def test_is_extended_real():
x = Symbol('x', extended_real=True)
y = Symbol('y', extended_real=False)
z = Symbol('z')
assert is_extended_real(x)
assert not is_extended_real(y)
assert is_extended_real(z) is None
assert is_extended_real(z, Q.extended_real(z))
def test_is_eq():
# test assumptions
assert is_eq(x, y, Q.infinite(x) & Q.finite(y)) is False
assert is_eq(
x, y,
Q.infinite(x) & Q.infinite(y) & Q.extended_real(x)
& ~Q.extended_real(y)) is False
assert is_eq(
x, y,
Q.infinite(x) & Q.infinite(y) & Q.extended_positive(x)
& Q.extended_negative(y)) is False
assert is_eq(x + I, y + I, Q.infinite(x) & Q.finite(y)) is False
assert is_eq(1 + x * I, 1 + y * I, Q.infinite(x) & Q.finite(y)) is False
assert is_eq(x, S(0), assumptions=Q.zero(x))
assert is_eq(x, S(0), assumptions=~Q.zero(x)) is False
assert is_eq(x, S(0), assumptions=Q.nonzero(x)) is False
assert is_neq(x, S(0), assumptions=Q.zero(x)) is False
assert is_neq(x, S(0), assumptions=~Q.zero(x))
assert is_neq(x, S(0), assumptions=Q.nonzero(x))
# test registration
class PowTest(Expr):
def __new__(cls, base, exp):
return Basic.__new__(cls, _sympify(base), _sympify(exp))
@dispatch(PowTest, PowTest)
def _eval_is_eq(lhs, rhs):
if type(lhs) == PowTest and type(rhs) == PowTest:
return fuzzy_and([
is_eq(lhs.args[0], rhs.args[0]),
is_eq(lhs.args[1], rhs.args[1])
])
assert is_eq(PowTest(3, 4), PowTest(3, 4))
assert is_eq(PowTest(3, 4), _sympify(4)) is None
assert is_neq(PowTest(3, 4), PowTest(3, 7))