a Эм>> from sympy import Q >>> from sympy.assumptions.cnf import Literal >>> from sympy.abc import x >>> Literal(Q.even(x)) Literal(Q.even(x), False) >>> Literal(~Q.even(x)) Literal(Q.even(x), True) FcsTt|tГr|jd}d}nt|tttfГr8|r4|S|StГа|б}||_||_ |S)NrT) ┌ isinstancer┌args┌AND┌ORr┌super┌__new__┌lit┌is_Not)┌clsrr┌objй┌ __class__й·e/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/assumptions/cnf.pyr&s zLiteral.__new__cCs|jSйNйrй┌selfr#r#r$┌arg1szLiteral.argcCsVt|jГr|а|б}n0z|jа|б}WntyD|jа|б}Yn0t|Г||jГSr%)┌callabler┌apply┌AttributeError┌rcall┌typer)r(┌exprrr#r#r$r-5s z Literal.rcallcCs|j}t|j|ГSr%)rrr)r(rr#r#r$┌ __invert__?szLiteral.__invert__cCsdаt|Гj|j|jбS)Nz {}({}, {}))┌formatr.┌__name__rrr'r#r#r$┌__str__CszLiteral.__str__cCs|j|jko|j|jkSr%)r)rйr(┌otherr#r#r$┌__eq__HszLiteral.__eq__cCstt|Гj|j|jfГ}|Sr%)┌hashr.r2r)r)r(┌hr#r#r$┌__hash__KszLiteral.__hash__)F)r2┌ __module__┌__qualname__┌__doc__r┌propertyr)r-r0r3┌__repr__r6r9┌ __classcell__r#r#r!r$rs rc@sPeZdZdZddДZeddДГZddДZdd ДZd dДZ dd ДZ ddДZeZdS)rz+ A low-level implementation for Or cGs ||_dSr%й┌_argsйr(rr#r#r$┌__init__TszOR.__init__cCst|jtdНSйN)┌keyй┌sortedrA┌strr'r#r#r$rWszOR.argscst|ГЗfddД|jDГОS)Ncsg|]}|аИбСqSr#йr-й┌.0r)йr/r#r$┌ \s zOR.rcall..йr.rAйr(r/r#rLr$r-[s zOR.rcallcCstddД|jDГОS)NcSsg|] }|СqSr#r#rJr#r#r$rMaєz!OR.__invert__..)rrAr'r#r#r$r0`sz OR.__invert__cCstt|Гjft|jГГSr%йr7r.r2┌tuplerr'r#r#r$r9cszOR.__hash__cCs|j|jkSr%йrr4r#r#r$r6fsz OR.__eq__cCs"ddаddД|jDГбd}|S)N·(· | cSsg|]}t|ГСqSr#йrHrJr#r#r$rMjrPzOR.__str__..·)й┌joinrйr(┌sr#r#r$r3isz OR.__str__N) r2r:r;r<rCr=rr-r0r9r6r3r>r#r#r#r$rPs rc@sPeZdZdZddДZddДZeddДГZdd ДZd dДZ dd ДZ ddДZeZdS)rz, A low-level implementation for And cGs ||_dSr%r@rBr#r#r$rCtszAND.__init__cCstddД|jDГОS)NcSsg|] }|СqSr#r#rJr#r#r$rMxrPz"AND.__invert__..)rrAr'r#r#r$r0wszAND.__invert__cCst|jtdНSrDrFr'r#r#r$rzszAND.argscst|ГЗfddД|jDГОS)Ncsg|]}|аИбСqSr#rIrJrLr#r$rMs zAND.rcall..rNrOr#rLr$r-~s z AND.rcallcCstt|Гjft|jГГSr%rQr'r#r#r$r9ГszAND.__hash__cCs|j|jkSr%rSr4r#r#r$r6Жsz AND.__eq__cCs"ddаddД|jDГбd}|S)NrT· & cSsg|]}t|ГСqSr#rVrJr#r#r$rMКrPzAND.__str__..rWrXrZr#r#r$r3ЙszAND.__str__N) r2r:r;r<rCr0r=rr-r9r6r3r>r#r#r#r$rps rNcsВddlm}ddlm}m}Иdur*tГЙt|jt|j t |jt|j t|jt|ji}t|Г|vrt|t|Г}||jО}t|tГrШ|jd}t|ИГ}|St|tГr╛tЗfddДtа|бDГОSt|tГrфtЗfddДtа|бDГОSt|tГРrtЗfddД|jDГО}|St|tГРr8tЗfd dД|jDГО}|St|tГРrжg} tdt |jГd dГD]>} t!|j| ГD]*ЙЗЗfddД|jDГ}| а"t|ОбРqnРq^t| ОSt|t#ГРrg} tdt |jГd dГD]>} t!|j| ГD]*ЙЗЗfd dД|jDГ}| а"t|ОбРq▄Рq╠t| ОSt|t$ГРrPt|jdИГt|jd ИГ}} t|| ГSt|t%ГРr║g} t&|j|jd dЕ|jddНD]0\}}t|ИГ}t|ИГ}| а"t||ГбРqАt| ОSt|t'ГРrt|jdИГ}t|jd ИГ}t|jdИГ} tt||Гt|| ГГSt||ГРrN|j(|j)}}Иа*|dб}|duРrNt|j+|ОИГSt||ГРrzИа*|dб}|duРrzt|ИГSt,|ГS)aК Generates the Negation Normal Form of any boolean expression in terms of AND, OR, and Literal objects. Examples ======== >>> from sympy import Q, Eq >>> from sympy.assumptions.cnf import to_NNF >>> from sympy.abc import x, y >>> expr = Q.even(x) & ~Q.positive(x) >>> to_NNF(expr) (Literal(Q.even(x), False) & Literal(Q.positive(x), True)) Supported boolean objects are converted to corresponding predicates. >>> to_NNF(Eq(x, y)) Literal(Q.eq(x, y), False) If ``composite_map`` argument is given, ``to_NNF`` decomposes the specified predicate into a combination of primitive predicates. >>> cmap = {Q.nonpositive: Q.negative | Q.zero} >>> to_NNF(Q.nonpositive, cmap) (Literal(Q.negative, False) | Literal(Q.zero, False)) >>> to_NNF(Q.nonpositive(x), cmap) (Literal(Q.negative(x), False) | Literal(Q.zero(x), False)) r)┌Q)┌AppliedPredicate┌ PredicateNcsg|]}t|ИГСqSr#й┌to_NNFйrK┌xй┌ composite_mapr#r$rM┐rPzto_NNF..csg|]}t|ИГСqSr#r`rbrdr#r$rM┬rPcsg|]}t|ИГСqSr#r`rbrdr#r$rM┼rPcsg|]}t|ИГСqSr#r`rbrdr#r$rM╔rPщщcs*g|]"}|Иvrt|ИГnt|ИГСqSr#r`йrKr[йre┌negr#r$rM╨s cs*g|]"}|Иvrt|ИГnt|ИГСqSr#r`rhrir#r$rM┘s )┌ fillvalue)-Zsympy.assumptions.askr]Zsympy.assumptions.assumer^r_┌dictr┌eqr┌ner ┌gtr┌ltr┌ger┌ler.rrrrarrZ make_argsrrrr r ┌range┌lenr┌appendrrrrr┌function┌ arguments┌getr-r)r/rer]r^r_Zbinrelpreds┌predr)┌tmp┌cnfs┌i┌clause┌L┌R┌a┌b┌MrZnewpredr#rir$raРsВ( "( racCspt|ttfГs,tГ}|аt|fГбt|ГSt|tГrLtjddД|jDГОSt|tГrltj ddД|jDГОSdS)zМ Distributes AND over OR in the NNF expression. Returns the result( Conjunctive Normal Form of expression) as a CNF object. cSsg|]}t|ГСqSr#й┌distribute_AND_over_ORrJr#r#r$rM s z*distribute_AND_over_OR..cSsg|]}t|ГСqSr#rГrJr#r#r$rMs N) rrr┌set┌add┌ frozenset┌CNF┌all_orrA┌all_and)r/rzr#r#r$rД■s rДc@sоeZdZdZd%ddДZddДZddДZd d ДZddДZd dДZ e ddДГZddДZddДZ ddДZddДZddДZddДZe ddДГZe dd ДГZe d!d"ДГZe d#d$ДГZdS)&rИa Class to represent CNF of a Boolean expression. Consists of set of clauses, which themselves are stored as frozenset of Literal objects. Examples ======== >>> from sympy import Q >>> from sympy.assumptions.cnf import CNF >>> from sympy.abc import x >>> cnf = CNF.from_prop(Q.real(x) & ~Q.zero(x)) >>> cnf.clauses {frozenset({Literal(Q.zero(x), True)}), frozenset({Literal(Q.negative(x), False), Literal(Q.positive(x), False), Literal(Q.zero(x), False)})} NcCs|s tГ}||_dSr%йrЕ┌clausesйr(rМr#r#r$rC$szCNF.__init__cCstа|бj}|а|бdSr%)rИ┌to_CNFrМ┌add_clauses)r(┌proprМr#r#r$rЖ)szCNF.addcCsdаddД|jDГб}|S)Nr\cSs(g|] }ddаddД|DГбdСqS)rTrUcSsg|]}t|ГСqSr#rV)rKrr#r#r$rM/rPz*CNF.__str__...rW)rYйrKr}r#r#r$rM/s zCNF.__str__..)rYrМrZr#r#r$r3-s zCNF.__str__cCs|D]}|а|бq|Sr%йrЖ)r(┌props┌pr#r#r$┌extend4sz CNF.extendcCstt|jГГSr%)rИrЕrМr'r#r#r$┌copy9szCNF.copycCs|j|O_dSr%)rМrНr#r#r$rП<szCNF.add_clausescCs|Г}|а|б|Sr%rТ)rrР┌resr#r#r$┌ from_prop?s z CNF.from_propcCs|а|jб|Sr%)rПrМr4r#r#r$┌__iand__EszCNF.__iand__cCs(tГ}|jD]}|ddД|DГO}q|S)NcSsh|] }|jТqSr#r&rJr#r#r$┌ LrPz%CNF.all_predicates..rЛ)r(Z predicates┌cr#r#r$┌all_predicatesIs zCNF.all_predicatescCsPtГ}t|j|jГD]2\}}t|Г}|D]}|а|бq(|аt|Гбqt|ГSr%)rЕrrМrЖrЗrИ)r(┌cnfrМrАrБrz┌tr#r#r$┌_orOszCNF._orcCs|jа|jб}t|ГSr%)rМ┌unionrИйr(rЭrМr#r#r$┌_andXszCNF._andcCs~t|jГ}tГ}|dD]}|аt|fГбqt|Г}|ddЕD]4}tГ}|D]}|аt|fГбqR|аt|Гб}qD|S)Nщ )┌listrМrЕrЖrЗrИrЯ)r(ZclssZllrc┌restrФr#r#r$┌_not\s zCNF._notcsBtГ}|jD]$}ЗfddД|DГ}|аt|Обqt|ОЙtИГS)Ncsg|]}|аИбСqSr#rIrJrLr#r$rMmrPzCNF.rcall..)rдrМrurrrД)r(r/Zclause_listr}Zlitsr#rLr$r-js z CNF.rcallcGs,|dаб}|ddЕD]}|а|б}q|SйNrrf)rЦrЯйrr{rБrеr#r#r$rЙrsz CNF.all_orcGs,|dаб}|ddЕD]}|а|б}q|Srз)rЦrвrиr#r#r$rКyszCNF.all_andcCs$ddlm}t||ГГ}t|Г}|S)Nr)┌get_composite_predicates)Zsympy.assumptions.factsrйrarД)rr/rйr#r#r$rОАsz CNF.to_CNFcs ddДЙtЗfddД|jDГОS)zm Converts CNF object to SymPy's boolean expression retaining the form of expression. cSs|jrt|jГS|jSr%)rrr)r)r#r#r$┌remove_literalНsz&CNF.CNF_to_cnf..remove_literalc3s$|]}tЗfddД|DГОVqdS)c3s|]}И|ГVqdSr%r#rJйrкr#r$┌ РrPz+CNF.CNF_to_cnf...N)rrСrлr#r$rмРrPz!CNF.CNF_to_cnf..)rrМ)rrЭr#rлr$┌ CNF_to_cnfЗszCNF.CNF_to_cnf)N)r2r:r;r<rCrЖr3rХrЦrП┌classmethodrШrЩrЬrЯrвrжr-rЙrКrОrнr#r#r#r$rИs. rИc@sbeZdZdZdddДZddДZeddДГZed d ДГZddДZ d dДZ ddДZddДZddДZ dS)┌ EncodedCNFz0 Class for encoding the CNF expression. 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