def random_even_arithgroup(index,nu2_max=None,nu3_max=None):
r"""
Return a random even arithmetic subgroup
EXAMPLES::
sage: import sage.modular.arithgroup.tests as tests
sage: G = tests.random_even_arithgroup(30); G # random
Arithmetic subgroup of index 30
sage: G.is_even()
True
"""
from sage.groups.perm_gps.permgroup import PermutationGroup
test = False
if nu2_max is None:
nu2_max = index//5
elif nu2_max == 0:
assert index%2 == 0
if nu3_max is None:
nu3_max = index//7
elif nu3_max == 0:
assert index%3 == 0
while not test:
nu2 = prandom.randint(0,nu2_max)
nu2 = index%2 + nu2*2
nu3 = prandom.randint(0,nu3_max)
nu3 = index%3 + nu3*3
l = range(1,index+1)
prandom.shuffle(l)
S2 = []
for i in xrange(nu2):
S2.append((l[i],))
for i in xrange(nu2,index,2):
S2.append((l[i],l[i+1]))
prandom.shuffle(l)
S3 = []
for i in xrange(nu3):
S3.append((l[i],))
for i in xrange(nu3,index,3):
S3.append((l[i],l[i+1],l[i+2]))
G = PermutationGroup([S2,S3])
test = G.is_transitive()
return ArithmeticSubgroup_Permutation(S2=S2,S3=S3)
def random_even_arithgroup(index, nu2_max=None, nu3_max=None):
r"""
Return a random even arithmetic subgroup
EXAMPLES::
sage: import sage.modular.arithgroup.tests as tests
sage: G = tests.random_even_arithgroup(30); G # random
Arithmetic subgroup of index 30
sage: G.is_even()
True
"""
from sage.groups.perm_gps.permgroup import PermutationGroup
test = False
if nu2_max is None:
nu2_max = index // 5
elif nu2_max == 0:
assert index % 2 == 0
if nu3_max is None:
nu3_max = index // 7
elif nu3_max == 0:
assert index % 3 == 0
while not test:
nu2 = prandom.randint(0, nu2_max)
nu2 = index % 2 + nu2 * 2
nu3 = prandom.randint(0, nu3_max)
nu3 = index % 3 + nu3 * 3
l = list(range(1, index + 1))
prandom.shuffle(l)
S2 = []
for i in range(nu2):
S2.append((l[i], ))
for i in range(nu2, index, 2):
S2.append((l[i], l[i + 1]))
prandom.shuffle(l)
S3 = []
for i in range(nu3):
S3.append((l[i], ))
for i in range(nu3, index, 3):
S3.append((l[i], l[i + 1], l[i + 2]))
G = PermutationGroup([S2, S3])
test = G.is_transitive()
return ArithmeticSubgroup_Permutation(S2=S2, S3=S3)
def _get_random_ribbon_graph(self):
r"""
Return a random ribbon graph with right parameters.
"""
n = random.randint(self.min_num_seps, self.max_num_seps)
S = SymmetricGroup(2 * n)
e = S([(2 * i + 1, 2 * i + 2) for i in range(n)])
f = S.random_element()
P = PermutationGroup([e, f])
while not P.is_transitive():
f = S.random_element()
P = PermutationGroup([e, f])
return RibbonGraph(edges=[e(i + 1) - 1 for i in range(2 * n)],
faces=[f(i + 1) - 1 for i in range(2 * n)])
def _get_random_ribbon_graph(self):
r"""
Return a random ribbon graph with right parameters.
"""
n = random.randint(self.min_num_seps,self.max_num_seps)
S = SymmetricGroup(2*n)
e = S([(2*i+1,2*i+2) for i in xrange(n)])
f = S.random_element()
P = PermutationGroup([e,f])
while not P.is_transitive():
f = S.random_element()
P = PermutationGroup([e,f])
return RibbonGraph(
edges=[e(i+1)-1 for i in xrange(2*n)],
faces=[f(i+1)-1 for i in xrange(2*n)])
