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Mini Shell
Mini Shell
from sympy import S, Symbol
from sympy.core.logic import fuzzy_and, fuzzy_bool, fuzzy_not, fuzzy_or
from sympy.core.relational import Eq
from sympy.sets.sets import FiniteSet, Interval, Set, Union, ProductSet
from sympy.sets.fancysets import Complexes, Reals, Range, Rationals
from sympy.multipledispatch import dispatch
_inf_sets = [S.Naturals, S.Naturals0, S.Integers, S.Rationals, S.Reals, S.Complexes]
@dispatch(Set, Set) # type: ignore # noqa:F811
def is_subset_sets(a, b): # noqa:F811
return None
@dispatch(Interval, Interval) # type: ignore # noqa:F811
def is_subset_sets(a, b): # noqa:F811
# This is correct but can be made more comprehensive...
if fuzzy_bool(a.start < b.start):
return False
if fuzzy_bool(a.end > b.end):
return False
if (b.left_open and not a.left_open and fuzzy_bool(Eq(a.start, b.start))):
return False
if (b.right_open and not a.right_open and fuzzy_bool(Eq(a.end, b.end))):
return False
@dispatch(Interval, FiniteSet) # type: ignore # noqa:F811
def is_subset_sets(a_interval, b_fs): # noqa:F811
# An Interval can only be a subset of a finite set if it is finite
# which can only happen if it has zero measure.
if fuzzy_not(a_interval.measure.is_zero):
return False
@dispatch(Interval, Union) # type: ignore # noqa:F811
def is_subset_sets(a_interval, b_u): # noqa:F811
if all(isinstance(s, (Interval, FiniteSet)) for s in b_u.args):
intervals = [s for s in b_u.args if isinstance(s, Interval)]
if all(fuzzy_bool(a_interval.start < s.start) for s in intervals):
return False
if all(fuzzy_bool(a_interval.end > s.end) for s in intervals):
return False
if a_interval.measure.is_nonzero:
no_overlap = lambda s1, s2: fuzzy_or([
fuzzy_bool(s1.end <= s2.start),
fuzzy_bool(s1.start >= s2.end),
])
if all(no_overlap(s, a_interval) for s in intervals):
return False
@dispatch(Range, Range) # type: ignore # noqa:F811
def is_subset_sets(a, b): # noqa:F811
if a.step == b.step == 1:
return fuzzy_and([fuzzy_bool(a.start >= b.start),
fuzzy_bool(a.stop <= b.stop)])
@dispatch(Range, Interval) # type: ignore # noqa:F811
def is_subset_sets(a_range, b_interval): # noqa:F811
if a_range.step.is_positive:
if b_interval.left_open and a_range.inf.is_finite:
cond_left = a_range.inf > b_interval.left
else:
cond_left = a_range.inf >= b_interval.left
if b_interval.right_open and a_range.sup.is_finite:
cond_right = a_range.sup < b_interval.right
else:
cond_right = a_range.sup <= b_interval.right
return fuzzy_and([cond_left, cond_right])
@dispatch(Range, FiniteSet) # type: ignore # noqa:F811
def is_subset_sets(a_range, b_finiteset): # noqa:F811
try:
a_size = a_range.size
except ValueError:
# symbolic Range of unknown size
return None
if a_size > len(b_finiteset):
return False
elif any(arg.has(Symbol) for arg in a_range.args):
return fuzzy_and(b_finiteset.contains(x) for x in a_range)
else:
# Checking A \ B == EmptySet is more efficient than repeated naive
# membership checks on an arbitrary FiniteSet.
a_set = set(a_range)
b_remaining = len(b_finiteset)
# Symbolic expressions and numbers of unknown type (integer or not) are
# all counted as "candidates", i.e. *potentially* matching some a in
# a_range.
cnt_candidate = 0
for b in b_finiteset:
if b.is_Integer:
a_set.discard(b)
elif fuzzy_not(b.is_integer):
pass
else:
cnt_candidate += 1
b_remaining -= 1
if len(a_set) > b_remaining + cnt_candidate:
return False
if len(a_set) == 0:
return True
return None
@dispatch(Interval, Range) # type: ignore # noqa:F811
def is_subset_sets(a_interval, b_range): # noqa:F811
if a_interval.measure.is_extended_nonzero:
return False
@dispatch(Interval, Rationals) # type: ignore # noqa:F811
def is_subset_sets(a_interval, b_rationals): # noqa:F811
if a_interval.measure.is_extended_nonzero:
return False
@dispatch(Range, Complexes) # type: ignore # noqa:F811
def is_subset_sets(a, b): # noqa:F811
return True
@dispatch(Complexes, Interval) # type: ignore # noqa:F811
def is_subset_sets(a, b): # noqa:F811
return False
@dispatch(Complexes, Range) # type: ignore # noqa:F811
def is_subset_sets(a, b): # noqa:F811
return False
@dispatch(Complexes, Rationals) # type: ignore # noqa:F811
def is_subset_sets(a, b): # noqa:F811
return False
@dispatch(Rationals, Reals) # type: ignore # noqa:F811
def is_subset_sets(a, b): # noqa:F811
return True
@dispatch(Rationals, Range) # type: ignore # noqa:F811
def is_subset_sets(a, b): # noqa:F811
return False
@dispatch(ProductSet, FiniteSet) # type: ignore # noqa:F811
def is_subset_sets(a_ps, b_fs): # noqa:F811
return fuzzy_and(b_fs.contains(x) for x in a_ps)
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