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