def Zn(n):
'''
Group of integers under addition modulo n
'''
addXY = lambda x, y : (x + y) % n
add_op = OperationFactory.create_operation(addXY, numeric_set.Zn(n))
return FiniteGroupFactory.create_group(add_op.get_set(), add_op)
def FiniteDirectSum(*rings):
'''
Given rings R1, R2, ..., represents
the set R1 (+) R2 (+) ...
'''
mulXY = lambda x, y : tuple([rings[i].multiply(x[i], y[i]) for i in range(len(rings))])
add_group = gFiniteDirectSum(*[ring.get_additive_group() for ring in rings])
mult_op = OperationFactory.create_operation(mulXY, add_group)
return FiniteRingFactory.create_ring(add_group, mult_op)
def Zn(n):
multXY = lambda x, y : (x * y) % n
mult_op = OperationFactory.create_operation(multXY, gZn(n))
return FiniteRingFactory.create_ring(gZn(n), mult_op)