\h-SrSSKJr SSKJr SSKJrJr SSKJ r J r SSK J r J r SSKJr SSKJr SS KJr SS KJrJr SS KJr S \ S \4S jrSrSSjrSrSSjrS \4Sjrg)zJ Module to evaluate the proposition with assumptions using SAT algorithm. )S)Symbol) NumberKind UndefinedKind)get_all_known_matrix_factsget_all_known_number_facts)global_assumptionsAppliedPredicate)class_fact_registry)oo) satisfiable)CNF EncodedCNF) MatrixKindTcL[R"U5n[R"U)5n[R"U5n[5nU(aURU5n[XQUX4S9nUR U5 U(aUR U5 [ XVU5$)a Function to evaluate the proposition with assumptions using SAT algorithm. This function extracts every fact relevant to the expressions composing proposition and assumptions. For example, if a predicate containing ``Abs(x)`` is proposed, then ``Q.zero(Abs(x)) | Q.positive(Abs(x))`` will be found and passed to SAT solver because ``Q.nonnegative`` is registered as a fact for ``Abs``. Proposition is evaluated to ``True`` or ``False`` if the truth value can be determined. If not, ``None`` is returned. Parameters ========== proposition : Any boolean expression. Proposition which will be evaluated to boolean value. 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. use_known_facts : bool, optional. If ``True``, facts from ``sympy.assumptions.ask_generated`` module are passed to SAT solver as well. iterations : int, optional. Number of times that relevant facts are recursively extracted. Default is infinite times until no new fact is found. Returns ======= ``True``, ``False``, or ``None`` Examples ======== >>> from sympy import Abs, Q >>> from sympy.assumptions.satask import satask >>> from sympy.abc import x >>> satask(Q.zero(Abs(x)), Q.zero(x)) True )use_known_facts iterations)r from_propextendget_all_relevant_facts add_from_cnfcheck_satisfiability) proposition assumptionscontextrrprops_props context_cnfsats P/var/www/auris/envauris/lib/python3.13/site-packages/sympy/assumptions/satask.pysataskr!sd MM+ &E ]]K< (F-- ,K%K!((1 [' @C[! % s 33cBUR5nUR5nURU5 URU5 [U5n[U5nU(aU(agU(aU(dgU(dU(agU(dU(d [S5egg)NTFzInconsistent assumptions)copyrr ValueError)prop_propfactbasesat_true sat_false can_be_true can_be_falses r rrUsz}}H I $ 5!h'Ky)L|< < |344 ,;r"Nc[U5nUR5n[5nU(aXQR5-nU(aXRR5-nU[R[R 1- nSnU[5:waL[5nUH$n[U5n X-[5:wdM Xy-nM& Xs- nX6-nU[5:waMLXEVs1sH!n[U5U-[5:wdMUiM# sn-n[5n UHCn [ U [5(aU [U R5-n M2U RU 5 ME U $s snf)a Extract every expression in the argument of predicates from *proposition*, *assumptions* and *context*. Parameters ========== proposition : sympy.assumptions.cnf.CNF assumptions : sympy.assumptions.cnf.CNF, optional. context : sympy.assumptions.cnf.CNF, optional. CNF generated from assumptions context. Examples ======== >>> from sympy import Q, Abs >>> from sympy.assumptions.cnf import CNF >>> from sympy.assumptions.satask import extract_predargs >>> from sympy.abc import x, y >>> props = CNF.from_prop(Q.zero(Abs(x*y))) >>> assump = CNF.from_prop(Q.zero(x) & Q.zero(y)) >>> extract_predargs(props, assump) {x, y, Abs(x*y)} N) find_symbolsall_predicatessetrtruefalse isinstancer argumentsadd) rrrreq_keyskeyslkeystmp_keystmplsymsexprskeys r extract_predargsr?ms28K(H  % % 'D EE ++-- '')) QVVQWW% %EH ce eA?DCE) > ce   E1a8!;su!DQ EED EE c+ , , S' 'E IIcN  L Fs E=Ec[U[5(a1[5nUR5HnU[ U5-nM U$UR [ 5$)zo Find every :obj:`~.Symbol` in *pred*. Parameters ========== pred : sympy.assumptions.cnf.CNF, or any Expr. )r3rr0r/r.atomsr)predsymbolsas r r.r.sM$%$$&A |A &G' ::f r"cTU(d [5n[5nUHn[U5Hpn[R"U5nUR U5nUR 5H2n[ U[5(dMU[UR5-nM4 Mr M X - U4$)a^ Extract relevant facts from the items in *exprs*. Facts are defined in ``assumptions.sathandlers`` module. This function is recursively called by ``get_all_relevant_facts()``. Parameters ========== exprs : set Expressions whose relevant facts are searched. relevant_facts : sympy.assumptions.cnf.CNF, optional. Pre-discovered relevant facts. Returns ======= exprs : set Candidates for next relevant fact searching. relevant_facts : sympy.assumptions.cnf.CNF Updated relevant facts. Examples ======== Here, we will see how facts relevant to ``Abs(x*y)`` are recursively extracted. On the first run, set containing the expression is passed without pre-discovered relevant facts. The result is a set containing candidates for next run, and ``CNF()`` instance containing facts which are relevant to ``Abs`` and its argument. >>> from sympy import Abs >>> from sympy.assumptions.satask import get_relevant_clsfacts >>> from sympy.abc import x, y >>> exprs = {Abs(x*y)} >>> exprs, facts = get_relevant_clsfacts(exprs) >>> exprs {x*y} >>> facts.clauses #doctest: +SKIP {frozenset({Literal(Q.odd(Abs(x*y)), False), Literal(Q.odd(x*y), True)}), frozenset({Literal(Q.zero(Abs(x*y)), False), Literal(Q.zero(x*y), True)}), frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.even(x*y), True)}), frozenset({Literal(Q.zero(Abs(x*y)), True), Literal(Q.zero(x*y), False)}), frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.odd(Abs(x*y)), False), Literal(Q.odd(x*y), True)}), frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.even(x*y), True), Literal(Q.odd(Abs(x*y)), False)}), frozenset({Literal(Q.positive(Abs(x*y)), False), Literal(Q.zero(Abs(x*y)), False)})} We pass the first run's results to the second run, and get the expressions for next run and updated facts. >>> exprs, facts = get_relevant_clsfacts(exprs, relevant_facts=facts) >>> exprs {x, y} On final run, no more candidate is returned thus we know that all relevant facts are successfully retrieved. >>> exprs, facts = get_relevant_clsfacts(exprs, relevant_facts=facts) >>> exprs set() ) rr0r to_CNF_andr/r3r r4)r=relevant_factsnewexprsexprfactnewfactr>s r get_relevant_clsfactsrMsL uH'-Djj&G+009N--/c#344CMM 22H0.  ^ ++r"c h^Sn[5n[5nUS:Xa [XU5nUW-n[X5upUS- nXT:aO U(dOM9U(Ga8[5n [ SU55(aU R [ 55 [ SU55(aU R [55 [5n U RU 5 SmU4Sjn /n /n [U R5n[U5HAup_XRVs/sH nU"U5PM sn- n X"U RX^-5- n MC [[[!U [#S[U 5S-5555n[U U5nO [5nUR%U5 U$s snf)a Extract all relevant facts from *proposition* and *assumptions*. This function extracts the facts by recursively calling ``get_relevant_clsfacts()``. Extracted facts are converted to ``EncodedCNF`` and returned. Parameters ========== proposition : sympy.assumptions.cnf.CNF CNF generated from proposition expression. assumptions : sympy.assumptions.cnf.CNF CNF generated from assumption expression. context : sympy.assumptions.cnf.CNF CNF generated from assumptions context. use_known_facts : bool, optional. If ``True``, facts from ``sympy.assumptions.ask_generated`` module are encoded as well. iterations : int, optional. Number of times that relevant facts are recursively extracted. Default is infinite times until no new fact is found. Returns ======= sympy.assumptions.cnf.EncodedCNF Examples ======== >>> from sympy import Q >>> from sympy.assumptions.cnf import CNF >>> from sympy.assumptions.satask import get_all_relevant_facts >>> from sympy.abc import x, y >>> props = CNF.from_prop(Q.nonzero(x*y)) >>> assump = CNF.from_prop(Q.nonzero(x)) >>> context = CNF.from_prop(Q.nonzero(y)) >>> get_all_relevant_facts(props, assump, context) #doctest: +SKIP rc3X# UH oR[[5:Hv M" g7fN)kindrr.0rJs r )get_all_relevant_facts..RsIytyyJz22ys(*c3z# UH1oR[:H=(d UR[:Hv M3 g7frQ)rRrrrSs r rUrVUs*aW`tj(Idii=.HIW`s9;cUS:aX-$X- $)Nr)litdeltas r translate_literal1get_all_relevant_facts..translate_literal[sQw{"{"r"c p>UVVs/sHo"Vs1sH nT"X15iM snPM snn$s snfs snnfrQrY)datar[clauseir\s r translate_data.get_all_relevant_facts..translate_dataas5PTUPTf&A&Q&q0&APTU UAUs 2- 22)rr0r?rMany add_clausesrrrfrom_cnflenrC enumerater_dictlistzipranger)rrrrrrarH all_exprsr=known_facts_CNF kf_encodedrbr_rCn_litrJrBencodingctxr\s @r rr sh AUNI  6$[wGEU 5e L Q ?   % IyI I I  ' '(B(D E aW`a a a  ' '(B(D E\ O, #  VJ&&' +GA /A/AB/AtT /AB BG N:??AI> >D,S%3w<>*BCDEx(l^$ JCsF/)NNrQ)__doc__sympy.core.singletonrsympy.core.symbolrsympy.core.kindrrsympy.assumptions.ask_generatedrrsympy.assumptions.assumer r sympy.assumptions.sathandlersr sympy.corer sympy.logic.inferencer sympy.assumptions.cnfrrsympy.matrices.kindrr!rr?r.rMrrYr"r r~sb#$5bI=-1*%)2DA4H507r$R,ldr"