reduced.matrix] row = ZZ((T * S).trace()) assert row >= 0 if row >= matrixRowCount: continue a_T = reduced.value(-HermWeight) M[row,column] += a_T M.set_immutable() return M
def test_herm_modform_indexset(D=-3, B_cF=7): """ This also tests `\curlF` iteration and `reduceGL()`. """ from helpers import herm_modform_indexset_py from algo import herm_modform_indexset indexset = herm_modform_indexset(D=D, B_cF=B_cF) indexset_py = herm_modform_indexset_py(D=D, B_cF=B_cF) assert indexset == indexset_py
def check_eisenstein_series_D3_weight6(vs, B_cF):
"""
We know that there must be an Eisenstein series in weight 6 with D=-3.
We check for that.
INPUT:
- `vs` - Hermitian modular form Fourier expansion supervectorspace
- `B_cF` - the limit of the precision index set for the Hermitian Fourier indices
OUTPUT:
- Not defined. We just raise a ValueError exception if this check fails.
"""
from algo import herm_modform_indexset
from helpers import M2T_Odual
D = -3
HermWeight = 6
indexset = herm_modform_indexset(D=D, B_cF=B_cF)
jacobi_coeffs_1 = {
(0, (0, 0)): 1,
(1, (0, 0)): -240,
(1, (1, 1)): -45,
(2, (0, 0)): -3690,
(2, (1, 1)): -1872,
(3, (0, 0)): -19680,
(3, (1, 1)): -11565,
(4, (0, 0)): -57840,
(4, (1, 1)): -43920
}
from reduceGL import reduce_GL
def reduce_matrix_jacobi1(key, value):
# In standard base of \cO^#.
a, (b1, b2) = key
m, char = reduce_GL((a, b1, b2, 1), D)
# Like reduce_character_evalutation::value() in reduceGL.hpp.
h = 6 # because D == -3
k = -HermWeight
detchar = char[1] * k
if detchar % h == 0: detvalue = 1
elif detchar % h == h/2: detvalue = -1
else: assert False, "detchar %i" % detchar
m = M2T_Odual(m, D)
return m, value * detvalue
jacobi_coeffs_1_transformed = dict(
[reduce_matrix_jacobi1(key,value) for (key,value) in jacobi_coeffs_1.items()])
indexmap = {}
for m in jacobi_coeffs_1_transformed.keys():
indexmap[m] = indexset.index(m)
reverse_indexlist = sorted([(value,key) for (key,value) in indexmap.items()])
def reduced_vector(v):
new_v = [None] * len(indexmap)
for i,(j,m) in enumerate(reverse_indexlist):
new_v[i] = v[j]
return vector(QQ, new_v)
reduced_vs_basis = map(reduced_vector, vs.basis())
reduced_vs_basis_matrix = matrix(QQ, reduced_vs_basis)
vector_jac = [None] * len(indexmap)
for i,(j,m) in enumerate(reverse_indexlist):
vector_jac[i] = jacobi_coeffs_1_transformed[m]
vector_jac = vector(QQ, vector_jac)
try:
lincomb = reduced_vs_basis_matrix.solve_left(vector_jac)
except ValueError as e:
if "no solutions" in str(e):
print "reduced_vs_basis_matrix =", reduced_vs_basis_matrix, ", rank =", reduced_vs_basis_matrix.rank()
print "vector_jac =", vector_jac
assert False
raise
return lincomb
