def __cmp__(self, other):
"""
Compare self to other.
The ordering on congruence subgroups of the form `\Gamma_H(N)` for
some H is first by level and then by the subgroup H. In
particular, this means that we have `\Gamma_1(N) < \Gamma_H(N) <
\Gamma_0(N)` for every nontrivial subgroup H.
EXAMPLES::
sage: G = Gamma1(86)
sage: G.__cmp__(G)
0
sage: G.__cmp__(GammaH(86, [11])) is not 0
True
sage: Gamma1(12) < Gamma0(12)
True
sage: Gamma1(10) < Gamma1(12)
True
sage: Gamma1(11) == GammaH(11, [])
True
sage: Gamma1(1) == SL2Z
True
sage: Gamma1(2) == Gamma0(2)
True
"""
from all import is_GammaH
if not is_CongruenceSubgroup(other):
return cmp(type(self), type(other))
c = cmp(self.level(), other.level())
if c: return c
# Since Gamma1(N) is GammaH(N) for H all of (Z/N)^\times,
# we know how to compare it to any other GammaH without having
# to look at self._list_of_elements_in_H().
if is_GammaH(other):
if is_Gamma1(other):
return 0
else:
H = other._generators_for_H()
return cmp(0,len(H))
return cmp(type(self), type(other))
def __cmp__(self, other):
"""
Compare self to other.
The ordering on congruence subgroups of the form `\Gamma_H(N)` for
some H is first by level and then by the subgroup H. In
particular, this means that we have `\Gamma_1(N) < \Gamma_H(N) <
\Gamma_0(N)` for every nontrivial subgroup H.
EXAMPLES::
sage: G = Gamma1(86)
sage: G.__cmp__(G)
0
sage: G.__cmp__(GammaH(86, [11])) is not 0
True
sage: Gamma1(12) < Gamma0(12)
True
sage: Gamma1(10) < Gamma1(12)
True
sage: Gamma1(11) == GammaH(11, [])
True
sage: Gamma1(1) == SL2Z
True
sage: Gamma1(2) == Gamma0(2)
True
"""
from all import is_GammaH
if not is_CongruenceSubgroup(other):
return cmp(type(self), type(other))
c = cmp(self.level(), other.level())
if c: return c
# Since Gamma1(N) is GammaH(N) for H all of (Z/N)^\times,
# we know how to compare it to any other GammaH without having
# to look at self._list_of_elements_in_H().
if is_GammaH(other):
if is_Gamma1(other):
return 0
else:
H = other._generators_for_H()
return cmp(0, len(H))
return cmp(type(self), type(other))