def test_ComplexPlane_measure():
a, b = Interval(2, 5), Interval(4, 8)
theta1, theta2 = Interval(0, 2*S.Pi), Interval(0, S.Pi)
c1 = ComplexPlane(a*b)
c2 = ComplexPlane(Union(a*theta1, b*theta2), polar=True)
assert c1.measure == 12
assert c2.measure == 9*pi
def test_ComplexPlane_FiniteSet():
x, y, z, a, b, c = symbols('x y z a b c')
# Issue #9669
assert ComplexPlane(FiniteSet(a, b, c)*FiniteSet(x, y, z)) == \
FiniteSet(a + I*x, a + I*y, a + I*z, b + I*x, b + I*y,
b + I*z, c + I*x, c + I*y, c + I*z)
assert ComplexPlane(FiniteSet(2) * FiniteSet(3)) == FiniteSet(2 + 3 * I)
def test_Complex():
assert 5 in S.Complexes
assert 5 + 4 * I in S.Complexes
assert S.Pi in S.Complexes
assert -sqrt(2) in S.Complexes
assert -I in S.Complexes
assert sqrt(-1) in S.Complexes
assert S.Complexes.intersect(S.Reals) == S.Reals
assert S.Complexes.union(S.Reals) == S.Complexes
assert S.Complexes == ComplexPlane(S.Reals * S.Reals)
def test_ComplexPlane_contains():
# contains in ComplexPlane
a = Interval(2, 3)
b = Interval(4, 6)
c = Interval(7, 9)
c1 = ComplexPlane(a*b)
c2 = ComplexPlane(Union(a*b, c*a))
assert 2.5 + 4.5*I in c1
assert 2 + 4*I in c1
assert 3 + 4*I in c1
assert 8 + 2.5*I in c2
assert 2.5 + 6.1*I not in c1
assert 4.5 + 3.2*I not in c1
r1 = Interval(0, 1)
theta1 = Interval(0, 2*S.Pi)
c3 = ComplexPlane(r1*theta1, polar=True)
assert 0.5 + 0.6*I in c3
assert I in c3
assert 1 in c3
assert 0 in c3
assert 1 + I not in c3
assert 1 - I not in c3
def test_ComplexPlane_union():
# Polar form
c1 = ComplexPlane(Interval(0, 1)*Interval(0, 2*S.Pi), polar=True)
c2 = ComplexPlane(Interval(0, 1)*Interval(0, S.Pi), polar=True)
c3 = ComplexPlane(Interval(0, oo)*Interval(0, S.Pi), polar=True)
c4 = ComplexPlane(Interval(0, oo)*Interval(S.Pi, 2*S.Pi), polar=True)
p1 = Union(Interval(0, 1)*Interval(0, 2*S.Pi), Interval(0, 1)*Interval(0, S.Pi))
p2 = Union(Interval(0, oo)*Interval(0, S.Pi), Interval(0, oo)*Interval(S.Pi, 2*S.Pi))
assert c1.union(c2) == ComplexPlane(p1, polar=True)
assert c3.union(c4) == ComplexPlane(p2, polar=True)
# Rectangular form
c5 = ComplexPlane(Interval(2, 5)*Interval(6, 9))
c6 = ComplexPlane(Interval(4, 6)*Interval(10, 12))
c7 = ComplexPlane(Interval(0, 10)*Interval(-10, 0))
c8 = ComplexPlane(Interval(12, 16)*Interval(14, 20))
p3 = Union(Interval(2, 5)*Interval(6, 9), Interval(4, 6)*Interval(10, 12))
p4 = Union(Interval(0, 10)*Interval(-10, 0), Interval(12, 16)*Interval(14, 20))
assert c5.union(c6) == ComplexPlane(p3)
assert c7.union(c8) == ComplexPlane(p4)
assert c1.union(Interval(2, 4)) == Union(c1, Interval(2, 4))
assert c5.union(Interval(2, 4)) == Union(c5, Interval(2, 4))
def test_ComplexPlane_intersect():
# Polar form
X_axis = ComplexPlane(Interval(0, oo)*FiniteSet(0, S.Pi), polar=True)
unit_disk = ComplexPlane(Interval(0, 1)*Interval(0, 2*S.Pi), polar=True)
upper_half_unit_disk = ComplexPlane(Interval(0, 1)*Interval(0, S.Pi), polar=True)
upper_half_disk = ComplexPlane(Interval(0, oo)*Interval(0, S.Pi), polar=True)
lower_half_disk = ComplexPlane(Interval(0, oo)*Interval(S.Pi, 2*S.Pi), polar=True)
right_half_disk = ComplexPlane(Interval(0, oo)*Interval(-S.Pi/2, S.Pi/2), polar=True)
first_quad_disk = ComplexPlane(Interval(0, oo)*Interval(0, S.Pi/2), polar=True)
assert upper_half_disk.intersect(unit_disk) == upper_half_unit_disk
assert right_half_disk.intersect(first_quad_disk) == first_quad_disk
assert upper_half_disk.intersect(right_half_disk) == first_quad_disk
assert upper_half_disk.intersect(lower_half_disk) == X_axis
c1 = ComplexPlane(Interval(0, 4)*Interval(0, 2*S.Pi), polar=True)
assert c1.intersect(Interval(1, 5)) == Interval(1, 4)
assert c1.intersect(Interval(4, 9)) == FiniteSet(4)
assert c1.intersect(Interval(5, 12)) == EmptySet()
# Rectangular form
X_axis = ComplexPlane(Interval(-oo, oo)*FiniteSet(0))
unit_square = ComplexPlane(Interval(-1, 1)*Interval(-1, 1))
upper_half_unit_square = ComplexPlane(Interval(-1, 1)*Interval(0, 1))
upper_half_plane = ComplexPlane(Interval(-oo, oo)*Interval(0, oo))
lower_half_plane = ComplexPlane(Interval(-oo, oo)*Interval(-oo, 0))
right_half_plane = ComplexPlane(Interval(0, oo)*Interval(-oo, oo))
first_quad_plane = ComplexPlane(Interval(0, oo)*Interval(0, oo))
assert upper_half_plane.intersect(unit_square) == upper_half_unit_square
assert right_half_plane.intersect(first_quad_plane) == first_quad_plane
assert upper_half_plane.intersect(right_half_plane) == first_quad_plane
assert upper_half_plane.intersect(lower_half_plane) == X_axis
c1 = ComplexPlane(Interval(-5, 5)*Interval(-10, 10))
assert c1.intersect(Interval(2, 7)) == Interval(2, 5)
assert c1.intersect(Interval(5, 7)) == FiniteSet(5)
assert c1.intersect(Interval(6, 9)) == EmptySet()
# unevaluated object
C1 = ComplexPlane(Interval(0, 1)*Interval(0, 2*S.Pi), polar=True)
C2 = ComplexPlane(Interval(-1, 1)*Interval(-1, 1))
assert C1.intersect(C2) == Intersection(C1, C2)
