\hTzSSKrSSKrSSKJrJr SSKJrJrJrJrJ r J r SSK J r J r SSKJrJrJrJrJrJrJr SSKJr SSKJrJrJr SSKJrJrJr SS K J!r!J"r" SS K#J$r$ SS K%J&r&J'r'J(r(J)r)J*r*J+r+J,r, SS K-J.r.J/r/J0r0J1r1J2r2 SS K-J3r3J4r4J5r5J6r6J7r7 SSK8J9r9 SSK:J;r; SSKr? SSK@JArA SSKBJCrC SSKDJErE SSKFJGrGJHrHJIrIJJrJJKrK "SS\95rLS#SjrMS\R\\ 4S\LS\R\P/S44SjrQS\S\LS\R\P/S44SjrRSS.S\ S \R\TS!\T4S"jjrUg)$N)AddMul)SymbolExprFloatRationalIntegerBasic)UndefinedFunctionFunction) Relational UnequalityEqualityLessThan GreaterThanStrictLessThanStrictGreaterThan)Abs)explogPow)sinhcoshtanh)MinMax) Piecewise)sincostanasinacosatanatan2)AndOrXorImpliesBoolean) BooleanTrue BooleanFalseBooleanFunctionNotITE)Printer)Interval) prec_to_dpsto_str)AppliedPredicate)AppliedBinaryRelation)Q)StrictGreaterThanPredicateStrictLessThanPredicateGreaterThanPredicateLessThanPredicateEqualityPredicatec\rSrSr%SrS\S\S\S000\S_\ S_\ S _\ S _\ S _\ S _\S _\"5S _\"5S _\"5S _\"5S _\"5S _\S_\S_\S_\S_\S_0\S_\S_\S_\S_\S_\S_\S_\ S_\!S_\"S_\#S_\$S_\%S_\&S _\'S!_\(S"_\)S#_ES$.r*\+\,S%'\+\,S&'SGS'\-R\\+4S(jjr/S)\04S*jr1S+\0S,\-Rd\3\44S-\04S.jr5S/r6S0\74S1jr8S0\94S2jr:S0\;4S3jrS0\?4S5jr@S0\A4S6jrBS0\C4S7jrDS0\C4S8jrES9\F4S:jrGS9\H4S;jrIS9\J4S<jrKS9\4S=jrLS9\M4S>jrNS9\O4S?jrPS9\4S@jrQS9\R4SAjrSSBrTSCrUSDrVSErWSFrXg)H SMTLibPrinter_smtlibNBoolIntReal+*=z<=z>=<>rrabsrrr arcsinarccosarctanarctan2rrrminmaxpowandorxornotitez=>) precision known_typesknown_constantsknown_functions_default_settings symbol_tablesettingscU=(d 0nU=(d 0Ul[R"X5 URSUl[ URS5Ul[ URS5Ul[ URS5UlUR R5Ho0RU5(aMe URR5Ho0RU5(aMe g)NrTrUrVrW) rYr/__init__ _settings _precisiondict _known_types_known_constants_known_functionsvalues_is_legal_name)selfrZrY_s M/var/www/auris/envauris/lib/python3.13/site-packages/sympy/printing/smtlib.pyr\SMTLibPrinter.__init__Ts>r(.B(..5  !>? $T^^4E%F G $T^^4E%F G""))+A4G4G4J4J-J4J+&&--/A8K8KA8N8N1N8N/schU(dgUSR5(ag[SU55$)NFrc3X# UH oR5=(d US:Hv M" g7f)rfN)isalnum).0rfs rg /SMTLibPrinter._is_legal_name..es 6Aq99;*!s(*As(*) isnumericall)rerjs rgrdSMTLibPrinter._is_legal_namebs+ Q4>>  E6A666riopargsreturncL^SRU4SjU55nSUSUS3$)N c3t># UH-n[U[5(aUOTRU5v M/ g7fN) isinstancestr_print)rnares rgro(SMTLibPrinter._s_expr..hs6 As##AQ s58())join)rertruargs_strs` rg_s_exprSMTLibPrinter._s_exprgs788    2$az##ricXR;aURUnO[U5UR;aUR[U5nO[[U55[:Xa URnOr[ U[ 5(aNUR UR;a4URUR nURX!R5$URUnURX!R5$rz) rbtyper namer{r4functionr argumentsru)reerts rg_print_FunctionSMTLibPrinter._print_Functionos %% %&&q)B !W-- -&&tAw/B $q']/ /B 0 1 1ajjDDYDY6Y&&qzz2B<<KK0 0&&q)B||B''rirc$URU5$rzrrers rg_print_RelationalSMTLibPrinter._print_Relational~##A&&ric$URU5$rzrrs rg_print_BooleanFunction$SMTLibPrinter._print_BooleanFunctionrric$URU5$rzrrs rg _print_ExprSMTLibPrinter._print_Exprrric[U5UR;aURU5$UR[nUR[nUR X0R X!R 5/5$rz)rrbrrr-rru)rereq_opnot_ops rg_print_UnequalitySMTLibPrinter._print_Unequalitysd 7d++ +))!, ,))(3E**3/F<<eVV)D(EF Fricv^^S[R[[44UU4SjjmT"UR5$)Nruc >USup[U5S:Xa-USLd[U[5(deTRU5$TR[ nTR UX!T"USS5/5$)NrT)lenr{r*r}rbr.r)rurcrS_print_Piecewise_recursiveres rgrBSMTLibPrinter._print_Piecewise.._print_Piecewise_recursivesy7DA4yA~T jK&@&@@@{{1~%++C0||C4T!"X>*ri)typingUnionlisttupleru)rerrs` @rg_print_PiecewiseSMTLibPrinter._print_Piecewises2 V\\$+-F  *!&&11ric$URR(aURR(agURRURR:wa[SUS35eSURSURS3$)NzOne-sided intervals (`z`) are not supported in SMT.[z, ])start is_infiniteend ValueErrorrs rg_print_IntervalSMTLibPrinter._print_Intervalsm 77  155#4#4 WW AEE$5$5 55aS8TUV Vqwwir!%%* *ricjUR[R:Xa&[R"URSS5nGO_UR[R :Xa&[R "URSS5nGOUR[R:Xa%[R"URSS5nOUR[R:Xa%[R"URSS5nOUR[R:Xa%[R"URSS5nORUR[R:Xa%[R"URSS5nO[SUS35eUR!U5$)Nrz Predicate (`z`) is not handled.)rr5positivegtrnegativeltzeroeq nonpositivele nonnegativegenonzeroner_print_AppliedBinaryRelation)rerrels rg_print_AppliedPredicate%SMTLibPrinter._print_AppliedPredicates :: #$$q{{1~a(C ZZ1:: %$$q{{1~q)C ZZ166 !$$q{{1~q)C ZZ1== ($$q{{1~q)C ZZ1== ($$q{{1~q)C ZZ199 $$$q{{1~q)C|A3.@AB B0055ricUR[R:Xa!UR[ UR 65$UR U5$rz)rr5rrrrrrs rgr*SMTLibPrinter._print_AppliedBinaryRelations= :: ))*akk*BC C''* *rixcg)Ntruerers rg_print_BooleanTrue SMTLibPrinter._print_BooleanTruesricg)Nfalserrs rg_print_BooleanFalse!SMTLibPrinter._print_BooleanFalsesric @[UR5n[URUSSSS9nSU;aZUR S5upEUSS:XaUSSnUR [ nUR [nSU<SU<S U<S U<S 3 $US ;a [S 5eU$)NT) strip_zeros min_fixed max_fixedrrrBrrrxz (z 10 z)))z+infz-infz)Infinite values are not supported in SMT.) r1_prec mlib_to_str_mpf_splitrbrrr)rerdpsstr_realmantrmulrNs rg _print_FloatSMTLibPrinter._print_Floats!''"qwwY]^ (?"..-KT1v}!"g'',C'',C,/sC@ @ ) )HI IOric6UR[U55$rz)r}rrs rg _print_floatSMTLibPrinter._print_floats{{58$$ricRURSURUR/5$)N/)rpqrs rg_print_RationalSMTLibPrinter._print_Rationals||C!##qss,,ricPURS:Xde[UR5$)Nr)rr|rrs rg_print_IntegerSMTLibPrinter._print_Integersssaxx133xric[U5$rz)r|rs rg _print_intSMTLibPrinter._print_ints 1v ric^URUR5(deUR$rzrdrrs rg _print_SymbolSMTLibPrinter._print_Symbol&""166****vv ricURRU5nU(aU$UR(aURUR5OUR5nUR U5$rz)ragetr^evalfr)rerrfs rg_print_NumberSymbol!SMTLibPrinter._print_NumberSymbolsQ$$((+ K,0OO(A$$Q' 'ric^URUR5(deUR$rzrrs rg_print_UndefinedFunction&SMTLibPrinter._print_UndefinedFunctionrric~[UR;aUR[SSS95$URU5$)NrF)evaluate)rrbrrrs rg _print_Exp1SMTLibPrinter._print_Exp1sCd+++  Q!7 8   $ $Q ' ricJ[S[U5S[U5S35e)NzCannot convert `z ` of type `z ` to SMT.)NotImplementedErrorreprr)reexprs rg emptyPrinterSMTLibPrinter.emptyPrinters'!$4T$ZL DQUJ$3$ (':''''T'G:G 2) 2++6)96$+.>+&K\e&%e%--Cv( crir<c U =(d Sn [U[5(dU/nUV s/sHn [R"U SSSS9PM nn U(d0n[ USU06n0n U(aXn[U5U R;dMUR (aM1UR&U_M@ M\ nnnUR)5Vs/sHn[+XU 5PM snUR)5Vs/sHn[+UX5PM sn-nUVs/sHnU(dM UPM nnU(aUVs/sHn[-XU 5PM nnSR//UVs/sH+n[U[05(aUOU R3U5PM- snQ[5SU55QUVs/sH+n[U[05(aUOU R3U5PM- snQU Vs/sH+n[U[05(aUOU R3U5PM- snQ5$s sn fs snnfs snnfs snfs snfs snfs snfs snfs snfs snf)aConverts ``expr`` to a string of smtlib code. Parameters ========== expr : Expr | List[Expr] A SymPy expression or system to be converted. auto_assert : bool, optional If false, do not modify expr and produce only the S-Expression equivalent of expr. If true, assume expr is a system and assert each boolean element. auto_declare : bool, optional If false, do not produce declarations for the symbols used in expr. If true, prepend all necessary declarations for variables used in expr based on symbol_table. precision : integer, optional The ``evalf(..)`` precision for numbers such as pi. symbol_table : dict, optional A dictionary where keys are ``Symbol`` or ``Function`` instances and values are their Python type i.e. ``bool``, ``int``, ``float``, or ``Callable[...]``. If incomplete, an attempt will be made to infer types from ``expr``. known_types: dict, optional A dictionary where keys are ``bool``, ``int``, ``float`` etc. and values are their corresponding SMT type names. If not given, a partial listing compatible with several solvers will be used. known_functions : dict, optional A dictionary where keys are ``Function``, ``Relational``, ``BooleanFunction``, or ``Expr`` instances and values are their SMT string representations. If not given, a partial listing optimized for dReal solver (but compatible with others) will be used. known_constants: dict, optional A dictionary where keys are ``NumberSymbol`` instances and values are their SMT variable names. When using this feature, extra caution must be taken to avoid naming collisions between user symbols and listed constants. If not given, constants will be expanded inline i.e. ``3.14159`` instead of ``MY_SMT_VARIABLE_FOR_PI``. prefix_expressions: list, optional A list of lists of ``str`` and/or expressions to convert into SMTLib and prefix to the output. suffix_expressions: list, optional A list of lists of ``str`` and/or expressions to convert into SMTLib and postfix to the output. log_warn: lambda function, optional A function to record all warnings during potentially risky operations. Soundness is a core value in SMT solving, so it is good to log all assumptions made. Examples ======== >>> from sympy import smtlib_code, symbols, sin, Eq >>> x = symbols('x') >>> smtlib_code(sin(x).series(x).removeO(), log_warn=print) Could not infer type of `x`. Defaulting to float. Non-Boolean expression `x**5/120 - x**3/6 + x` will not be asserted. Converting to SMTLib verbatim. '(declare-const x Real)\n(+ x (* (/ -1 6) (pow x 3)) (* (/ 1 120) (pow x 5)))' >>> from sympy import Rational >>> x, y, tau = symbols("x, y, tau") >>> smtlib_code((2*tau)**Rational(7, 2), log_warn=print) Could not infer type of `tau`. Defaulting to float. Non-Boolean expression `8*sqrt(2)*tau**(7/2)` will not be asserted. Converting to SMTLib verbatim. '(declare-const tau Real)\n(* 8 (pow 2 (/ 1 2)) (pow tau (/ 7 2)))' ``Piecewise`` expressions are implemented with ``ite`` expressions by default. Note that if the ``Piecewise`` lacks a default term, represented by ``(expr, True)`` then an error will be thrown. This is to prevent generating an expression that may not evaluate to anything. >>> from sympy import Piecewise >>> pw = Piecewise((x + 1, x > 0), (x, True)) >>> smtlib_code(Eq(pw, 3), symbol_table={x: float}, log_warn=print) '(declare-const x Real)\n(assert (= (ite (> x 0) (+ 1 x) x) 3))' Custom printing can be defined for certain types by passing a dictionary of PythonType : "SMT Name" to the ``known_types``, ``known_constants``, and ``known_functions`` kwargs. >>> from typing import Callable >>> from sympy import Function, Add >>> f = Function('f') >>> g = Function('g') >>> smt_builtin_funcs = { # functions our SMT solver will understand ... f: "existing_smtlib_fcn", ... Add: "sum", ... } >>> user_def_funcs = { # functions defined by the user must have their types specified explicitly ... g: Callable[[int], float], ... } >>> smtlib_code(f(x) + g(x), symbol_table=user_def_funcs, known_functions=smt_builtin_funcs, log_warn=print) Non-Boolean expression `f(x) + g(x)` will not be asserted. Converting to SMTLib verbatim. '(declare-const x Int)\n(declare-fun g (Int) Real)\n(sum (existing_smtlib_fcn x) (g x))' cgrzr)rfs rgsmtlib_code..dsdriTF)strictr convert_xorrYrTrUrWrVCould not infer type of `z`. Defaulting to float.z$Unknown type of undefined function `z^`. Must be mapped to ``str`` in known_functions or mapped to ``Callable[..]`` in symbol_table. c3$# UHov M g7frzr)rnrs rgrosmtlib_code..s(>)4SE9PQR&+s#S !3!33S /$$$6se >=ABT#A(3TB 99( 'As##A1 5'  (<( ( As##A1 5 &( 'As##A1 5' # O j7V ?C    sS!N* "N/N/#5N5N5/N5N;O" O1OO ,2O 72O 02O r0rr/c4UR(aHURUn[U[5(deURUnUR SX/5$UR (aUR[U5n[U5(deURVs/sHoARUPM nn[U5S:deSSRUSS5S3nUSnUR S[U5XV/5$U"SUS 35 gs snf) Nz declare-constrrrxrz declare-funzNon-Symbol/Function `z` will not be declared.) r"rYr{rr`rr#callable__args__rr)r0rr/type_signaturerfparams_signaturereturn_signatures rgr'r's }},.$////7yy3*?@@ S 2''''5C5L5LM5L..+5LM>"Q&&&sxxs(;<=Q?)"-yyc4D(WXX (-DEFNs#Drch[U[5(d}XR;aURU[:XdWUR(aY[ U5UR;a@UR[ U5R S[:XaURSU/5$U"SUS35 U$)Nr8assertzNon-Boolean expression `z6` will not be asserted. Converting to SMTLib verbatim.)r{r)rYrr#rr:r)rrr/s rgr(r(s!W ^^q 1T 9  Q1>>! tAw((,4yyA3''+A3.defri)rYexprsrYrvc^U(a [U5O0mS[4U4SjjnU"UVs1sHnUR(dMUiM sn[5 U"UVVVs1sHInUR [ 5H,nUR HnUR(dMUiM M. MK snnn[5 U"UVVVVs1sHnUR [5Hkn[U5T;dM[UR T[U5R5H&upVUR(dMU[:XdM$UiM( Mm M snnnn[5 U"UVVVVs1sHnUR [5Hkn[U5T;dM[UR T[U5R5H&upVUR(dMU[:XdM$UiM( Mm M snnnn[5 U"UVVs1sH5nUR [5HnUR(dMUiM M7 snn[5 U"UVVs1sHHnUR [5H+nUR(dMUR(aM)UiM- MJ snn[5 UVV s/sH oR [ 5HoPM M" n nn U V s/sH7oR"R(dMU R"U R$4PM9 sn U V s/sH7oR$R(dMU R$U R"4PM9 sn -n U HupU T;aTU OU T;aTU OU R&(a*[U 5T;aT[U 5RSOWU R((a[O@U R(dU R*(a[OU R(a[OSnU(dMU"U 1U5 M T$s snfs snnnfs snnnnfs snnnnfs snnfs snnfs sn nfs sn fs sn f)Nsymsc >UHAnUR(deTRX!5=o1:wdM.[SUSUSUS35e g)Nrz`. Apparently both `z` and `z`?)r" setdefaultr%)rBinfrjold_type_symbolss rg safe_update-_auto_infer_smtlib_types..safe_updatesWA;; ;$//77?";A3>RS[R\\cdgchhj kllrir8)r_setr"rr!r,rur rzipr:rr is_integeris_realrrlhsrhsr# is_Boolean is_Integer)rYr@rHrboolfuncsymbolparamintfuncrrrels_eqrelsinferreltd inferencerGs @rgr r s"&2tL!rHm#mA ;;   A0HmmF    $ 0    A)H >X % !h0H0Q0QRMF     !& S )   Awwx(G =H $ !xW /F/O/OPMF     !& Q (   AggfoF    %    AggfoF >> #)"3"3 %    %Eut 80Ds0DsuGE-4 -4c8I8I!!W .5 -4c8I8I!!W  D  $0HUO$0HUO  T%[H%< T%[ ! * *2 .$$D##u'7'7C]]E   9k5'95 OI F  sP?P?>Q Q ,Q 4AQ 9Q Q +,QAQ Q,Q.Q  Q .Q! Q! % Q! 'Q'/Q-Q-3Q2Q2) TTNNNNNNNN)Vrr sympy.corerrrrrrr r sympy.core.functionr r sympy.core.relationalr rrrrrr$sympy.functions.elementary.complexesr&sympy.functions.elementary.exponentialrrr%sympy.functions.elementary.hyperbolicrrr(sympy.functions.elementary.miscellaneousrr$sympy.functions.elementary.piecewiser(sympy.functions.elementary.trigonometricrrr r!r"r#r$sympy.logic.boolalgr%r&r'r(r)r*r+r,r-r.sympy.printing.printerr/ sympy.setsr0mpmath.libmp.libmpfr1r2rsympy.assumptions.assumer3!sympy.assumptions.relation.binrelr4sympy.assumptions.askr5#sympy.assumptions.relation.equalityr6r7r8r9r:r<r6rCallabler|r'r(rr_r rrirgrms- DD;|||4@@BB=:[[[>>TT*B5C#``ocGoch$(<@04 xvfll68+;<Z`ZiZiknjoqujuZv* 4 M V__cUTX[=Y  +/^ ^//$'^ ^ri