def test_Eq():
assert Eq(Interval(0, 1), Interval(0, 1))
assert Eq(Interval(0, 1), Union(Interval(2, 3),
Interval(4, 5))).is_Equality
assert Eq(Interval(0, 1), Interval(0, 2)) is S.false
s1 = FiniteSet(0, 1)
s2 = FiniteSet(1, 2)
assert Eq(s1, s1)
assert Eq(s1, s2) is S.false
assert Eq(FiniteSet(1, 2), FiniteSet(3, 4, 5)) is S.false
assert Eq(s1*s2, s1*s2)
assert Eq(s1*s2, s2*s1) is S.false
p1 = ProductSet(FiniteSet(1), FiniteSet(2))
assert Eq(p1, s1).is_Equality
p2 = ProductSet(FiniteSet(1), FiniteSet(2), FiniteSet(3))
assert Eq(p1, p2) is S.false
def test_union():
assert Union(Interval(1, 2), Interval(2, 3)) == Interval(1, 3)
assert Union(Interval(1, 2), Interval(2, 3, True)) == Interval(1, 3)
assert Union(Interval(1, 3), Interval(2, 4)) == Interval(1, 4)
assert Union(Interval(1, 2), Interval(1, 3)) == Interval(1, 3)
assert Union(Interval(1, 3), Interval(1, 2)) == Interval(1, 3)
assert Union(Interval(1, 3, False, True), Interval(1, 2)) == \
Interval(1, 3, False, True)
assert Union(Interval(1, 3), Interval(1, 2, False, True)) == Interval(1, 3)
assert Union(Interval(1, 2, True), Interval(1, 3)) == Interval(1, 3)
assert Union(Interval(1, 2, True), Interval(1, 3, True)) == \
Interval(1, 3, True)
assert Union(Interval(1, 2, True), Interval(1, 3, True, True)) == \
Interval(1, 3, True, True)
assert Union(Interval(1, 2, True, True), Interval(1, 3, True)) == \
Interval(1, 3, True)
assert Union(Interval(1, 3), Interval(2, 3)) == Interval(1, 3)
assert Union(Interval(1, 3, False, True), Interval(2, 3)) == \
Interval(1, 3)
assert Union(Interval(1, 2, False, True), Interval(2, 3, True)) != \
Interval(1, 3)
assert Union(Interval(1, 2), S.EmptySet) == Interval(1, 2)
assert Union(S.EmptySet) == S.EmptySet
assert Union(Interval(0, 1), [FiniteSet(1.0/n) for n in range(1, 10)]) == \
Interval(0, 1)
assert Interval(1, 2).union(Interval(2, 3)) == \
Interval(1, 2) + Interval(2, 3)
assert Interval(1, 2).union(Interval(2, 3)) == Interval(1, 3)
assert Union(Set()) == Set()
assert FiniteSet(1) + FiniteSet(2) + FiniteSet(3) == FiniteSet(1, 2, 3)
assert FiniteSet('ham') + FiniteSet('eggs') == FiniteSet('ham', 'eggs')
assert FiniteSet(1, 2, 3) + S.EmptySet == FiniteSet(1, 2, 3)
assert FiniteSet(1, 2, 3) & FiniteSet(2, 3, 4) == FiniteSet(2, 3)
assert FiniteSet(1, 2, 3) | FiniteSet(2, 3, 4) == FiniteSet(1, 2, 3, 4)
assert S.EmptySet | FiniteSet(x, FiniteSet(y, z)) == \
FiniteSet(x, FiniteSet(y, z))
# Test that Intervals and FiniteSets play nicely
assert Interval(1, 3) + FiniteSet(2) == Interval(1, 3)
assert Interval(1, 3, True, True) + FiniteSet(3) == \
Interval(1, 3, True, False)
X = Interval(1, 3) + FiniteSet(5)
Y = Interval(1, 2) + FiniteSet(3)
XandY = X.intersection(Y)
assert 2 in X and 3 in X and 3 in XandY
assert XandY.is_subset(X) and XandY.is_subset(Y)
pytest.raises(TypeError, lambda: Union(1, 2, 3))
assert X.is_iterable is False
Z = Union(FiniteSet(1, 2)*FiniteSet(3, 4), FiniteSet(1, 2, 3, 4))
assert Z.is_iterable
# issue sympy/sympy#7843
assert Union(S.EmptySet, FiniteSet(-sqrt(-I), sqrt(-I))) == FiniteSet(-sqrt(-I), sqrt(-I))
assert Union(ProductSet(FiniteSet(1), FiniteSet(2)), Interval(0, 1)).is_Union
assert Union(ProductSet(FiniteSet(1), FiniteSet(2)),
ProductSet(FiniteSet(1), FiniteSet(2), FiniteSet(3))).is_Union
assert list(Union(FiniteSet(1, 2), FiniteSet(3, 4), evaluate=False)) == [1, 3, 2, 4]
pytest.raises(TypeError, lambda: iter(Union(FiniteSet(1, 2), Interval(0, 1))))
assert (Union(FiniteSet(E), FiniteSet(pi), evaluate=False).evalf() ==
FiniteSet(Float('2.7182818284590451', prec=15),
Float('3.1415926535897931', prec=15)))
def test_ProductSet_iter():
pytest.raises(TypeError, lambda: iter(ProductSet(Set(1), Set(2))))
def test_pow_args():
pytest.raises(ValueError, lambda: Interval(0, 1)**-1)
pytest.raises(TypeError, lambda: ProductSet(2))
def test_ProductSet_of_single_arg_is_arg():
assert ProductSet(Interval(0, 1)) == Interval(0, 1)
def test_intersection():
pytest.raises(TypeError, lambda: Intersection(1))
pytest.raises(TypeError, lambda: Intersection())
assert Interval(0, 2).intersection(Interval(1, 2)) == Interval(1, 2)
assert Interval(0, 2).intersection(Interval(1, 2, True)) == \
Interval(1, 2, True)
assert Interval(0, 2, True).intersection(Interval(1, 2)) == \
Interval(1, 2, False, False)
assert Interval(0, 2, True, True).intersection(Interval(1, 2)) == \
Interval(1, 2, False, True)
assert Interval(0, 2).intersection(Union(Interval(0, 1), Interval(2, 3))) == \
Union(Interval(0, 1), Interval(2, 2))
x = Symbol('x')
assert Intersection(Interval(0, 1), FiniteSet(x)).is_iterable
assert not Intersection(Interval(0, 1), Interval(0, x)).is_iterable
assert FiniteSet(1, 2, x).intersection(FiniteSet(x)) == FiniteSet(x)
assert FiniteSet('ham', 'eggs').intersection(FiniteSet('ham')) == \
FiniteSet('ham')
assert FiniteSet(1, 2, 3, 4, 5).intersection(S.EmptySet) == S.EmptySet
assert Interval(0, 5).intersection(FiniteSet(1, 3)) == FiniteSet(1, 3)
assert Interval(0, 1, True, True).intersection(FiniteSet(1)) == S.EmptySet
assert Union(Interval(0, 1), Interval(2, 3)).intersection(Interval(1, 2)) == \
Union(Interval(1, 1), Interval(2, 2))
assert Union(Interval(0, 1), Interval(2, 3)).intersection(Interval(0, 2)) == \
Union(Interval(0, 1), Interval(2, 2))
assert Union(Interval(0, 1), Interval(2, 3)).intersection(Interval(1, 2, True, True)) == \
S.EmptySet
assert Union(Interval(0, 1), Interval(2, 3)).intersection(S.EmptySet) == \
S.EmptySet
assert Union(Interval(0, 5), FiniteSet('ham')).intersection(FiniteSet(2, 3, 4, 5, 6)) == \
Union(FiniteSet(2, 3, 4, 5), Intersection(FiniteSet(6), Union(Interval(0, 5), FiniteSet('ham'))))
# issue sympy/sympy#8217
assert Intersection(FiniteSet(x), FiniteSet(y)) == \
Intersection(FiniteSet(x), FiniteSet(y), evaluate=False)
assert FiniteSet(x).intersection(S.Reals) == \
Intersection(S.Reals, FiniteSet(x), evaluate=False)
# tests for the intersection alias
assert Interval(0, 5).intersection(FiniteSet(1, 3)) == FiniteSet(1, 3)
assert Interval(0, 1, True, True).intersection(FiniteSet(1)) == S.EmptySet
assert Union(Interval(0, 1), Interval(2, 3)).intersection(Interval(1, 2)) == \
Union(Interval(1, 1), Interval(2, 2))
assert ProductSet(FiniteSet(1),
FiniteSet(2)).intersection(Interval(1, 2)).is_Intersection
# iterable
i = Intersection(FiniteSet(1, 2, 3), Interval(2, 5), evaluate=False)
assert i.is_iterable
assert set(i) == {Integer(2), Integer(3)}
# challenging intervals
x = Symbol('x', extended_real=True)
i = Intersection(Interval(0, 3), Interval(x, 6))
assert (5 in i) is False
pytest.raises(TypeError, lambda: 2 in i)
# Singleton special cases
assert Intersection(Interval(0, 1), S.EmptySet) == S.EmptySet
assert Intersection(S.Reals, Interval(-oo, x, True)) == Interval(-oo, x, True)
# Products
line = Interval(0, 5)
i = Intersection(line**2, line**3, evaluate=False)
assert (2, 2) not in i
assert (2, 2, 2) not in i
pytest.raises(ValueError, lambda: list(i))
assert (Intersection(Intersection(S.Integers, S.Naturals, evaluate=False),
S.Reals, evaluate=False) ==
Intersection(S.Integers, S.Naturals, S.Reals, evaluate=False))
assert (imageset(Lambda(x, x**2),
Intersection(FiniteSet(1, 2), FiniteSet(2, 3),
evaluate=False)) == FiniteSet(4))
