def test_sympyissue_9447():
a = Interval(0, 1) + Interval(2, 3)
assert (Complement(S.UniversalSet, a) ==
Complement(S.UniversalSet,
Union(Interval(0, 1), Interval(2, 3)), evaluate=False))
# issue sympy/sympy#10305:
assert (Complement(S.Naturals, a) ==
Complement(S.Naturals,
Union(Interval(0, 1), Interval(2, 3)), evaluate=False))
def test_sympyissue_9808():
assert (Complement(FiniteSet(y),
FiniteSet(1)) == Complement(FiniteSet(y),
FiniteSet(1),
evaluate=False))
assert (Complement(FiniteSet(1, 2, x),
FiniteSet(x, y, 2, 3)) == Complement(FiniteSet(1),
FiniteSet(y),
evaluate=False))
def test_sympyissue_9637():
n = Symbol('n')
a = FiniteSet(n)
b = FiniteSet(2, n)
assert Complement(S.Reals, a) == Complement(S.Reals, a, evaluate=False)
assert Complement(Interval(1, 3), a) == Complement(Interval(1, 3), a, evaluate=False)
assert (Complement(Interval(1, 3), b) ==
Complement(Union(Interval(1, 2, right_open=True),
Interval(2, 3, left_open=True)), a, evaluate=False))
assert Complement(a, S.Reals) == Complement(a, S.Reals, evaluate=False)
assert Complement(a, Interval(1, 3)) == Complement(a, Interval(1, 3), evaluate=False)
def test_complement():
assert Interval(0, 1).complement(S.Reals) == \
Union(Interval(-oo, 0, True, True), Interval(1, oo, True, True))
assert Interval(0, 1, True, False).complement(S.Reals) == \
Union(Interval(-oo, 0, True, False), Interval(1, oo, True, True))
assert Interval(0, 1, False, True).complement(S.Reals) == \
Union(Interval(-oo, 0, True, True), Interval(1, oo, False, True))
assert Interval(0, 1, True, True).complement(S.Reals) == \
Union(Interval(-oo, 0, True, False), Interval(1, oo, False, True))
assert S.UniversalSet.complement(S.EmptySet) == S.EmptySet
assert S.UniversalSet.complement(S.Reals) == S.EmptySet
assert S.UniversalSet.complement(S.UniversalSet) == S.EmptySet
assert S.EmptySet.complement(S.Reals) == S.Reals
assert Union(Interval(0, 1), Interval(2, 3)).complement(S.Reals) == \
Union(Interval(-oo, 0, True, True), Interval(1, 2, True, True),
Interval(3, oo, True, True))
assert FiniteSet(0).complement(S.Reals) == \
Union(Interval(-oo, 0, True, True), Interval(0, oo, True, True))
assert (FiniteSet(5) + Interval(-oo,
0)).complement(S.Reals) == \
Interval(0, 5, True, True) + Interval(5, oo, True, True)
assert FiniteSet(1, 2, 3).complement(S.Reals) == \
Interval(-oo, 1, True, True) + \
Interval(1, 2, True, True) + Interval(2, 3, True, True) +\
Interval(3, oo, True, True)
assert FiniteSet(x).complement(S.Reals) == Complement(
S.Reals, FiniteSet(x))
assert FiniteSet(0, x).complement(S.Reals) == Complement(
Interval(-oo, 0, True, True) + Interval(0, oo, True, True),
FiniteSet(x),
evaluate=False)
square = Interval(0, 1) * Interval(0, 1)
notsquare = square.complement(S.Reals * S.Reals)
assert all(pt in square for pt in [(0, 0), (.5, .5), (1, 0), (1, 1)])
assert not any(pt in notsquare
for pt in [(0, 0), (.5, .5), (1, 0), (1, 1)])
assert not any(pt in square for pt in [(-1, 0), (1.5, .5), (10, 10)])
assert all(pt in notsquare for pt in [(-1, 0), (1.5, .5), (10, 10)])
def test_difference():
assert Interval(1, 3) - Interval(1, 2) == Interval(2, 3, True)
assert Interval(1, 3) - Interval(2, 3) == Interval(1, 2, False, True)
assert Interval(1, 3, True) - Interval(2, 3) == Interval(1, 2, True, True)
assert Interval(1, 3, True) - Interval(2, 3, True) == \
Interval(1, 2, True, False)
assert Interval(0, 2) - FiniteSet(1) == \
Union(Interval(0, 1, False, True), Interval(1, 2, True, False))
assert FiniteSet(1, 2, 3) - FiniteSet(2) == FiniteSet(1, 3)
assert (FiniteSet('ham', 'eggs') - FiniteSet('eggs') ==
Complement(FiniteSet('ham'), FiniteSet('eggs')))
assert FiniteSet(1, 2, 3, 4) - Interval(2, 10, True, False) == \
FiniteSet(1, 2)
assert FiniteSet(1, 2, 3, 4) - S.EmptySet == FiniteSet(1, 2, 3, 4)
assert Union(Interval(0, 2), FiniteSet(2, 3, 4)) - Interval(1, 3) == \
Union(Interval(0, 1, False, True), FiniteSet(4))
assert -1 in S.Reals - S.Naturals
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_Complement():
assert str(Complement(S.Reals, S.Naturals)) == '(-oo, oo) \ Naturals()'
