def _projective_general_unitary_order(n, field):
q = field.order
return (Integer({field.char: field.pow * (n * (n - 1) / 2)}) *
prod((Integer(q ** i - 1) *
Integer(q ** i + 1) for i in xrange(1, n // 2 + 1))) *
prod((Integer(q ** (2 * i + 1) + 1)) for i in xrange(1,
(n + 1) // 2)))
def _projective_general_unitary_order(n, field):
q = field.order
return (Integer({field.char: field.pow * (n * (n - 1) // 2)}) *
prod((Integer(q ** i - 1) *
Integer(q ** i + 1) for i in range(1, n // 2 + 1))) *
prod((Integer(q ** (2 * i + 1) + 1)) for i in range(1,
(n + 1) // 2)))
def _projective_special_unitary_order(n, field):
q = field.order
return (Integer({field.char: field.pow * (n * (n - 1) / 2)}) * prod(
(Integer(q**i - 1) * Integer(q**i + 1)
for i in xrange(2, n // 2 + 1))) * prod(
(Integer(q**(2 * i + 1) + 1))
for i in xrange(1, (n + 1) // 2)) * Integer(q - 1) * Integer(
(q + 1) // gcd(n, q + 1)))
def order(n, field):
q = field.order
n //= 2
o = (Integer({field.char: field.pow * n * (n - 1)}) *
Integer(q**n - e) * prod((Integer(q**i - 1) * Integer(q**i + 1)
for i in xrange(1, n))))
if field.char != 2:
o.div_by_prime(2)
return o
def order(n, field):
q = field.order
n //= 2
o = (Integer({field.char: field.pow * n * (n - 1)}) *
Integer(q ** n - e) *
prod((Integer(q ** i - 1) *
Integer(q ** i + 1) for i in xrange(1, n))))
if field.char != 2:
o.div_by_prime(2)
return o
def order(n, field):
q = field.order
n //= 2
part = prod(
(Integer(q**k - 1) * Integer(q**k + 1) for k in xrange(1, n)))
if not e:
return (part * Integer({field.char: field.pow * n * n}) *
Integer(q**n - 1) * Integer(q**n + 1))
if field.char == 2:
part *= 2
return (part * Integer({field.char: field.pow * n * (n - 1)}) *
Integer(q**n - e))
def order(n, field):
q = field.order
n //= 2
part = prod((Integer(q ** k - 1) *
Integer(q ** k + 1) for k in xrange(1, n)))
if not e:
return (part * Integer({field.char: field.pow * n * n}) *
Integer(q ** n - 1) * Integer(q ** n + 1))
if field.char == 2:
part *= 2
return (part * Integer({field.char: field.pow * n * (n - 1)}) *
Integer(q ** n - e))
def order(self):
if self._order is None:
# n!/2
self._order = numeric.prod(xrange(3, self._degree + 1))
return self._order
def _symplectic_order(n, field):
n //= 2
q = field.order
return (Integer({field.char: field.pow * n * n}) * prod(
(Integer(q**i - 1) * Integer(q**i + 1) for i in xrange(1, n + 1))))
def _order_product(field, pow, pluses, minuses):
q = field.order
return (Integer({field.char: field.pow * pow}) * prod(
(Integer(q**i + 1) for i in pluses)) * prod(
(Integer(q**i - 1) for i in minuses)))
def _projective_general_linear_order(n, field):
q = field.order
return (Integer({field.char: field.pow * (n * (n - 1) / 2)}) *
prod((Integer(q ** i - 1) for i in xrange(2, n + 1))))
def _projective_special_linear_order(n, field):
q = field.order
return (Integer({field.char: field.pow * (n * (n - 1) / 2)}) * prod(
(Integer(q**i - 1)
for i in xrange(3, n + 1))) * Integer(q + 1) * Integer(
(q - 1) // gcd(n, q - 1)))
def _projective_general_linear_order(n, field):
q = field.order
return (Integer({field.char: field.pow * (n * (n - 1) / 2)}) * prod(
(Integer(q**i - 1) for i in xrange(2, n + 1))))
def order(self):
if self._order is None:
# n!/2
self._order = numeric.prod(xrange(3, self._degree + 1))
return self._order
def _symplectic_order(n, field):
n //= 2
q = field.order
return (Integer({field.char: field.pow * n * n}) *
prod((Integer(q ** i - 1) *
Integer(q ** i + 1) for i in xrange(1, n + 1))))
def _order_product(field, pow, pluses, minuses):
q = field.order
return (Integer({field.char: field.pow * pow}) *
prod((Integer(q ** i + 1) for i in pluses)) *
prod((Integer(q ** i - 1) for i in minuses)))
def _projective_special_linear_order(n, field):
q = field.order
return (Integer({field.char: field.pow * (n * (n - 1) / 2)}) *
prod((Integer(q ** i - 1) for i in xrange(3, n + 1))) *
Integer(q + 1) * Integer((q - 1) // gcd(n, q - 1)))
