You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
108 lines
3.1 KiB
108 lines
3.1 KiB
from sympy.core import Basic, Expr
|
|
from sympy.core.function import Lambda
|
|
from sympy.core.numbers import oo, Infinity, NegativeInfinity, Zero, Integer
|
|
from sympy.core.singleton import S
|
|
from sympy.core.symbol import symbols
|
|
from sympy.functions.elementary.miscellaneous import (Max, Min)
|
|
from sympy.sets.fancysets import ImageSet
|
|
from sympy.sets.setexpr import set_div
|
|
from sympy.sets.sets import Set, Interval, FiniteSet, Union
|
|
from sympy.multipledispatch import Dispatcher
|
|
|
|
|
|
_x, _y = symbols("x y")
|
|
|
|
|
|
_set_pow = Dispatcher('_set_pow')
|
|
|
|
|
|
@_set_pow.register(Basic, Basic)
|
|
def _(x, y):
|
|
return None
|
|
|
|
@_set_pow.register(Set, Set)
|
|
def _(x, y):
|
|
return ImageSet(Lambda((_x, _y), (_x ** _y)), x, y)
|
|
|
|
@_set_pow.register(Expr, Expr)
|
|
def _(x, y):
|
|
return x**y
|
|
|
|
@_set_pow.register(Interval, Zero)
|
|
def _(x, z):
|
|
return FiniteSet(S.One)
|
|
|
|
@_set_pow.register(Interval, Integer)
|
|
def _(x, exponent):
|
|
"""
|
|
Powers in interval arithmetic
|
|
https://en.wikipedia.org/wiki/Interval_arithmetic
|
|
"""
|
|
s1 = x.start**exponent
|
|
s2 = x.end**exponent
|
|
if ((s2 > s1) if exponent > 0 else (x.end > -x.start)) == True:
|
|
left_open = x.left_open
|
|
right_open = x.right_open
|
|
# TODO: handle unevaluated condition.
|
|
sleft = s2
|
|
else:
|
|
# TODO: `s2 > s1` could be unevaluated.
|
|
left_open = x.right_open
|
|
right_open = x.left_open
|
|
sleft = s1
|
|
|
|
if x.start.is_positive:
|
|
return Interval(
|
|
Min(s1, s2),
|
|
Max(s1, s2), left_open, right_open)
|
|
elif x.end.is_negative:
|
|
return Interval(
|
|
Min(s1, s2),
|
|
Max(s1, s2), left_open, right_open)
|
|
|
|
# Case where x.start < 0 and x.end > 0:
|
|
if exponent.is_odd:
|
|
if exponent.is_negative:
|
|
if x.start.is_zero:
|
|
return Interval(s2, oo, x.right_open)
|
|
if x.end.is_zero:
|
|
return Interval(-oo, s1, True, x.left_open)
|
|
return Union(Interval(-oo, s1, True, x.left_open), Interval(s2, oo, x.right_open))
|
|
else:
|
|
return Interval(s1, s2, x.left_open, x.right_open)
|
|
elif exponent.is_even:
|
|
if exponent.is_negative:
|
|
if x.start.is_zero:
|
|
return Interval(s2, oo, x.right_open)
|
|
if x.end.is_zero:
|
|
return Interval(s1, oo, x.left_open)
|
|
return Interval(0, oo)
|
|
else:
|
|
return Interval(S.Zero, sleft, S.Zero not in x, left_open)
|
|
|
|
@_set_pow.register(Interval, Infinity)
|
|
def _(b, e):
|
|
# TODO: add logic for open intervals?
|
|
if b.start.is_nonnegative:
|
|
if b.end < 1:
|
|
return FiniteSet(S.Zero)
|
|
if b.start > 1:
|
|
return FiniteSet(S.Infinity)
|
|
return Interval(0, oo)
|
|
elif b.end.is_negative:
|
|
if b.start > -1:
|
|
return FiniteSet(S.Zero)
|
|
if b.end < -1:
|
|
return FiniteSet(-oo, oo)
|
|
return Interval(-oo, oo)
|
|
else:
|
|
if b.start > -1:
|
|
if b.end < 1:
|
|
return FiniteSet(S.Zero)
|
|
return Interval(0, oo)
|
|
return Interval(-oo, oo)
|
|
|
|
@_set_pow.register(Interval, NegativeInfinity)
|
|
def _(b, e):
|
|
return _set_pow(set_div(S.One, b), oo)
|