o 8VaG@sdZddlmZmZmZddlmZmZmZddl m Z ddl m Z ddl mZmZmZmZmZmZddlmZddlmZdd lmZGd d d ZeZd d ZdefddZddZddZddZ ddl!m"Z"m#Z#dS)z4Module for querying SymPy objects about assumptions.)global_assumptions PredicateAppliedPredicate)CNF EncodedCNFLiteral)sympify) BooleanKind)EqNeGtLtGeLe) satisfiable)memoize_property)SymPyDeprecationWarningc@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;dpS)qAssumptionKeyszy This class contains all the supported keys by ``ask``. It should be accessed via the instance ``sympy.Q``. cCddlm}|S)N)HermitianPredicate) handlers.setsr)selfrr7/usr/lib/python3/dist-packages/sympy/assumptions/ask.py hermitian zAssumptionKeys.hermitiancCr)Nr)AntihermitianPredicate)rr)rrrrr antihermitian#rzAssumptionKeys.antihermitiancCr)Nr) RealPredicate)rr)rrrrrreal(rzAssumptionKeys.realcCr)Nr)ExtendedRealPredicate)rr!)rr!rrr extended_real-rzAssumptionKeys.extended_realcCr)Nr)ImaginaryPredicate)rr#)rr#rrr imaginary2rzAssumptionKeys.imaginarycCr)Nr)ComplexPredicate)rr%)rr%rrrcomplex7rzAssumptionKeys.complexcCr)Nr)AlgebraicPredicate)rr')rr'rrr algebraic<rzAssumptionKeys.algebraiccCr)Nr)TranscendentalPredicate)Zpredicates.setsr))rr)rrrtranscendentalArzAssumptionKeys.transcendentalcCr)Nr)IntegerPredicate)rr+)rr+rrrintegerFrzAssumptionKeys.integercCr)Nr)RationalPredicate)rr-)rr-rrrrationalKrzAssumptionKeys.rationalcCr)Nr)IrrationalPredicate)rr/)rr/rrr irrationalPrzAssumptionKeys.irrationalcCr)Nr)FinitePredicate)handlers.calculusr1)rr1rrrfiniteUrzAssumptionKeys.finitecCr)Nr)InfinitePredicate)r2r4)rr4rrrinfiniteZrzAssumptionKeys.infinitecCr)Nr)PositiveInfinitePredicate)r2r6)rr6rrrpositive_infinite_rz AssumptionKeys.positive_infinitecCr)Nr)NegativeInfinitePredicate)r2r8)rr8rrrnegative_infinitedrz AssumptionKeys.negative_infinitecCr)Nr)PositivePredicate)handlers.orderr:)rr:rrrpositiveirzAssumptionKeys.positivecCr)Nr)NegativePredicate)r;r=)rr=rrrnegativenrzAssumptionKeys.negativecCr)Nr) ZeroPredicate)r;r?)rr?rrrzerosrzAssumptionKeys.zerocCr)Nr)ExtendedPositivePredicate)r;rA)rrArrrextended_positivexrz AssumptionKeys.extended_positivecCr)Nr)ExtendedNegativePredicate)r;rC)rrCrrrextended_negative}rz AssumptionKeys.extended_negativecCr)Nr)NonZeroPredicate)r;rE)rrErrrnonzerorzAssumptionKeys.nonzerocCr)Nr)NonPositivePredicate)r;rG)rrGrrr nonpositiverzAssumptionKeys.nonpositivecCr)Nr)NonNegativePredicate)r;rI)rrIrrr nonnegativerzAssumptionKeys.nonnegativecCr)Nr)ExtendedNonZeroPredicate)r;rK)rrKrrrextended_nonzerorzAssumptionKeys.extended_nonzerocCr)Nr)ExtendedNonPositivePredicate)r;rM)rrMrrrextended_nonpositiverz#AssumptionKeys.extended_nonpositivecCr)Nr)ExtendedNonNegativePredicate)r;rO)rrOrrrextended_nonnegativerz#AssumptionKeys.extended_nonnegativecCr)Nr) EvenPredicate)handlers.ntheoryrQ)rrQrrrevenrzAssumptionKeys.evencCr)Nr) OddPredicate)rRrT)rrTrrroddrzAssumptionKeys.oddcCr)Nr)PrimePredicate)rRrV)rrVrrrprimerzAssumptionKeys.primecCr)Nr)CompositePredicate)rRrX)rrXrrr compositerzAssumptionKeys.compositecCr)Nr)CommutativePredicate)handlers.commonrZ)rrZrrr commutativerzAssumptionKeys.commutativecCr)Nr)IsTruePredicate)r[r])rr]rrris_truerzAssumptionKeys.is_truecCr)Nr)SymmetricPredicate)handlers.matricesr_)rr_rrr symmetricrzAssumptionKeys.symmetriccCr)Nr)InvertiblePredicate)r`rb)rrbrrr invertiblerzAssumptionKeys.invertiblecCr)Nr)OrthogonalPredicate)r`rd)rrdrrr orthogonalrzAssumptionKeys.orthogonalcCr)Nr)UnitaryPredicate)r`rf)rrfrrrunitaryrzAssumptionKeys.unitarycCr)Nr)PositiveDefinitePredicate)r`rh)rrhrrrpositive_definiterz AssumptionKeys.positive_definitecCr)Nr)UpperTriangularPredicate)r`rj)rrjrrrupper_triangularrzAssumptionKeys.upper_triangularcCr)Nr)LowerTriangularPredicate)r`rl)rrlrrrlower_triangularrzAssumptionKeys.lower_triangularcCr)Nr)DiagonalPredicate)r`rn)rrnrrrdiagonalrzAssumptionKeys.diagonalcCr)Nr)FullRankPredicate)r`rp)rrprrrfullrankrzAssumptionKeys.fullrankcCr)Nr)SquarePredicate)r`rr)rrrrrrsquarerzAssumptionKeys.squarecCr)Nr)IntegerElementsPredicate)r`rt)rrtrrrinteger_elementsrzAssumptionKeys.integer_elementscCr)Nr)RealElementsPredicate)r`rv)rrvrrr real_elementsrzAssumptionKeys.real_elementscCr)Nr)ComplexElementsPredicate)r`rx)rrxrrrcomplex_elementsrzAssumptionKeys.complex_elementscCr)Nr)SingularPredicate)predicates.matricesrz)rrzrrrsingularrzAssumptionKeys.singularcCr)Nr)NormalPredicate)r{r})rr}rrrnormalrzAssumptionKeys.normalcCr)Nr)TriangularPredicate)r{r)rrrrr triangular rzAssumptionKeys.triangularcCr)Nr)UnitTriangularPredicate)r{r)rrrrrunit_triangularrzAssumptionKeys.unit_triangularcCr)Nr)EqualityPredicate)relation.equalityr)rrrrreqrzAssumptionKeys.eqcCr)Nr)UnequalityPredicate)rr)rrrrrnerzAssumptionKeys.necCr)Nr)StrictGreaterThanPredicate)rr)rrrrrgtrzAssumptionKeys.gtcCr)Nr)GreaterThanPredicate)rr)rrrrrge"rzAssumptionKeys.gecCr)Nr)StrictLessThanPredicate)rr)rrrrrlt'rzAssumptionKeys.ltcCr)Nr)LessThanPredicate)rr)rrrrrle,rzAssumptionKeys.leN)<__name__ __module__ __qualname____doc__rrrr r"r$r&r(r*r,r.r0r3r5r7r9r<r>r@rBrDrFrHrJrLrNrPrSrUrWrYr\r^rarcrergrirkrmrorqrsrurwryr|r~rrrrrrrrrrrrrs                                                      rcCs~t}|jD]4}g}|D]$}t|jtr0t|jjdkr0|jj|vr.|t |jj |j q n q |r:| t |qt|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_facts4s  rTc Cshddlm}t|}t|}t|ts|jturtdt|ts&|jtur*tdtt j t t j t t jtt jtt jtt ji}t|trK|j|j}}n|j|vrZ||j|j}}nt j|f}}t|}||t||}t} t } | !t| | "||j#rt$| durt%d|t&||} | dur| S||'|} | durt(| S||||d} | S) a 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 : Any boolean expression. Proposition which will be evaluated to boolean value. If this is not ``AppliedPredicate``, it will be wrapped by ``Q.is_true``. assumptions : Any boolean expression, 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)sataskz.proposition must be a valid logical expressionz.assumptions must be a valid logical expressionFzinconsistent assumptions %sN) assumptionscontext))Zsympy.assumptions.sataskrrrrkindr TypeErrorr Qrr rr rr rrrrrrrrfuncrr^rZ from_propextendrget_all_known_factsrZfrom_cnfZ add_from_cnfrr ValueError_ask_single_factZ _eval_askbool) Z propositionrrrZ binrelpredskeyrZ assump_cnf local_factsZknown_facts_cnfZenc_cnfresrrraskds< Z(        rc Cs|jrgt}t|jdkr5|j\}t|dkr5|\}||d}|dur(|dnt}|jr5|j|vr5dS|jD].}t|dkrf|\}|jsM||jdnd}|durTq8|\}}||vr_dS||vrfdSq8dS)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_dictZclfZ prop_factsZprop_reqrZprop_rejrrrrs.3    rcCsbtdddddt|tr|jj}tt|d}|dur$||dStt|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`. zregister_handler() function%multipledispatch handler of PredicateQ1.8ZfeatureZ useinsteadZissueZdeprecated_since_versionN)handlers) rwarnrrnamegetattrrZ add_handlersetattr)rhandlerZQkeyrrrregister_handlerDs   rcCs:tdddddt|tr|jj}tt||dS)z Removes a handler from the ask system. Same syntax as register_handler .. deprecated:: 1.8. Use multipledispatch handler instead. See :obj:`~.Predicate`. zremove_handler() functionrrrrN)rrrrrrrremove_handler)rrrrrr\s r)rrN)$rZsympy.assumptions.assumerrrZsympy.assumptions.cnfrrrZ sympy.corerZsympy.core.kindr Zsympy.core.relationalr r r r rrZsympy.logic.inferencerZsympy.utilities.decoratorrZsympy.utilities.exceptionsrrrrrrrrZsympy.assumptions.ask_generatedrrrrrrs(      !0S