def integral_cuspidal_subspace(self):
"""
In certatain cases this might return the integral structure of the cuspidal subspace.
This code is mainly a way to compute the integral structe faster than sage does now.
It returns None if it cannot find the integral subspace.
"""
if self.verbose: tm = cputime(); mem = get_memory_usage(); print "Int struct start"
#This code is the same as the firs part of self.M.integral_structure
G = set([i for i, _ in self.M._mod2term])
G = list(G)
G.sort()
#if there is a two term relation between two manin symbols we only need one of the two
#so that's why we only use elements from G instead of all manin symbols.
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "G"
B = self.M._manin_gens_to_basis.matrix_from_rows(list(G)).sparse_matrix()
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "B"
#The collums of B now span self.M.integral_structure as ZZ-module
B, d = B._clear_denom()
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "Clear denom"
if d == 1:
#for explanation see d == 2
assert len(set([B.nonzero_positions_in_row(i)[0] for i in xrange(B.nrows()) if len(B.nonzero_positions_in_row(i)) == 1 and B[i, B.nonzero_positions_in_row(i)[0]] == 1])) == B.ncols(), "B doesn't contain the Identity"
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "Check Id"
ZZbasis = MatrixSpace(QQ, B.ncols(), sparse=True)(1)
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "ZZbasis"
elif d == 2:
#in this case the matrix B will contain 2*Id as a minor this allows us to compute the hermite normal form of B in a very efficient way. This will give us the integral basis ZZbasis.
#if it turns out to be nessecarry this can be generalized to the case d%4==2 if we don't mind to only get the right structure localized at 2
assert len(set([B.nonzero_positions_in_row(i)[0] for i in xrange(B.nrows()) if len(B.nonzero_positions_in_row(i)) == 1 and B[i, B.nonzero_positions_in_row(i)[0]] == 2])) == B.ncols(), "B doesn't contain 2*Identity"
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "Check 2*Id"
E = matrix_modp(B,sparse=True)
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "matmodp"
E = E.echelon_form()
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "echelon"
ZZbasis = MatrixSpace(QQ, B.ncols(), sparse=True)(1)
for (pivot_row, pivot_col) in zip(E.pivot_rows(), E.pivots()):
for j in E.nonzero_positions_in_row(pivot_row):
ZZbasis[pivot_col, j] = QQ(1) / 2
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "ZZbasis"
else:
return None
#now we compute the integral kernel of the boundary map with respect to the integral basis. This will give us the integral cuspidal submodule.
boundary_matrix = self.M.boundary_map().matrix()
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "Boundary matrix"
ZZboundary_matrix=(ZZbasis*boundary_matrix).change_ring(ZZ)
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "ZZBoundary matrix"
left_kernel_matrix=ZZboundary_matrix.transpose().dense_matrix()._right_kernel_matrix(algorithm='pari')
if type(left_kernel_matrix)==tuple:
left_kernel_matrix=left_kernel_matrix[1]
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "kernel matrix"
ZZcuspidal_basis=left_kernel_matrix*ZZbasis
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "ZZkernel matrix"
assert ZZcuspidal_basis.change_ring(QQ).echelon_form()==self.S.basis_matrix() , "the calculated integral basis does not span the right QQ vector space" # a little sanity check. This shows that the colums of ZZcuspidal_basis really span the right QQ vectorspace
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "check"
#finally create the sub-module, we delibarately do this as a QQ vector space with custom basis, because this is faster then dooing the calculations over ZZ since sage will then use a slow hermite normal form algorithm.
ambient_module=VectorSpace(QQ,ZZcuspidal_basis.ncols())
int_struct = ambient_module.submodule_with_basis(ZZcuspidal_basis.rows())
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "finnished"
return int_struct
def integral_cuspidal_subspace(self):
"""
In certatain cases this might return the integral structure of the cuspidal subspace.
This code is mainly a way to compute the integral structe faster than sage does now.
It returns None if it cannot find the integral subspace.
"""
if self.verbose: tm = cputime(); mem = get_memory_usage(); print("Int struct start")
#This code is the same as the firs part of self.M.integral_structure
G = set([i for i, _ in self.M._mod2term])
G = list(G)
G.sort()
#if there is a two term relation between two manin symbols we only need one of the two
#so that's why we only use elements from G instead of all manin symbols.
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "G")
B = self.M._manin_gens_to_basis.matrix_from_rows(list(G)).sparse_matrix()
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "B")
#The collums of B now span self.M.integral_structure as ZZ-module
B, d = B._clear_denom()
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "Clear denom")
if d == 1:
#for explanation see d == 2
assert len(set([B.nonzero_positions_in_row(i)[0] for i in range(B.nrows()) if len(B.nonzero_positions_in_row(i)) == 1 and B[i, B.nonzero_positions_in_row(i)[0]] == 1])) == B.ncols(), "B doesn't contain the Identity"
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "Check Id")
ZZbasis = MatrixSpace(QQ, B.ncols(), sparse=True)(1)
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "ZZbasis")
elif d == 2:
#in this case the matrix B will contain 2*Id as a minor this allows us to compute the hermite normal form of B in a very efficient way. This will give us the integral basis ZZbasis.
#if it turns out to be nessecarry this can be generalized to the case d%4==2 if we don't mind to only get the right structure localized at 2
assert len(set([B.nonzero_positions_in_row(i)[0] for i in range(B.nrows()) if len(B.nonzero_positions_in_row(i)) == 1 and B[i, B.nonzero_positions_in_row(i)[0]] == 2])) == B.ncols(), "B doesn't contain 2*Identity"
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "Check 2*Id")
E = matrix_modp(B,sparse=True)
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "matmodp")
E = E.echelon_form()
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "echelon")
ZZbasis = MatrixSpace(QQ, B.ncols(), sparse=True)(1)
for (pivot_row, pivot_col) in zip(E.pivot_rows(), E.pivots()):
for j in E.nonzero_positions_in_row(pivot_row):
ZZbasis[pivot_col, j] = QQ(1) / 2
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "ZZbasis")
else:
return None
#now we compute the integral kernel of the boundary map with respect to the integral basis. This will give us the integral cuspidal submodule.
boundary_matrix = self.M.boundary_map().matrix()
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "Boundary matrix")
ZZboundary_matrix=(ZZbasis*boundary_matrix).change_ring(ZZ)
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "ZZBoundary matrix")
left_kernel_matrix=ZZboundary_matrix.transpose().dense_matrix()._right_kernel_matrix(algorithm='pari')
if type(left_kernel_matrix)==tuple:
left_kernel_matrix=left_kernel_matrix[1]
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "kernel matrix")
ZZcuspidal_basis=left_kernel_matrix*ZZbasis
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "ZZkernel matrix")
assert ZZcuspidal_basis.change_ring(QQ).echelon_form()==self.S.basis_matrix() , "the calculated integral basis does not span the right QQ vector space" # a little sanity check. This shows that the colums of ZZcuspidal_basis really span the right QQ vectorspace
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "check")
#finally create the sub-module, we delibarately do this as a QQ vector space with custom basis, because this is faster then dooing the calculations over ZZ since sage will then use a slow hermite normal form algorithm.
ambient_module=VectorSpace(QQ,ZZcuspidal_basis.ncols())
int_struct = ambient_module.submodule_with_basis(ZZcuspidal_basis.rows())
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "finnished")
return int_struct
def _get_labels(M, x, rows, L):
from sage.all import VectorSpace, Set, Matrix
# If non-central, then this is true iff not intersecting.
not_e1 = lambda v: list(v)[1:] != [0] * (len(v) - 1)
# Determine new hyperplanes and group like rows together.
V = VectorSpace(M.base_ring(), M.ncols())
lines = []
labels = []
for r in range(M.nrows()):
v = M[r]
is_new = not_e1(v)
i = 0
while i < len(lines) and is_new:
if v in V.subspace([lines[i]]):
is_new = False
labels[i] = labels[i].union(Set([r]))
else:
i += 1
if is_new:
lines.append(v)
labels.append(Set([r]))
# Adjust the labels because we are missing rows.
fix_sets = lambda F: lambda S: Set(list(map(lambda s: F(s), S)))
for k in rows:
adjust = lambda i: i + (k <= i) * 1
labels = list(map(fix_sets(adjust), labels))
labels = [Set(rows)] + labels
# Adjust the row labels to hyperplane labels
HL = L.hyperplane_labels
A = L.hyperplane_arrangement
HL_lab = lambda i: list(filter(lambda j: HL[j] == A[i], HL.keys()))[0]
labels = list(map(fix_sets(HL_lab), labels))
# Get the new hyperplanes
FL = L.flat_labels
new_hyp = [labels[k].union(labels[0]) for k in range(1, len(labels))]
P = L.poset
flat = lambda S: list(filter(lambda j: FL[j] == S, P.upper_covers(x)))[0]
new_hyp = list(map(flat, new_hyp))
def last_adj(S):
l_hyp = labels[1:]
T = S.difference(labels[0])
new_T = Set([])
for k in range(len(l_hyp)):
if l_hyp[k].issubset(T):
new_T = new_T.union(Set([new_hyp[k]]))
return new_T
return Matrix(lines), last_adj, {
new_hyp[i]: i
for i in range(len(new_hyp))
}
def monics(F, d, u=1):
"""Iterate through all degree d polynomials over F with leading coefficient u.
NB Use u=1 to get monics, and u=0 to give all polys of degree <d.
"""
Fx = PolynomialRing(F, 'x')
for v in VectorSpace(F, d):
yield Fx(v.list() + [u])
def _random_ini(dop):
import random
from sage.all import VectorSpace, QQ
ind = dop.indicial_polynomial(dop.base_ring().gen())
sl_decomp = my_shiftless_decomposition(ind)
pol, shifts = random.choice(sl_decomp)
expo = random.choice(pol.roots(QQbar))[0]
values = {
shift: tuple(VectorSpace(QQ, mult).random_element(10))
for shift, mult in shifts
}
return LogSeriesInitialValues(expo, values, dop)
def randomize(self, prime):
assert not self.randomized
MSZp = MatrixSpace(ZZ.residue_field(ZZ.ideal(prime)), self.size)
def random_matrix():
while True:
m = MSZp.random_element()
if not m.is_singular() and m.rank() == self.size:
return m, m.inverse()
m0, m0i = random_matrix()
self.bp[0] = self.bp[0].group(MSZp, prime).mult_left(m0)
for i in xrange(1, len(self.bp)):
mi, mii = random_matrix()
self.bp[i-1] = self.bp[i-1].group(MSZp, prime).mult_right(mii)
self.bp[i] = self.bp[i].group(MSZp, prime).mult_left(mi)
self.bp[-1] = self.bp[-1].group(MSZp, prime).mult_right(m0i)
VSZp = VectorSpace(ZZ.residue_field(ZZ.ideal(prime)), self.size)
self.s = copy(VSZp.zero())
self.s[0] = 1
self.t = copy(VSZp.zero())
self.t[len(self.t) - 1] = 1
self.m0, self.m0i = m0, m0i
self.randomized = True
def random_ini(dop):
import random
from sage.all import VectorSpace
ind = dop.indicial_polynomial(dop.base_ring().gen())
sl_decomp = my_shiftless_decomposition(ind)
pol, shifts = random.choice(sl_decomp)
expo = random.choice(pol.roots(QQbar))[0]
expo = utilities.as_embedded_number_field_element(expo)
values = {}
while all(a.is_zero() for v in values.values() for a in v):
values = {
shift: tuple(VectorSpace(QQ, mult).random_element(10))
for shift, mult in shifts
}
return LogSeriesInitialValues(expo, values, dop)
def randomize(self, prime):
assert not self.randomized
MSZp = MatrixSpace(ZZ.residue_field(ZZ.ideal(prime)), self.size)
def random_matrix():
while True:
m = MSZp.random_element()
if not m.is_singular() and m.rank() == self.size:
return m, m.inverse()
m0, m0i = random_matrix()
self.bp[0] = self.bp[0].group(MSZp, prime).mult_left(m0)
for i in xrange(1, len(self.bp)):
mi, mii = random_matrix()
self.bp[i - 1] = self.bp[i - 1].group(MSZp, prime).mult_right(mii)
self.bp[i] = self.bp[i].group(MSZp, prime).mult_left(mi)
self.bp[-1] = self.bp[-1].group(MSZp, prime).mult_right(m0i)
VSZp = VectorSpace(ZZ.residue_field(ZZ.ideal(prime)), self.size)
self.s = copy(VSZp.zero())
self.s[0] = 1
self.t = copy(VSZp.zero())
self.t[len(self.t) - 1] = 1
self.m0, self.m0i = m0, m0i
self.randomized = True
def __pow__(self, n, _=None):
r"""
Return the vector space of dimension ``n`` over this field.
EXAMPLES::
sage: from pyeantic import RealEmbeddedNumberField
sage: K = NumberField(x**2 - 2, 'a', embedding=sqrt(AA(2)))
sage: K = RealEmbeddedNumberField(K)
sage: K^3
Vector space of dimension 3 over Real Embedded Number Field in a with defining polynomial x^2 - 2 with a = 1.414213562373095?
"""
if isinstance(n, tuple):
m, n = n
from sage.all import MatrixSpace
return MatrixSpace(self, m, n)
else:
from sage.all import VectorSpace
return VectorSpace(self, n)
def _para_intersection_poset(A):
from sage.geometry.hyperplane_arrangement.affine_subspace import AffineSubspace
from sage.all import exists, flatten, Set, QQ, VectorSpace, Poset
from .Globals import __SANITY
N = _N
K = A.base_ring()
whole_space = AffineSubspace(0, VectorSpace(K, A.dimension()))
# L is the ranked list of affine subspaces in L(A).
L = [[whole_space], list(map(lambda H: H._affine_subspace(), A))]
# hyp_cont is the ranked list describing which hyperplanes contain the
# corresponding intersection.
hyp_cont = [[Set([])], [Set([k]) for k in range(len(A))]]
c = A.is_central() * (-1)
for r in range(2, A.rank() + c + 1):
print("{1}Working on elements of rank {0}".format(r, _time()))
m = len(L[r - 1])
pmax = lambda k: (k + 1) * (m // N) + (k == N - 1) * (m % N)
pmin = lambda k: k * (m // N)
all_input = lambda k: tuple([
A,
range(pmin(k), pmax(k)), hyp_cont[r - 1][pmin(k):pmax(k)], L[r - 1]
[pmin(k):pmax(k)]
])
data = list(
build_next([all_input(k) for k in range(N) if pmin(k) != pmax(k)]))
data = _reduce(lambda x, y: x + y[1], data, [])
new_lev, new_hyp = list(zip(*data))
new_lev = list(new_lev)
new_hyp = list(new_hyp)
i = 0
# Merge the lists down
print("{0}Merging the lists from the {1} workers".format(_time(), N))
# First we check the affine spaces
while i < len(new_lev):
U = new_lev[i]
B1 = U.linear_part().basis_matrix()
p1 = U.point()
j = i + 1
while j < len(new_lev):
V = new_lev[j]
B2 = V.linear_part().basis_matrix()
p2 = V.point()
if B1 == B2 and p1 == p2:
new_lev = new_lev[:j] + new_lev[j + 1:]
new_hyp[i] = new_hyp[i].union(new_hyp[j])
new_hyp = new_hyp[:j] + new_hyp[j + 1:]
else:
j += 1
i += 1
# Second we check the labels of intersection (don't want duplicates)
i = 0
while i < len(new_lev):
j = i + 1
while j < len(new_lev):
if new_hyp[i] == new_hyp[j]:
new_lev = new_lev[:j] + new_lev[j + 1:]
new_hyp = new_hyp[:j] + new_hyp[j + 1:]
else:
j += 1
i += 1
L.append(new_lev)
hyp_cont.append(new_hyp)
# A silly optimization for centrals.
if A.is_central() and len(A) > 1:
inter = lambda X, Y: X.intersection(Y._affine_subspace())
L.append([_reduce(inter, A[1:], A[0]._affine_subspace())])
hyp_cont.append([Set(list(range(len(A))))])
L_flat = list(_reduce(lambda x, y: x + y, L, []))
hc_flat = list(_reduce(lambda x, y: x + y, hyp_cont, []))
# Sanity checks
if __SANITY:
print("{0}Running sanity check".format(_time()))
assert len(L_flat) == len(hc_flat)
for i in range(len(hc_flat)):
for j in range(i + 1, len(hc_flat)):
assert hc_flat[i] != hc_flat[j], "{0} vs {1}".format(i, j)
for i in range(len(L_flat)):
I = list(map(lambda x: A[x], hc_flat[i]))
U = _reduce(lambda x, y: x.intersection(y._affine_subspace()), I,
whole_space)
assert U == L_flat[i], "{0} vs {1}".format(U, L_flat[i])
print("{0}Constructing lattice of flats".format(_time()))
t = {}
for i in range(len(hc_flat)):
t[i] = Set(list(map(lambda x: x + 1, hc_flat[i])))
cmp_fn = lambda p, q: t[p].issubset(t[q])
label_dict = {i: t[i] for i in range(len(hc_flat))}
get_hyp = lambda i: A[label_dict[i].an_element() - 1]
hyp_dict = {i + 1: get_hyp(i + 1) for i in range(len(A))}
return [Poset((t, cmp_fn)), label_dict, hyp_dict]
def vector_to_double_char(v):
assert len(v) == 2
return CHARSET[v[0]] + CHARSET[v[1]]
def encrypt(msg, K):
assert all(c in CHARSET for c in msg)
assert len(msg) % 2 == 0
A, v = K
ciphertext = ""
for i in range(0, len(msg), 2):
tmp = A * double_char_to_vector(msg[i:i + 2]) + v
ciphertext += vector_to_double_char(tmp)
return ciphertext
if __name__ == '__main__':
from secret import flag
assert flag.startswith('kmactf')
A = MatrixSpace(Fp, 2, 2).random_element()
v = VectorSpace(Fp, 2).random_element()
assert A.determinant() != 0
print('ciphertext =', repr(encrypt(flag, (A, v))))
# Output:
# ciphertext = 'u_rm3eefa}_7det1znb{sce{qo0h7yf0b}sktse8xtr6'
def solve(vectors, goal): M = MatrixSpace(GF(2), len(vectors), len(vectors[0])) V = VectorSpace(GF(2), len(goal)) A = M(vectors) b = V(goal) return A.solve_left(b)
def __init__(self, p, congruence_type=1, sign=1, algorithm="custom", verbose=False, dump_dir=None):
"""
Create a Kamienny criterion object.
INPUT:
- `p` -- prime -- verify that there is no order p torsion
over a degree `d` field
- `sign` -- 1 (default),-1 or 0 -- the sign of the modular symbols space to use
- ``algorithm`` -- "default" or "custom" whether to use a custom (faster)
integral structure algorithm or to use the sage builtin algortihm
- ``verbose`` -- bool; whether to print extra stuff while
running.
EXAMPLES::
sage: from mdsage import *
sage: C = KamiennyCriterion(29, algorithm="custom", verbose=False); C
Kamienny's Criterion for p=29
sage: C.use_custom_algorithm
True
sage: C.p
29
sage: C.verbose
False
"""
self.verbose = verbose
self.dump_dir = dump_dir
if self.verbose: tm = cputime(); mem = get_memory_usage(); print "init"
assert congruence_type == 0 or congruence_type == 1
self.congruence_type=congruence_type
try:
p = ZZ(p)
if congruence_type==0:
self.congruence_group = Gamma0(p)
if congruence_type==1:
self.congruence_group = GammaH(p,[-1])
except TypeError:
self.congruence_group = GammaH(p.level(),[-1]+p._generators_for_H())
self.congruence_type = ("H",self.congruence_group._list_of_elements_in_H())
self.p = self.congruence_group.level()
self.algorithm=algorithm
self.sign=sign
self.M = ModularSymbols(self.congruence_group, sign=sign)
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "modsym"
self.S = self.M.cuspidal_submodule()
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "cuspsub"
self.use_custom_algorithm = False
if algorithm=="custom":
self.use_custom_algorithm = True
if self.use_custom_algorithm:
int_struct = self.integral_cuspidal_subspace()
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "custom int_struct"
else:
int_struct = self.S.integral_structure()
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "sage int_struct"
self.S_integral = int_struct
v = VectorSpace(GF(2), self.S.dimension()).random_element()
self.v=v
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "rand_vect"
if dump_dir:
v.dump(dump_dir+"/vector%s_%s" % (p,congruence_type))
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "dump"
def __init__(self, p, congruence_type=1, sign=1, algorithm="custom", verbose=False, dump_dir=None):
"""
Create a Kamienny criterion object.
INPUT:
- `p` -- prime -- verify that there is no order p torsion
over a degree `d` field
- `sign` -- 1 (default),-1 or 0 -- the sign of the modular symbols space to use
- ``algorithm`` -- "default" or "custom" whether to use a custom (faster)
integral structure algorithm or to use the sage builtin algortihm
- ``verbose`` -- bool; whether to print extra stuff while
running.
EXAMPLES::
sage: from mdsage import *
sage: C = KamiennyCriterion(29, algorithm="custom", verbose=False); C
Kamienny's Criterion for p=29
sage: C.use_custom_algorithm
True
sage: C.p
29
sage: C.verbose
False
"""
self.verbose = verbose
self.dump_dir = dump_dir
if self.verbose: tm = cputime(); mem = get_memory_usage(); print("init")
assert congruence_type == 0 or congruence_type == 1
self.congruence_type=congruence_type
try:
p = ZZ(p)
if congruence_type==0:
self.congruence_group = Gamma0(p)
if congruence_type==1:
self.congruence_group = GammaH(p,[-1])
except TypeError:
self.congruence_group = GammaH(p.level(),[-1]+p._generators_for_H())
self.congruence_type = ("H",self.congruence_group._list_of_elements_in_H())
self.p = self.congruence_group.level()
self.algorithm=algorithm
self.sign=sign
self.M = ModularSymbols(self.congruence_group, sign=sign)
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "modsym")
self.S = self.M.cuspidal_submodule()
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "cuspsub")
self.use_custom_algorithm = False
if algorithm=="custom":
self.use_custom_algorithm = True
if self.use_custom_algorithm:
int_struct = self.integral_cuspidal_subspace()
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "custom int_struct")
else:
int_struct = self.S.integral_structure()
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "sage int_struct")
self.S_integral = int_struct
v = VectorSpace(GF(2), self.S.dimension()).random_element()
self.v=v
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "rand_vect")
if dump_dir:
v.dump(dump_dir+"/vector%s_%s" % (p,congruence_type))
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "dump")
