ó ¡¼™\c@ sddlmZmZddlmZddlmZddlmZddl m Z ddl m Z ddl mZddlmZmZdd lmZmZdd lmZdd lmZmZmZmZdd lmZdd lmZdefd„ƒYZ dS(iÿÿÿÿ(tprint_functiontdivision(tS(tBasic(tTuple(tExpr(tLambda(t fuzzy_bool(tSymboltDummy(tAndt as_Boolean(tContains(tSettEmptySettUniont FiniteSet(tsift(t filldedentt ConditionSetcB sweZdZejd„Zed„ƒZed„ƒZed„ƒZ ed„ƒZ d„Z d„Z d d„ZRS( s Set of elements which satisfies a given condition. {x | condition(x) is True for x in S} Examples ======== >>> from sympy import Symbol, S, ConditionSet, pi, Eq, sin, Interval >>> from sympy.abc import x, y, z >>> sin_sols = ConditionSet(x, Eq(sin(x), 0), Interval(0, 2*pi)) >>> 2*pi in sin_sols True >>> pi/2 in sin_sols False >>> 3*pi in sin_sols False >>> 5 in ConditionSet(x, x**2 > 4, S.Reals) True If the value is not in the base set, the result is false: >>> 5 in ConditionSet(x, x**2 > 4, Interval(2, 4)) False Notes ===== Symbols with assumptions should be avoided or else the condition may evaluate without consideration of the set: >>> n = Symbol('n', negative=True) >>> cond = (n > 0); cond False >>> ConditionSet(n, cond, S.Integers) EmptySet() In addition, substitution of a dummy symbol can only be done with a generic symbol with matching commutativity or else a symbol that has identical assumptions. If the base set contains the dummy symbol it is logically distinct and will be the target of substitution. >>> c = ConditionSet(x, x < 1, {x, z}) >>> c.subs(x, y) ConditionSet(x, x < 1, {y, z}) A second substitution is needed to change the dummy symbol, too: >>> _.subs(x, y) ConditionSet(y, y < 1, {y, z}) And trying to replace the dummy symbol with anything but a symbol is ignored: the only change possible will be in the base set: >>> ConditionSet(y, y < 1, {y, z}).subs(y, 1) ConditionSet(y, y < 1, {z}) >>> _.subs(y, 1) ConditionSet(y, y < 1, {z}) Notes ===== If no base set is specified, the universal set is implied: >>> ConditionSet(x, x < 1).base_set UniversalSet() Although expressions other than symbols may be used, this is discouraged and will raise an error if the expression is not found in the condition: >>> ConditionSet(x + 1, x + 1 < 1, S.Integers) ConditionSet(x + 1, x + 1 < 1, Integers) >>> ConditionSet(x + 1, x < 1, S.Integers) Traceback (most recent call last): ... ValueError: non-symbol dummy not recognized in condition Although the name is usually respected, it must be replaced if the base set is another ConditionSet and the dummy symbol and appears as a free symbol in the base set and the dummy symbol of the base set appears as a free symbol in the condition: >>> ConditionSet(x, x < y, ConditionSet(y, x + y < 2, S.Integers)) ConditionSet(lambda, (lambda < y) & (lambda + x < 2), Integers) The best way to do anything with the dummy symbol is to access it with the sym property. >>> _.subs(_.sym, Symbol('_x')) ConditionSet(_x, (_x < y) & (_x + x < 2), Integers) c  sÔtˆttfƒrCtˆŒ‰tˆŒ‰tj|ˆˆ|ƒStˆƒ‰t|tƒrmt|Œ}nt|tƒs‹t dƒ‚nˆt j kr¡t j Sˆt j kr´|St|t ƒrÇ|Sd}t|tƒr5t|‡‡fd†ƒ}|dr$t|tŒ}t|dŒ}q5t|tŒSnt||ƒrS|j\}}}ˆ|krttˆ|ƒ‰qSˆ|jkr¥tˆ|jiˆ|6ƒƒ‰qS|ˆjkrÜtˆji|ˆ6ƒ|ƒ‰|‰qStdƒ}|ˆjks||jkrtt|ƒƒ}ntˆji|ˆ6ƒ|ji||6ƒƒ‰|‰ntˆtƒsŸtdƒ}|ˆji|ˆ6ƒjkrŸtdƒ‚qŸntj|ˆˆ|ƒ} |dkrÇ| St|| ƒS(Nsexpecting set for base_setc stˆjˆ|ƒƒS(N(Rtsubs(t_(t conditiontsym(s6lib/python2.7/site-packages/sympy/sets/conditionset.pyt‡stlambdas,non-symbol dummy not recognized in condition(t isinstanceRttupleRRt__new__R tsetR t TypeErrorRtfalseRttruetNoneRtTruetargsR t free_symbolstxreplaceRR tstrt ValueErrorR( tclsRRtbase_settknowtsiftedtstctdumtrv((RRs6lib/python2.7/site-packages/sympy/sets/conditionset.pyRqs^     "    cC s |jdS(Ni(R#(tself((s6lib/python2.7/site-packages/sympy/sets/conditionset.pyR©tcC s |jdS(Ni(R#(R0((s6lib/python2.7/site-packages/sympy/sets/conditionset.pyRªR1cC s |jdS(Ni(R#(R0((s6lib/python2.7/site-packages/sympy/sets/conditionset.pyR«R1cC s'|j\}}}|j|j|jBS(N(R#R$(R0R,R-tb((s6lib/python2.7/site-packages/sympy/sets/conditionset.pyR$­scC s.tt|j|jƒ|ƒ|jj|ƒƒS(N(R RRRR)tcontains(R0tother((s6lib/python2.7/site-packages/sympy/sets/conditionset.pyR3²scC sbt|jtƒs|S|j\}}}||krú|j||ƒ}t|tƒrç|j|jksŽt|jƒdkrÒ|j|jkrÒ||j kr°|j |||ƒS|j ||j||ƒ|ƒSnt t dƒƒ‚n|j |||ƒS|j j||ƒ}|j j||ƒ}|tjkrLt|t||ƒ|ƒS|j |j||ƒS(Nisð A dummy symbol can only be replaced with a symbol having the same assumptions or one having a single assumption having the same commutativity. (RRRR#RRt assumptions0tlentis_commutativeR)tfuncR'RRRR RR (R0toldtnewRtcondtbase((s6lib/python2.7/site-packages/sympy/sets/conditionset.pyt _eval_subs¶s( "cC sºt||jƒstSt|jtƒt|jtƒkr>tS|rStdƒ‚n|}t|jtƒr°t|jtƒr°|j|j|jj|j|jƒ|jƒ}n||kS(Ns)symbol arg not supported for ConditionSet( RR8tFalseRRR'RRR)(R0R4tsymbolto((s6lib/python2.7/site-packages/sympy/sets/conditionset.pytdummy_eqßs$$ N(t__name__t __module__t__doc__Rt UniversalSetRtpropertyRRR)R$R3R=R!RA(((s6lib/python2.7/site-packages/sympy/sets/conditionset.pyRs_8  )N(!t __future__RRtsympyRtsympy.core.basicRtsympy.core.containersRtsympy.core.exprRtsympy.core.functionRtsympy.core.logicRtsympy.core.symbolRR tsympy.logic.boolalgR R tsympy.sets.containsR tsympy.sets.setsR RRRtsympy.utilities.iterablesRtsympy.utilities.miscRR(((s6lib/python2.7/site-packages/sympy/sets/conditionset.pyts"