def test_Range():
assert Range(5) == Range(0, 5) == Range(0, 5, 1)
r = Range(10, 20, 2)
assert 12 in r
assert 8 not in r
assert 11 not in r
assert 30 not in r
assert list(Range(0, 5)) == list(range(5))
assert list(Range(5, 0, -1)) == list(range(1, 6))
assert Range(0, 10, -1) == S.EmptySet
assert Range(5, 15).sup == 14
assert Range(5, 15).inf == 5
assert Range(15, 5, -1).sup == 15
assert Range(15, 5, -1).inf == 6
assert Range(10, 67, 10).sup == 60
assert Range(60, 7, -10).inf == 10
assert len(Range(10, 38, 10)) == 3
assert Range(0, 0, 5) == S.EmptySet
assert Range(1, 1) == S.EmptySet
pytest.raises(ValueError, lambda: Range(0, oo, oo))
pytest.raises(ValueError, lambda: Range(0, pi, 1))
assert 5 in Range(0, oo, 5)
assert -5 in Range(-oo, 0, 5)
assert Range(0, oo)
assert Range(-oo, 0)
assert Range(0, -oo, -1)
assert Range(1, oo)
assert Range(-oo, oo)
assert Range(0, oo, 2)._last_element is oo
assert Range(-oo, 1, 1)._last_element is Integer(0)
it = iter(Range(-oo, 0, 2))
assert (next(it), next(it)) == (-2, -4)
assert Range(-1, 10, 1).intersection(S.Integers) == Range(-1, 10, 1)
assert Range(-1, 10, 1).intersection(S.Naturals) == Range(1, 10, 1)
assert (Range(-1, 10,
1).intersection(Set(x)) == Intersection(Range(-1, 10, 1),
Set(x),
evaluate=False))
assert Range(1, 10, 1)._ith_element(5) == 6 # the index starts from zero
assert Range(1, 10, 1)._last_element == 9
assert Range(1, 10, 1).boundary == Range(1, 10, 1)
assert Range(range(10)) == Range(10)
assert Range(range(1, 10)) == Range(1, 10)
assert Range(range(1, 10, 2)) == Range(1, 10, 2)
assert Range(range(1000000000000)) == Range(1000000000000)
def test_naturals():
N = S.Naturals
assert 5 in N
assert -5 not in N
assert 5.5 not in N
ni = iter(N)
a, b, c, d = next(ni), next(ni), next(ni), next(ni)
assert (a, b, c, d) == (1, 2, 3, 4)
assert isinstance(a, Basic)
assert N.intersection(Interval(-5, 5)) == Range(1, 6)
assert N.intersection(Interval(-5, 5, True, True)) == Range(1, 5)
assert N.intersection(Set(x)) == Intersection(N, Set(x), evaluate=False)
assert N.boundary == N
assert N.inf == 1
assert N.sup == oo
def test_integers():
Z = S.Integers
assert 5 in Z
assert -5 in Z
assert 5.5 not in Z
zi = iter(Z)
a, b, c, d = next(zi), next(zi), next(zi), next(zi)
assert (a, b, c, d) == (0, 1, -1, 2)
assert isinstance(a, Basic)
assert Z.intersection(Interval(-5, 5)) == Range(-5, 6)
assert Z.intersection(Interval(-5, 5, True, True)) == Range(-4, 5)
assert Z.intersection(Set(x)) == Intersection(Z, Set(x), evaluate=False)
assert Z.inf == -oo
assert Z.sup == oo
assert Z.boundary == Z
assert imageset(Lambda((x, y), x * y),
Z) == ImageSet(Lambda((x, y), x * y), Z)
def test_SymmetricDifference():
assert (SymmetricDifference(FiniteSet(0, 1, 2, 3, 4, 5),
FiniteSet(2, 4, 6, 8, 10)) == FiniteSet(
0, 1, 3, 5, 6, 8, 10))
assert (SymmetricDifference(FiniteSet(2, 3, 4),
FiniteSet(2, 3, 4, 5)) == FiniteSet(5))
assert FiniteSet(2).symmetric_difference(FiniteSet(2, 5)) == FiniteSet(5)
assert (FiniteSet(1, 2, 3, 4, 5) ^ FiniteSet(1, 2, 5, 6) == FiniteSet(
3, 4, 6))
assert (Set(Integer(1), Integer(2), Integer(3))
^ Set(Integer(2), Integer(3), Integer(4)) == Union(
Set(Integer(1), Integer(2), Integer(3)) -
Set(Integer(2), Integer(3), Integer(4)),
Set(Integer(2), Integer(3), Integer(4)) -
Set(Integer(1), Integer(2), Integer(3))))
assert (Interval(0, 4) ^ Interval(2, 5) == Union(
Interval(0, 4) - Interval(2, 5),
Interval(2, 5) - Interval(0, 4)))
class TestSet(Set):
def _symmetric_difference(self, other):
return
t1, t2 = TestSet(1), TestSet(2)
assert t1.symmetric_difference(t2) == SymmetricDifference(t1,
t2,
evaluate=False)
def test_SymmetricDifference():
assert (SymmetricDifference(FiniteSet(0, 1, 2, 3, 4, 5),
FiniteSet(2, 4, 6, 8, 10)) == FiniteSet(
0, 1, 3, 5, 6, 8, 10))
assert (SymmetricDifference(FiniteSet(2, 3, 4),
FiniteSet(2, 3, 4, 5)) == FiniteSet(5))
assert (FiniteSet(1, 2, 3, 4, 5) ^ FiniteSet(1, 2, 5, 6) == FiniteSet(
3, 4, 6))
assert (Set(1, 2, 3) ^ Set(2, 3, 4) == Union(
Set(1, 2, 3) - Set(2, 3, 4),
Set(2, 3, 4) - Set(1, 2, 3)))
assert (Interval(0, 4) ^ Interval(2, 5) == Union(
Interval(0, 4) - Interval(2, 5),
Interval(2, 5) - Interval(0, 4)))
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_is_number():
assert Interval(0, 1).is_number is False
assert Set().is_number is False
def test_ProductSet_iter():
pytest.raises(TypeError, lambda: iter(ProductSet(Set(1), Set(2))))
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.intersect(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
# issue 7843
assert Union(S.EmptySet,
FiniteSet(-sqrt(-I),
sqrt(-I))) == FiniteSet(-sqrt(-I), sqrt(-I))