def test_relabel(self):
r"""
Try the function canonic labels for a random even modular subgroup.
EXAMPLES::
sage: from sage.modular.arithgroup.tests import Test
sage: Test().test_relabel() # random
"""
if prandom.uniform(0,1) < self.odd_probability:
G = random_odd_arithgroup(self.index)
else:
G = random_even_arithgroup(self.index)
G.relabel()
s2 = G._S2
s3 = G._S3
l = G._L
r = G._R
# 0 should be stabilized by the mapping
# used for renumbering so we start at 1
p = range(1,self.index)
for _ in xrange(10):
prandom.shuffle(p)
# we add 0 to the mapping
pp = [0] + p
ss2 = [None]*self.index
ss3 = [None]*self.index
ll = [None]*self.index
rr = [None]*self.index
for i in xrange(self.index):
ss2[pp[i]] = pp[s2[i]]
ss3[pp[i]] = pp[s3[i]]
ll[pp[i]] = pp[l[i]]
rr[pp[i]] = pp[r[i]]
if G.is_even():
GG = EvenArithmeticSubgroup_Permutation(ss2,ss3,ll,rr)
else:
GG = OddArithmeticSubgroup_Permutation(ss2,ss3,ll,rr)
GG.relabel()
for elt in ['_S2','_S3','_L','_R']:
if getattr(G,elt) != getattr(GG,elt):
print "s2 = %s" %str(s2)
print "s3 = %s" %str(s3)
print "ss2 = %s" %str(ss2)
print "ss3 = %s" %str(ss3)
print "pp = %s" %str(pp)
raise AssertionError("%s does not coincide" %elt)
def test_relabel(self):
r"""
Try the function canonical labels for a random even modular subgroup.
EXAMPLES::
sage: from sage.modular.arithgroup.tests import Test
sage: Test().test_relabel() # random
"""
if prandom.uniform(0, 1) < self.odd_probability:
G = random_odd_arithgroup(self.index)
else:
G = random_even_arithgroup(self.index)
G.relabel()
s2 = G._S2
s3 = G._S3
l = G._L
r = G._R
# 0 should be stabilized by the mapping
# used for renumbering so we start at 1
p = list(range(1, self.index))
for _ in range(10):
prandom.shuffle(p)
# we add 0 to the mapping
pp = [0] + p
ss2 = [None] * self.index
ss3 = [None] * self.index
ll = [None] * self.index
rr = [None] * self.index
for i in range(self.index):
ss2[pp[i]] = pp[s2[i]]
ss3[pp[i]] = pp[s3[i]]
ll[pp[i]] = pp[l[i]]
rr[pp[i]] = pp[r[i]]
if G.is_even():
GG = EvenArithmeticSubgroup_Permutation(ss2, ss3, ll, rr)
else:
GG = OddArithmeticSubgroup_Permutation(ss2, ss3, ll, rr)
GG.relabel()
for elt in ['_S2', '_S3', '_L', '_R']:
if getattr(G, elt) != getattr(GG, elt):
print("s2 = %s" % str(s2))
print("s3 = %s" % str(s3))
print("ss2 = %s" % str(ss2))
print("ss3 = %s" % str(ss3))
print("pp = %s" % str(pp))
raise AssertionError("%s does not coincide" % elt)
def test_contains(self):
r"""
Test whether the random generator for arithgroup perms gives matrices in
the group.
EXAMPLES::
sage: from sage.modular.arithgroup.tests import Test
sage: Test().test_contains() #random
"""
if prandom.uniform(0,1) < self.odd_probability:
G = random_odd_arithgroup(self.index)
else:
G = random_even_arithgroup(self.index)
for _ in xrange(20):
g = G.random_element()
if G.random_element() not in G:
raise AssertionError("%s not in %s" %(g,G))
def test_contains(self):
r"""
Test whether the random generator for arithgroup perms gives matrices in
the group.
EXAMPLES::
sage: from sage.modular.arithgroup.tests import Test
sage: Test().test_contains() #random
"""
if prandom.uniform(0, 1) < self.odd_probability:
G = random_odd_arithgroup(self.index)
else:
G = random_even_arithgroup(self.index)
for _ in range(20):
g = G.random_element()
if G.random_element() not in G:
raise AssertionError("%s not in %s" % (g, G))
def m(): if prandom.randint(0,1): return prandom.uniform(-1,1) else: return prandom.gauss(0,2)