def __cmp__(self, other):
"""
Compare self to other.
The ordering on congruence subgroups of the form GammaH(N) for
some H is first by level and then by the subgroup H. In
particular, this means that we have Gamma1(N) < GammaH(N) <
Gamma0(N) for every nontrivial subgroup H.
EXAMPLES::
sage: G = GammaH(86, [9])
sage: G.__cmp__(G)
0
sage: G.__cmp__(GammaH(86, [11])) is not 0
True
sage: Gamma1(11) < Gamma0(11)
True
sage: Gamma1(11) == GammaH(11, [])
True
sage: Gamma0(11) == GammaH(11, [2])
True
"""
if is_GammaH(other):
t = cmp(self.level(), other.level())
if t:
return t
else:
return cmp(self._list_of_elements_in_H(),
other._list_of_elements_in_H())
else:
return CongruenceSubgroup.__cmp__(self, other)
def __cmp__(self, other):
"""
Compare self to other.
The ordering on congruence subgroups of the form GammaH(N) for
some H is first by level and then by the subgroup H. In
particular, this means that we have Gamma1(N) < GammaH(N) <
Gamma0(N) for every nontrivial subgroup H.
EXAMPLES::
sage: G = GammaH(86, [9])
sage: G.__cmp__(G)
0
sage: G.__cmp__(GammaH(86, [11])) is not 0
True
sage: Gamma1(11) < Gamma0(11)
True
sage: Gamma1(11) == GammaH(11, [])
True
sage: Gamma0(11) == GammaH(11, [2])
True
"""
if is_GammaH(other):
t = cmp(self.level(), other.level())
if t:
return t
else:
return cmp(self._list_of_elements_in_H(), other._list_of_elements_in_H())
else:
return CongruenceSubgroup.__cmp__(self, other)
def __cmp__(self, other):
"""
Compare self to other.
The ordering on congruence subgroups of the form GammaH(N) for some H
is first by level, then by the order of H, then lexicographically by H.
In particular, this means that we have Gamma1(N) < GammaH(N) <
Gamma0(N) for every nontrivial proper subgroup H.
EXAMPLES::
sage: G = GammaH(86, [9])
sage: G.__cmp__(G)
0
sage: G.__cmp__(GammaH(86, [11])) is not 0
True
sage: Gamma1(11) < Gamma0(11)
True
sage: Gamma1(11) == GammaH(11, [])
True
sage: Gamma0(11) == GammaH(11, [2])
True
sage: G = Gamma0(86)
sage: G.__cmp__(G)
0
sage: G.__cmp__(GammaH(86, [11])) is not 0
True
sage: Gamma1(17) < Gamma0(17)
True
sage: Gamma0(1) == SL2Z
True
sage: Gamma0(2) == Gamma1(2)
True
sage: [x._list_of_elements_in_H() for x in sorted(Gamma0(24).gamma_h_subgroups())]
[[1],
[1, 5],
[1, 7],
[1, 11],
[1, 13],
[1, 17],
[1, 19],
[1, 23],
[1, 5, 7, 11],
[1, 5, 13, 17],
[1, 5, 19, 23],
[1, 7, 13, 19],
[1, 7, 17, 23],
[1, 11, 13, 23],
[1, 11, 17, 19],
[1, 5, 7, 11, 13, 17, 19, 23]]
"""
if is_GammaH(other):
return (cmp(self.level(), other.level())
or -cmp(self.index(), other.index())
or cmp(self._list_of_elements_in_H(),
other._list_of_elements_in_H()))
else:
return CongruenceSubgroup.__cmp__(self, other)
def __cmp__(self, other):
"""
Compare self to other.
The ordering on congruence subgroups of the form GammaH(N) for some H
is first by level, then by the order of H, then lexicographically by H.
In particular, this means that we have Gamma1(N) < GammaH(N) <
Gamma0(N) for every nontrivial proper subgroup H.
EXAMPLES::
sage: G = GammaH(86, [9])
sage: G.__cmp__(G)
0
sage: G.__cmp__(GammaH(86, [11])) is not 0
True
sage: Gamma1(11) < Gamma0(11)
True
sage: Gamma1(11) == GammaH(11, [])
True
sage: Gamma0(11) == GammaH(11, [2])
True
sage: G = Gamma0(86)
sage: G.__cmp__(G)
0
sage: G.__cmp__(GammaH(86, [11])) is not 0
True
sage: Gamma1(17) < Gamma0(17)
True
sage: Gamma0(1) == SL2Z
True
sage: Gamma0(2) == Gamma1(2)
True
sage: [x._list_of_elements_in_H() for x in sorted(Gamma0(24).gamma_h_subgroups())]
[[1],
[1, 5],
[1, 7],
[1, 11],
[1, 13],
[1, 17],
[1, 19],
[1, 23],
[1, 5, 7, 11],
[1, 5, 13, 17],
[1, 5, 19, 23],
[1, 7, 13, 19],
[1, 7, 17, 23],
[1, 11, 13, 23],
[1, 11, 17, 19],
[1, 5, 7, 11, 13, 17, 19, 23]]
"""
if is_GammaH(other):
return (cmp(self.level(), other.level())
or -cmp(self.index(), other.index())
or cmp(self._list_of_elements_in_H(), other._list_of_elements_in_H()))
else:
return CongruenceSubgroup.__cmp__(self, other)
def __cmp__(self, other):
r"""
Compare self to other.
EXAMPLES::
sage: Gamma(3) == SymmetricGroup(8)
False
sage: Gamma(3) == Gamma1(3)
False
sage: Gamma(5) < Gamma(6)
True
sage: Gamma(5) == Gamma(5)
True
sage: Gamma(3) == Gamma(3).as_permutation_group()
True
"""
if is_Gamma(other):
return cmp(self.level(), other.level())
else:
return CongruenceSubgroup.__cmp__(self, other)
def __cmp__(self, other):
r"""
Compare self to other.
EXAMPLES::
sage: Gamma(3) == SymmetricGroup(8)
False
sage: Gamma(3) == Gamma1(3)
False
sage: Gamma(5) < Gamma(6)
True
sage: Gamma(5) == Gamma(5)
True
sage: Gamma(3) == Gamma(3).as_permutation_group()
True
"""
if is_Gamma(other):
return cmp(self.level(), other.level())
else:
return CongruenceSubgroup.__cmp__(self, other)
