ó ~9­\c@ sdZddlmZmZddlmZmZd„Zed„Z d„Z d„Z d„Z d „Z d efd „ƒYZd efd „ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZeejd>> from sympy.core.logic import _torf >>> _torf((True, True)) True >>> _torf((False, False)) False >>> _torf((True, False)) N(tFalsetTrue(targstsawTtsawFta((s/lib/python2.7/site-packages/sympy/core/logic.pyt_torfs      cC sTt}xF|D]>}|tkr%q n|dkr5dS|rE|rEdSt}q W| S(síReturn 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 N(RRtNone(Rt quick_exitt saw_otherR ((s/lib/python2.7/site-packages/sympy/core/logic.pyt _fuzzy_group(s%     cC s0|dkrdS|ttfkr,t|ƒSdS(s‡Return 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(R RRtbool(tx((s/lib/python2.7/site-packages/sympy/core/logic.pyt fuzzy_boolYs cC sFt}x9|D]1}t|ƒ}|tkr/tS|r |}q q W|S(sÌReturn 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 (RRR(Rtrvtai((s/lib/python2.7/site-packages/sympy/core/logic.pyt fuzzy_andps    cC s|dkr|S| SdS(sò 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 N(R (tv((s/lib/python2.7/site-packages/sympy/core/logic.pyt fuzzy_not”s cC sttd„|DƒƒƒS(s³ 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 cs s|]}t|ƒVqdS(N(R(t.0ti((s/lib/python2.7/site-packages/sympy/core/logic.pys ½s(RR(R((s/lib/python2.7/site-packages/sympy/core/logic.pytfuzzy_or«stLogiccB sqeZdZiZd„Zd„Zd„Zd„Zd„Zd„Z d„Z d„Z e Z e d „ƒZRS( sLogical expressioncG stj|ƒ}||_|S(N(tobjectt__new__R(tclsRtobj((s/lib/python2.7/site-packages/sympy/core/logic.pyRÅs cC s|jS(N(R(tself((s/lib/python2.7/site-packages/sympy/core/logic.pyt__getnewargs__ÊscC s#tt|ƒjft|jƒƒS(N(thashttypet__name__ttupleR(R((s/lib/python2.7/site-packages/sympy/core/logic.pyt__hash__ÍscC s-t|t|ƒƒstS|j|jkSdS(N(t isinstanceR"RR(R tb((s/lib/python2.7/site-packages/sympy/core/logic.pyt__eq__ÐscC s-t|t|ƒƒstS|j|jkSdS(N(R&R"RR(R R'((s/lib/python2.7/site-packages/sympy/core/logic.pyt__ne__ÖscC s|j|ƒdkrtStS(Niÿÿÿÿ(t__cmp__RR(Rtother((s/lib/python2.7/site-packages/sympy/core/logic.pyt__lt__ÜscC set|ƒt|ƒk r?tt|ƒƒ}tt|ƒƒ}n|j}|j}||k||kS(N(R"tstrR(RR+R R'((s/lib/python2.7/site-packages/sympy/core/logic.pyR*ás   cC s*d|jjdjd„|jDƒƒfS(Ns%s(%s)s, cs s|]}t|ƒVqdS(N(R-(RR ((s/lib/python2.7/site-packages/sympy/core/logic.pys ìs(t __class__R#tjoinR(R((s/lib/python2.7/site-packages/sympy/core/logic.pyt__str__ês cC sd}d}x.|jƒD] }|dkr{|dk rPtd||fƒ‚n|dkrotd|ƒ‚n|}qnd|ks“d|kr¢tdƒ‚n|ddkræt|ƒd krÓtd ƒ‚nt|d ƒ}n|rtj|||ƒ}d}qn|dk r3td ||fƒ‚n|}qW|dk r\td |ƒ‚n|dkr{td |ƒ‚n|S(snLogic from string with space around & and | but none after !. e.g. !a & b | c s&|sdouble op forbidden: "%s %s"s+%s cannot be in the beginning of expressiont&t|s#& and | must have space around themit!isdo not include space after "!"s missing op between "%s" and "%s"s#premature end-of-expression in "%s"s "%s" is emptyN(R tsplitt ValueErrortlentNotRt op_2class(ttexttlexprtschedoptterm((s/lib/python2.7/site-packages/sympy/core/logic.pyt fromstringðs>       (R#t __module__t__doc__R8RR R%R(R)R,R*R0t__repr__t staticmethodR=(((s/lib/python2.7/site-packages/sympy/core/logic.pyRÀs       t AndOr_BasecB s eZd„Zed„ƒZRS(cG sÞg}xD|D]<}||jkr&|S||j kr<q n|j|ƒq Wtt|j|ƒƒdtƒ}x'|D]}t|ƒ|kru|jSquWt|ƒdkr´|jƒSt|ƒdkrÎ|j St j ||ŒS(Ntkeyii( t op_x_notxtappendtsortedtsettflattenR!R7R6tpopRR(RRtbargsR ((s/lib/python2.7/site-packages/sympy/core/logic.pyR%s  !   cC s›t|ƒ}g}xvtrŠy|jdƒ}Wntk rBPnXt|tƒrzt||ƒrz|j|jƒqqzn|j|ƒqWt |ƒ}|S(Ni( tlistRRIt IndexErrorR&RtextendRRER$(RRt args_queuetrestarg((s/lib/python2.7/site-packages/sympy/core/logic.pyRH;s     (R#R>Rt classmethodRH(((s/lib/python2.7/site-packages/sympy/core/logic.pyRB#s tAndcB s eZeZd„Zd„ZRS(cC s&tg|jD]}t|ƒ^q ŒS(N(tOrRR7(RR ((s/lib/python2.7/site-packages/sympy/core/logic.pyt_eval_propagate_notSscC sàxÙtt|jƒƒD]¾}|j|}t|tƒr|j| |j|d}g|jD]}t||fŒ^q^}xDtt|ƒƒD]0}t||tƒr||jƒ||RRDRTRU(((s/lib/python2.7/site-packages/sympy/core/logic.pyRRPs RScB seZeZd„ZRS(cC s&tg|jD]}t|ƒ^q ŒS(N(RRRR7(RR ((s/lib/python2.7/site-packages/sympy/core/logic.pyRTos(R#R>RRDRT(((s/lib/python2.7/site-packages/sympy/core/logic.pyRSlsR7cB s eZd„Zed„ƒZRS(cC sƒt|tƒrtj||ƒSt|tƒr3| St|tƒrM|jdSt|tƒrl|jƒ}|Std|fƒ‚dS(NisNot: unknown argument %r( R&RRRRR7RRTR5(RRP((s/lib/python2.7/site-packages/sympy/core/logic.pyRvs  cC s |jdS(Ni(R(R((s/lib/python2.7/site-packages/sympy/core/logic.pyRP‡s(R#R>RtpropertyRP(((s/lib/python2.7/site-packages/sympy/core/logic.pyR7ts R1R2R3N(R?t __future__RRtsympy.core.compatibilityRRR RRRRRRRRRBRRRSR7R8(((s/lib/python2.7/site-packages/sympy/core/logic.pyts   1  $  c-