Current File : //lib/python3/dist-packages/sympy/sets/handlers/union.py
from sympy import (Interval, Intersection, Set, EmptySet, S, sympify,
FiniteSet, Union, ComplexRegion, ProductSet)
from sympy.multipledispatch import dispatch
from sympy.sets.fancysets import (Naturals, Naturals0, Integers, Rationals,
Reals)
from sympy.sets.sets import UniversalSet
@dispatch(Naturals0, Naturals) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return a
@dispatch(Rationals, Naturals) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return a
@dispatch(Rationals, Naturals0) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return a
@dispatch(Reals, Naturals) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return a
@dispatch(Reals, Naturals0) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return a
@dispatch(Reals, Rationals) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return a
@dispatch(Integers, Set) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
intersect = Intersection(a, b)
if intersect == a:
return b
elif intersect == b:
return a
@dispatch(ComplexRegion, Set) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
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
@dispatch(type(EmptySet), Set) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return b
@dispatch(UniversalSet, Set) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return a
@dispatch(ProductSet, ProductSet) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
if b.is_subset(a):
return a
if len(b.sets) != len(a.sets):
return None
if len(a.sets) == 2:
a1, a2 = a.sets
b1, b2 = b.sets
if a1 == b1:
return a1 * Union(a2, b2)
if a2 == b2:
return Union(a1, b1) * a2
return None
@dispatch(ProductSet, Set) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
if b.is_subset(a):
return a
return None
@dispatch(Interval, Interval) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
if a._is_comparable(b):
from sympy.functions.elementary.miscellaneous import Min, Max
# Non-overlapping intervals
end = Min(a.end, b.end)
start = Max(a.start, b.start)
if (end < start or
(end == start and (end not in a and end not in b))):
return None
else:
start = Min(a.start, b.start)
end = Max(a.end, b.end)
left_open = ((a.start != start or a.left_open) and
(b.start != start or b.left_open))
right_open = ((a.end != end or a.right_open) and
(b.end != end or b.right_open))
return Interval(start, end, left_open, right_open)
@dispatch(Interval, UniversalSet) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return S.UniversalSet
@dispatch(Interval, Set) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
# If I have open end points and these endpoints are contained in b
# But only in case, when endpoints are finite. Because
# interval does not contain oo or -oo.
open_left_in_b_and_finite = (a.left_open and
sympify(b.contains(a.start)) is S.true and
a.start.is_finite)
open_right_in_b_and_finite = (a.right_open and
sympify(b.contains(a.end)) is S.true and
a.end.is_finite)
if open_left_in_b_and_finite or open_right_in_b_and_finite:
# Fill in my end points and return
open_left = a.left_open and a.start not in b
open_right = a.right_open and a.end not in b
new_a = Interval(a.start, a.end, open_left, open_right)
return {new_a, b}
return None
@dispatch(FiniteSet, FiniteSet) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return FiniteSet(*(a._elements | b._elements))
@dispatch(FiniteSet, Set) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
# If `b` set contains one of my elements, remove it from `a`
if any(b.contains(x) == True for x in a):
return {
FiniteSet(*[x for x in a if b.contains(x) != True]), b}
return None
@dispatch(Set, Set) # type: ignore # noqa:F811
def union_sets(a, b): # noqa:F811
return None
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