def __init__(self, mapping, inv_mapping, l_edges, r_edges, s2_edges,
s3_edges):
N = len(s2_edges)
ss2 = [None] * len(s2_edges)
ss3 = [None] * len(s3_edges)
ll = [None] * len(l_edges)
rr = [None] * len(r_edges)
for i in range(N):
ss2[s2_edges[i]] = i
ss3[s3_edges[i]] = i
ll[l_edges[i]] = i
rr[r_edges[i]] = i
if mapping[0].is_orientation_cover():
self._veech_group = EvenArithmeticSubgroup_Permutation(
ss2, ss3, ll, rr)
else:
self._veech_group = OddArithmeticSubgroup_Permutation(
ss2, ss3, ll, rr)
self._l_edges = l_edges
self._li_edges = ll
self._r_edges = r_edges
self._ri_edges = rr
self._s2_edges = s2_edges
self._s2i_edges = ss2
self._s3_edges = s3_edges
self._s3i_edges = ss3
self._mapping = mapping
self._inv_mapping = inv_mapping
def as_permutation_group(self):
r"""
Return self as an arithmetic subgroup defined in terms of the
permutation action of `SL(2,\ZZ)` on its right cosets.
This method uses Todd-Coxeter enumeration (via the method
:meth:`~todd_coxeter`) which can be extremely slow for arithmetic
subgroups with relatively large index in `SL(2,\ZZ)`.
EXAMPLES::
sage: G = Gamma(3)
sage: P = G.as_permutation_group(); P
Arithmetic subgroup of index 24
sage: G.ncusps() == P.ncusps()
True
sage: G.nu2() == P.nu2()
True
sage: G.nu3() == P.nu3()
True
sage: G.an_element() in P
True
sage: P.an_element() in G
True
"""
_, _, l_edges, s2_edges = self.todd_coxeter()
n = len(l_edges)
s3_edges = [None] * n
r_edges = [None] * n
for i in xrange(n):
ii = s2_edges[l_edges[i]]
s3_edges[ii] = i
r_edges[ii] = s2_edges[i]
if self.is_even():
from sage.modular.arithgroup.arithgroup_perm import EvenArithmeticSubgroup_Permutation
g = EvenArithmeticSubgroup_Permutation(S2=s2_edges,
S3=s3_edges,
L=l_edges,
R=r_edges)
else:
from sage.modular.arithgroup.arithgroup_perm import OddArithmeticSubgroup_Permutation
g = OddArithmeticSubgroup_Permutation(S2=s2_edges,
S3=s3_edges,
L=l_edges,
R=r_edges)
g.relabel()
return g
def as_permutation_group(self):
r"""
Return self as an arithmetic subgroup defined in terms of the
permutation action of `SL(2,\ZZ)` on its right cosets.
This method uses Todd-Coxeter enumeration (via the method
:meth:`~todd_coxeter`) which can be extremely slow for arithmetic
subgroups with relatively large index in `SL(2,\ZZ)`.
EXAMPLES::
sage: G = Gamma(3)
sage: P = G.as_permutation_group(); P
Arithmetic subgroup of index 24
sage: G.ncusps() == P.ncusps()
True
sage: G.nu2() == P.nu2()
True
sage: G.nu3() == P.nu3()
True
sage: G.an_element() in P
True
sage: P.an_element() in G
True
"""
_, _, l_edges, s2_edges = self.todd_coxeter()
n = len(l_edges)
s3_edges = [None] * n
r_edges = [None] * n
for i in xrange(n):
ii = s2_edges[l_edges[i]]
s3_edges[ii] = i
r_edges[ii] = s2_edges[i]
if self.is_even():
from sage.modular.arithgroup.arithgroup_perm import EvenArithmeticSubgroup_Permutation
g = EvenArithmeticSubgroup_Permutation(
S2=s2_edges, S3=s3_edges, L=l_edges, R=r_edges)
else:
from sage.modular.arithgroup.arithgroup_perm import OddArithmeticSubgroup_Permutation
g = OddArithmeticSubgroup_Permutation(
S2=s2_edges, S3=s3_edges, L=l_edges, R=r_edges)
g.relabel()
return g