def intersection_sets(self, other):
if other.is_ComplexRegion:
# self in rectangular form
if (not self.polar) and (not other.polar):
return ComplexRegion(Intersection(self.sets, other.sets))
# self in polar form
elif self.polar and other.polar:
r1, theta1 = self.a_interval, self.b_interval
r2, theta2 = other.a_interval, other.b_interval
new_r_interval = Intersection(r1, r2)
new_theta_interval = Intersection(theta1, theta2)
# 0 and 2*Pi means the same
if ((2 * S.Pi in theta1 and S.Zero in theta2)
or (2 * S.Pi in theta2 and S.Zero in theta1)):
new_theta_interval = Union(new_theta_interval, FiniteSet(0))
return ComplexRegion(new_r_interval * new_theta_interval,
polar=True)
if other.is_subset(S.Reals):
new_interval = []
x = symbols("x", cls=Dummy, real=True)
# self in rectangular form
if not self.polar:
for element in self.psets:
if S.Zero in element.args[1]:
new_interval.append(element.args[0])
new_interval = Union(*new_interval)
return Intersection(new_interval, other)
# self in polar form
elif self.polar:
for element in self.psets:
if S.Zero in element.args[1]:
new_interval.append(element.args[0])
if S.Pi in element.args[1]:
new_interval.append(
ImageSet(Lambda(x, -x), element.args[0]))
if S.Zero in element.args[0]:
new_interval.append(FiniteSet(0))
new_interval = Union(*new_interval)
return Intersection(new_interval, other)
def union_sets(a, b):
if b.is_subset(S.Reals):
# treat a subset of reals as a complex region
b = ComplexRegion.from_real(b)
if b.is_ComplexRegion:
# a in rectangular form
if (not a.polar) and (not b.polar):
return ComplexRegion(Union(a.sets, b.sets))
# a in polar form
elif a.polar and b.polar:
return ComplexRegion(Union(a.sets, b.sets), polar=True)
return None