U L?hK@sdZddlmZmZmZddlmZmZmZddl m Z ddl m Z ddl mZmZmZmZmZmZddlmZddlmZdd lmZmZmZGd d d ZeZd d ZdefddZddZ ddZ!ddZ"ddl#m$Z$m%Z%dS)z4Module for querying SymPy objects about assumptions.)global_assumptions PredicateAppliedPredicate)CNF EncodedCNFLiteral)sympify) BooleanKind)EqNeGtLtGeLe) satisfiable)memoize_property)sympy_deprecation_warningSymPyDeprecationWarningignore_warningsc@seZdZdZeddZeddZeddZedd Zed d Z ed d Z eddZ eddZ eddZ eddZeddZeddZeddZeddZeddZed d!Zed"d#Zed$d%Zed&d'Zed(d)Zed*d+Zed,d-Zed.d/Zed0d1Zed2d3Zed4d5Zed6d7Zed8d9Z ed:d;Z!edd?Z#ed@dAZ$edBdCZ%edDdEZ&edFdGZ'edHdIZ(edJdKZ)edLdMZ*edNdOZ+edPdQZ,edRdSZ-edTdUZ.edVdWZ/edXdYZ0edZd[Z1ed\d]Z2ed^d_Z3ed`daZ4edbdcZ5edddeZ6edfdgZ7edhdiZ8edjdkZ9edldmZ:edndoZ;edpdqZs zAssumptionKeys.algebraiccCsddlm}|S)Nr)TranscendentalPredicate)predicates.setsr))rr)rrrtranscendentalCs zAssumptionKeys.transcendentalcCsddlm}|S)Nr)IntegerPredicate)rr,)rr,rrrintegerHs zAssumptionKeys.integercCsddlm}|S)Nr)NonIntegerPredicate)r*r.)rr.rrr nonintegerMs zAssumptionKeys.nonintegercCsddlm}|S)Nr)RationalPredicate)rr0)rr0rrrrationalRs zAssumptionKeys.rationalcCsddlm}|S)Nr)IrrationalPredicate)rr2)rr2rrr irrationalWs zAssumptionKeys.irrationalcCsddlm}|S)Nr)FinitePredicate)handlers.calculusr4)rr4rrrfinite\s zAssumptionKeys.finitecCsddlm}|S)Nr)InfinitePredicate)r5r7)rr7rrrinfiniteas zAssumptionKeys.infinitecCsddlm}|S)Nr)PositiveInfinitePredicate)r5r9)rr9rrrpositive_infinitefs z AssumptionKeys.positive_infinitecCsddlm}|S)Nr)NegativeInfinitePredicate)r5r;)rr;rrrnegative_infiniteks z AssumptionKeys.negative_infinitecCsddlm}|S)Nr)PositivePredicate)handlers.orderr=)rr=rrrpositiveps zAssumptionKeys.positivecCsddlm}|S)Nr)NegativePredicate)r>r@)rr@rrrnegativeus zAssumptionKeys.negativecCsddlm}|S)Nr) ZeroPredicate)r>rB)rrBrrrzerozs zAssumptionKeys.zerocCsddlm}|S)Nr)ExtendedPositivePredicate)r>rD)rrDrrrextended_positives z AssumptionKeys.extended_positivecCsddlm}|S)Nr)ExtendedNegativePredicate)r>rF)rrFrrrextended_negatives z AssumptionKeys.extended_negativecCsddlm}|S)Nr)NonZeroPredicate)r>rH)rrHrrrnonzeros zAssumptionKeys.nonzerocCsddlm}|S)Nr)NonPositivePredicate)r>rJ)rrJrrr nonpositives zAssumptionKeys.nonpositivecCsddlm}|S)Nr)NonNegativePredicate)r>rL)rrLrrr nonnegatives zAssumptionKeys.nonnegativecCsddlm}|S)Nr)ExtendedNonZeroPredicate)r>rN)rrNrrrextended_nonzeros zAssumptionKeys.extended_nonzerocCsddlm}|S)Nr)ExtendedNonPositivePredicate)r>rP)rrPrrrextended_nonpositives z#AssumptionKeys.extended_nonpositivecCsddlm}|S)Nr)ExtendedNonNegativePredicate)r>rR)rrRrrrextended_nonnegatives z#AssumptionKeys.extended_nonnegativecCsddlm}|S)Nr) EvenPredicate)handlers.ntheoryrT)rrTrrrevens zAssumptionKeys.evencCsddlm}|S)Nr) OddPredicate)rUrW)rrWrrrodds zAssumptionKeys.oddcCsddlm}|S)Nr)PrimePredicate)rUrY)rrYrrrprimes zAssumptionKeys.primecCsddlm}|S)Nr)CompositePredicate)rUr[)rr[rrr composites zAssumptionKeys.compositecCsddlm}|S)Nr)CommutativePredicate)handlers.commonr])rr]rrr commutatives zAssumptionKeys.commutativecCsddlm}|S)Nr)IsTruePredicate)r^r`)rr`rrris_trues zAssumptionKeys.is_truecCsddlm}|S)Nr)SymmetricPredicate)handlers.matricesrb)rrbrrr symmetrics zAssumptionKeys.symmetriccCsddlm}|S)Nr)InvertiblePredicate)rcre)rrerrr invertibles zAssumptionKeys.invertiblecCsddlm}|S)Nr)OrthogonalPredicate)rcrg)rrgrrr orthogonals zAssumptionKeys.orthogonalcCsddlm}|S)Nr)UnitaryPredicate)rcri)rrirrrunitarys zAssumptionKeys.unitarycCsddlm}|S)Nr)PositiveDefinitePredicate)rcrk)rrkrrrpositive_definites z AssumptionKeys.positive_definitecCsddlm}|S)Nr)UpperTriangularPredicate)rcrm)rrmrrrupper_triangulars zAssumptionKeys.upper_triangularcCsddlm}|S)Nr)LowerTriangularPredicate)rcro)rrorrrlower_triangulars zAssumptionKeys.lower_triangularcCsddlm}|S)Nr)DiagonalPredicate)rcrq)rrqrrrdiagonals zAssumptionKeys.diagonalcCsddlm}|S)Nr)FullRankPredicate)rcrs)rrsrrrfullranks zAssumptionKeys.fullrankcCsddlm}|S)Nr)SquarePredicate)rcru)rrurrrsquares zAssumptionKeys.squarecCsddlm}|S)Nr)IntegerElementsPredicate)rcrw)rrwrrrinteger_elementss zAssumptionKeys.integer_elementscCsddlm}|S)Nr)RealElementsPredicate)rcry)rryrrr real_elementss zAssumptionKeys.real_elementscCsddlm}|S)Nr)ComplexElementsPredicate)rcr{)rr{rrrcomplex_elementss zAssumptionKeys.complex_elementscCsddlm}|S)Nr)SingularPredicate)predicates.matricesr})rr}rrrsingulars zAssumptionKeys.singularcCsddlm}|S)Nr)NormalPredicate)r~r)rrrrrnormal s zAssumptionKeys.normalcCsddlm}|S)Nr)TriangularPredicate)r~r)rrrrr triangulars zAssumptionKeys.triangularcCsddlm}|S)Nr)UnitTriangularPredicate)r~r)rrrrrunit_triangulars zAssumptionKeys.unit_triangularcCsddlm}|S)Nr)EqualityPredicate)relation.equalityr)rrrrreqs zAssumptionKeys.eqcCsddlm}|S)Nr)UnequalityPredicate)rr)rrrrrnes zAssumptionKeys.necCsddlm}|S)Nr)StrictGreaterThanPredicate)rr)rrrrrgt$s zAssumptionKeys.gtcCsddlm}|S)Nr)GreaterThanPredicate)rr)rrrrrge)s zAssumptionKeys.gecCsddlm}|S)Nr)StrictLessThanPredicate)rr)rrrrrlt.s zAssumptionKeys.ltcCsddlm}|S)Nr)LessThanPredicate)rr)rrrrrle3s zAssumptionKeys.leN)=__name__ __module__ __qualname____doc__rrrr r"r$r&r(r+r-r/r1r3r6r8r:r<r?rArCrErGrIrKrMrOrQrSrVrXrZr\r_rardrfrhrjrlrnrprrrtrvrxrzr|rrrrrrrrrrrrrrrs                                                        rcCst}|jD]n}g}|D]N}t|jtrbt|jjdkrb|jj|kr\|t |jj |j qfq qq q|r | t |q t|S)a Extract all relevant assumptions from *assump* with respect to given *exprs*. Parameters ========== assump : sympy.assumptions.cnf.CNF exprs : tuple of expressions Returns ======= sympy.assumptions.cnf.CNF Examples ======== >>> from sympy import Q >>> from sympy.assumptions.cnf import CNF >>> from sympy.assumptions.ask import _extract_all_facts >>> from sympy.abc import x, y >>> assump = CNF.from_prop(Q.positive(x) & Q.integer(y)) >>> exprs = (x,) >>> cnf = _extract_all_facts(assump, exprs) >>> cnf.clauses {frozenset({Literal(Q.positive, False)})} r)setclauses isinstanceZlitrlen argumentsargappendrfunctionis_Notadd frozensetr)ZassumpZexprsZfactsclauseargsliteralrrr_extract_all_facts;s  rTc Csddlm}ddlm}ddlm}t|}t|}t|tsH|j t k rPt dt|tsd|j t k rlt dt t jtt jtt jtt jtt jtt ji}t|tr|j|j}}n.|j|kr|t||j}}nt j|f}}t !|} | "|t#| |} t$} t%} | &t | | '| | j(r@t)| dkr@t*d|t+|| } | d k rX| S||,|} | d k rxt-| S||||d } | d k r| Sz||||d } Wn|k rYd SX| S) ay Function to evaluate the proposition with assumptions. Explanation =========== This function evaluates the proposition to ``True`` or ``False`` if the truth value can be determined. If not, it returns ``None``. It should be discerned from :func:`~.refine` which, when applied to a proposition, simplifies the argument to symbolic ``Boolean`` instead of Python built-in ``True``, ``False`` or ``None``. **Syntax** * ask(proposition) Evaluate the *proposition* in global assumption context. * ask(proposition, assumptions) Evaluate the *proposition* with respect to *assumptions* in global assumption context. Parameters ========== proposition : Boolean Proposition which will be evaluated to boolean value. If this is not ``AppliedPredicate``, it will be wrapped by ``Q.is_true``. assumptions : Boolean, optional Local assumptions to evaluate the *proposition*. context : AssumptionsContext, optional Default assumptions to evaluate the *proposition*. By default, this is ``sympy.assumptions.global_assumptions`` variable. Returns ======= ``True``, ``False``, or ``None`` Raises ====== TypeError : *proposition* or *assumptions* is not valid logical expression. ValueError : assumptions are inconsistent. Examples ======== >>> from sympy import ask, Q, pi >>> from sympy.abc import x, y >>> ask(Q.rational(pi)) False >>> ask(Q.even(x*y), Q.even(x) & Q.integer(y)) True >>> ask(Q.prime(4*x), Q.integer(x)) False If the truth value cannot be determined, ``None`` will be returned. >>> print(ask(Q.odd(3*x))) # cannot determine unless we know x None ``ValueError`` is raised if assumptions are inconsistent. >>> ask(Q.integer(x), Q.even(x) & Q.odd(x)) Traceback (most recent call last): ... ValueError: inconsistent assumptions Q.even(x) & Q.odd(x) Notes ===== Relations in assumptions are not implemented (yet), so the following will not give a meaningful result. >>> ask(Q.positive(x), x > 0) It is however a work in progress. See Also ======== sympy.assumptions.refine.refine : Simplification using assumptions. Proposition is not reduced to ``None`` if the truth value cannot be determined. r)satask) lra_satask)UnhandledInputz.proposition must be a valid logical expressionz.assumptions must be a valid logical expressionFzinconsistent assumptions %sN) assumptionscontext).Zsympy.assumptions.sataskrZsympy.assumptions.lra_sataskrZ!sympy.logic.algorithms.lra_theoryrrrrkindr TypeErrorr Qrr rr rr rrrrrrrrfunctyperrarZ from_propextendrget_all_known_factsrZfrom_cnfZ add_from_cnfrr ValueError_ask_single_factZ _eval_askbool)Z propositionrrrrrZ binrelpredskeyrZ assump_cnf local_factsZknown_facts_cnfZenc_cnfresrrraskosLZ   (           rc Cs|jrt}t|jdkrj|j\}t|dkrj|\}||d}|dk rP|dnt}|jrj|j|krjdS|jD]\}t|dkrp|\}|js||jdnd}|dkrqp|\}}||krdS||krpdSqpdS)a Compute the truth value of single predicate using assumptions. Parameters ========== key : sympy.assumptions.assume.Predicate Proposition predicate. local_facts : sympy.assumptions.cnf.CNF Local assumption in CNF form. Returns ======= ``True``, ``False`` or ``None`` Examples ======== >>> from sympy import Q >>> from sympy.assumptions.cnf import CNF >>> from sympy.assumptions.ask import _ask_single_fact If prerequisite of proposition is rejected by the assumption, return ``False``. >>> key, assump = Q.zero, ~Q.zero >>> local_facts = CNF.from_prop(assump) >>> _ask_single_fact(key, local_facts) False >>> key, assump = Q.zero, ~Q.even >>> local_facts = CNF.from_prop(assump) >>> _ask_single_fact(key, local_facts) False If assumption implies the proposition, return ``True``. >>> key, assump = Q.even, Q.zero >>> local_facts = CNF.from_prop(assump) >>> _ask_single_fact(key, local_facts) True If proposition rejects the assumption, return ``False``. >>> key, assump = Q.even, Q.odd >>> local_facts = CNF.from_prop(assump) >>> _ask_single_fact(key, local_facts) False rNrFT)rget_known_facts_dictrgetrrr) rrZknown_facts_dictclfZ prop_factsZprop_reqrZprop_rejrrrrs,3    rcCsZtddddt|tr |jj}tt|d}|dk r@||ntt|t||gddS)z Register a handler in the ask system. key must be a string and handler a class inheriting from AskHandler. .. deprecated:: 1.8. Use multipledispatch handler instead. See :obj:`~.Predicate`. z The AskHandler system is deprecated. The register_handler() function should be replaced with the multipledispatch handler of Predicate. 1.8deprecated-askhandlerZdeprecated_since_versionZactive_deprecations_targetN)handlers)rrrnamegetattrr add_handlersetattr)rhandlerZQkeyrrrregister_handlerYs    rc CsHtddddt|tr |jj}tttt||W5QRXdS)z Removes a handler from the ask system. .. deprecated:: 1.8. Use multipledispatch handler instead. See :obj:`~.Predicate`. z The AskHandler system is deprecated. The remove_handler() function should be replaced with the multipledispatch handler of Predicate. rrrN) rrrrrrrrremove_handler)rrrrrrss  r)rrN)&rZsympy.assumptions.assumerrrZsympy.assumptions.cnfrrrZ sympy.corerZsympy.core.kindr Zsympy.core.relationalr r r r rrZsympy.logic.inferencerZsympy.utilities.decoratorrZsympy.utilities.exceptionsrrrrrrrrrrZsympy.assumptions.ask_generatedrrrrrrs&      &4S