Source code for sympy.assumptions.assume

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)
def _sympystr(self, printer): if not self: return "%s()" % self.__class__.__name__ return "%s(%s)" % (self.__class__.__name__, printer._print_set(self))
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): 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) @property def binary_symbols(self): from sympy.core.relational import Eq, Ne if self.func.name in ['is_true', 'is_false']: i = self.arg if i.is_Boolean or i.is_Symbol or isinstance(i, (Eq, Ne)): return i.binary_symbols return set()
[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 >>> type(Q.prime) <class 'sympy.assumptions.assume.Predicate'> >>> Q.prime.name 'prime' >>> Q.prime(7) Q.prime(7) >>> _.func.name 'prime' 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: >>> from sympy.abc import x >>> Q.is_true(x > 1) Q.is_true(x > 1) """ 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
[docs]@contextmanager 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)