from __future__ import print_function, division
import inspect
from sympy.core.cache import cacheit
from sympy.core.singleton import S
from sympy.core.sympify import _sympify
from sympy.logic.boolalg import Boolean
from sympy.utilities.source import get_class
from contextlib import contextmanager
[docs]class AssumptionsContext(set):
"""Set representing assumptions.
This is used to represent global assumptions, but you can also use this
class to create your own local assumptions contexts. It is basically a thin
wrapper to Python's set, so see its documentation for advanced usage.
Examples
========
>>> from sympy import AppliedPredicate, Q
>>> from sympy.assumptions.assume import global_assumptions
>>> global_assumptions
AssumptionsContext()
>>> from sympy.abc import x
>>> global_assumptions.add(Q.real(x))
>>> global_assumptions
AssumptionsContext([Q.real(x)])
>>> global_assumptions.remove(Q.real(x))
>>> global_assumptions
AssumptionsContext()
>>> global_assumptions.clear()
"""
[docs] def add(self, *assumptions):
"""Add an assumption."""
for a in assumptions:
super(AssumptionsContext, self).add(a)
global_assumptions = AssumptionsContext()
[docs]class AppliedPredicate(Boolean):
"""The class of expressions resulting from applying a Predicate.
Examples
========
>>> from sympy import Q, Symbol
>>> x = Symbol('x')
>>> Q.integer(x)
Q.integer(x)
>>> type(Q.integer(x))
<class 'sympy.assumptions.assume.AppliedPredicate'>
"""
__slots__ = []
def __new__(cls, predicate, arg):
if not isinstance(arg, bool):
# XXX: There is not yet a Basic type for True and False
arg = _sympify(arg)
return Boolean.__new__(cls, predicate, arg)
is_Atom = True # do not attempt to decompose this
@property
def arg(self):
"""
Return the expression used by this assumption.
Examples
========
>>> from sympy import Q, Symbol
>>> x = Symbol('x')
>>> a = Q.integer(x + 1)
>>> a.arg
x + 1
"""
return self._args[1]
@property
def args(self):
return self._args[1:]
@property
def func(self):
return self._args[0]
@cacheit
def sort_key(self, order=None):
return (self.class_key(), (2, (self.func.name, self.arg.sort_key())),
S.One.sort_key(), S.One)
def __eq__(self, other):
if type(other) is AppliedPredicate:
return self._args == other._args
return False
def __hash__(self):
return super(AppliedPredicate, self).__hash__()
def _eval_ask(self, assumptions):
return self.func.eval(self.arg, assumptions)
[docs]class Predicate(Boolean):
"""A predicate is a function that returns a boolean value.
Predicates merely wrap their argument and remain unevaluated:
>>> from sympy import Q, ask, Symbol, S
>>> x = Symbol('x')
>>> Q.prime(7)
Q.prime(7)
To obtain the truth value of an expression containing predicates, use
the function `ask`:
>>> ask(Q.prime(7))
True
The tautological predicate `Q.is_true` can be used to wrap other objects:
>>> Q.is_true(x > 1)
Q.is_true(x > 1)
>>> Q.is_true(S(1) < x)
Q.is_true(1 < x)
"""
is_Atom = True
def __new__(cls, name, handlers=None):
obj = Boolean.__new__(cls)
obj.name = name
obj.handlers = handlers or []
return obj
def _hashable_content(self):
return (self.name,)
def __getnewargs__(self):
return (self.name,)
def __call__(self, expr):
return AppliedPredicate(self, expr)
def add_handler(self, handler):
self.handlers.append(handler)
def remove_handler(self, handler):
self.handlers.remove(handler)
@cacheit
def sort_key(self, order=None):
return self.class_key(), (1, (self.name,)), S.One.sort_key(), S.One
[docs] 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)
# 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
@contextmanager
[docs]def assuming(*assumptions):
""" Context manager for assumptions
Examples
========
>>> from sympy.assumptions import assuming, Q, ask
>>> from sympy.abc import x, y
>>> print(ask(Q.integer(x + y)))
None
>>> with assuming(Q.integer(x), Q.integer(y)):
... print(ask(Q.integer(x + y)))
True
"""
old_global_assumptions = global_assumptions.copy()
global_assumptions.update(assumptions)
try:
yield
finally:
global_assumptions.clear()
global_assumptions.update(old_global_assumptions)
