EddZddlmZddlmZddlmZddlmZddl m Z m Z m Z m Z mZmZddlmZedZedd Zd Zed Zd ZdZd S)z Known facts in assumptions module. This module defines the facts between unary predicates in ``get_known_facts()``, and supports functions to generate the contents in ``sympy.assumptions.ask_generated`` file. )Q)AppliedPredicate)cacheit)Symbol)to_cnfAndNotImplies Equivalent Exclusive) satisfiablectjtjtjztjztjtjtjztjtjtjztj tjtjztj tjtjztj tj tjztjztjztj ztjtjtj ztjtjtj ztjtj tjztjztj ztjtj tjztjztjtjtjztj ztjtjtjzi SN)rrealnegativezeropositiveintegerevenodd nonpositivenonzero nonnegative extended_realnegative_infinitepositive_infiniteextended_positiveextended_negativeextended_nonzeroextended_nonpositiveextended_nonnegativecomplex algebraictranscendental7lib/python3.11/site-packages/sympy/assumptions/facts.pyget_composite_predicatesr(s af$qz1 AFQUN  QV+ AJ+ + !- :QVCajPSTSff QZ!*== QZ!*== A/!*><  !,q//1:a==11<   1 q{1~~..<  !&))QU1XX&&!< "  ! ajmm,,#< $ q 16!99%%%< & !+a..!'!**--'< (  A+QYq\\AJqMM-IJJ)< * q AJqMM)QWQZZK7QHH+< 0 q 1;q>>**1< 2  A 2 2333< 4 q 1;q>>AOA,>,>>??5< : !*Q--!--;< <  ! ahqkk**=< > #A&&)>E< J  Q!4Q!7!788K< L  Q1..M< N  ! qq1111<??CCO< P  ! ahqkk**Q< R  ! al1oo..S< T  QXa[[))U< V  1 qx{{++W< X #A&& Q88Y< Z  1 q1!4455[< \  1 q1!4455]< ^ "1%%q|A77_< ` "1%%q|A77a< b  Q!3A!6!69KA9N9N!NOOc< d "1%%(:1(=(==qz!}}MMe< f  1 q{1~~..g< h !!$$al1oo66i< j  QA//k< l  Q!--m< n  A ,,o< p  1  +Q\!__==q< r 1<??QZ]]N33s< t "1%%qq'9'9::u< v ""A$6q$9$9::w< < < Dz Kr&ct|}t||}i}|D]\}}t}t}|D]n} t | t r|| j2t | tr'| j d} || jo||f||j<|S)a Computes and returns a dictionary which contains the relations between unary predicates. Each key is a predicate, and item is two groups of predicates. First group contains the predicates which are implied by the key, and second group contains the predicates which are rejected by the key. All predicates in *keys* and *fact* must be unary and have same placeholder symbol. Parameters ========== keys : list of AppliedPredicate instances. fact : Fact between predicates in conjugated normal form. Examples ======== >>> from sympy import Q, And, Implies >>> from sympy.assumptions.facts import generate_known_facts_dict >>> from sympy.abc import x >>> keys = [Q.even(x), Q.odd(x), Q.zero(x)] >>> fact = And(Implies(Q.even(x), ~Q.odd(x)), ... Implies(Q.zero(x), Q.even(x))) >>> generate_known_facts_dict(keys, fact) {Q.even: ({Q.even}, {Q.odd}), Q.odd: ({Q.odd}, {Q.even, Q.zero}), Q.zero: ({Q.even, Q.zero}, {Q.odd})} r) rsingle_fact_lookupitemsset isinstanceraddfunctionr args) keysrFfact_cnfmappingretkeyvalueimpliedrejectedexprpreds r'generate_known_facts_dictrZzsBd||H x00G Cmmoo 0 0 U%%55 , ,D$ 011 , DM****D#&& ,y| T]+++$h/CL Jr&ct}tjtjtjtjtjtjfD]}||g}tj j D]G}| drtt|}||vr2| |H|S)z Return every unary predicates registered to ``Q``. This function is used to generate the keys for ``generate_known_facts_dict``. __)rKreqnegtltgelerM __class____dict__ startswithgetattrappend)excluderYresultattrs r'get_known_facts_keysrkseeGqtQT14qt4 D F $ ??4   q$ 7?   d Mr&ci}|D]m}|h||<|D]b}||krZt|||r|||t|||r|||cn|Sr)ask_full_inferencerM)known_facts_keysknown_facts_cnfrRrT other_keys r'rIrIsG11u ) 1 1IC 1%ioFF0CL$$Y///%yj#GG1CL$$iZ000  1 Nr&c tt|||sdStt||t|sdSdS)z9 Method for inferring properties about objects. FTN)r rr ) proposition assumptionsros r'rmrmsS s?KEE F Fu s?K[9I9IJJ K Kt 4r&r)__doc__sympy.assumptions.askrsympy.assumptions.assumersympy.core.cachersympy.core.symbolrsympy.logic.boolalgrrr r r r sympy.logic.inferencer r(rGrZrkrIrmr%r&r'r{sN$#####555555$$$$$$$$$$$$------  & PPP Pf///d  0        r&