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)])
def _get_random_cylinder_diagram(self):
r"""
Return a random cylinder diagram with right parameters
"""
test = False
while test:
n = random.randint(self.min_num_seps,self.max_num_seps)
S = SymmetricGroup(2*n)
bot = S.random_element()
b = [[i-1 for i in c] for c in bot.cycle_tuples(singletons=True)]
p = Partitions(2*n,length=len(b)).random_element()
top = S([i+1 for i in canonical_perm(p)])
t = [[i-1 for i in c] for c in top.cycle_tuples(singletons=True)]
prandom.shuffle(t)
c = CylinderDiagram(zip(b,t))
test = c.is_connected()
return c
def _get_random_cylinder_diagram(self):
r"""
Return a random cylinder diagram with right parameters
"""
test = False
while test:
n = random.randint(self.min_num_seps, self.max_num_seps)
S = SymmetricGroup(2 * n)
bot = S.random_element()
b = [[i - 1 for i in c] for c in bot.cycle_tuples(singletons=True)]
p = Partitions(2 * n, length=len(b)).random_element()
top = S([i + 1 for i in canonical_perm(p)])
t = [[i - 1 for i in c] for c in top.cycle_tuples(singletons=True)]
prandom.shuffle(t)
c = CylinderDiagram(zip(b, t))
test = c.is_connected()
return c