def is_subgroup(self, other):
r"""
Return True if self is a subgroup of right, and False
otherwise.
EXAMPLES::
sage: GammaH(24,[7]).is_subgroup(SL2Z)
True
sage: GammaH(24,[7]).is_subgroup(Gamma0(8))
True
sage: GammaH(24, []).is_subgroup(GammaH(24, [7]))
True
sage: GammaH(24, []).is_subgroup(Gamma1(24))
True
sage: GammaH(24, [17]).is_subgroup(GammaH(24, [7]))
False
sage: GammaH(1371, [169]).is_subgroup(GammaH(457, [169]))
True
"""
from all import is_Gamma0, is_Gamma1
if not isinstance(other, GammaH_class):
raise NotImplementedError
# level of self should divide level of other
if self.level() % other.level():
return False
# easy cases
if is_Gamma0(other):
return True # recall self is a GammaH, so it's contained in Gamma0
if is_Gamma1(other) and len(self._generators_for_H()) > 0:
return False
else:
# difficult case
t = other._list_of_elements_in_H()
for x in self._generators_for_H():
if not (x in t):
return False
return True
def is_subgroup(self, other):
r"""
Return True if self is a subgroup of right, and False
otherwise.
EXAMPLES::
sage: GammaH(24,[7]).is_subgroup(SL2Z)
True
sage: GammaH(24,[7]).is_subgroup(Gamma0(8))
True
sage: GammaH(24, []).is_subgroup(GammaH(24, [7]))
True
sage: GammaH(24, []).is_subgroup(Gamma1(24))
True
sage: GammaH(24, [17]).is_subgroup(GammaH(24, [7]))
False
sage: GammaH(1371, [169]).is_subgroup(GammaH(457, [169]))
True
"""
from all import is_Gamma0, is_Gamma1
if not isinstance(other, GammaH_class):
raise NotImplementedError
# level of self should divide level of other
if self.level() % other.level():
return False
# easy cases
if is_Gamma0(other):
return True # recall self is a GammaH, so it's contained in Gamma0
if is_Gamma1(other) and len(self._generators_for_H()) > 0:
return False
else:
# difficult case
t = other._list_of_elements_in_H()
for x in self._generators_for_H():
if not (x in t):
return False
return True