def is_subgroup(self, right):
"""
Return True if self is a subgroup of right.
EXAMPLES::
sage: G = Gamma0(20)
sage: G.is_subgroup(SL2Z)
True
sage: G.is_subgroup(Gamma0(4))
True
sage: G.is_subgroup(Gamma0(20))
True
sage: G.is_subgroup(Gamma0(7))
False
sage: G.is_subgroup(Gamma1(20))
False
sage: G.is_subgroup(GammaH(40, []))
False
sage: Gamma0(80).is_subgroup(GammaH(40, [31, 21, 17]))
True
sage: Gamma0(2).is_subgroup(Gamma1(2))
True
"""
if right.level() == 1:
return True
if is_Gamma0(right):
return self.level() % right.level() == 0
if is_Gamma1(right):
if right.level() >= 3:
return False
elif right.level() == 2:
return self.level() == 2
# case level 1 dealt with above
else:
return GammaH_class.is_subgroup(self, right)
def is_subgroup(self, right):
"""
Return True if self is a subgroup of right.
EXAMPLES::
sage: G = Gamma0(20)
sage: G.is_subgroup(SL2Z)
True
sage: G.is_subgroup(Gamma0(4))
True
sage: G.is_subgroup(Gamma0(20))
True
sage: G.is_subgroup(Gamma0(7))
False
sage: G.is_subgroup(Gamma1(20))
False
sage: G.is_subgroup(GammaH(40, []))
False
sage: Gamma0(80).is_subgroup(GammaH(40, [31, 21, 17]))
True
sage: Gamma0(2).is_subgroup(Gamma1(2))
True
"""
if right.level() == 1:
return True
if is_Gamma0(right):
return self.level() % right.level() == 0
if is_Gamma1(right):
if right.level() >= 3:
return False
elif right.level() == 2:
return self.level() == 2
# case level 1 dealt with above
else:
return GammaH_class.is_subgroup(self, right)
