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Mini Shell
Mini Shell
from sympy import Min, Max, Set, Lambda, symbols, S, oo
from sympy.core import Basic, Expr, Integer
from sympy.core.numbers import Infinity, NegativeInfinity, Zero
from sympy.multipledispatch import dispatch
from sympy.sets import Interval, FiniteSet, Union, ImageSet
_x, _y = symbols("x y")
@dispatch(Basic, Basic) # type: ignore # noqa:F811
def _set_pow(x, y): # noqa:F811
return None
@dispatch(Set, Set) # type: ignore # noqa:F811
def _set_pow(x, y): # noqa:F811
return ImageSet(Lambda((_x, _y), (_x ** _y)), x, y)
@dispatch(Expr, Expr) # type: ignore # noqa:F811
def _set_pow(x, y): # noqa:F811
return x**y
@dispatch(Interval, Zero) # type: ignore # noqa:F811
def _set_pow(x, z): # noqa:F811
return FiniteSet(S.One)
@dispatch(Interval, Integer) # type: ignore # noqa:F811
def _set_pow(x, exponent): # noqa:F811
"""
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)
@dispatch(Interval, Infinity) # type: ignore # noqa:F811
def _set_pow(b, e): # noqa:F811
# 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)
@dispatch(Interval, NegativeInfinity) # type: ignore # noqa:F811
def _set_pow(b, e): # noqa:F811
from sympy.sets.setexpr import set_div
return _set_pow(set_div(S.One, b), oo)
Zerion Mini Shell 1.0