def test_infinitely_indexed_set_1():
assert imageset(Lambda(n, n),
S.Integers) == imageset(Lambda(m, m), S.Integers)
assert (imageset(Lambda(n, 2 * n), S.Integers).intersection(
imageset(Lambda(m, 2 * m + 1), S.Integers)) == EmptySet())
assert (imageset(Lambda(n, 2 * n), S.Integers).intersection(
imageset(Lambda(n, 2 * n + 1), S.Integers)) == EmptySet())
assert (imageset(Lambda(m, 2 * m), S.Integers).intersection(
imageset(Lambda(n, 3 * n),
S.Integers)) == ImageSet(Lambda(t, 6 * t), S.Integers))
def test_booleans():
"""Test basic unions and intersections."""
assert Union(l1, l2).equal(l1)
assert Intersection(l1, l2).equal(l1)
assert Intersection(l1, l4) == FiniteSet(Point(1, 1))
assert Intersection(Union(l1, l4),
l3) == FiniteSet(Point(-1 / 3, -1 / 3), Point(5, 1))
assert Intersection(l1, FiniteSet(Point(7, -7))) == EmptySet()
assert Intersection(Circle(Point(0, 0), 3),
Line(p1, p2)) == FiniteSet(Point(-3, 0), Point(3, 0))
fs = FiniteSet(Point(1 / 3, 1), Point(2 / 3, 0), Point(9 / 5, 1 / 5),
Point(7 / 3, 1))
# test the intersection of polygons
assert Intersection(poly1, poly2) == fs
# make sure if we union polygons with subsets, the subsets go away
assert Union(poly1, poly2, fs) == Union(poly1, poly2)
# make sure that if we union with a FiniteSet that isn't a subset,
# that the points in the intersection stop being listed
assert Union(poly1, FiniteSet(Point(0, 0),
Point(3,
5))) == Union(poly1,
FiniteSet(Point(3, 5)))
# intersect two polygons that share an edge
assert Intersection(poly1, poly3) == Union(
FiniteSet(Point(3 / 2, 1), Point(2, 1)),
Segment(Point(0, 0), Point(1, 0)))
def test_bool_as_set():
assert And(x <= 2, x >= -2).as_set() == Interval(-2, 2)
assert Or(x >= 2, x <= -2).as_set() == (Interval(-oo, -2, True) +
Interval(2, oo, False, True))
assert Not(x > 2, evaluate=False).as_set() == Interval(-oo, 2, True)
# issue sympy/sympy#10240
assert Not(And(x > 2, x < 3)).as_set() == \
Union(Interval(-oo, 2, True), Interval(3, oo, False, True))
assert true.as_set() == S.UniversalSet
assert false.as_set() == EmptySet()
def test_Complement():
assert Complement(Interval(1, 3), Interval(1, 2)) == Interval(2, 3, True)
assert Complement(FiniteSet(1, 3, 4), FiniteSet(3, 4)) == FiniteSet(1)
assert Complement(Union(Interval(0, 2),
FiniteSet(2, 3, 4)), Interval(1, 3)) == \
Union(Interval(0, 1, False, True), FiniteSet(4))
assert 3 not in Complement(Interval(0, 5), Interval(1, 4), evaluate=False)
assert -1 in Complement(S.Reals, S.Naturals, evaluate=False)
assert 1 not in Complement(S.Reals, S.Naturals, evaluate=False)
assert Complement(S.Integers, S.UniversalSet) == EmptySet()
assert S.UniversalSet.complement(S.Integers) == EmptySet()
assert (0 not in S.Reals.intersection(S.Integers - FiniteSet(0)))
assert S.EmptySet - S.Integers == S.EmptySet
assert (S.Integers - FiniteSet(0)) - FiniteSet(1) == S.Integers - FiniteSet(0, 1)
assert (S.Reals - Union(S.Naturals, FiniteSet(pi)) ==
Intersection(S.Reals - S.Naturals, S.Reals - FiniteSet(pi)))
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 Interval(0, 2) not in Interval(0, 2)
# issue sympy/sympy#10326
assert S.Reals.contains(oo) is false
assert S.Reals.contains(-oo) is false
assert Interval(-oo, oo, True).contains(oo) is true
assert Interval(-oo, oo).contains(-oo) is true
bad = [EmptySet(), FiniteSet(1), Interval(1, 2), zoo,
I, oo, nan, -oo]
assert all(i not in Interval(0, 5) for i in bad)
assert FiniteSet(1, 2, 3).contains(2) is true
assert FiniteSet(1, 2, x).contains(x) is true
# issue sympy/sympy#8197
assert isinstance(FiniteSet(b).contains(-a), Contains)
assert isinstance(FiniteSet(b).contains(a), Contains)
assert isinstance(FiniteSet(a).contains(1), Contains)
pytest.raises(TypeError, lambda: 1 in FiniteSet(a))
# issue sympy/sympy#8209
rad1 = Integer(4)
rad2 = Pow(2, 2, evaluate=False)
s1 = FiniteSet(rad1)
s2 = FiniteSet(rad2)
assert s1 - s2 == S.EmptySet
items = [1, 2, oo, Symbol('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
assert FiniteSet(RootOf(x**3 + x - 1, 0)).contains(oo) is 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_bool_as_set():
assert ((x <= 2) & (x >= -2)).as_set() == Interval(-2, 2)
assert ((x >= 2) | (x <= -2)).as_set() == (Interval(-oo, -2) + Interval(2, oo, False))
assert Not(x > 2, evaluate=False).as_set() == Interval(-oo, 2, True)
assert true.as_set() == S.UniversalSet
assert false.as_set() == EmptySet()
