def test_contains():
assert Interval(0, 2).contains(1) is S.true
assert Interval(0, 2).contains(3) is S.false
assert Interval(0, 2, True, False).contains(0) is S.false
assert Interval(0, 2, True, False).contains(2) is S.true
assert Interval(0, 2, False, True).contains(0) is S.true
assert Interval(0, 2, False, True).contains(2) is S.false
assert Interval(0, 2, True, True).contains(0) is S.false
assert Interval(0, 2, True, True).contains(2) is S.false
assert (Interval(0, 2) in Interval(0, 2)) is False
assert FiniteSet(1, 2, 3).contains(2) is S.true
assert FiniteSet(1, 2, Symbol('x')).contains(Symbol('x')) is S.true
assert FiniteSet(y)._contains(x) is None
raises(TypeError, lambda: x in FiniteSet(y))
assert FiniteSet({x, y})._contains({x}) is None
assert FiniteSet({x, y}).subs(y, x)._contains({x}) is True
assert FiniteSet({x, y}).subs(y, x + 1)._contains({x}) is False
# issue 8197
from sympy.abc import a, b
assert isinstance(FiniteSet(b).contains(-a), Contains)
assert isinstance(FiniteSet(b).contains(a), Contains)
assert isinstance(FiniteSet(a).contains(1), Contains)
raises(TypeError, lambda: 1 in FiniteSet(a))
# issue 8209
rad1 = Pow(Pow(2, S(1) / 3) - 1, S(1) / 3)
rad2 = Pow(S(1) / 9,
S(1) / 3) - Pow(S(2) / 9,
S(1) / 3) + Pow(S(4) / 9,
S(1) / 3)
s1 = FiniteSet(rad1)
s2 = FiniteSet(rad2)
assert s1 - s2 == S.EmptySet
items = [1, 2, S.Infinity, S('ham'), -1.1]
fset = FiniteSet(*items)
assert all(item in fset for item in items)
assert all(fset.contains(item) is S.true for item in items)
assert Union(Interval(0, 1), Interval(2, 5)).contains(3) is S.true
assert Union(Interval(0, 1), Interval(2, 5)).contains(6) is S.false
assert Union(Interval(0, 1), FiniteSet(2, 5)).contains(3) is S.false
assert S.EmptySet.contains(1) is S.false
assert FiniteSet(rootof(x**3 + x - 1, 0)).contains(S.Infinity) is S.false
assert rootof(x**5 + x**3 + 1, 0) in S.Reals
assert not rootof(x**5 + x**3 + 1, 1) in S.Reals
# non-bool results
assert Union(Interval(1, 2), Interval(3, 4)).contains(x) == \
Or(And(S(1) <= x, x <= 2), And(S(3) <= x, x <= 4))
assert Intersection(Interval(1, x), Interval(2, 3)).contains(y) == \
And(y <= 3, y <= x, S(1) <= y, S(2) <= y)
assert (S.Complexes).contains(S.ComplexInfinity) == S.false
def test_contains():
assert Interval(0, 2).contains(1) is S.true
assert Interval(0, 2).contains(3) is S.false
assert Interval(0, 2, True, False).contains(0) is S.false
assert Interval(0, 2, True, False).contains(2) is S.true
assert Interval(0, 2, False, True).contains(0) is S.true
assert Interval(0, 2, False, True).contains(2) is S.false
assert Interval(0, 2, True, True).contains(0) is S.false
assert Interval(0, 2, True, True).contains(2) is S.false
assert (Interval(0, 2) in Interval(0, 2)) is False
assert FiniteSet(1, 2, 3).contains(2) is S.true
assert FiniteSet(1, 2, Symbol('x')).contains(Symbol('x')) is S.true
# issue 8197
from sympy.abc import a, b
assert isinstance(FiniteSet(b).contains(-a), Contains)
assert isinstance(FiniteSet(b).contains(a), Contains)
assert isinstance(FiniteSet(a).contains(1), Contains)
raises(TypeError, lambda: 1 in FiniteSet(a))
# issue 8209
rad1 = Pow(Pow(2, S(1)/3) - 1, S(1)/3)
rad2 = Pow(S(1)/9, S(1)/3) - Pow(S(2)/9, S(1)/3) + Pow(S(4)/9, S(1)/3)
s1 = FiniteSet(rad1)
s2 = FiniteSet(rad2)
assert s1 - s2 == S.EmptySet
items = [1, 2, S.Infinity, S('ham'), -1.1]
fset = FiniteSet(*items)
assert all(item in fset for item in items)
assert all(fset.contains(item) is S.true for item in items)
assert Union(Interval(0, 1), Interval(2, 5)).contains(3) is S.true
assert Union(Interval(0, 1), Interval(2, 5)).contains(6) is S.false
assert Union(Interval(0, 1), FiniteSet(2, 5)).contains(3) is S.false
assert S.EmptySet.contains(1) is S.false
assert FiniteSet(rootof(x**3 + x - 1, 0)).contains(S.Infinity) is S.false
assert rootof(x**5 + x**3 + 1, 0) in S.Reals
assert not rootof(x**5 + x**3 + 1, 1) in S.Reals
# non-bool results
assert Union(Interval(1, 2), Interval(3, 4)).contains(x) == \
Or(And(x <= 2, x >= 1), And(x <= 4, x >= 3))
assert Intersection(Interval(1, x), Interval(2, 3)).contains(y) == \
And(y <= 3, y <= x, y >= 1, y >= 2)
assert (S.Complexes).contains(S.ComplexInfinity) == S.false
def test_contains():
assert Interval(0, 2).contains(1) is S.true
assert Interval(0, 2).contains(3) is S.false
assert Interval(0, 2, True, False).contains(0) is S.false
assert Interval(0, 2, True, False).contains(2) is S.true
assert Interval(0, 2, False, True).contains(0) is S.true
assert Interval(0, 2, False, True).contains(2) is S.false
assert Interval(0, 2, True, True).contains(0) is S.false
assert Interval(0, 2, True, True).contains(2) is S.false
assert FiniteSet(1, 2, 3).contains(2) is S.true
assert FiniteSet(1, 2, Symbol('x')).contains(Symbol('x')) is S.true
# issue 8197
from sympy.abc import a, b
assert isinstance(FiniteSet(b).contains(-a), Contains)
assert isinstance(FiniteSet(b).contains(a), Contains)
assert isinstance(FiniteSet(a).contains(1), Contains)
raises(TypeError, lambda: 1 in FiniteSet(a))
# issue 8209
rad1 = Pow(Pow(2, S(1) / 3) - 1, S(1) / 3)
rad2 = Pow(S(1) / 9,
S(1) / 3) - Pow(S(2) / 9,
S(1) / 3) + Pow(S(4) / 9,
S(1) / 3)
s1 = FiniteSet(rad1)
s2 = FiniteSet(rad2)
assert s1 - s2 == S.EmptySet
items = [1, 2, S.Infinity, S('ham'), -1.1]
fset = FiniteSet(*items)
assert all(item in fset for item in items)
assert all(fset.contains(item) is S.true for item in items)
assert Union(Interval(0, 1), Interval(2, 5)).contains(3) is S.true
assert Union(Interval(0, 1), Interval(2, 5)).contains(6) is S.false
assert Union(Interval(0, 1), FiniteSet(2, 5)).contains(3) is S.false
assert S.EmptySet.contains(1) is S.false
assert FiniteSet(RootOf(x**3 + x - 1, 0)).contains(S.Infinity) is S.false
assert RootOf(x**5 + x**3 + 1, 0) in S.Reals
assert not RootOf(x**5 + x**3 + 1, 1) in S.Reals
def test_contains():
assert Interval(0, 2).contains(1) is S.true
assert Interval(0, 2).contains(3) is S.false
assert Interval(0, 2, True, False).contains(0) is S.false
assert Interval(0, 2, True, False).contains(2) is S.true
assert Interval(0, 2, False, True).contains(0) is S.true
assert Interval(0, 2, False, True).contains(2) is S.false
assert Interval(0, 2, True, True).contains(0) is S.false
assert Interval(0, 2, True, True).contains(2) is S.false
assert FiniteSet(1, 2, 3).contains(2) is S.true
assert FiniteSet(1, 2, Symbol("x")).contains(Symbol("x")) is S.true
# issue 8197
from sympy.abc import a, b
assert isinstance(FiniteSet(b).contains(-a), Contains)
assert isinstance(FiniteSet(b).contains(a), Contains)
assert isinstance(FiniteSet(a).contains(1), Contains)
raises(TypeError, lambda: 1 in FiniteSet(a))
# issue 8209
rad1 = Pow(Pow(2, S(1) / 3) - 1, S(1) / 3)
rad2 = Pow(S(1) / 9, S(1) / 3) - Pow(S(2) / 9, S(1) / 3) + Pow(S(4) / 9, S(1) / 3)
s1 = FiniteSet(rad1)
s2 = FiniteSet(rad2)
assert s1 - s2 == S.EmptySet
items = [1, 2, S.Infinity, S("ham"), -1.1]
fset = FiniteSet(*items)
assert all(item in fset for item in items)
assert all(fset.contains(item) is S.true for item in items)
assert Union(Interval(0, 1), Interval(2, 5)).contains(3) is S.true
assert Union(Interval(0, 1), Interval(2, 5)).contains(6) is S.false
assert Union(Interval(0, 1), FiniteSet(2, 5)).contains(3) is S.false
assert S.EmptySet.contains(1) is S.false
assert FiniteSet(RootOf(x ** 3 + x - 1, 0)).contains(S.Infinity) is S.false
assert RootOf(x ** 5 + x ** 3 + 1, 0) in S.Reals
assert not RootOf(x ** 5 + x ** 3 + 1, 1) in S.Reals
def test_contains():
assert Interval(0, 2).contains(1) is True
assert Interval(0, 2).contains(3) is False
assert Interval(0, 2, True, False).contains(0) is False
assert Interval(0, 2, True, False).contains(2) is True
assert Interval(0, 2, False, True).contains(0) is True
assert Interval(0, 2, False, True).contains(2) is False
assert Interval(0, 2, True, True).contains(0) is False
assert Interval(0, 2, True, True).contains(2) is False
assert FiniteSet(1, 2, 3).contains(2)
assert FiniteSet(1, 2, Symbol('x')).contains(Symbol('x'))
items = [1, 2, S.Infinity, S('ham'), -1.1]
fset = FiniteSet(*items)
assert all(item in fset for item in items)
assert all(fset.contains(item) is True for item in items)
assert Union(Interval(0, 1), Interval(2, 5)).contains(3) is True
assert Union(Interval(0, 1), Interval(2, 5)).contains(6) is False
assert Union(Interval(0, 1), FiniteSet(2, 5)).contains(3) is False
assert S.EmptySet.contains(1) is False
def test_contains():
assert Interval(0, 2).contains(1) == True
assert Interval(0, 2).contains(3) == False
assert Interval(0, 2, True, False).contains(0) == False
assert Interval(0, 2, True, False).contains(2) == True
assert Interval(0, 2, False, True).contains(0) == True
assert Interval(0, 2, False, True).contains(2) == False
assert Interval(0, 2, True, True).contains(0) == False
assert Interval(0, 2, True, True).contains(2) == False
assert FiniteSet(1,2,3).contains(2)
assert FiniteSet(1,2,Symbol('x')).contains(Symbol('x'))
items = [1, 2, S.Infinity, S('ham'), -1.1]
fset = FiniteSet(*items)
assert all(item in fset for item in items)
assert all(fset.contains(item) is True for item in items)
assert Union(Interval(0, 1), Interval(2, 5)).contains(3) == True
assert Union(Interval(0, 1), Interval(2, 5)).contains(6) == False
assert Union(Interval(0, 1), FiniteSet(2, 5)).contains(3) == False
assert S.EmptySet.contains(1) == False
