def degeneracy_matrix(self, p=None):
"""
Map from self to QuaterniocModule of level self/p.
EXAMPLES::
sage: from sage.modular.hilbert.sqrt5_hmf import F, QuaternionicModule
sage: H = QuaternionicModule(2*F.prime_above(31)); H
Quaternionic module of dimension 4, level 10*a-4 (of norm 124=2^2*31) over QQ(sqrt(5))
sage: H.degeneracy_matrix(2)
[1 0]
[0 1]
[0 1]
[0 1]
sage: H.degeneracy_matrix(F.prime_above(31))
[1]
[1]
[1]
[1]
sage: H.degeneracy_matrix()
[1 0 1]
[0 1 1]
[0 1 1]
[0 1 1]
sage: H.degeneracy_matrix() is H.degeneracy_matrix()
False
sage: H.degeneracy_matrix(2) is H.degeneracy_matrix(2)
True
"""
if self.level().is_prime():
return matrix(QQ, self.dimension(), 0, sparse=True)
if self._degeneracy_matrices.has_key(p):
return self._degeneracy_matrices[p]
if p is None:
A = None
for p in prime_divisors(self._level):
A = self.degeneracy_matrix(p) if A is None else A.augment(self.degeneracy_matrix(p))
A.set_immutable()
self._degeneracy_matrices[None] = A
return A
p = sqrt5_ideal(p)
if self._degeneracy_matrices.has_key(p):
return self._degeneracy_matrices[p]
d = self._icosians_mod_p1.degeneracy_matrix(p)
d.set_immutable()
self._degeneracy_matrices[p] = d
return d
def degeneracy_matrix(self, p=None):
if self.level().is_prime():
return matrix(QQ, self.dimension(), 0, sparse=True)
if p is None:
A = None
for p in prime_divisors(self._level):
if A is None:
A = self.degeneracy_matrix(p)
else:
A = A.augment(self.degeneracy_matrix(p))
return A
p = ideal(p)
if self._degeneracy_matrices.has_key(p):
return self._degeneracy_matrices[p]
d = self._icosians_mod_p1.degeneracy_matrix(p)
d.set_immutable()
self._degeneracy_matrices[p] = d
return d
def degeneracy_matrix(self, p=None):
if self.level().is_prime():
return matrix(QQ, self.dimension(), 0, sparse=True)
if p is None:
A = None
for p in prime_divisors(self._level):
if A is None:
A = self.degeneracy_matrix(p)
else:
A = A.augment(self.degeneracy_matrix(p))
return A
p = ideal(p)
if self._degeneracy_matrices.has_key(p):
return self._degeneracy_matrices[p]
d = self._icosians_mod_p1.degeneracy_matrix(p)
d.set_immutable()
self._degeneracy_matrices[p] = d
return d
