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)