\hKSrSSKJrJrJr SSKJrJrJr SSK J r SSK J r SSK JrJrJrJrJrJr SSKJr SSKJr SS KJrJrJr "S S 5r\"5rS rS \4SjrSr Sr!Sr"SSK#J$r$J%r% g)z4Module for querying SymPy objects about assumptions.)global_assumptions PredicateAppliedPredicate)CNF EncodedCNFLiteral)sympify) BooleanKind)EqNeGtLtGeLe) satisfiable)memoize_property)sympy_deprecation_warningSymPyDeprecationWarningignore_warningsc\rSrSrSr\S5r\S5r\S5r\S5r \S5r \S5r \S 5r \S 5r \S 5r\S 5r\S 5r\S5r\S5r\S5r\S5r\S5r\S5r\S5r\S5r\S5r\S5r\S5r\S5r\S5r\S5r\S5r\S5r \S5r!\S5r"\S 5r#\S!5r$\S"5r%\S#5r&\S$5r'\S%5r(\S&5r)\S'5r*\S(5r+\S)5r,\S*5r-\S+5r.\S,5r/\S-5r0\S.5r1\S/5r2\S05r3\S15r4\S25r5\S35r6\S45r7\S55r8\S65r9\S75r:\S85r;\S95r<\S:5r=S;r>g<)=AssumptionKeyszm This class contains all the supported keys by ``ask``. It should be accessed via the instance ``sympy.Q``. cSSKJn U"5$)N)HermitianPredicate) handlers.setsr)selfrs M/var/www/auris/envauris/lib/python3.13/site-packages/sympy/assumptions/ask.py hermitianAssumptionKeys.hermitian 5!##cSSKJn U"5$)Nr)AntihermitianPredicate)rr$)rr$s r antihermitianAssumptionKeys.antihermitian%s9%''r"cSSKJn U"5$)Nr) RealPredicate)rr()rr(s rrealAssumptionKeys.real*s 0r"cSSKJn U"5$)Nr)ExtendedRealPredicate)rr,)rr,s r extended_realAssumptionKeys.extended_real/s8$&&r"cSSKJn U"5$)Nr)ImaginaryPredicate)rr0)rr0s r imaginaryAssumptionKeys.imaginary4r!r"cSSKJn U"5$)Nr)ComplexPredicate)rr4)rr4s rcomplexAssumptionKeys.complex93!!r"cSSKJn U"5$)Nr)AlgebraicPredicate)rr9)rr9s r algebraicAssumptionKeys.algebraic>r!r"cSSKJn U"5$)Nr)TranscendentalPredicate)predicates.setsr=)rr=s rtranscendentalAssumptionKeys.transcendentalCs<&((r"cSSKJn U"5$)Nr)IntegerPredicate)rrB)rrBs rintegerAssumptionKeys.integerHr7r"cSSKJn U"5$)Nr)NonIntegerPredicate)r>rF)rrFs r nonintegerAssumptionKeys.nonintegerMs8"$$r"cSSKJn U"5$)Nr)RationalPredicate)rrJ)rrJs rrationalAssumptionKeys.rationalRs4 ""r"cSSKJn U"5$)Nr)IrrationalPredicate)rrN)rrNs r irrationalAssumptionKeys.irrationalWs6"$$r"cSSKJn U"5$)Nr)FinitePredicate)handlers.calculusrR)rrRs rfiniteAssumptionKeys.finite\6  r"cSSKJn U"5$)Nr)InfinitePredicate)rSrX)rrXs rinfiniteAssumptionKeys.infinitea8 ""r"cSSKJn U"5$)Nr)PositiveInfinitePredicate)rSr])rr]s rpositive_infinite AssumptionKeys.positive_infinitef@(**r"cSSKJn U"5$)Nr)NegativeInfinitePredicate)rSrb)rrbs rnegative_infinite AssumptionKeys.negative_infinitekr`r"cSSKJn U"5$)Nr)PositivePredicate)handlers.orderrf)rrfs rpositiveAssumptionKeys.positivep5 ""r"cSSKJn U"5$)Nr)NegativePredicate)rgrl)rrls rnegativeAssumptionKeys.negativeurjr"cSSKJn U"5$)Nr) ZeroPredicate)rgrp)rrps rzeroAssumptionKeys.zerozs 1r"cSSKJn U"5$)Nr)ExtendedPositivePredicate)rgrt)rrts rextended_positive AssumptionKeys.extended_positive=(**r"cSSKJn U"5$)Nr)ExtendedNegativePredicate)rgry)rrys rextended_negative AssumptionKeys.extended_negativerwr"cSSKJn U"5$)Nr)NonZeroPredicate)rgr})rr}s rnonzeroAssumptionKeys.nonzeros4!!r"cSSKJn U"5$)Nr)NonPositivePredicate)rgr)rrs r nonpositiveAssumptionKeys.nonpositive8#%%r"cSSKJn U"5$)Nr)NonNegativePredicate)rgr)rrs r nonnegativeAssumptionKeys.nonnegativerr"cSSKJn U"5$)Nr)ExtendedNonZeroPredicate)rgr)rrs rextended_nonzeroAssumptionKeys.extended_nonzeros<'))r"cSSKJn U"5$)Nr)ExtendedNonPositivePredicate)rgr)rrs rextended_nonpositive#AssumptionKeys.extended_nonpositive@+--r"cSSKJn U"5$)Nr)ExtendedNonNegativePredicate)rgr)rrs rextended_nonnegative#AssumptionKeys.extended_nonnegativerr"cSSKJn U"5$)Nr) EvenPredicate)handlers.ntheoryr)rrs revenAssumptionKeys.evens 3r"cSSKJn U"5$)Nr) OddPredicate)rr)rrs roddAssumptionKeys.odds 2~r"cSSKJn U"5$)Nr)PrimePredicate)rr)rrs rprimeAssumptionKeys.primes4r"cSSKJn U"5$)Nr)CompositePredicate)rr)rrs r compositeAssumptionKeys.composites8!##r"cSSKJn U"5$)Nr)CommutativePredicate)handlers.commonr)rrs r commutativeAssumptionKeys.commutatives9#%%r"cSSKJn U"5$)Nr)IsTruePredicate)rr)rrs ris_trueAssumptionKeys.is_trues4  r"cSSKJn U"5$)Nr)SymmetricPredicate)handlers.matricesr)rrs r symmetricAssumptionKeys.symmetrics9!##r"cSSKJn U"5$)Nr)InvertiblePredicate)rr)rrs r invertibleAssumptionKeys.invertible:"$$r"cSSKJn U"5$)Nr)OrthogonalPredicate)rr)rrs r orthogonalAssumptionKeys.orthogonalrr"cSSKJn U"5$)Nr)UnitaryPredicate)rr)rrs runitaryAssumptionKeys.unitarys7!!r"cSSKJn U"5$)Nr)PositiveDefinitePredicate)rr)rrs rpositive_definite AssumptionKeys.positive_definiter`r"cSSKJn U"5$)Nr)UpperTriangularPredicate)rr)rrs rupper_triangularAssumptionKeys.upper_triangular?'))r"cSSKJn U"5$)Nr)LowerTriangularPredicate)rr)rrs rlower_triangularAssumptionKeys.lower_triangularrr"cSSKJn U"5$)Nr)DiagonalPredicate)rr)rrs rdiagonalAssumptionKeys.diagonalr[r"cSSKJn U"5$)Nr)FullRankPredicate)rr)rrs rfullrankAssumptionKeys.fullrankr[r"cSSKJn U"5$)Nr)SquarePredicate)rr)rrs rsquareAssumptionKeys.squarerVr"cSSKJn U"5$)Nr)IntegerElementsPredicate)rr)rrs rinteger_elementsAssumptionKeys.integer_elementsrr"cSSKJn U"5$)Nr)RealElementsPredicate)rr)rrs r real_elementsAssumptionKeys.real_elementss<$&&r"cSSKJn U"5$)Nr)ComplexElementsPredicate)rr)rrs rcomplex_elementsAssumptionKeys.complex_elementsrr"cSSKJn U"5$)Nr)SingularPredicate)predicates.matricesr)rrs rsingularAssumptionKeys.singulars: ""r"cSSKJn U"5$)Nr)NormalPredicate)rr)rrs rnormalAssumptionKeys.normal s8  r"cSSKJn U"5$)Nr)TriangularPredicate)rr)rrs r triangularAssumptionKeys.triangulars<"$$r"cSSKJn U"5$)Nr)UnitTriangularPredicate)rr)rrs runit_triangularAssumptionKeys.unit_triangulars@&((r"cSSKJn U"5$)Nr)EqualityPredicate)relation.equalityr)rrs reqAssumptionKeys.eqr[r"cSSKJn U"5$)Nr)UnequalityPredicate)rr)rrs rneAssumptionKeys.nerr"cSSKJn U"5$)Nr)StrictGreaterThanPredicate)rr)rrs rgtAssumptionKeys.gt$sA)++r"cSSKJn U"5$)Nr)GreaterThanPredicate)rr)rrs rgeAssumptionKeys.ge)s;#%%r"cSSKJn U"5$)Nr)StrictLessThanPredicate)rr )rr s rltAssumptionKeys.lt.s>&((r"cSSKJn U"5$)Nr)LessThanPredicate)rr)rrs rleAssumptionKeys.le3r[r"N)?__name__ __module__ __qualname____firstlineno____doc__rrr%r)r-r1r5r:r?rCrGrKrOrTrYr^rcrhrmrqrurzr~rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr r__static_attributes__rr"rrrsg$$((''$$""$$))""%%##%%!!##++++####++++""&&&&**....  $$&&!!$$%%%%""++****####!!**''**##!!%%))##%%,,&&))##r"rc[5nURHn/nUHn[UR[5(a{[ URR 5S:XaXURRU;a;UR[URRUR55 M M M U(dMUR[U55 M [U5$)a3 Extract all relevant assumptions from *assump* with respect to given *exprs*. Parameters ========== assump : sympy.assumptions.cnf.CNF exprs : tuple of expressions Returns ======= sympy.assumptions.cnf.CNF Examples ======== >>> from sympy import Q >>> from sympy.assumptions.cnf import CNF >>> from sympy.assumptions.ask import _extract_all_facts >>> from sympy.abc import x, y >>> assump = CNF.from_prop(Q.positive(x) & Q.integer(y)) >>> exprs = (x,) >>> cnf = _extract_all_facts(assump, exprs) >>> cnf.clauses {frozenset({Literal(Q.positive, False)})} r)setclauses isinstancelitrlen argumentsargappendrfunctionis_Notadd frozensetr)assumpexprsfactsclauseargsliterals r_extract_all_factsr+;s< EE..G'++'788SAVAV=W[\=\;;??e+KK (<(U4p[@RB"U5n U REU5 [GX5n [I5n [K5n U RM[AU 55 U ROU 5 U RP(a[SU 5SLa[USU-5e[WXz5n U bU $U"U6RYU5n U b [[U 5$U"XUS 9n U bU $U"XUS 9n U $!Ua g f=f) a Function to evaluate the proposition with assumptions. Explanation =========== This function evaluates the proposition to ``True`` or ``False`` if the truth value can be determined. If not, it returns ``None``. It should be discerned from :func:`~.refine` which, when applied to a proposition, simplifies the argument to symbolic ``Boolean`` instead of Python built-in ``True``, ``False`` or ``None``. **Syntax** * ask(proposition) Evaluate the *proposition* in global assumption context. * ask(proposition, assumptions) Evaluate the *proposition* with respect to *assumptions* in global assumption context. Parameters ========== proposition : Boolean Proposition which will be evaluated to boolean value. If this is not ``AppliedPredicate``, it will be wrapped by ``Q.is_true``. assumptions : Boolean, optional Local assumptions to evaluate the *proposition*. context : AssumptionsContext, optional Default assumptions to evaluate the *proposition*. By default, this is ``sympy.assumptions.global_assumptions`` variable. Returns ======= ``True``, ``False``, or ``None`` Raises ====== TypeError : *proposition* or *assumptions* is not valid logical expression. ValueError : assumptions are inconsistent. Examples ======== >>> from sympy import ask, Q, pi >>> from sympy.abc import x, y >>> ask(Q.rational(pi)) False >>> ask(Q.even(x*y), Q.even(x) & Q.integer(y)) True >>> ask(Q.prime(4*x), Q.integer(x)) False If the truth value cannot be determined, ``None`` will be returned. >>> print(ask(Q.odd(3*x))) # cannot determine unless we know x None ``ValueError`` is raised if assumptions are inconsistent. >>> ask(Q.integer(x), Q.even(x) & Q.odd(x)) Traceback (most recent call last): ... ValueError: inconsistent assumptions Q.even(x) & Q.odd(x) Notes ===== Relations in assumptions are not implemented (yet), so the following will not give a meaningful result. >>> ask(Q.positive(x), x > 0) It is however a work in progress. See Also ======== sympy.assumptions.refine.refine : Simplification using assumptions. Proposition is not reduced to ``None`` if the truth value cannot be determined. r)satask) lra_satask)UnhandledInputz.proposition must be a valid logical expressionz.assumptions must be a valid logical expressionFzinconsistent assumptions %sN) assumptionscontext).sympy.assumptions.sataskr-sympy.assumptions.lra_sataskr.!sympy.logic.algorithms.lra_theoryr/r rrkindr TypeErrorr Qrr rr rrr rrrrrr!rfunctyper)rr from_propextendr+get_all_known_factsrfrom_cnf add_from_cnfrr ValueError_ask_single_fact _eval_askbool) propositionr0r1r-r.r/ binrelpredskeyr) assump_cnf local_factsknown_facts_cnfenc_cnfress raskrKost07@+&K+&K+y))[-=-=[-PHII+y))[-=-=[-PHIIqttRr144QTT2qttRNK+/00((+*?*?T   [ ([ 12K4D4DTII ~T{+Jg%Z6K*+OlG S)* %{73u<6DEE 3 ,C   t*  { +C Cy w GC  wO J sII! I!cUR(a[5n[UR5S:XagURun[U5S:XaJUunURUS5nUbUSO [ 5nUR (aUR U;agURH^n[U5S:XdMUunUR (dURUR S5OSnUcMLUuphX;a gX;dM^ g g)aE Compute the truth value of single predicate using assumptions. Parameters ========== key : sympy.assumptions.assume.Predicate Proposition predicate. local_facts : sympy.assumptions.cnf.CNF Local assumption in CNF form. Returns ======= ``True``, ``False`` or ``None`` Examples ======== >>> from sympy import Q >>> from sympy.assumptions.cnf import CNF >>> from sympy.assumptions.ask import _ask_single_fact If prerequisite of proposition is rejected by the assumption, return ``False``. >>> key, assump = Q.zero, ~Q.zero >>> local_facts = CNF.from_prop(assump) >>> _ask_single_fact(key, local_facts) False >>> key, assump = Q.zero, ~Q.even >>> local_facts = CNF.from_prop(assump) >>> _ask_single_fact(key, local_facts) False If assumption implies the proposition, return ``True``. >>> key, assump = Q.even, Q.zero >>> local_facts = CNF.from_prop(assump) >>> _ask_single_fact(key, local_facts) True If proposition rejects the assumption, return ``False``. >>> key, assump = Q.even, Q.odd >>> local_facts = CNF.from_prop(assump) >>> _ask_single_fact(key, local_facts) False rNrFT)rget_known_facts_dictrgetrr"r) rErGknown_facts_dictclf prop_factsprop_reqr(prop_rejs rr@r@sf/1 {"" #q (%%CB2w!|-11#t< ,6,B:a=88 1 !))F6{aFGhh-11!%%>TX %%/"?_ * r"c [SSSS9 [U[5(aURRn[ [ US5nUbUR U5 g[[ U[X/S95 g)z Register a handler in the ask system. key must be a string and handler a class inheriting from AskHandler. .. deprecated:: 1.8. Use multipledispatch handler instead. See :obj:`~.Predicate`. z The AskHandler system is deprecated. The register_handler() function should be replaced with the multipledispatch handler of Predicate. 1.8deprecated-askhandlerdeprecated_since_versionactive_deprecations_targetN)handlers)rrrnamegetattrr7 add_handlersetattr)rEhandlerQkeys rregister_handlerrbYsj "'#: #y!!hhmm 1c4 D  !3 # :;r"c[SSSS9 [U[5(aURRn[ [ 5 [ [U5RU5 SSS5 g!,(df  g=f)z Removes a handler from the ask system. .. deprecated:: 1.8. Use multipledispatch handler instead. See :obj:`~.Predicate`. z The AskHandler system is deprecated. The remove_handler() function should be replaced with the multipledispatch handler of Predicate. rVrWrXN) rrrr\rrr]r7remove_handler)rEr`s rrdrdss^ "'#: #y!!hhmm 0 13&&w/ 2 1 1s  A// A=)r<rMN)&rsympy.assumptions.assumerrrsympy.assumptions.cnfrrr sympy.corer sympy.core.kindr sympy.core.relationalr r r rrrsympy.logic.inferencersympy.utilities.decoratorrsympy.utilities.exceptionsrrrrr7r+rKr@rbrdsympy.assumptions.ask_generatedr<rMrr"rrns{:::'88-699a#a#H 1h"&/ATnPf<40.r"