def test_imageset_intersection_real():
assert (imageset(Lambda(n, n + (n - 1)*(n + 1)*I),
S.Integers).intersection(S.Reals) ==
FiniteSet(-1, 1))
s = ImageSet(Lambda(n, -I*(I*(2*pi*n - pi/4) + log(Abs(sqrt(-I))))), S.Integers)
assert s.intersection(S.Reals) == imageset(Lambda(n, 2*n*pi - pi/4), S.Integers)
def test_imageset_intersection_real():
assert (imageset(Lambda(n, n + (n - 1)*(n + 1)*I),
S.Integers).intersection(S.Reals) ==
FiniteSet(-1, 1))
s = ImageSet(Lambda(n, -I*(I*(2*pi*n - pi/4) + log(Abs(sqrt(-I))))), S.Integers)
assert s.intersection(S.Reals) == imageset(Lambda(n, 2*n*pi - pi/4), S.Integers)
def test_ImageSet():
squares = ImageSet(Lambda(x, x**2), S.Naturals)
assert 4 in squares
assert 5 not in squares
assert FiniteSet(*range(10)).intersection(squares) == FiniteSet(1, 4, 9)
assert 16 not in squares.intersection(Interval(0, 10))
si = iter(squares)
a, b, c, d = next(si), next(si), next(si), next(si)
assert (a, b, c, d) == (1, 4, 9, 16)
harmonics = ImageSet(Lambda(x, 1 / x), S.Naturals)
assert Rational(1, 5) in harmonics
assert Rational(.25) in harmonics
assert 0.25 not in harmonics
assert Rational(.3) not in harmonics
assert harmonics.is_iterable
def test_ImageSet():
squares = ImageSet(Lambda(x, x**2), S.Naturals)
assert 4 in squares
assert 5 not in squares
assert FiniteSet(*range(10)).intersection(squares) == FiniteSet(1, 4, 9)
assert 16 not in squares.intersection(Interval(0, 10))
si = iter(squares)
a, b, c, d = next(si), next(si), next(si), next(si)
assert (a, b, c, d) == (1, 4, 9, 16)
harmonics = ImageSet(Lambda(x, 1/x), S.Naturals)
assert Rational(1, 5) in harmonics
assert Rational(.25) in harmonics
assert 0.25 not in harmonics
assert Rational(.3) not in harmonics
assert harmonics.is_iterable