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.intersect(Interval(-5, 5)) == Range(1, 6)
assert N.intersect(Interval(-5, 5, True, True)) == Range(1, 5)
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.intersect(Interval(-5, 5)) == Range(-5, 6)
assert Z.intersect(Interval(-5, 5, True, True)) == Range(-4, 5)
assert Z.inf == -oo
assert Z.sup == oo
assert Z.boundary == Z
def test_range_interval_intersection():
# Intersection with intervals
assert FiniteSet(*Range(0, 10, 1).intersect(Interval(2, 6))) == \
FiniteSet(2, 3, 4, 5, 6)
# Open Intervals are removed
assert (FiniteSet(*Range(0, 10, 1).intersect(Interval(2, 6,
True, True))) ==
FiniteSet(3, 4, 5))
# Try this with large steps
assert (FiniteSet(*Range(0, 100, 10).intersect(Interval(15, 55))) ==
FiniteSet(20, 30, 40, 50))
# Going backwards
assert (FiniteSet(*Range(10, -9, -3).intersect(Interval(-5, 6))) ==
FiniteSet(-5, -2, 1, 4))
assert (FiniteSet(*Range(10, -9, -3).intersect(Interval(-5, 6, True))) ==
FiniteSet(-2, 1, 4))
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_fun():
assert (FiniteSet(*ImageSet(Lambda(x, sin(pi*x/4)), Range(-10, 11))) ==
FiniteSet(-1, -sqrt(2)/2, 0, sqrt(2)/2, 1))
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(-oo, oo))
pytest.raises(ValueError, lambda: Range(-oo, oo, 2))
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(0, oo, 2)._last_element is oo
assert Range(-oo, 1, 1)._last_element is S.Zero
it = iter(Range(-oo, 0, 2))
assert (next(it), next(it)) == (-2, -4)
assert Range(-1, 10, 1).intersect(S.Integers) == Range(-1, 10, 1)
assert Range(-1, 10, 1).intersect(S.Naturals) == Range(1, 10, 1)
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)
def test_image_is_ImageSet():
assert isinstance(imageset(x, sqrt(sin(x)), Range(5)), ImageSet)