def unit_group_exponent(self):
"""
EXAMPLES::
sage: R = IntegerModRing(17)
sage: R.unit_group_exponent()
16
sage: R = IntegerModRing(18)
sage: R.unit_group_exponent()
6
"""
if self.__unit_group_exponent != None:
return self.__unit_group_exponent
a = []
for p, r in self.factored_order():
if p != 2:
a.append((p - 1) * (p**(r - 1))) # phi(p**r)
else: # p=2
if r == 2:
a.append(2)
elif r > 2:
a.append(2**(r - 2))
#endif
#endfor
self.__unit_group_exponent = int(LCM(a))
return self.__unit_group_exponent
def unit_group_exponent(self):
"""
EXAMPLES::
sage: R = IntegerModRing(17)
sage: R.unit_group_exponent()
16
sage: R = IntegerModRing(18)
sage: R.unit_group_exponent()
6
"""
if self.__unit_group_exponent != None:
return self.__unit_group_exponent
a = []
for p, r in self.factored_order():
if p != 2:
a.append((p-1)*(p**(r-1))) # phi(p**r)
else: # p=2
if r==2:
a.append(2)
elif r>2:
a.append(2**(r-2))
#endif
#endfor
self.__unit_group_exponent = int(LCM(a))
return self.__unit_group_exponent
def unit_group_exponent(self):
"""
EXAMPLES::
sage: R = IntegerModRing(17)
sage: R.unit_group_exponent()
16
sage: R = IntegerModRing(18)
sage: R.unit_group_exponent()
6
"""
a = []
for p, r in self.factored_order():
if p != 2:
a.append((p-1)*(p**(r-1))) # phi(p**r)
elif r==2: # p=2 from this point on
a.append(2)
elif r>2:
a.append(2**(r-2))
return int(LCM(a))
def unit_group_exponent(self):
"""
EXAMPLES::
sage: R = IntegerModRing(17)
sage: R.unit_group_exponent()
16
sage: R = IntegerModRing(18)
sage: R.unit_group_exponent()
6
"""
a = []
for p, r in self.factored_order():
if p != 2:
a.append((p - 1) * (p**(r - 1))) # phi(p**r)
elif r == 2: # p=2 from this point on
a.append(2)
elif r > 2:
a.append(2**(r - 2))
return int(LCM(a))