+ i-Rt^RIHt^RIHt^RIHtHt^RIH t H t ^RI H t H t ^RIHt^RIHt^RIHt^R IHtHt^R IHtR ] R ]3R ltR tRRltRtRRltR ]3RltR#)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) MatrixKindTcV\P!V4p\P!V(4p\P!V4p\4pV'dVPV4p\WQVW4R7pVP V4V'dVP V4\ WVV4#)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 &&&&& V/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/assumptions/satask.pysataskr sd MM+ &E ]]K< (F-- ,K%K!((1 [' @C[! % s 33c\VP4pVP4pVPV4VPV4\V4p\V4pV'd V'dR#V'd V'gR#V'g V'dR#V'gV'g \R4hR#R#)NTFzInconsistent assumptions)copyrr ValueError)prop_propfactbasesat_true sat_false can_be_true can_be_falses&&& rrrUsz}}H I $ 5!h'Ky)L|< < |344 ,;r!Nc\V4pVP4p\4pV'dWQP4,pV'dWRP4,pV\P\P 0, pRpV\48wdP\4pVF-p\V4p W,\48wgK%Wy,pK/ Ws, pW6,pK^YEUu0uF&p\V4V,\48wgK$VkK( up,p\4p VFHp \ V \4'dV \V P4,p K7V PV 4KJ V #uupi)a Extract every expression in the argument of predicates from *proposition*, *assumptions* and *context*. Parameters ========== proposition : sympy.assumptions.cnf.CNF assumptions : sympy.assumptions.cnf.CNF, optional. context : sympy.assumptions.cnf.CNF, optional. CNF generated from assumptions context. Examples ======== >>> from sympy import Q, Abs >>> from sympy.assumptions.cnf import CNF >>> from sympy.assumptions.satask import extract_predargs >>> from sympy.abc import x, y >>> props = CNF.from_prop(Q.zero(Abs(x*y))) >>> assump = CNF.from_prop(Q.zero(x) & Q.zero(y)) >>> extract_predargs(props, assump) {x, y, Abs(x*y)} N) find_symbolsall_predicatessetrtruefalse isinstancer argumentsadd) rrrreq_keyskeyslkeystmp_keystmplsymsexprskeys &&& rextract_predargsr>ms&8K(H  % % 'D EE ++-- '')) QVVQWW% %EH ce eA?DCE) > E1a8!;su!DQQ EED EE c+ , , S' 'E IIcN  L Fs -!E<E<c\V\4'd6\4pVP4FpV\ V4,pK V#VP \ 4#)zo Find every :obj:`~.Symbol` in *pred*. Parameters ========== pred : sympy.assumptions.cnf.CNF, or any Expr. )r2r r/r.r-atomsr)predsymbolsas& rr-r-sM$%$$&A |A &G' ::f r!chV'g \4p\4pVFp\V4Fup\P!V4pVP V4pVP 4F7p\ V\4'gKV\VP4,pK9 Kw K W , V3#)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() ) r r/r to_CNF_andr.r2r r3)r<relevant_factsnewexprsexprfactnewfactr=s&& rget_relevant_clsfactsrLsL uH'-Djj&G+009N--/c#344CMM 22H0.  ^ ++r!c *a^p\4p\4pV^8Xd \WV4pVX,p\W4wrV^, pWT8dM V'dKDV'Ed\4p \;QJdRV4F 'gK RM RM !RV44'dV P \ 44\;QJdRV4F 'gK RM RM !RV44'dV P \44\4p V PV 4RoV3Rlp .p .p \V P4p\V4FLwr_YPUu.uF pV!V4NK up, p W!V PW^,4, p KN \\\!V \#^\V 4^,4444p\V V4pM \4pVP%V4V#uupi)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 Tc3X"TF qP\\48HxK" R#5iN)kindrr.0rIs& r )get_all_relevant_facts..RsIytyyJz22ys(*Fc3|"TF2qP\8H;'gVP\8HxK4 R#5irO)rPrrrQs& rrSrTUs-aW`tj(IIdii=.HIW`s<<c0V^8d W,#W, #))litdeltas&&rtranslate_literal1get_all_relevant_facts..translate_literal[sQw{"{"r!c l<VUUu.uFq"Uu0uF pS!W14kK upNK upp#uupiuuppirOrX)datarZclauseir[s&& rtranslate_data.get_all_relevant_facts..translate_dataas5PTUPTf&A&Q&q0&APTU UAUs0+ 00)r r/r>rLany add_clausesrrrfrom_cnflenrB enumerater^dictlistzipranger)rrrrrr`rG all_exprsr<known_facts_CNF kf_encodedrar^rBn_litrIrAencodingctxr[s&&&&& @rrr sh AUNI  6$[wGEU 5e L Q ? u % 3IyI333IyI I I  ' '(B(D E 3aW`a333aW`a a a  ' '(B(D E\ O, #  VJ&&' +GA /A/AB/AtT /AB BG N:??AI> >D,S%3w<>*BCDEx(l^$ JCs1H)NNrO)__doc__sympy.core.singletonrsympy.core.symbolrsympy.core.kindrrsympy.assumptions.ask_generatedrrsympy.assumptions.assumerr sympy.assumptions.sathandlersr sympy.corer sympy.logic.inferencer sympy.assumptions.cnfr rsympy.matrices.kindrr rr>r-rLrrXr!rr}sb#$5bI=-1*%)2DA4H507r$R,ldr!