ó ¡¼™\c@ sàddlmZmZddlZddlmZddlmZddlm Z ddl m Z ddl m Z ddlmZd efd „ƒYZeƒZd e fd „ƒYZd e fd„ƒYZed„ƒZdS(iÿÿÿÿ(tprint_functiontdivisionN(tcacheit(tS(t_sympify(tBoolean(t get_class(tcontextmanagertAssumptionsContextcB s eZdZd„Zd„ZRS(sÕSet 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() cG s+x$|D]}tt|ƒj|ƒqWdS(sAdd an assumption.N(tsuperRtadd(tselft assumptionsta((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyR $s cC s1|sd|jjSd|jj|j|ƒfS(Ns%s()s%s(%s)(t __class__t__name__t _print_set(R tprinter((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyt _sympystr)s(Rt __module__t__doc__R R(((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyR s tAppliedPredicatecB sŒeZdZgZd„ZeZed„ƒZed„ƒZ ed„ƒZ e d d„ƒZ d„Zd„Zd„Zed „ƒZRS( sThe 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)) cC st|ƒ}tj|||ƒS(N(RRt__new__(tclst predicatetarg((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyRAs cC s |jdS(sê 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 i(t_args(R ((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyRGscC s |jdS(Ni(R(R ((s7lib/python2.7/site-packages/sympy/assumptions/assume.pytargsXscC s |jdS(Ni(R(R ((s7lib/python2.7/site-packages/sympy/assumptions/assume.pytfunc\scC s=|jƒd|jj|jjƒfftjjƒtjfS(Ni(t class_keyRtnameRtsort_keyRtOne(R torder((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyR`s'cC s&t|ƒtkr"|j|jkStS(N(ttypeRRtFalse(R tother((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyt__eq__escC stt|ƒjƒS(N(R Rt__hash__(R ((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyR&jscC s|jj|j|ƒS(N(RtevalR(R R ((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyt _eval_askmscC siddlm}m}|jjdkrb|j}|jsX|jsXt|||fƒrb|j Snt ƒS(Niÿÿÿÿ(tEqtNetis_truetis_false(R+R,( tsympy.core.relationalR)R*RRRt is_Booleant is_Symbolt isinstancetbinary_symbolstset(R R)R*ti((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyR1ps  ' N(RRRt __slots__RtTruetis_AtomtpropertyRRRRtNoneRR%R&R(R1(((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyR1s     t PredicatecB skeZdZeZd d„Zd„Zd„Zd„Z d„Z d„Z e d d„ƒZ ed„ZRS( s«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) >>> 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) cC s+tj|ƒ}||_|p!g|_|S(N(RRRthandlers(RRR:tobj((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyR™s cC s |jfS(N(R(R ((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyt_hashable_contentŸscC s |jfS(N(R(R ((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyt__getnewargs__¢scC s t||ƒS(N(R(R texpr((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyt__call__¥scC s|jj|ƒdS(N(R:tappend(R thandler((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyt add_handler¨scC s|jj|ƒdS(N(R:tremove(R RA((s7lib/python2.7/site-packages/sympy/assumptions/assume.pytremove_handler«scC s.|jƒd|jfftjjƒtjfS(Ni(RRRR R(R R!((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyR®sc C säd\}}tjt|ƒƒ}x¼|jD]±}t|ƒ}xœ|D]”}t||jdƒ} | dkrqqDn| ||ƒ}|dkr’qDn|dkr§|}n0|dkr¼|}n||kr×tdƒ‚nPqDWq+W|S(sŒ Evaluate self(expr) under the given assumptions. This uses only direct resolution methods, not logical inference. sincompatible resolutorsN(NN( R8tinspecttgetmroR"R:RtgetattrRt ValueError( R R>R trest_restmroRARtsubclassteval_((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyR'²s&           N(RRRR5R6R8RR<R=R?RBRDRRR'(((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyR9zs      cg sAtjƒ}tj|ƒz dVWdtjƒtj|ƒXdS(s0 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 N(tglobal_assumptionstcopytupdatetclear(R told_global_assumptions((s7lib/python2.7/site-packages/sympy/assumptions/assume.pytassumingÒs     (t __future__RRREtsympy.core.cacheRtsympy.core.singletonRtsympy.core.sympifyRtsympy.logic.boolalgRtsympy.utilities.sourceRt contextlibRR2RRNRR9RS(((s7lib/python2.7/site-packages/sympy/assumptions/assume.pyts # IX