def definition(self):
e, S = self.args
from sympy.concrete.expr_with_limits import Exists
condition_set = S.condition_set()
if condition_set:
condition = condition_set.condition
if condition_set.variable != e:
condition = condition._subs(condition_set.variable, e)
return And(condition,
self.func(e, condition_set.base_set),
equivalent=self)
image_set = S.image_set()
if image_set is not None:
expr, variables, base_set = image_set
from sympy import Wild
variables_ = Wild(variables.name, **variables.dtype.dict)
assert variables_.shape == variables.shape
e = e.subs_limits_with_epitome(expr)
dic = e.match(expr.subs(variables, variables_))
if dic:
variables_ = dic[variables_]
if variables.dtype != variables_.dtype:
assert len(variables.shape) == 1
variables_ = variables_[:variables.shape[-1]]
return Contains(variables_, base_set, equivalent=self)
if e._has(variables):
_variables = base_set.element_symbol(e.free_symbols)
assert _variables.dtype == variables.dtype
expr = expr._subs(variables, _variables)
variables = _variables
assert not e._has(variables)
return Exists(Equality(e, expr, evaluate=False),
(variables, base_set),
equivalent=self)
if S.is_UNION:
for v in S.variables:
if self.lhs._has(v):
_v = v.generate_free_symbol(self.free_symbols,
**v.dtype.dict)
S = S.limits_subs(v, _v)
contains = Contains(self.lhs, S.function).simplify()
contains.equivalent = None
return Exists(contains, *S.limits, equivalent=self).simplify()
return self
def definition(self):
e, S = self.args
from sympy.concrete.expr_with_limits import ForAll
image_set = S.image_set()
if image_set is not None:
expr, variables, base_set = image_set
from sympy import Wild
variables_ = Wild(variables.name, **variables.dtype.dict)
e = e.subs_limits_with_epitome(expr)
dic = e.match(expr.subs(variables, variables_))
if dic:
variables_ = dic[variables_]
if variables.dtype != variables_.dtype:
assert len(variables.shape) == 1
variables_ = variables_[:variables.shape[-1]]
return self.func(variables_, base_set, equivalent=self)
if e.has(variables):
_variables = base_set.element_symbol(e.free_symbols)
assert _variables.dtype == variables.dtype
expr = expr._subs(variables, _variables)
variables = _variables
assert not e.has(variables)
return ForAll(Unequality(e, expr, evaluate=False),
(variables, base_set),
equivalent=self)
condition_set = S.condition_set()
if condition_set:
return Or(
~condition_set.condition._subs(condition_set.variable, e),
~self.func(e, condition_set.base_set),
equivalent=self)
if S.is_UNION:
contains = self.func(self.lhs, S.function).simplify()
contains.equivalent = None
return ForAll(contains, *S.limits, equivalent=self).simplify()
return self
