80 lines
2 KiB
Python
80 lines
2 KiB
Python
|
|
from .euclidean import *
|
|
from .numbertype import *
|
|
|
|
# so all IntegersModP are instances of the same base class
|
|
class _Modular(FieldElement):
|
|
pass
|
|
|
|
|
|
@memoize
|
|
def IntegersModP(p):
|
|
# assume p is prime
|
|
|
|
class IntegerModP(_Modular):
|
|
def __init__(self, n):
|
|
try:
|
|
self.n = int(n) % IntegerModP.p
|
|
except:
|
|
raise TypeError("Can't cast type %s to %s in __init__" % (type(n).__name__, type(self).__name__))
|
|
|
|
self.field = IntegerModP
|
|
|
|
@typecheck
|
|
def __add__(self, other):
|
|
return IntegerModP(self.n + other.n)
|
|
|
|
@typecheck
|
|
def __sub__(self, other):
|
|
return IntegerModP(self.n - other.n)
|
|
|
|
@typecheck
|
|
def __mul__(self, other):
|
|
return IntegerModP(self.n * other.n)
|
|
|
|
def __neg__(self):
|
|
return IntegerModP(-self.n)
|
|
|
|
@typecheck
|
|
def __eq__(self, other):
|
|
return isinstance(other, IntegerModP) and self.n == other.n
|
|
|
|
@typecheck
|
|
def __ne__(self, other):
|
|
return isinstance(other, IntegerModP) is False or self.n != other.n
|
|
|
|
@typecheck
|
|
def __divmod__(self, divisor):
|
|
q,r = divmod(self.n, divisor.n)
|
|
return (IntegerModP(q), IntegerModP(r))
|
|
|
|
def inverse(self):
|
|
# need to use the division algorithm *as integers* because we're
|
|
# doing it on the modulus itself (which would otherwise be zero)
|
|
x,y,d = extendedEuclideanAlgorithm(self.n, self.p)
|
|
|
|
if d != 1:
|
|
raise Exception("Error: p is not prime in %s!" % (self.__name__))
|
|
|
|
return IntegerModP(x)
|
|
|
|
def __abs__(self):
|
|
return abs(self.n)
|
|
|
|
def __str__(self):
|
|
return str(self.n)
|
|
|
|
def __repr__(self):
|
|
return '%d (mod %d)' % (self.n, self.p)
|
|
|
|
def __int__(self):
|
|
return self.n
|
|
|
|
IntegerModP.p = p
|
|
IntegerModP.__name__ = 'Z/%d' % (p)
|
|
IntegerModP.englishName = 'IntegersMod%d' % (p)
|
|
return IntegerModP
|
|
|
|
|
|
if __name__ == "__main__":
|
|
mod7 = IntegersModP(7)
|