def maximal_isotropic_subgroup(self):
r"""
Returns the maximal isotropic subgroup of self.
"""
S=list()
for a in self._D:
if(self.Q(a)==0 and a<>0):
S.append(a)
# S is now a list of all isotropic elements except 0
PS=list(powerset(S))
PS.reverse()
# PS now contains all subsets of isotropic elements (except 0)
# with decreasing sizes. We now need to find the first, which together with 0
# is a group.
#print "PS=",PS
for A in PS:
A.append(0)
#print "Test the isotropic set: S=",A
ok=True
for x in A:
for y in A:
z=red_mod1(x+y)
if(not z in A):
#print "S was not a subgroup!"
ok=False
if(ok):
A.sort()
return A
raise ArithmeticError, "Could not find maximal isotropic subgroup!"
def maximal_isotropic_subgroup(self):
r"""
Returns the maximal isotropic subgroup of self.
"""
S=list()
for a in self._D:
if self.Q(a) == 0 and a != 0:
S.append(a)
# S is now a list of all isotropic elements except 0
PS=list(powerset(S))
PS.reverse()
# PS now contains all subsets of isotropic elements (except 0)
# with decreasing sizes. We now need to find the first, which together with 0
# is a group.
#print "PS=",PS
for A in PS:
A.append(0)
#print "Test the isotropic set: S=",A
ok=True
for x in A:
for y in A:
z=red_mod1(x+y)
if(not z in A):
#print "S was not a subgroup!"
ok=False
if(ok):
A.sort()
return A
raise ArithmeticError("Could not find maximal isotropic subgroup!")
def invariant_trace_field_generators(self):
gens = self.generators()
if min([abs(self(g).trace()) for g in gens]) < 0.001:
raise ValueError(
"Algorithm fails when a generator has trace 0, see page 125 of ML"
)
gens = [2 * g for g in gens]
enough_elts = [
''.join(sorted(s)) for s in powerset(gens) if len(s) > 0
]
return [self(w).trace() for w in enough_elts]
def trace_field_generators(self):
gens = self.generators()
enough_elts = [
''.join(sorted(s)) for s in powerset(gens) if len(s) > 0
]
return [self(w).trace() for w in enough_elts]