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Mini Shell
Mini Shell
from sympy import Set, symbols
from sympy.core import Basic, Expr
from sympy.multipledispatch import dispatch
from sympy.sets import Interval
_x, _y = symbols("x y")
@dispatch(Basic, Basic) # type: ignore # noqa:F811
def _set_mul(x, y): # noqa:F811
return None
@dispatch(Set, Set) # type: ignore # noqa:F811
def _set_mul(x, y): # noqa:F811
return None
@dispatch(Expr, Expr) # type: ignore # noqa:F811
def _set_mul(x, y): # noqa:F811
return x*y
@dispatch(Interval, Interval) # type: ignore # noqa:F811
def _set_mul(x, y): # noqa:F811
"""
Multiplications in interval arithmetic
https://en.wikipedia.org/wiki/Interval_arithmetic
"""
# TODO: some intervals containing 0 and oo will fail as 0*oo returns nan.
comvals = (
(x.start * y.start, bool(x.left_open or y.left_open)),
(x.start * y.end, bool(x.left_open or y.right_open)),
(x.end * y.start, bool(x.right_open or y.left_open)),
(x.end * y.end, bool(x.right_open or y.right_open)),
)
# TODO: handle symbolic intervals
minval, minopen = min(comvals)
maxval, maxopen = max(comvals)
return Interval(
minval,
maxval,
minopen,
maxopen
)
@dispatch(Basic, Basic) # type: ignore # noqa:F811
def _set_div(x, y): # noqa:F811
return None
@dispatch(Expr, Expr) # type: ignore # noqa:F811
def _set_div(x, y): # noqa:F811
return x/y
@dispatch(Set, Set) # type: ignore # noqa:F811 # noqa:F811
def _set_div(x, y): # noqa:F811
return None
@dispatch(Interval, Interval) # type: ignore # noqa:F811
def _set_div(x, y): # noqa:F811
"""
Divisions in interval arithmetic
https://en.wikipedia.org/wiki/Interval_arithmetic
"""
from sympy.sets.setexpr import set_mul
from sympy import oo
if (y.start*y.end).is_negative:
return Interval(-oo, oo)
if y.start == 0:
s2 = oo
else:
s2 = 1/y.start
if y.end == 0:
s1 = -oo
else:
s1 = 1/y.end
return set_mul(x, Interval(s1, s2, y.right_open, y.left_open))
Zerion Mini Shell 1.0