+ iKRt^RIHtHtHt^RIHtHtHt^RI H t ^RI H t ^RI HtHtHtHtHtHt^RIHt^RIHt^RIHtHtHt!R R 4t]!4tR tR ]3R ltRt Rt!Rt"^RI#H$t$H%t%R#)z4Module for querying SymPy objects about assumptions.)global_assumptions PredicateAppliedPredicate)CNF EncodedCNFLiteral)sympify) BooleanKind)EqNeGtLtGeLe) satisfiable)memoize_property)sympy_deprecation_warningSymPyDeprecationWarningignore_warningsca]tRt^toRt]R4t]R4t]R4t]R4t ]R4t ]R4t ]R4t ]R 4t ]R 4t]R 4t]R 4t]R 4t]R4t]R4t]R4t]R4t]R4t]R4t]R4t]R4t]R4t]R4t]R4t]R4t]R4t]R4t]R4t ]R4t!]R4t"]R4t#]R 4t$]R!4t%]R"4t&]R#4t']R$4t(]R%4t)]R&4t*]R'4t+]R(4t,]R)4t-]R*4t.]R+4t/]R,4t0]R-4t1]R.4t2]R/4t3]R04t4]R14t5]R24t6]R34t7]R44t8]R54t9]R64t:]R74t;]R84t<]R94t=R:t>Vt?R;#)<AssumptionKeyszm This class contains all the supported keys by ``ask``. It should be accessed via the instance ``sympy.Q``. c^RIHpV!4#))HermitianPredicate) handlers.setsr)selfrs& u/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/assumptions/ask.py hermitianAssumptionKeys.hermitian 5!##c^RIHpV!4#)r)AntihermitianPredicate)rr")rr"s& r antihermitianAssumptionKeys.antihermitian%s9%''r c^RIHpV!4#)r) RealPredicate)rr&)rr&s& rrealAssumptionKeys.real*s 0r c^RIHpV!4#)r)ExtendedRealPredicate)rr*)rr*s& r extended_realAssumptionKeys.extended_real/s8$&&r c^RIHpV!4#)r)ImaginaryPredicate)rr.)rr.s& r imaginaryAssumptionKeys.imaginary4rr c^RIHpV!4#)r)ComplexPredicate)rr2)rr2s& rcomplexAssumptionKeys.complex93!!r c^RIHpV!4#)r)AlgebraicPredicate)rr7)rr7s& r algebraicAssumptionKeys.algebraic>rr c^RIHpV!4#)r)TranscendentalPredicate)predicates.setsr;)rr;s& rtranscendentalAssumptionKeys.transcendentalCs<&((r c^RIHpV!4#)r)IntegerPredicate)rr@)rr@s& rintegerAssumptionKeys.integerHr5r c^RIHpV!4#)r)NonIntegerPredicate)r<rD)rrDs& r nonintegerAssumptionKeys.nonintegerMs8"$$r c^RIHpV!4#)r)RationalPredicate)rrH)rrHs& rrationalAssumptionKeys.rationalRs4 ""r c^RIHpV!4#)r)IrrationalPredicate)rrL)rrLs& r irrationalAssumptionKeys.irrationalWs6"$$r c^RIHpV!4#)r)FinitePredicate)handlers.calculusrP)rrPs& rfiniteAssumptionKeys.finite\6  r c^RIHpV!4#)r)InfinitePredicate)rQrV)rrVs& rinfiniteAssumptionKeys.infinitea8 ""r c^RIHpV!4#)r)PositiveInfinitePredicate)rQr[)rr[s& rpositive_infinite AssumptionKeys.positive_infinitef@(**r c^RIHpV!4#)r)NegativeInfinitePredicate)rQr`)rr`s& rnegative_infinite AssumptionKeys.negative_infinitekr^r c^RIHpV!4#)r)PositivePredicate)handlers.orderrd)rrds& rpositiveAssumptionKeys.positivep5 ""r c^RIHpV!4#)r)NegativePredicate)rerj)rrjs& rnegativeAssumptionKeys.negativeurhr c^RIHpV!4#)r) ZeroPredicate)rern)rrns& rzeroAssumptionKeys.zerozs 1r c^RIHpV!4#)r)ExtendedPositivePredicate)rerr)rrrs& rextended_positive AssumptionKeys.extended_positive=(**r c^RIHpV!4#)r)ExtendedNegativePredicate)rerw)rrws& rextended_negative AssumptionKeys.extended_negativerur c^RIHpV!4#)r)NonZeroPredicate)rer{)rr{s& rnonzeroAssumptionKeys.nonzeros4!!r c^RIHpV!4#)r)NonPositivePredicate)rer)rrs& r nonpositiveAssumptionKeys.nonpositive8#%%r c^RIHpV!4#)r)NonNegativePredicate)rer)rrs& r nonnegativeAssumptionKeys.nonnegativerr c^RIHpV!4#)r)ExtendedNonZeroPredicate)rer)rrs& rextended_nonzeroAssumptionKeys.extended_nonzeros<'))r c^RIHpV!4#)r)ExtendedNonPositivePredicate)rer)rrs& rextended_nonpositive#AssumptionKeys.extended_nonpositive@+--r c^RIHpV!4#)r)ExtendedNonNegativePredicate)rer)rrs& rextended_nonnegative#AssumptionKeys.extended_nonnegativerr c^RIHpV!4#)r) EvenPredicate)handlers.ntheoryr)rrs& revenAssumptionKeys.evens 3r c^RIHpV!4#)r) OddPredicate)rr)rrs& roddAssumptionKeys.odds 2~r c^RIHpV!4#)r)PrimePredicate)rr)rrs& rprimeAssumptionKeys.primes4r c^RIHpV!4#)r)CompositePredicate)rr)rrs& r compositeAssumptionKeys.composites8!##r c^RIHpV!4#)r)CommutativePredicate)handlers.commonr)rrs& r commutativeAssumptionKeys.commutatives9#%%r c^RIHpV!4#)r)IsTruePredicate)rr)rrs& ris_trueAssumptionKeys.is_trues4  r c^RIHpV!4#)r)SymmetricPredicate)handlers.matricesr)rrs& r symmetricAssumptionKeys.symmetrics9!##r c^RIHpV!4#)r)InvertiblePredicate)rr)rrs& r invertibleAssumptionKeys.invertible:"$$r c^RIHpV!4#)r)OrthogonalPredicate)rr)rrs& r orthogonalAssumptionKeys.orthogonalrr c^RIHpV!4#)r)UnitaryPredicate)rr)rrs& runitaryAssumptionKeys.unitarys7!!r c^RIHpV!4#)r)PositiveDefinitePredicate)rr)rrs& rpositive_definite AssumptionKeys.positive_definiter^r c^RIHpV!4#)r)UpperTriangularPredicate)rr)rrs& rupper_triangularAssumptionKeys.upper_triangular?'))r c^RIHpV!4#)r)LowerTriangularPredicate)rr)rrs& rlower_triangularAssumptionKeys.lower_triangularrr c^RIHpV!4#)r)DiagonalPredicate)rr)rrs& rdiagonalAssumptionKeys.diagonalrYr c^RIHpV!4#)r)FullRankPredicate)rr)rrs& rfullrankAssumptionKeys.fullrankrYr c^RIHpV!4#)r)SquarePredicate)rr)rrs& rsquareAssumptionKeys.squarerTr c^RIHpV!4#)r)IntegerElementsPredicate)rr)rrs& rinteger_elementsAssumptionKeys.integer_elementsrr c^RIHpV!4#)r)RealElementsPredicate)rr)rrs& r real_elementsAssumptionKeys.real_elementss<$&&r c^RIHpV!4#)r)ComplexElementsPredicate)rr)rrs& rcomplex_elementsAssumptionKeys.complex_elementsrr c^RIHpV!4#)r)SingularPredicate)predicates.matricesr)rrs& rsingularAssumptionKeys.singulars: ""r c^RIHpV!4#)r)NormalPredicate)rr)rrs& rnormalAssumptionKeys.normal s8  r c^RIHpV!4#)r)TriangularPredicate)rr)rrs& r triangularAssumptionKeys.triangulars<"$$r c^RIHpV!4#)r)UnitTriangularPredicate)rr)rrs& runit_triangularAssumptionKeys.unit_triangulars@&((r c^RIHpV!4#)r)EqualityPredicate)relation.equalityr)rrs& reqAssumptionKeys.eqrYr c^RIHpV!4#)r)UnequalityPredicate)rr)rrs& rneAssumptionKeys.nerr c^RIHpV!4#)r)StrictGreaterThanPredicate)rr)rrs& rgtAssumptionKeys.gt$sA)++r c^RIHpV!4#)r)GreaterThanPredicate)rr)rrs& rgeAssumptionKeys.ge)s;#%%r c^RIHpV!4#)r)StrictLessThanPredicate)rr)rrs& rltAssumptionKeys.lt.s>&((r c^RIHpV!4#)r)LessThanPredicate)rr )rr s& rleAssumptionKeys.le3rYr N)@__name__ __module__ __qualname____firstlineno____doc__rrr#r'r+r/r3r8r=rArErIrMrRrWr\rarfrkrorsrxr|rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr r __static_attributes____classdictcell__) __classdict__s@rrrsj$$((''$$""$$))""%%##%%!!##++++####++++""&&&&**....  $$&&!!$$%%%%""++****####!!**''**##!!%%))##%%,,&&))##r rc\4pVPFp.pVFp\VP\4'd~\ VPP 4^8XdZVPPV9d<VP\VPPVP44KKK V'gKVP\V44K \V4#)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)})} )setclauses isinstancelitrlen argumentsargappendrfunctionis_Notadd frozensetr)assumpexprsfactsclauseargsliterals&& r_extract_all_factsr+;s< EE..G'++'788SAVAV=W[\=\;;??e+KK (<(V3r\@PB!V4p V PEV4\GW4p \I4p \K4p V PM\AV 44V POV 4V PP'd"\SV 4RJd\URV,4h\WWz4p V eV #V!V!PYV4p V e \[V 4#V!WVR 7p V eV #V!WVR 7p V # TdR#i;i) 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. )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/rrrkindr TypeErrorr Qrr rr rr r rrrr rr!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 s& I22I=<I=c>VP'Ed \4p\VP4^8XdqVPwp\V4^8XdSVwpVPVR4pVe V^,M \ 4pVP 'dVP V9dR#VPFep\V4^8XgKVwpVP 'gVPVP R4MRpVfKOVwrhW9dR#W9gKdR# R#)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 NFT)rget_known_facts_dictrgetrr"r) rErGknown_facts_dictclf prop_factsprop_reqr(prop_rejs && rr@r@sf/1 {"" #q (%%CB2w!|-11#t< ,6,B:a=888 1 !))F6{aFGhhh-11!%%>TX %%/"?_ * r c \RRRR7\V\4'dVPPp\ \ VR4pVeVP V4R#\\ V\W.R74R#)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 \RRRR7\V\4'dVPPp\ \ 4;_uu_4\ \V4PV4RRR4R# +'giR#;i)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&&rrdrdssd "'#: #y!!hhmm 0 1 13&&w/ 2 1 1 1s  A<< B )r<rMN)&rsympy.assumptions.assumerrrsympy.assumptions.cnfrrr sympy.corersympy.core.kindr sympy.core.relationalr r r r rrsympy.logic.inferencersympy.utilities.decoratorrsympy.utilities.exceptionsrrrrr7r+rKr@rbrdsympy.assumptions.ask_generatedr<rMrr rrns{:::'88-699a#a#H 1h"&/ATnPf<40.r