def eval_predicate(predicate, expr, assumptions=True):
"""
Evaluate predicate(expr) under the given assumptions.
This uses only direct resolution methods, not logical inference.
"""
res, _res = None, None
mro = inspect.getmro(type(expr))
for handler in predicate.handlers:
cls = get_class(handler)
for subclass in mro:
try:
eval = getattr(cls, subclass.__name__)
except AttributeError:
continue
res = eval(expr, assumptions)
if _res is None:
_res = res
elif res is None:
# since first resolutor was conclusive, we keep that value
res = _res
else:
# only check consistency if both resolutors have concluded
if _res != res:
raise ValueError('incompatible resolutors')
break
return res
def eval(self, expr, assumptions=True):
"""
Evaluate self(expr) under the given assumptions.
This uses only direct resolution methods, not logical inference.
"""
res, _res = None, None
mro = inspect.getmro(type(expr))
for handler in self.handlers:
cls = get_class(handler)
for subclass in mro:
try:
eval = getattr(cls, subclass.__name__)
except AttributeError:
continue
res = eval(expr, assumptions)
if _res is None:
_res = res
elif res is None:
# since first resolutor was conclusive, we keep that value
res = _res
else:
# only check consistency if both resolutors have concluded
if _res != res:
raise ValueError('incompatible resolutors')
break
return res
def eval(self, args, assumptions=True):
# Support for deprecated design
# When old design is removed, this will always return None
SymPyDeprecationWarning(
feature="Evaluating UndefinedPredicate",
useinstead="multipledispatch handler of Predicate",
issue=20873,
deprecated_since_version="1.8").warn()
expr, = args
res, _res = None, None
mro = inspect.getmro(type(expr))
for handler in self.handlers:
cls = get_class(handler)
for subclass in mro:
eval_ = getattr(cls, subclass.__name__, None)
if eval_ is None:
continue
res = eval_(expr, assumptions)
# Do not stop if value returned is None
# Try to check for higher classes
if res is None:
continue
if _res is None:
_res = res
elif res is None:
# since first resolutor was conclusive, we keep that value
res = _res
else:
# only check consistency if both resolutors have concluded
if _res != res:
raise ValueError('incompatible resolutors')
break
return res
def eval(self, args, assumptions=True):
# Support for deprecated design
# When old design is removed, this will always return None
expr, = args
res, _res = None, None
mro = inspect.getmro(type(expr))
for handler in self.handlers:
cls = get_class(handler)
for subclass in mro:
eval_ = getattr(cls, subclass.__name__, None)
if eval_ is None:
continue
res = eval_(expr, assumptions)
# Do not stop if value returned is None
# Try to check for higher classes
if res is None:
continue
if _res is None:
_res = res
elif res is None:
# since first resolutor was conclusive, we keep that value
res = _res
else:
# only check consistency if both resolutors have concluded
if _res != res:
raise ValueError('incompatible resolutors')
break
return res
def eval(self, args, assumptions=True):
# Support for deprecated design
# When old design is removed, this will always return None
sympy_deprecation_warning(
"""
The AskHandler system is deprecated. Evaluating UndefinedPredicate
objects should be replaced with the multipledispatch handler of
Predicate.
""",
deprecated_since_version="1.8",
active_deprecations_target='deprecated-askhandler',
stacklevel=5,
)
expr, = args
res, _res = None, None
mro = inspect.getmro(type(expr))
for handler in self.handlers:
cls = get_class(handler)
for subclass in mro:
eval_ = getattr(cls, subclass.__name__, None)
if eval_ is None:
continue
res = eval_(expr, assumptions)
# Do not stop if value returned is None
# Try to check for higher classes
if res is None:
continue
if _res is None:
_res = res
else:
# only check consistency if both resolutors have concluded
if _res != res:
raise ValueError('incompatible resolutors')
break
return res
def eval(self, expr, assumptions=True):
"""
Evaluate self(expr) under the given assumptions.
This uses only direct resolution methods, not logical inference.
"""
res, _res = None, None
mro = inspect.getmro(type(expr))
for handler in self.handlers:
cls = get_class(handler)
for subclass in mro:
eval_ = getattr(cls, subclass.__name__, None)
if eval_ is None:
continue
res = eval_(expr, assumptions)
# Do not stop if value returned is None
# Try to check for higher classes
if res is None:
continue
if _res is None:
_res = res
elif res is None:
# since first resolutor was conclusive, we keep that value
res = _res
else:
# only check consistency if both resolutors have concluded
if _res != res:
raise ValueError('incompatible resolutors')
break
return res
def test_get_class():
_basic = get_class('sympy.core.basic.Basic')
assert _basic.__name__ == 'Basic'
def ask(expr, key, assumptions=True):
"""
Method for inferring properties about objects.
**Syntax**
* ask(expression, key)
* ask(expression, key, assumptions)
where expression is any SymPy expression
**Examples**
>>> from sympy import ask, Q, Assume, pi
>>> from sympy.abc import x, y
>>> ask(pi, Q.rational)
False
>>> ask(x*y, Q.even, Assume(x, Q.even) & Assume(y, Q.integer))
True
>>> ask(x*y, Q.prime, Assume(x, Q.integer) & Assume(y, Q.integer))
False
**Remarks**
Relations in assumptions are not implemented (yet), so the following
will not give a meaningful result.
>> ask(x, positive=True, Assume(x>0))
It is however a work in progress and should be available before
the official release
"""
expr = sympify(expr)
assumptions = And(assumptions, And(*global_assumptions))
# direct resolution method, no logic
resolutors = []
for handler in handlers_dict[key]:
resolutors.append( get_class(handler) )
res, _res = None, None
mro = inspect.getmro(type(expr))
for handler in resolutors:
for subclass in mro:
if hasattr(handler, subclass.__name__):
res = getattr(handler, subclass.__name__)(expr, assumptions)
if _res is None: _res = res
elif res is None:
# since first resolutor was conclusive, we keep that value
res = _res
else:
# only check consistency if both resolutors have concluded
if _res != res: raise ValueError, 'incompatible resolutors'
break
if res is not None:
return res
if assumptions is True: return
# use logic inference
if not expr.is_Atom: return
clauses = copy.deepcopy(known_facts_compiled)
assumptions = conjuncts(to_cnf(assumptions))
# add assumptions to the knowledge base
for assump in assumptions:
conj = eliminate_assume(assump, symbol=expr)
if conj:
out = []
for sym in conjuncts(to_cnf(conj)):
lit, pos = literal_symbol(sym), type(sym) is not Not
if pos:
out.extend([known_facts_keys.index(str(l))+1 for l in disjuncts(lit)])
else:
out.extend([-(known_facts_keys.index(str(l))+1) for l in disjuncts(lit)])
clauses.append(out)
n = len(known_facts_keys)
clauses.append([known_facts_keys.index(key)+1])
if not dpll_int_repr(clauses, range(1, n+1), {}):
return False
clauses[-1][0] = -clauses[-1][0]
if not dpll_int_repr(clauses, range(1, n+1), {}):
# if the negation is satisfiable, it is entailed
return True
del clauses
def test_get_class():
_basic = get_class('sympy.core.basic.Basic')
assert _basic.__name__ == 'Basic'
def test_get_class():
_basic = get_class("sympy.core.basic.Basic")
assert _basic.__name__ == "Basic"
def ask(expr, key, assumptions=True):
"""
Method for inferring properties about objects.
**Syntax**
* ask(expression, key)
* ask(expression, key, assumptions)
where expression is any SymPy expression
**Examples**
>>> from sympy import ask, Q, Assume, pi
>>> from sympy.abc import x, y
>>> ask(pi, Q.rational)
False
>>> ask(x*y, Q.even, Assume(x, Q.even) & Assume(y, Q.integer))
True
>>> ask(x*y, Q.prime, Assume(x, Q.integer) & Assume(y, Q.integer))
False
**Remarks**
Relations in assumptions are not implemented (yet), so the following
will not give a meaningful result.
>> ask(x, positive=True, Assume(x>0))
It is however a work in progress and should be available before
the official release
"""
expr = sympify(expr)
assumptions = And(assumptions, And(*global_assumptions))
# direct resolution method, no logic
resolutors = []
for handler in handlers_dict[key]:
resolutors.append(get_class(handler))
res, _res = None, None
mro = inspect.getmro(type(expr))
for handler in resolutors:
for subclass in mro:
if hasattr(handler, subclass.__name__):
res = getattr(handler, subclass.__name__)(expr, assumptions)
if _res is None:
_res = res
elif res is None:
# since first resolutor was conclusive, we keep that value
res = _res
else:
# only check consistency if both resolutors have concluded
if _res != res:
raise ValueError('incompatible resolutors')
break
if res is not None:
return res
if assumptions is True:
return
# use logic inference
if not expr.is_Atom:
return
clauses = copy.deepcopy(known_facts_compiled)
assumptions = conjuncts(to_cnf(assumptions))
# add assumptions to the knowledge base
for assump in assumptions:
conj = eliminate_assume(assump, symbol=expr)
if conj:
out = set()
for sym in conjuncts(to_cnf(conj)):
lit, pos = literal_symbol(sym), type(sym) is not Not
if pos:
out.update([
known_facts_keys.index(str(l)) + 1
for l in disjuncts(lit)
])
else:
out.update([
-(known_facts_keys.index(str(l)) + 1)
for l in disjuncts(lit)
])
clauses.append(out)
n = len(known_facts_keys)
clauses.append(set([known_facts_keys.index(key) + 1]))
if not dpll_int_repr(clauses, set(range(1, n + 1)), {}):
return False
clauses[-1] = set([-(known_facts_keys.index(key) + 1)])
if not dpll_int_repr(clauses, set(range(1, n + 1)), {}):
# if the negation is satisfiable, it is entailed
return True
del clauses