o jgÇ ã@s¾dZddlmZddlmZddlmZddlmZddl m Z m Z m Z m Z mZmZddlmZedd „ƒZedd d „ƒZedd d„ƒZeddd„ƒZdd„Zedd„ƒZdd„Zdd„Zd S)zÓ 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. é)ÚQ)ÚAppliedPredicate)Úcacheit)ÚSymbol)Úto_cnfÚAndÚNotÚImpliesÚ EquivalentÚ Exclusive)Ú satisfiablecCsÜtjtjtjBtjBtjtjtjBtjtjtjBtj tjtjBtj tjtjBtj tj tjBtjBtjBtj Btjtjtj Btjtjtj Btjtj tjBtjBtj Btjtj tjBtjBtjtjtjBtj BtjtjtjBi S©N)rÚrealÚnegativeÚzeroÚpositiveÚintegerÚevenÚoddÚ nonpositiveÚnonzeroÚ nonnegativeÚ extended_realÚnegative_infiniteÚpositive_infiniteÚextended_positiveÚextended_negativeÚextended_nonzeroÚextended_nonpositiveÚextended_nonnegativeÚcomplexÚ algebraicÚtranscendental©r#r#úO/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/assumptions/facts.pyÚget_composite_predicatess ôr%NcCs&|durtdƒ}tt|ƒt|ƒƒ}|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. NÚx)rrÚget_number_factsÚget_matrix_facts©r&Úfactr#r#r$Úget_known_facts&sþr+cCs|durtdƒ}ttt |¡t |¡t |¡t |¡t |¡ƒtt  |¡t  |¡ƒt t  |¡t  |¡Bt  |¡ƒtt  |¡t |¡ƒtt  |¡t |¡t |¡Bƒtt |¡t |¡ƒt t |¡t |¡ƒtt |¡t |¡ƒt t |¡t |¡ƒt t |¡t |¡ƒtt |¡t |¡ƒt t |¡t |¡Bt |¡t |¡@ƒt t |¡t |¡@t |¡@t |¡ƒt t  |¡t |¡ƒt t  |¡t |¡ƒt t |¡t |¡t |¡Bƒtt |¡t |¡ƒt t  |¡t |¡ƒt t |¡t |¡Bt |¡ƒt t |¡t |¡Bt |¡ƒƒ}|S)zþ Facts between unary number predicates. Parameters ========== x : Symbol, optional Placeholder symbol for unary facts. Default is ``Symbol('x')``. Returns ======= fact : Known facts in conjugated normal form. Nr&)rrr rrrrrrrÚ imaginaryr r r"r!r ÚrationalÚ irrationalrrrÚ compositeÚprimeÚ hermitianÚ antihermitianÚinfiniteÚfiniteÚ commutativer)r#r#r$r'As6ÿ(*Þ$r'cCs|durtdƒ}ttt |¡t |¡ƒtt |¡t |¡ƒtt |¡t |¡@t |¡ƒtt |¡t |¡ƒtt |¡t  |¡ƒtt |¡t  |¡ƒtt  |¡t |¡ƒtt |¡t  |¡ƒtt  |¡t  |¡ƒtt  |¡t  |¡ƒtt  |¡t |¡ƒtt  |¡t |¡ƒtt |¡t  |¡t  |¡Bƒtt  |¡t  |¡@t  |¡ƒtt  |¡t |¡ƒtt |¡t |¡ƒtt  |¡t |¡ƒtt  |¡t  |¡ƒtt |¡t  |¡ƒtt |¡t  |¡@t  |¡ƒtt  |¡t |¡ƒtt |¡t |¡ƒtt |¡t |¡ƒƒ}|S)zþ Facts between unary matrix predicates. Parameters ========== x : Symbol, optional Placeholder symbol for unary facts. Default is ``Symbol('x')``. Returns ======= fact : Known facts in conjugated normal form. Nr&)rrr rÚ orthogonalÚpositive_definiteÚunitaryÚ real_elementsÚnormalÚ invertibleÚsquareÚdiagonalÚupper_triangularÚlower_triangularÚ triangularÚ symmetricÚunit_triangularÚfullrankr ÚsingularÚinteger_elementsÚcomplex_elementsr)r#r#r$r(|s8èr(c Csˆt|ƒ}t||ƒ}i}| ¡D]2\}}tƒ}tƒ}|D]} t| tƒr)| | j¡qt| tƒr9| j d} | | j¡q||f||j<q|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) rÚsingle_fact_lookupÚitemsÚsetÚ isinstancerÚaddÚfunctionrÚargs) Úkeysr*Úfact_cnfÚmappingÚretÚkeyÚvalueÚimpliedÚrejectedÚexprÚpredr#r#r$Úgenerate_known_facts_dict®s!     €rXcCs\tjtjtjtjtjtjh}g}tjjD]}|  d¡rqt t|ƒ}||vr&q|  |¡q|S)z” Return every unary predicates registered to ``Q``. This function is used to generate the keys for ``generate_known_facts_dict``. Ú__) rÚeqÚneÚgtÚltÚgeÚleÚ __class__Ú__dict__Ú startswithÚgetattrÚappend)ÚexcludeÚresultÚattrrWr#r#r$Úget_known_facts_keysàs     rhcCsfi}|D],}|h||<|D]"}||kr/t|||ƒr || |¡t|||ƒr/|| |¡q q|Sr )Úask_full_inferencerK)Úknown_facts_keysÚknown_facts_cnfrPrRÚ other_keyr#r#r$rG÷s  €ûrGcCs0tt|||ƒƒs dStt||t|ƒƒƒsdSdS)z9 Method for inferring properties about objects. FTN)r rr)Ú propositionÚ assumptionsrkr#r#r$ris rir )Ú__doc__Úsympy.assumptions.askrÚsympy.assumptions.assumerÚsympy.core.cacherÚsympy.core.symbolrÚsympy.logic.boolalgrrrr r r Úsympy.logic.inferencer r%r+r'r(rXrhrGrir#r#r#r$Ús(         : 12