MZddZddlmZddlmZddlmZddlmZddl m Z m Z m Z m Z mZmZddlmZedZedd Zd Zed Zd ZdZy )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) satisfiablec~tjtjtjztjztj tj tjztjtjtjztjtjtjztjtjtjztjtjtjztjztjztjztjtjtjztjtjtjztj tjtjztjztjztj"tjtjztjztj$tjtjztjztj&tj(tj*zi SN)rrealnegativezeropositiveintegerevenodd nonpositivenonzero nonnegative extended_realnegative_infinitepositive_infiniteextended_positiveextended_negativeextended_nonzeroextended_nonpositiveextended_nonnegativecomplex algebraictranscendental9/usr/lib/python3/dist-packages/sympy/assumptions/facts.pyget_composite_predicatesr(sz aff$qzz1 AFFQUUN  QVV+ AJJ+ + !-- :QVVCajjPSTSfSff QZZ!*=*== QZZ!*=*== A//!**|ztj8|ttj<|tj@|ttj<|tjB|ttj@|tjD|ttjF|tj@|ttj:|tjB|ttjF|tjH|ttjF|tjJ|ttjJ|tjL|ttjH|tjL|ttjL|tjH|tjJ|zttjH|tjJ|ztjF|ttjF|tjN|ttjP|tjL|ttjB|tjR|ttjB|tjD|ttjN|tjD|ttjR|tjD|ztjB|ttjB|tjT|ttjV|tj>|ttj>|tjX|}|S)z Facts between unary predicates. Parameters ========== x : Symbol, optional Placeholder symbol for unary facts. Default is ``Symbol('x')``. Returns ======= fact : Known facts in conjugated normal form. x)-rrr rrrrrrr imaginaryr r"r$r#r rational irrationalrrr compositeprime hermitian antihermitianinfinitefinite commutative orthogonalpositive_definiteunitary real_elementsnormal invertiblesquarediagonalupper_triangularlower_triangular triangular symmetricunit_triangularfullranksingularinteger_elementscomplex_elements)r*facts r'get_known_factsrG&s" y 3K < !%%a(!**Q- JJqM1..q1 3<  !&&)Q[[^, <  q AKKN*AIIaL9<  !""1%q{{1~6<  166!9ajjmall1o=><  !,,q/1::a=1<   1 q{{1~.<  !&&)QUU1X&!< "  ! ajjm,#< $ q 166!9%%< & !++a.!''!*-'< (  A+QYYq\AJJqM-IJ)< * q AJJqM)QWWQZK7QH+< 0 q 1;;q>*1< 2  A 233< 4 q 1;;q>AOOA,>>?5< : !**Q-!-;< <  ! ahhqk*=< > ##A&)<)E< J  Q!4!4Q!78K< L  Q1.M< N  ! qq111<<?CO< P  ! ahhqk*Q< R  ! all1o.S< T  QXXa[)U< V  1 qxx{+W< X ##A& Q8Y< Z  1 q11!45[< \  1 q11!45]< ^ ""1%q||A7_< ` ""1%q||A7a< b  Q!3!3A!69K9KA9N!NOc< d ""1%(:(:1(==qzz!}Me< f  1 q{{1~.g< h !!!$all1o6i< j  QA/k< l  Q!-m< n  A ,o< p  1  +Q\\!_=q< r 1<<?QZZ]N3s< t ""1%qq'9:u< v "A$6$6q$9:w< Dz Kr&ct|}t||}i}|jD]\}}t}t}|D]i} t | t r|j | j/t | ts@| jd} |j | jk||f||j<|S)a Computes and returns a dictionary which contains the relations between unary predicates. Each key is a predicate, and item is two groups of predicates. First group contains the predicates which are implied by the key, and second group contains the predicates which are rejected by the key. All predicates in *keys* and *fact* must be unary and have same placeholder symbol. Parameters ========== keys : list of AppliedPredicate instances. fact : Fact between predicates in conjugated normal form. Examples ======== >>> from sympy import Q, And, Implies >>> from sympy.assumptions.facts import generate_known_facts_dict >>> from sympy.abc import x >>> keys = [Q.even(x), Q.odd(x), Q.zero(x)] >>> fact = And(Implies(Q.even(x), ~Q.odd(x)), ... Implies(Q.zero(x), Q.even(x))) >>> generate_known_facts_dict(keys, fact) {Q.even: ({Q.even}, {Q.odd}), Q.odd: ({Q.odd}, {Q.even, Q.zero}), Q.zero: ({Q.even, Q.zero}, {Q.odd})} r) rsingle_fact_lookupitemsset isinstanceraddfunctionr args) keysrFfact_cnfmappingretkeyvalueimpliedrejectedexprpreds r'generate_known_facts_dictrZzsBd|H x0G Cmmo 0 U%5 ,D$ 01 DMM*D#&yy| T]]+  , %h/CLL 0 Jr&ct}tjtjtjtj tj tjfD]}|j|g}tjjD]:}|jdrtt|}||vr*|j|<|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_keysrkseGqttQTT144qtt4 DF $$ ??4 q$ 7?  d  Mr&ci}|D]Z}|h||<|D]M}||k7s t|||r||j|t|||s9||j|O\|Sr)ask_full_inferencerM)known_facts_keysknown_facts_cnfrRrT other_keys r'rIrIsG1u ) 1IC%ioFCL$$Y/%yj#GCL$$iZ0  11 Nr&c rtt|||sytt||t|syy)z9 Method for inferring properties about objects. FTN)r rr ) proposition assumptionsros r'rmrms4 s?KE F s?K[9IJ K r&r)__doc__sympy.assumptions.askrsympy.assumptions.assumersympy.core.cachersympy.core.symbolrsympy.logic.boolalgrrr r r r sympy.logic.inferencer r(rGrZrkrIrmr%r&r'r{st$5$$-  & P Pf/d  0  r&