def test_normalize():
# this should be 0
z = Z.cons(pos=Nat(1), neg=Nat(1))
# we normalize it
assert z.normalize() == Z(0)
z = Z.cons(pos=Nat(1), neg=Nat(0))
assert z.normalize() == Z(1)
z = Z.cons(pos=Nat(0), neg=Nat(1))
assert z.normalize() == Z(-1)
def test_generator():
# because the Z.zero == Z.cons(pos=Nat(0), neg=Nat(0))
assert Z.zero()._generator == Z.cons
assert Z.cons(pos=Nat(0), neg=Nat(0))._generator == Z.cons
def test_constructor():
assert Z(0) == Z.cons(pos=Nat(0), neg=Nat(0))
assert Z(1) == Z.cons(pos=Nat(1), neg=Nat(0))
assert Z(-1) == Z.cons(pos=Nat(0), neg=Nat(1))