B ™‘[Ä#ã@sÜddlmZmZddlmZddlmZddlmZddl m Z ddl m Z ddl mZddlmZdd lmZmZdd lmZmZdd lmZmZmZmZmZmZdd lmZdd l m!Z!ddl"m#Z#Gdd„deƒZ$dS)é)Úprint_functionÚdivision)ÚS)ÚContains)ÚBasic)ÚTuple)ÚExpr)ÚLambda)Ú fuzzy_bool)ÚSymbolÚDummy)ÚAndÚ as_Boolean)ÚSetÚIntervalÚ IntersectionÚEmptySetÚUnionÚ FiniteSet)Úsift)Ú filldedent)Údispatchc@sheZdZdZejfdd„Zedd„ƒZedd„ƒZ edd„ƒZ edd „ƒZ d d „Z d d „Z ddd„ZdS)Ú ConditionSeta 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 sötˆttfƒr.tˆŽ‰tˆŽ‰t |ˆˆ|¡Stˆƒ‰t|tƒrJt|Ž}nt|tƒs\t dƒ‚ˆt j krlt j Sˆt j krz|St|t ƒrˆ|Sd}t|tƒrØt|‡‡fdd„ƒ}|drÌt|dŽ}t|dŽ}n t|dŽSt||ƒrœ|j\}}}ˆ|krtˆ|ƒ‰n–ˆ|jkr(tˆ| |ˆi¡ƒ‰nt|ˆjkrNtˆ ˆ|i¡|ƒ‰|‰nNtdƒ}|ˆjksn||jkrztt|ƒƒ}tˆ ˆ|i¡| ||i¡ƒ‰|‰tˆtƒsÎtdƒ}|ˆ ˆ|i¡jkrÎtdƒ‚t |ˆˆ|¡} |dkrì| St|| ƒS)Nzexpecting set for base_setcstˆ ˆ|¡ƒS)N)r Úsubs)Ú_)Ú conditionÚsym©ú6lib/python3.7/site-packages/sympy/sets/conditionset.pyÚ‰sz&ConditionSet.__new__..TÚlambdaz,non-symbol dummy not recognized in condition)Ú isinstancerÚtuplerrÚ__new__rÚsetrÚ TypeErrorrZfalserÚtruerÚargsr Ú free_symbolsZxreplacer r ÚstrÚ ValueErrorr) ÚclsrrÚbase_setZknowZsiftedÚsÚcZdumÚrvr)rrrr#ss^                    zConditionSet.__new__cCs |jdS)Nr)r')Úselfrrrr«szConditionSet.cCs |jdS)Né)r')r0rrrr¬scCs |jdS)Né)r')r0rrrr­scCs|j\}}}|j|j|jBS)N)r'r()r0r-r.Úbrrrr(¯s zConditionSet.free_symbolscCs tt|j|jƒ|ƒ|j |¡ƒS)N)r r rrr,Úcontains)r0Úotherrrrr4´szConditionSet.containscCsðt|jtƒs|S|j\}}}||kr¨| ||¡}t|tƒrš|j|jks`t|jƒdkrŽ|j|jkrŽ||j krx|  |||¡S|  || ||¡|¡St t dƒƒ‚|  |||¡S|j  ||¡}|j  ||¡}|tjkràt|t||ƒ|ƒS|  |j||¡S)Nr1zð A dummy symbol can only be replaced with a symbol having the same assumptions or one having a single assumption having the same commutativity. )r!rrr'rr Z assumptions0ÚlenZis_commutativer,Úfuncr*rrrr&rr)r0ÚoldÚnewrZcondÚbaserrrÚ _eval_subs¸s(        zConditionSet._eval_subsNcCs|t||jƒsdSt|jtƒt|jtƒkr,dS|r8tdƒ‚|}t|jtƒrtt|jtƒrt| |j|j |j|j¡|j¡}||kS)NFz)symbol arg not supported for ConditionSet)r!r7rr r*rrr,)r0r5ZsymbolÚorrrÚdummy_eqás zConditionSet.dummy_eq)N)Ú__name__Ú __module__Ú __qualname__Ú__doc__rZ UniversalSetr#Úpropertyrrr,r(r4r;r=rrrrrs_8    )rN)%Z __future__rrZsympyrZsympy.sets.containsrZsympy.core.basicrZsympy.core.containersrZsympy.core.exprrZsympy.core.functionr Zsympy.core.logicr Zsympy.core.symbolr r Zsympy.logic.boolalgr rZsympy.sets.setsrrrrrrZsympy.utilities.iterablesrZsympy.utilities.miscrZsympy.multipledispatchrrrrrrÚs