def test_zero_positive():
assert satask(Q.zero(x + y), Q.positive(x) & Q.positive(y)) is False
assert satask(Q.positive(x) & Q.positive(y), Q.zero(x + y)) is False
assert satask(Q.nonzero(x + y), Q.positive(x) & Q.positive(y)) is True
assert satask(Q.positive(x) & Q.positive(y), Q.nonzero(x + y)) is None
# This one requires several levels of forward chaining
assert satask(Q.zero(x*(x + y)), Q.positive(x) & Q.positive(y)) is False
assert satask(Q.positive(pi*x*y + 1), Q.positive(x) & Q.positive(y)) is True
assert satask(Q.positive(pi*x*y - 5), Q.positive(x) & Q.positive(y)) is None
def test_zero_pow():
assert satask(Q.zero(x**y), Q.zero(x) & Q.positive(y)) is True
assert satask(Q.zero(x**y), Q.nonzero(x) & Q.zero(y)) is False
assert satask(Q.zero(x), Q.zero(x**y)) is True
assert satask(Q.zero(x**y), Q.zero(x)) is None
def test_abs():
assert satask(Q.nonnegative(abs(x))) is True
assert satask(Q.positive(abs(x)), ~Q.zero(x)) is True
assert satask(Q.zero(x), ~Q.zero(abs(x))) is False
assert satask(Q.zero(x), Q.zero(abs(x))) is True
assert satask(Q.nonzero(x), ~Q.zero(abs(x))) is None # x could be complex
assert satask(Q.zero(abs(x)), Q.zero(x)) is True
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))
def test_sign():
x = Symbol('x', real = True)
assert refine(sign(x), Q.positive(x)) == 1
assert refine(sign(x), Q.negative(x)) == -1
assert refine(sign(x), Q.zero(x)) == 0
assert refine(sign(x), True) == sign(x)
assert refine(sign(Abs(x)), Q.nonzero(x)) == 1
x = Symbol('x', imaginary=True)
assert refine(sign(x), Q.positive(im(x))) == S.ImaginaryUnit
assert refine(sign(x), Q.negative(im(x))) == -S.ImaginaryUnit
assert refine(sign(x), True) == sign(x)
x = Symbol('x', complex=True)
assert refine(sign(x), Q.zero(x)) == 0
def test_old_assump():
assert satask(Q.positive(1)) is True
assert satask(Q.positive(-1)) is False
assert satask(Q.positive(0)) is False
assert satask(Q.positive(I)) is False
assert satask(Q.positive(pi)) is True
assert satask(Q.negative(1)) is False
assert satask(Q.negative(-1)) is True
assert satask(Q.negative(0)) is False
assert satask(Q.negative(I)) is False
assert satask(Q.negative(pi)) is False
assert satask(Q.zero(1)) is False
assert satask(Q.zero(-1)) is False
assert satask(Q.zero(0)) is True
assert satask(Q.zero(I)) is False
assert satask(Q.zero(pi)) is False
assert satask(Q.nonzero(1)) is True
assert satask(Q.nonzero(-1)) is True
assert satask(Q.nonzero(0)) is False
assert satask(Q.nonzero(I)) is False
assert satask(Q.nonzero(pi)) is True
assert satask(Q.nonpositive(1)) is False
assert satask(Q.nonpositive(-1)) is True
assert satask(Q.nonpositive(0)) is True
assert satask(Q.nonpositive(I)) is False
assert satask(Q.nonpositive(pi)) is False
assert satask(Q.nonnegative(1)) is True
assert satask(Q.nonnegative(-1)) is False
assert satask(Q.nonnegative(0)) is True
assert satask(Q.nonnegative(I)) is False
assert satask(Q.nonnegative(pi)) is True
def test_zero():
"""
Everything in this test doesn't work with the ask handlers, and most
things would be very difficult or impossible to make work under that
model.
"""
assert satask(Q.zero(x) | Q.zero(y), Q.zero(x*y)) is True
assert satask(Q.zero(x*y), Q.zero(x) | Q.zero(y)) is True
assert satask(Implies(Q.zero(x), Q.zero(x*y))) is True
# This one in particular requires computing the fixed-point of the
# relevant facts, because going from Q.nonzero(x*y) -> ~Q.zero(x*y) and
# Q.zero(x*y) -> Equivalent(Q.zero(x*y), Q.zero(x) | Q.zero(y)) takes two
# steps.
assert satask(Q.zero(x) | Q.zero(y), Q.nonzero(x*y)) is False
assert satask(Q.zero(x), Q.zero(x**2)) is True
def test_satask():
# No relevant facts
assert satask(Q.real(x), Q.real(x)) is True
assert satask(Q.real(x), ~Q.real(x)) is False
assert satask(Q.real(x)) is None
assert satask(Q.real(x), Q.positive(x)) is True
assert satask(Q.positive(x), Q.real(x)) is None
assert satask(Q.real(x), ~Q.positive(x)) is None
assert satask(Q.positive(x), ~Q.real(x)) is False
raises(ValueError, lambda: satask(Q.real(x), Q.real(x) & ~Q.real(x)))
with assuming(Q.positive(x)):
assert satask(Q.real(x)) is True
assert satask(~Q.positive(x)) is False
raises(ValueError, lambda: satask(Q.real(x), ~Q.positive(x)))
assert satask(Q.zero(x), Q.nonzero(x)) is False
assert satask(Q.positive(x), Q.zero(x)) is False
assert satask(Q.real(x), Q.zero(x)) is True
assert satask(Q.zero(x), Q.zero(x*y)) is None
assert satask(Q.zero(x*y), Q.zero(x))