a >> 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 Z from_propextendget_all_relevant_facts add_from_cnfcheck_satisfiability) proposition assumptionscontextr r propsZ_propsZ context_cnfsatrh/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/assumptions/satask.pysatasks2      rcCsl|}|}||||t|}t|}|r@|r@dS|rL|sLdS|sX|rXdS|sh|shtddS)NTFzInconsistent assumptions)copyrr ValueError)propZ_propZfactbaseZsat_trueZ sat_falseZ can_be_trueZ can_be_falserrrrSs  rNc st||}t}|r&||O}|r6||O}|tjtjh}d}|tkrt}|D]"}t|}|@tkr^||O}q^|}|OqJ|fdd|DO}t} |D](} t| tr| t| jO} q| | q| S)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)} Ncs"h|]}t|@tkr|qSr) find_symbolsset).0lZreq_keysrr z#extract_predargs..) rall_predicatesrrtruefalse isinstancer argumentsadd) rrrkeysZlkeysZtmp_keystmpr Zsymsexprskeyrr!rextract_predargsks0       r.cCs8t|tr.t}|D]}|t|O}q|S|tS)z Find every :obj:`~.Symbol` in *pred*. Parameters ========== pred : sympy.assumptions.cnf.CNF, or any Expr. )r'r rr$rZatomsr)predsymbolsarrrrs  rcCsn|s t}t}|D]L}t|D]>}t|}||}|D]}t|tr@|t|jO}q@q q|||fS)a1 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 containig 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 rrZto_CNFZ_andr$r'rr()r,relevant_factsZnewexprsexprZfactZnewfactr-rrrget_relevant_clsfactssF     r4cs d}t}t}|dkr$t|||}||O}t||\}}|d7}||krLqT|sqTq|r t} | tt} | | ddfdd} g} g} t| j }t |D]4\}| fdd| j D7} | | | j ||7} qt t t| tdt| d}t| |}nt}|||S) al 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 rcSs|dkr||S||SdS)Nrr)Zlitdeltarrrtranslate_literalSsz1get_all_relevant_facts..translate_literalcsfdd|DS)Ncs g|]}fdd|DqS)csh|]}|qSrr)rir6r7rrr"Zr#zLget_all_relevant_facts..translate_data...r)rZclauser9rr Zr#zBget_all_relevant_facts..translate_data..r)datar6)r7)r6rtranslate_dataYsz.get_all_relevant_facts..translate_datacsg|] }|qSrr)rr/)r3rrr:_r#z*get_all_relevant_facts..)r rr.r4Z add_clausesrr Zfrom_cnflenr0 enumerater;dictlistzipranger)rrrr r r8r2Z all_exprsr,Zknown_facts_CNFZ kf_encodedr<r;r0Zn_litencodingctxr)r3r7rr s<4        r)NN)N)__doc__Zsympy.core.singletonrZsympy.core.symbolrZsympy.assumptions.ask_generatedrZsympy.assumptions.assumerrZsympy.assumptions.sathandlersrZ sympy.corerZsympy.logic.inferencer Zsympy.assumptions.cnfr r rrr.rr4rrrrrs"       D 9 V