gKdZddlmZmZmZddlmZmZmZddl m Z ddl m Z ddl mZmZmZmZmZmZddlmZddlmZdd lmZmZmZGd d ZeZd Zd efdZdZ dZ!dZ"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_warningsceZdZdZedZedZedZedZedZ edZ edZ ed Z ed Z ed Zed Zed ZedZedZedZedZedZedZedZedZedZedZedZedZedZedZedZedZ edZ!edZ"ed Z#ed!Z$ed"Z%ed#Z&ed$Z'ed%Z(ed&Z)ed'Z*ed(Z+ed)Z,ed*Z-ed+Z.ed,Z/ed-Z0ed.Z1ed/Z2ed0Z3ed1Z4ed2Z5ed3Z6ed4Z7ed5Z8ed6Z9ed7Z:ed8Z;ed9Zrr c"ddlm}|S)Nr)TranscendentalPredicate)predicates.setsr5)rr5s rtranscendentalzAssumptionKeys.transcendentalCs#<<<<<<&&(((r c"ddlm}|S)Nr)IntegerPredicate)rr9)rr9s rintegerzAssumptionKeys.integerHr0r c"ddlm}|S)Nr)NonIntegerPredicate)r6r<)rr<s r nonintegerzAssumptionKeys.nonintegerMs#888888""$$$r c"ddlm}|S)Nr)RationalPredicate)rr?)rr?s rrationalzAssumptionKeys.rationalRs#444444  """r c"ddlm}|S)Nr)IrrationalPredicate)rrB)rrBs r irrationalzAssumptionKeys.irrationalWs#666666""$$$r c"ddlm}|S)Nr)FinitePredicate)handlers.calculusrE)rrEs rfinitezAssumptionKeys.finite\"666666   r c"ddlm}|S)Nr)InfinitePredicate)rFrJ)rrJs rinfinitezAssumptionKeys.infinitea#888888  """r c"ddlm}|S)Nr)PositiveInfinitePredicate)rFrN)rrNs rpositive_infinitez AssumptionKeys.positive_infinitef#@@@@@@((***r c"ddlm}|S)Nr)NegativeInfinitePredicate)rFrR)rrRs rnegative_infinitez AssumptionKeys.negative_infinitekrPr c"ddlm}|S)Nr)PositivePredicate)handlers.orderrU)rrUs rpositivezAssumptionKeys.positivep#555555  """r c"ddlm}|S)Nr)NegativePredicate)rVrZ)rrZs rnegativezAssumptionKeys.negativeurXr c"ddlm}|S)Nr) ZeroPredicate)rVr])rr]s rzerozAssumptionKeys.zerozs 111111}r c"ddlm}|S)Nr)ExtendedPositivePredicate)rVr`)rr`s rextended_positivez AssumptionKeys.extended_positive#======((***r c"ddlm}|S)Nr)ExtendedNegativePredicate)rVrd)rrds rextended_negativez AssumptionKeys.extended_negativerbr c"ddlm}|S)Nr)NonZeroPredicate)rVrg)rrgs rnonzerozAssumptionKeys.nonzeros#444444!!!r c"ddlm}|S)Nr)NonPositivePredicate)rVrj)rrjs r nonpositivezAssumptionKeys.nonpositive#888888##%%%r c"ddlm}|S)Nr)NonNegativePredicate)rVrn)rrns r nonnegativezAssumptionKeys.nonnegativerlr c"ddlm}|S)Nr)ExtendedNonZeroPredicate)rVrq)rrqs rextended_nonzerozAssumptionKeys.extended_nonzeros#<<<<<<'')))r c"ddlm}|S)Nr)ExtendedNonPositivePredicate)rVrt)rrts rextended_nonpositivez#AssumptionKeys.extended_nonpositive#@@@@@@++---r c"ddlm}|S)Nr)ExtendedNonNegativePredicate)rVrx)rrxs rextended_nonnegativez#AssumptionKeys.extended_nonnegativervr c"ddlm}|S)Nr) EvenPredicate)handlers.ntheoryr{)rr{s revenzAssumptionKeys.evens 333333}r c"ddlm}|S)Nr) OddPredicate)r|r)rrs roddzAssumptionKeys.odds 222222|~~r c"ddlm}|S)Nr)PrimePredicate)r|r)rrs rprimezAssumptionKeys.primes"444444~r c"ddlm}|S)Nr)CompositePredicate)r|r)rrs r compositezAssumptionKeys.composites#888888!!###r c"ddlm}|S)Nr)CommutativePredicate)handlers.commonr)rrs r commutativezAssumptionKeys.commutatives#999999##%%%r c"ddlm}|S)Nr)IsTruePredicate)rr)rrs ris_truezAssumptionKeys.is_trues"444444   r c"ddlm}|S)Nr)SymmetricPredicate)handlers.matricesr)rrs r symmetriczAssumptionKeys.symmetrics#999999!!###r c"ddlm}|S)Nr)InvertiblePredicate)rr)rrs r invertiblezAssumptionKeys.invertible#::::::""$$$r c"ddlm}|S)Nr)OrthogonalPredicate)rr)rrs r orthogonalzAssumptionKeys.orthogonalrr c"ddlm}|S)Nr)UnitaryPredicate)rr)rrs runitaryzAssumptionKeys.unitarys#777777!!!r c"ddlm}|S)Nr)PositiveDefinitePredicate)rr)rrs rpositive_definitez AssumptionKeys.positive_definiterPr c"ddlm}|S)Nr)UpperTriangularPredicate)rr)rrs rupper_triangularzAssumptionKeys.upper_triangular#??????'')))r c"ddlm}|S)Nr)LowerTriangularPredicate)rr)rrs rlower_triangularzAssumptionKeys.lower_triangularrr c"ddlm}|S)Nr)DiagonalPredicate)rr)rrs rdiagonalzAssumptionKeys.diagonalrLr c"ddlm}|S)Nr)FullRankPredicate)rr)rrs rfullrankzAssumptionKeys.fullrankrLr c"ddlm}|S)Nr)SquarePredicate)rr)rrs rsquarezAssumptionKeys.squarerHr c"ddlm}|S)Nr)IntegerElementsPredicate)rr)rrs rinteger_elementszAssumptionKeys.integer_elementsrr c"ddlm}|S)Nr)RealElementsPredicate)rr)rrs r real_elementszAssumptionKeys.real_elementss#<<<<<<$$&&&r c"ddlm}|S)Nr)ComplexElementsPredicate)rr)rrs rcomplex_elementszAssumptionKeys.complex_elementsrr c"ddlm}|S)Nr)SingularPredicate)predicates.matricesr)rrs rsingularzAssumptionKeys.singulars#::::::  """r c"ddlm}|S)Nr)NormalPredicate)rr)rrs rnormalzAssumptionKeys.normal s"888888   r c"ddlm}|S)Nr)TriangularPredicate)rr)rrs r triangularzAssumptionKeys.triangulars#<<<<<<""$$$r c"ddlm}|S)Nr)UnitTriangularPredicate)rr)rrs runit_triangularzAssumptionKeys.unit_triangulars#@@@@@@&&(((r c"ddlm}|S)Nr)EqualityPredicate)relation.equalityr)rrs reqzAssumptionKeys.eqrLr c"ddlm}|S)Nr)UnequalityPredicate)rr)rrs rnezAssumptionKeys.nerr c"ddlm}|S)Nr)StrictGreaterThanPredicate)rr)rrs rgtzAssumptionKeys.gt$s#AAAAAA))+++r c"ddlm}|S)Nr)GreaterThanPredicate)rr)rrs rgezAssumptionKeys.ge)s#;;;;;;##%%%r c"ddlm}|S)Nr)StrictLessThanPredicate)rr)rrs rltzAssumptionKeys.lt.s#>>>>>>&&(((r c"ddlm}|S)Nr)LessThanPredicate)rr)rrs rlezAssumptionKeys.le3rLr N)=__name__ __module__ __qualname____doc__rrr#r&r)r,r/r3r7r:r=r@rCrGrKrOrSrWr[r^rarerhrkrorrruryr}rrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrs>$$$((('''$$$"""$$$)))"""%%%###%%%!!!###++++++######++++++"""&&&&&&***......   $$$&&&!!!$$$%%%%%%"""+++******######!!!***'''***###!!!%%%)))###%%%,,,&&&)))#####r rct}|jD]}g}|D]}}t|jtr`t |jjdkrC|jj|vr3|t|jj |j zn&n$|r"| t|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 isinstancelitrlen argumentsargappendrfunctionis_Notadd frozensetr)assumpexprsfactsclauseargsliterals r_extract_all_factsr;s< EEE.++ + +G'+'788 SAV=W=W[\=\=\;?e++KK (>> 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).sympy.assumptions.sataskrsympy.assumptions.lra_sataskr!sympy.logic.algorithms.lra_theoryrr rrkindr TypeErrorr Qrr rr rrrrrrrrrrfunctyperrr from_propextendrget_all_known_factsrfrom_cnf add_from_cnfrr ValueError_ask_single_fact _eval_askbool) propositionrrrrr binrelpredskeyr assump_cnf local_factsknown_facts_cnfenc_cnfress raskrost0/////777777@@@@@@+&&K+&&K+y))J[-=[-P-PHIII+y))J[-=[-P-PHIIIqtRr14QT2qtRNK+/00.(+*?T  [ ( ([ 1 12K4DTI ~T{++Jg%Z66K*++OllG S))*** %%%F{733u<<6DEEE 3 , ,C   #t*  { + +C Cyy &+w G G GC  j+wOOO tt JsI++I43I4c|jrt}t|jdkr`|j\}t|dkrD|\}||d}||dn t }|jr |j|vrdS|jD]S}t|dkr>|\}|js||jdnd}|@|\}}||vrdS||vrdSTdS)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) r r known_facts_dictclf prop_factsprop_reqrprop_rejs rrrs f!/11 {" # #q ( (%CB2ww!||-11#t<< ,6,B:a==8! 1 1 5!) ! !F6{{aFGhX-11!%>>>TX %%/"((??44H__ 55 4r ctdddt|tr |jj}t t |d}|||dStt |t||gdS)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-askhandlerdeprecated_since_versionactive_deprecations_targetN)handlers)rrrnamegetattrr add_handlersetattr)r handlerQkeys rregister_handlerr'Ys "'#: #y!!hm 1c4 D  !!!!!3 # :::;;;;;r ctdddt|tr |jj}t t 5t t||ddddS#1swxYwYdS)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) rrrr!rrr"rremove_handler)r r%s rr)r)ss "'#: #y!!hm 0 1 1003&&w///000000000000000000s)A>>BB)rrN)&rsympy.assumptions.assumerrrsympy.assumptions.cnfrrr sympy.corer sympy.core.kindr sympy.core.relationalr r r rrrsympy.logic.inferencersympy.utilities.decoratorrsympy.utilities.exceptionsrrrrrrrrr'r)sympy.assumptions.ask_generatedrrrr rr3s::::::::::::''''''8888888888888888------6666669999999999a#a#a#a#a#a#a#a#H N111h"&/ATTTTnPPPf<<<4000.r