def test_ComplexRegion_union():
# Polar form
c1 = ComplexRegion(Interval(0, 1)*Interval(0, 2*S.Pi), polar=True)
c2 = ComplexRegion(Interval(0, 1)*Interval(0, S.Pi), polar=True)
c3 = ComplexRegion(Interval(0, oo)*Interval(0, S.Pi), polar=True)
c4 = ComplexRegion(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) == ComplexRegion(p1, polar=True)
assert c3.union(c4) == ComplexRegion(p2, polar=True)
# Rectangular form
c5 = ComplexRegion(Interval(2, 5)*Interval(6, 9))
c6 = ComplexRegion(Interval(4, 6)*Interval(10, 12))
c7 = ComplexRegion(Interval(0, 10)*Interval(-10, 0))
c8 = ComplexRegion(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) == ComplexRegion(p3)
assert c7.union(c8) == ComplexRegion(p4)
assert c1.union(Interval(2, 4)) == Union(c1, Interval(2, 4), evaluate=False)
assert c5.union(Interval(2, 4)) == Union(c5, ComplexRegion.from_real(Interval(2, 4)))
def test_ComplexRegion_union():
# Polar form
c1 = ComplexRegion(Interval(0, 1)*Interval(0, 2*S.Pi), polar=True)
c2 = ComplexRegion(Interval(0, 1)*Interval(0, S.Pi), polar=True)
c3 = ComplexRegion(Interval(0, oo)*Interval(0, S.Pi), polar=True)
c4 = ComplexRegion(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) == ComplexRegion(p1, polar=True)
assert c3.union(c4) == ComplexRegion(p2, polar=True)
# Rectangular form
c5 = ComplexRegion(Interval(2, 5)*Interval(6, 9))
c6 = ComplexRegion(Interval(4, 6)*Interval(10, 12))
c7 = ComplexRegion(Interval(0, 10)*Interval(-10, 0))
c8 = ComplexRegion(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) == ComplexRegion(p3)
assert c7.union(c8) == ComplexRegion(p4)
assert c1.union(Interval(2, 4)) == Union(c1, Interval(2, 4), evaluate=False)
assert c5.union(Interval(2, 4)) == Union(c5, ComplexRegion.from_real(Interval(2, 4)))
def _(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
def test_ComplexRegion_from_real():
c1 = ComplexRegion(Interval(0, 1) * Interval(0, 2 * S.Pi), polar=True)
raises(ValueError, lambda: c1.from_real(c1))
assert c1.from_real(Interval(-1, 1)) == ComplexRegion(
Interval(-1, 1) * FiniteSet(0), False)
