gq*"dZddlmZddlmZeeZdZddZdZ dZ dZ d Z d Z d ZGd d ZGddeZGddeZGddeZGddeZeej(d<eej(d<eej(d<y)zLogic expressions handling NOTE ---- at present this is mainly needed for facts.py, feel free however to improve this stuff for general purpose. ) annotations)OptionalcJdx}}|D]}|dur|ryd}|dur|ryd}y|S)zReturn True if all args are True, False if they are all False, else None. >>> from sympy.core.logic import _torf >>> _torf((True, True)) True >>> _torf((False, False)) False >>> _torf((True, False)) FTN)argssawTsawFas E/var/www/openai/venv/lib/python3.12/site-packages/sympy/core/logic.py_torfr sFD4  9D %ZD  Kc<d}|D]}|dur|y|r|ryd}| S)aReturn True if all args are True, None if there is any None else False unless ``quick_exit`` is True (then return None as soon as a second False is seen. ``_fuzzy_group`` is like ``fuzzy_and`` except that it is more conservative in returning a False, waiting to make sure that all arguments are True or False and returning None if any arguments are None. It also has the capability of permiting only a single False and returning None if more than one is seen. For example, the presence of a single transcendental amongst rationals would indicate that the group is no longer rational; but a second transcendental in the group would make the determination impossible. Examples ======== >>> from sympy.core.logic import _fuzzy_group By default, multiple Falses mean the group is broken: >>> _fuzzy_group([False, False, True]) False If multiple Falses mean the group status is unknown then set `quick_exit` to True so None can be returned when the 2nd False is seen: >>> _fuzzy_group([False, False, True], quick_exit=True) But if only a single False is seen then the group is known to be broken: >>> _fuzzy_group([False, True, True], quick_exit=True) False FTNr)r quick_exit saw_otherr s r _fuzzy_groupr+s=JI  9  9  )  =r c(|y|dvr t|Sy)aReturn True, False or None according to x. Whereas bool(x) returns True or False, fuzzy_bool allows for the None value and non-false values (which become None), too. Examples ======== >>> from sympy.core.logic import fuzzy_bool >>> from sympy.abc import x >>> fuzzy_bool(x), fuzzy_bool(None) (None, None) >>> bool(x), bool(None) (True, False) N)TF)bool)xs r fuzzy_boolr\s"" yMAwr cDd}|D]}t|}|dury|s|}|S)aReturn True (all True), False (any False) or None. Examples ======== >>> from sympy.core.logic import fuzzy_and >>> from sympy import Dummy If you had a list of objects to test the commutivity of and you want the fuzzy_and logic applied, passing an iterator will allow the commutativity to only be computed as many times as necessary. With this list, False can be returned after analyzing the first symbol: >>> syms = [Dummy(commutative=False), Dummy()] >>> fuzzy_and(s.is_commutative for s in syms) False That False would require less work than if a list of pre-computed items was sent: >>> fuzzy_and([s.is_commutative for s in syms]) False TFrrrvais r fuzzy_andrss54 B ^ ; B  Ir c||S| S)z Not in fuzzy logic Return None if `v` is None else `not v`. Examples ======== >>> from sympy.core.logic import fuzzy_not >>> fuzzy_not(True) False >>> fuzzy_not(None) >>> fuzzy_not(False) True r)vs r fuzzy_notrs" yu r cHd}|D]}t|}|dury|dus|}|S)a Or in fuzzy logic. Returns True (any True), False (all False), or None See the docstrings of fuzzy_and and fuzzy_not for more info. fuzzy_or is related to the two by the standard De Morgan's law. >>> from sympy.core.logic import fuzzy_or >>> fuzzy_or([True, False]) True >>> fuzzy_or([True, None]) True >>> fuzzy_or([False, False]) False >>> print(fuzzy_or([False, None])) None FTrrs r fuzzy_orr s9$ B ^ : ;B  Ir cddx}}|D] }t|}|r|dz }|dur|dz } y|dzdk(S)zReturn None if any element of args is not True or False, else True (if there are an odd number of True elements), else False.rFNr)rtfr rs r fuzzy_xorr&sO IA  ] FA 5[ FA  q5A:r c*tt|S)zMReturn False if all args are True, True if they are all False, else None.)rrrs r fuzzy_nandr)s Yt_ %%r cdeZdZUdZiZded<dZdZdZdZ dZ d Z d Z d Z e Zed Zy )LogiczLogical expressionzdict[str, type[Logic]] op_2classc>tj|}||_|SN)object__new__r)clsrobjs r r0z Logic.__new__snnS! r c|jSr.r(selfs r __getnewargs__zLogic.__getnewargs__s yyr cltt|jft|jzSr.)hashtype__name__tuplerr4s r __hash__zLogic.__hash__s(T$Z((*U499-==>>r c`t|t|sy|j|jk(S)NF isinstancer9rr bs r __eq__z Logic.__eq__s&!T!W%66QVV# #r c`t|t|sy|j|jk7S)NTr>r@s r __ne__z Logic.__ne__s&!T!W%66QVV# #r c.|j|dk(ryy)NTF)__cmp__)r5others r __lt__z Logic.__lt__s << " $r ct|t|ur)tt|}tt|}n|j}|j}||kD||kz Sr.)r9strr)r5rHr rAs r rGz Logic.__cmp__sR :T%[ (DJADK A A AA!a%  r cz|jjddjd|jDdS)N(z, c32K|]}t|ywr.)rK).0r s r z Logic.__str__.. s$?YSVYs)) __class__r:joinrr4s r __str__z Logic.__str__ s1>>2299$?TYY$??A Ar cd}d}|jD]}|dvr'|td|d|d|td|z|}.d|vsd|vr td |d d k(r't|d k(r td t|d d}|rt j |||}d}|td|d|d|}|td|z|td|z|S)znLogic from string with space around & and | but none after !. e.g. !a & b | c Nz&|zdouble op forbidden: " "z+%s cannot be in the beginning of expression&|z#& and | must have space around themr!r"zdo not include space after "!"zmissing op between "z" and "z#premature end-of-expression in "%s"z "%s" is empty)split ValueErrorlenNotr+r,)textlexprschedopterms r fromstringzLogic.fromstrings.JJLDt|&$:>HJJ=$ELNNd{cTk !FGGAw#~t9>$%EFF48}0=  :?FHHE;!@  BTIJ J =_t34 4 r N)r: __module__ __qualname____doc__r,__annotations__r0r6r<rBrDrIrGrT__repr__ staticmethodrcrr r r+r+sR(*I%* ?$ $  !AH//r r+c"eZdZdZedZy) AndOr_Basecg}|D]7}||jk(r|cS||j k(r'|j|9tt|j |t }|D]}t ||vs|jcSt|dk(r|jSt|dk(r |j Stj|g|S)N)keyr"r) op_x_notxappendsortedsetflattenr8r^r]popr+r0)r1rbargsr s r r0zAndOr_Base.__new__DsACMM!3==() LLO c#++e,-48A1v~}}$ t9>88:  Y!^}}$ $}}S(4((r ct|}g} |jd}t|tr(t||r|j |j K|j|\#t$rYnwxYwt|}|SNr) listrs IndexErrorr?r+extendrror;)r1r args_queueresargs r rrzAndOr_Base.flattenZs$Z   nnQ'#u%c3'%%chh/ JJsO  Sz sA++ A76A7N)r:rdrer0 classmethodrrrr r rkrkBs),r rkceZdZdZdZdZy)AndFc^t|jDcgc] }t|c}Scc}wr.)Orrr^r5r s r _eval_propagate_notzAnd._eval_propagate_notrs'DII.IqCFI.//.*ct|jD]\}}t|ts|jd||j|dzdz}|jDcgc]}t ||fz}}t t |D],}t||ts||j||<.t|}|cS|Scc}w)Nr") enumeraterr?rrranger]r+expand)r5ir|arestr ortermsjr{s r rz And.expandws  *FAs#r" "1  !a%&(999<BA3!/Bs7|,A!'!*e4%,QZ%6%6%8 -'l + CsCN)r:rdrernrrrr r rrosI0 r rceZdZdZdZy)rTc^t|jDcgc] }t|c}Scc}wr.)rrr^rs r rzOr._eval_propagate_nots'TYY/YSVY/00/rN)r:rdrernrrr r rrs I1r rc"eZdZdZedZy)r^ct|trtj||St|tr| St|t r|j dSt|tr|j}|Std|)NrzNot: unknown argument ) r?rKr+r0rr^rrr\)r1r|s r r0z Not.__new__ss c3 ==c* * T "7N S !88A;  U #))+CJ3@A Ar c |jdSrvr(r4s r r|zNot.argsyy|r N)r:rdrer0propertyr|rr r r^r^sB"r r^rXrYrZN)F)rf __future__rtypingrr FuzzyBoolr rrrrr r&r)r+rkrrr^r,rr r rs# TN 4.b.!H.8 & ``F**Z*411%0r