JThTSSKrSSKrSSKrSSKrSSKJrJrJrJrJ r J r SSK J r J r SSKrSSKJr SSKJr SSKJr SSKJr SSKJrJrJr SS KJr SS KJrJr SS KJ r SS K!J"r" SS K#J$r$ SSK%J&r& SSK'J(r( \(aSSK)J*r* \ "S\S9r+\ "S5r,/SQr-S\R&S\.4Sjr/S\\ \,/\+4S\\ \,/\ \+\R`444Sjr1S\\.S\\.S\\.4Sjr2S\RfS\RfS\Rf4S jr4"S!S"\Rj5r6"S#S$\Rj5r7"S%S&\Rj5r8"S'S(\Rj5r9"S)S*\Rj5r:"S+S,\65r;"S-S.\Rj5r<"S/S0\Rj5r="S1S2\Rj5r>"S3S4\Rj5r?"S5S6\Rj5r@"S7S8\\5rA"S9S:\A\5rB"S;S<\A\5rCS=rDS>rE"S?S@\Rj5rF"SASB\Rj5rG"SCSD\Rj5rH"SESF\Rj5rI"SGSH\Rj5rJ"SISJ\Rj5rK"SKSL\Rj5rL"SMSN\Rj5rM"SOSP\Rj5rN"SQSR\Rj5rO"SSST\Rj5rPSUrQ\Q"SV5rR\Q"SW5rS\Q"SX5rT\Q"SY5rU\Q"SZ5rV\Q"S[5rW\Q"S\5rX\Q"S]5rY\Q"S^5rZ\Q"S_5r[\Q"S`5r\\Q"Sa5r]\Q"Sb5r^\Q"Sc5r_Sdr`\`"SeSf5ra\`"SgSh5rbg)iN)CallableOptional SupportsFloat TYPE_CHECKINGTypeVarUnion) TypeVarTupleUnpack)Ssympify)Expr) Application)_torf fuzzy_andfuzzy_or) equal_valued) LatticeOp ShortCircuit)ordered)walk) PRECEDENCE)sift)int_oo)Iterable_T)bound_Ts)FloorDivModularIndexingWhere PythonModModCleanDiv CeilToInt FloorToIntCeilDiv IntTrueDiv FloatTrueDivLShiftRShift!IsNonOverlappingAndDenseIndicator TruncToFloat TruncToInt RoundToInt RoundDecimalToFloatFloatPow PowByNaturalIdentityexprreturnc"UR=(a} [UR5S:H=(a^ URSR=(a> URSR=(a URSURSL$)Nrr)is_Addlen_args is_symbol)r6s T/var/www/auris/envauris/lib/python3.13/site-packages/torch/utils/_sympy/functions.py_is_symbols_binary_summationr?Ysr  /  Oq  / JJqM # # / JJqM # # / JJqMA . fc^[R"T5S[[S[[ [ R44U4Sjj5nU$)Nargsr7c>T"U6n[SU55(a>[U[R5(d[R"[ U55nU$)Nc3V# UHn[U[R5v M! g7fN) isinstancesympyFloat.0as r> -_keep_float..inner..js84az!U[[))4'))anyrGrHrIfloat)rCrrAs r>inner_keep_float..innergsM$%tH 848 8 8 u{{B B  E!H%Ar@) functoolswrapsr rrrrHrI)rArSs` r> _keep_floatrWdsF__QVC[U2u{{?%; Lr@xycSX4;agX:H$rF)rXrYs r>fuzzy_eqr\ss v~ 6Mr@pqc^^S[RS[4SjmS[RS[4U4Sjjn[R"U"U5U"U55nX- X- p[ [ [RR[RRU555n[RRU5nUH$m[U4SjU55(dMUT-nM& U$)a Fast path for sympy.gcd, using a simple factoring strategy. We try to rewrite p and q in the form n*e*p1 + n*e*p2 and n*e*q0, where n is the greatest common integer factor and e is the largest syntactic common factor (i.e., common sub-expression) in p and q. Then the gcd returned is n*e, cancelling which we would be left with p1 + p2 and q0. Note that further factoring of p1 + p2 and q0 might be possible with sympy.factor (which uses domain-specific theories). E.g., we are unable to find that x*y + x + y + 1 is divisible by x + 1. More generally, when q is of the form q1 + q2 (instead of being already factored) it might be necessary to fall back on sympy.gcd. rXr7c[RRU5Vs/sH>n[U[[R 45(dM*[ [ U55PM@ nn[R"U5$s snfrF) rHMul make_argsrGintIntegerabsmathprod)rXarginteger_coefficientss r>integer_coefficient0simple_floordiv_gcd..integer_coefficientsgyy**1-+ -#U]]34 CCM- + yy-.. + s )A?A?r6c>[T[RRU55n[R "[ RU5$rF)maprHAddrbrUreducerfgcd)r6integer_factorsrjs r>integer_factor+simple_floordiv_gcd..integer_factors:), !4!4T!:* /::r@c3.># UH nTU;v M g7frFr[)rK base_splitrXs r>rM&simple_floordiv_gcd..s=:qJs) rHBasicrcrfrplistrmrarbrnall)r]r^rrrp base_splits divisor_splitrjrXs @@r>simple_floordiv_gcdr|ys"/u{{/s/;U[[;S; xxq)>!+<=C 7AGq15 EII  !4!4Q!782K.3YY-@-@-CM  == = ='C Jr@c L\rSrSr%SrSr\\S4\S'Sr \\S'Sr \ \S '\ S \ R4S j5r\ S \ R4S j5rS \ R"R$S \4Sjr\S\ R,S\ R,S \\ RS44Sj5rSrSrg)r z We maintain this so that: 1. We can use divisibility guards to simplify FloorDiv(a, b) to a / b. 2. Printing out the expression is nicer (compared to say, representing a//b as (a - a % b) / b) NB: This is Python-style floor division, round to -Inf r9.nargs# precedenceT is_integerr7c URS$NrrCselfs r>base FloorDiv.baseyy|r@c URS$Nrrrs r>divisorFloorDiv.divisorrr@printercURUR[SS- 5nURUR[SS- 5nSUSUS3$)NAtom?(z//) parenthesizerrrrrrrs r> _sympystrFloorDiv._sympystrsW##DIIz&/AC/GH&&t||Z5G#5MN4&7)1%%r@rrNc* UR(a [S5eU[[*[R[R*4;a@U[[*[R[R*4;a[R $U[R LdU[R La[R $UR(a[R R$UR(a[US5(aU$UR(a([US5(a[R"US5$[U[R5(Ga"[U[R5(GaU[[*[R[R*4;d0U[[*[R[R*4;a[U5[U5- nU[R:Xa[$U[R*:Xa[*$[R "U5(a[R $[R""[R$"U55$[U[R"5(aJ[U[R"5(a+[R""['U5['U5-5$[U[(5(a)[)UR*SUR*SU-5$[U[R"5(aSn/n[R,R/U5H/nXb- nUR(dMUR1U5 XG- nM1 [3U5S:wa&[)U[R,"USS06- U5U-$[5X5n[US5(a5[U[R,5(a[R6"X5n[US5(d8[)[R8"X- 5[R8"X(- 55$g![R:a gf=f)Ndivision by zerorrevaluateF)is_zeroZeroDivisionErrorrrHoonanr ZerorrrarGNumberrQrfinfisnanrdfloorrcr rCrnrbappendr;r|rpsimplifyPolynomialError) clsrrrR quotientstermstermquotientrps r>eval FloorDiv.evals1 ??#$67 7 FVGUXXy9 9g  G HH XXI J ? 99  599 599 499  <<77<<  ??|GQ77K ??|GR8899T2& & tU\\ * *7ELL11&%((UXXI>>vw588)DDd eGn,ADHH} txxiwAyy }}TZZ]33 dEMM * *z'5==/Q/Q==Tc'l!:; ; dH % %DIIaL$))A,*@A A gu}} - -IE ++D1>&&&LL&)I 25zQTEIIu$Eu$EEwO  %d4CC## 7EII(F(Fii.Q''NN4:.w}0M($$   sBQ;;RRcURUR[SS- 5nURUR[SS- 5nSUSUS3$)Nrrzfloor(/rrrs r>_ccodeFloorDiv._ccode&sW##DIIz&/AC/GH&&t||Z5G#5MNvQwiq))r@r[)__name__ __module__ __qualname____firstlineno____doc__rtuplerc__annotations__rrboolpropertyrHrwrrprinting StrPrinterstrr classmethodrdrrr__static_attributes__r[r@r>r r s"E5c?!JJ ekk&!:!:&s&P==P+0==P u{{D !PPd*r@r c \rSrSr%SrSr\\S4\S'Sr \ \S'Sr \\S '\ S \ RS \ RS \ RS \\ R 4Sj5rS \\ 4SjrS \\ 4SjrSrg)r!i,zC ModularIndexing(a, b, c) => (a // b) % c where % is the C modulus .rTrrrrrmodulusr7cUS:XdUS:Xa[RR$[U[R5(aE[U[R5(a&[U[R5(aX-U-$US:waU[R "X5nUS:wa9[ [R"X- 5[R"X$- 5U5$[U[R5(Ga/nSnURHn[R "XsU-5X2-:wdM$[U[R5(aUS:d^[U[R5(aC[URS[R5(aURSS:aSn OURU5 M [U5[UR5:waU(a[ [U5X#5$[U[5(a*[ URSURSU-U5$g![Ra GNf=f)NrrTF)rHr rrGrdrpr!rrrnrCrarr;sumr )rrrrrp new_terms all_positivers r>rModularIndexing.eval5s 191 77<<  tU]] + +7EMM227EMM22Ow. . !|ii.!8*tz2w}5 dEII & &-/I!%L 99TW#459JJ"477D1H"433&tyy|U]]CC IIaL1, (- !((." 9~TYY/L&s9~wHH dH % %"499Q<11GQ Q9$$   s AII-,I-cdURSSup[URUR5$Nr9)rCr\is_nonnegativerr]r^s r>_eval_is_nonnegative$ModularIndexing._eval_is_nonnegativejs,yy!}((!*:*:;;r@cdURSSup[URUR5$r)rCr\ is_positivers r>_eval_is_positive!ModularIndexing._eval_is_positivens(yy!} q}}55r@r[N)rrrrrrrrcrrrrrrHrdrrwrrrrr[r@r>r!r!,s"E5c?!JJ2==2+0==2CH==2 %++ 22h6r@r!c \rSrSr%SrSr\\S4\S'Sr \\S'S\ \ 4S jr S\ \ 4S jr S\ \ 4S jr\S \R"S \R"S\R"S\ \R"4Sj5rSrg)r"isz Good ol' ternary operator r.rrrr7cURSR(a URSR(aS$S$Nrr9TrCrrs r>_eval_is_integerWhere._eval_is_integer{s.yy|..499Q<3J3JtTPTTr@cURSR(a URSR(aS$S$r)rCrrs r>rWhere._eval_is_nonnegative~s9yy|**tyy|/J/J   r@cURSR(a URSR(aS$S$rrCrrs r>rWhere._eval_is_positives.yy|//DIIaL4L4LtVRVVr@cr]r^c\U[R:XaU$U[R:XaU$grF)rHtruefalse)rrr]r^s r>r Where.evals(  ?H %++ Hr@r[N)rrrrrrrrcrrrrrrrrrHrwrrr[r@r>r"r"ss"E5c?!JU(4.U htn W8D>W  % 05  %++ r@r"c\rSrSr%Sr\\S4\S'Sr\\S'Sr \ \S'\ S \ RS \ RS \\ R4S j5rS \\ 4S jrS \\ 4SjrSrg)r#ir.rrrTrr]r^r7cUR(a [S5eU[RLdXU*4;dUS:Xa[R$UR(aUR(aX-$UR(aHUS:XaBUR (a[R$UR (a[R$X- nUR(a[R$X:nUR(a#[U5(aUR(aU$[R"X5S:Xa[R$g)NModulo by zerorr9r)rrr r is_Numberis_evenis_oddOner is_BooleanrrrHr$rr]r^rRlesss r>rPythonMod.evals 99#$45 5 ;!A2w,!q&66M ;;1;;5L ;;16yyvv xxuu  E <<66M u ??tDzzammH 99Q?a 66Mr@cFURSR(aS$S$NrTrrs r>rPythonMod._eval_is_nonnegativeyy|//t9T9r@cFURSR(aS$S$r)rC is_negativers r>_eval_is_nonpositivePythonMod._eval_is_nonpositiverr@r[N)rrrrrrrcrrrrrrHrrrrrrr[r@r>r#r#s!E5c?!JJ*UZZ*EJJ*8EJJ3G**Z:htn::htn:r@r#c@\rSrSr%SrSr\\S'SrSr \ S5r Sr g) r$irrrTcUR(a [S5eU[RLdXU*4;dUS:Xa[R$UR(a/UR(aUS:dU5eUS:dU5eX-$UR(aHUS:XaBUR (a[R$UR (a[R$X- nUR(a[R$X:nUR(a%[U5(aUR(aU$ggg)Nrrrr9) rrr rrrrrrrrrrs r>rMod.evals 99#$45 5 ;!A2w,!q&66M ;;1;;6 1 66 1 65L ;;16yyvv xxuu  E <<66M u ??tDzzammH/r$r$s- EJJN))r@r$c\rSrSrSrSrg)r%izN Div where we can assume no rounding. This is to enable future optimizations. r[N)rrrrrrr[r@r>r%r%sr@r%c(\rSrSrSr\S5rSrg)r&i Tc.U[R[4;a[$U[R*[*4;a[*$[U[R5(a3[R "[ R"[U555$grF) rHrrrGrrdrfceilrQrnumbers r>rCeilToInt.evalsh ehh' 'M uxxi&) )7N fell + +==5=!9: : ,r@r[Nrrrrrrrrr[r@r>r&r& sJ;;r@r&c(\rSrSrSr\S5rSrg)r'iTcnU[R[4;a[$U[R*[4;a[*$[U[R5(aU$[U[R 5(a3[R"[ R"[U555$grF) rHrrrGrdrrfrrQrs r>rFloorToInt.evalsz ehh' 'M uxxi( (7N femm , ,M fell + +==E&M!:; ; ,r@r[Nrr[r@r>r'r'sJ<__new__CeilDiv.__new__1sN}}T"--( 99T #w .D* *DaK0': :r@r[N)rrrrrrr rr[r@r>r(r(*sJ;r@r(c(\rSrSrSr\S5rSrg)r+i:Tc4US:a [S5eUSU--$Nrznegative shift countr9) ValueErrorrrshifts r>r LShift.eval=s# 1934 4ahr@r[Nrr[r@r>r+r+:sJr@r+c(\rSrSrSr\S5rSrg)r,iDTcBUS:a [S5e[USU-5$r)rr rs r>r RShift.evalGs& 1934 4ah''r@r[Nrr[r@r>r,r,DsJ((r@r,c\rSrSrSr\S\\\RRR4Sj5r \S&S\\\RRRS\\\RRR4Sjj5r \S5r\S 5r\S 5rS rS rS rSrSrSrSrSrSrSrSrSrSrSrSrSr Sr!Sr"Sr#Sr$Sr%S r&S!r'S"r(S#r)S$r*S%r+g)' MinMaxBaseiNcHSSKJn URSUR5nSU5nU(dSOUR U5nU(aD[ UR U55nUc&UR"U40UD6nUR"U40UD6n[ U5nU(d UR$[U5S:Xa[U5R5$[R"U/[!U5Q70UD6nXWlXglU$![a URs$f=f)Nr)global_parametersrc38# UHn[U5v M g7frFr )rKrhs r>rM%MinMaxBase.__new__..Ss6  r)sympy.core.parametersrpopr"_satisfy_unique_summations_symbols frozenset_new_args_filterrzero_collapse_arguments_find_localzerosidentityr;rxrr r_argsetunique_summations_symbols)r original_args assumptionsrrrCr(objs r>r MinMaxBase.__new__Os;??:/@/I/IJ6 6  77 F "  !!5!5d!;< )0..tC{C++D@K@<<  t9>:>># #ll3>>+> (A% 3  xx sDD! D!r7cT[U5S:wag[US[5(a USUS4O USUS4up#[U5(dg[U5(aUR U5$[U[5(a#[ USS5nUbUR U/U5$g)au One common case in some models is building expressions of the form max(max(max(a+b...), c+d), e+f) which is simplified to max(a+b, c+d, e+f, ...). For such expressions, we call the Max constructor X times (once for each nested max) and the expression gets flattened. An expensive cost in constructing those expressions is running _collapse_arguments and _find_localzeros. However, those two optimizations are unnecessary when the args to max are all of the form a+b, c+d, ..etc where each term uses a unique set of symbols. This function is used to detect such properties of the expressions we are building and if so inform that we do not need to run those optimizations. To detect those, we store a property in the expression that tells that this expression is a min/max operation over terms that use unique symbols "unique_summations_symbols". This property also memoize the set of symbols used in all the terms to make it faster to detect this property inductively. When we apply max to add a new term, all we need to do is check if the new term uses unique symbols (with respect to existing terms and itself). Example: t = Max(a+b, c+d) ==> satisfies the property Max(t, h+j) ==> h,j not in [a,b,c,d] => satisfy the property. The function returns None if the new expression does not satisfy the unique_summations_symbols property. Otherwise, it returns a new set of unique symbols. r9Nrrr()r;rGrr?_unique_symbolsgetattr)rrClhsrhslhs_unique_summations_symbolss r>r -MinMaxBase._satisfy_unique_summations_symbols|s< t9>$q':..!Wd1g q'47#  ,C00 ( , ,&&t, , c: & &,30$- )-8**C52OPPr@N initial_setcUc [5OUnUHinUR5HRn[U[RR R 5(d gXS;a gURU5 MT Mk U$)z Return seen_symbols if all atoms in all args are all unique symbols, else returns None. initial_set can be used to represent initial value for seen_symbols N)setatomsrGrHcoresymbolSymboladd)rrCr4 seen_symbolsrhelements r>r.MinMaxBase._unique_symbolssk!, 3su C99;!'5::+<+<+C+CDD, $$W- 'r@c |^^^U(dU$[[U55nT[La[mO[mUSR(Ga//4=nupEUHan[ U[[5HEnUR SR(dM#U[U[5RU5 MG Mc [RnUH1nUR SnUR(dM%Xx:S:XdM/UnM3 [Rn UH1nUR SnUR(dM%Xy:S:XdM/Un M3 T[La)UH"n U R(d OCX:S:XdM U nM$ O2T[:Xa(UH"n U R(d OX:S:XdM U n M$ Sn T[LaU[R:wa[mUn OU [R:wa[mU n U bg[[U55HOnXn [U T5(dMU R Sn T[:XaX:OX:S:XdMATRX'MQ UU4Sjm[U5H(uplXS-SVs/sH nT"X5PM snXS-S&M* UU4Sjn[U5S:aU"U5nU$s snf)aRemove redundant args. Examples ======== >>> from sympy import Min, Max >>> from sympy.abc import a, b, c, d, e Any arg in parent that appears in any parent-like function in any of the flat args of parent can be removed from that sub-arg: >>> Min(a, Max(b, Min(a, c, d))) Min(a, Max(b, Min(c, d))) If the arg of parent appears in an opposite-than parent function in any of the flat args of parent that function can be replaced with the arg: >>> Min(a, Max(b, Min(c, d, Max(a, e)))) Min(a, Max(b, Min(a, c, d))) rTNc |>[U[[45(dU$XR;nU(d3UR"URVs/sH nT"X15PM snSS06$[UT5(a:UR"URVs/sHo3U:wdM T"X15PM snSS06$U$s snfs snf)NrF)rGMinMaxrCfunc)airLcondirdos r>rG*MinMaxBase._collapse_arguments..dosb3*-- U4Sjn[XSS9up#U(dU$UVs/sHn[UR5PM nn[R"U6nU(dU$[ U5nUVs/sHoU- PM n n[ U 5(a/U V s/sH n T"U SS06PM n n UR T "U SS065 T"USS06n X[UT5$rF)rG)rhothers r>GMinMaxBase._collapse_arguments..factor_minmax..3s :c5#9r@T)binaryrF)rr6rC intersectionrxryr)rCis_other other_argsremaining_argsrharg_setscommonnew_other_argsarg_set arg_sets_diffsother_args_diffother_args_factoredrrKs r> factor_minmax5MinMaxBase._collapse_arguments..factor_minmax2s9H)-dT)J &J 2<<#CHH H<%%x0F !&\N=EFX'v-XMF=!!FS"Tm5!#r$MinMaxBase._collapse_argumentssb0KGDM" #:EE 7   "$b& (FZTac*Avvay...z!S1299!<+LLEFF1I;;;AI$#6E,,CFF1I;;;AG#4CczC== , #  C== d*!  AczCLL(EA $}s4y)AA!!U++VVAY(- RV26!"'*llDG* dODA15!eg?2RY?DQM$ :0 t9q= &D I@s;J9c#v# UHn[U[5(a1URSLd"UR(a UR(d[ SUS35eX R :Xa [U5eX R:XaMURU:XaURShvN MUv M gN7f)z Generator filtering args. first standard filter, for cls.zero and cls.identity. Also reshape ``Max(a, Max(b, c))`` to ``Max(a, b, c)``, and check arguments for comparability FzThe argument 'z' is not comparable.N) rGris_extended_realr]r^rr#rr&rCrC)r arg_sequencerhs r>r"MinMaxBase._new_args_filterOs CsD))''50MM#*;*; >#6J!KLLhh"3'' $S88## ! $sB%B9'B7(B9c [5nSnUHfnUR(aAUcUnMU[La [XE5nM1U[La [ XE5nMG[ SU35eURU5 Mh UcU$[U5S:XaU1$[U5S:Xa^[[U55nUS;aUR(aU[LaU$U1$US:XaUR(aU[LaU$U1$URU5 U$)aV Sequentially allocate values to localzeros. When a value is identified as being more extreme than another member it replaces that member; if this is never true, then the value is simply appended to the localzeros. Unlike the sympy implementation, we only look for zero and one, we don't do generic is connected test pairwise which is slow Nz impossible rr)gr) r6rrBmaxrAminAssertionErrorr;r;nextiterrr)rvaluesoptions other_values num_valuerh other_values r>r%MinMaxBase._find_localzerosjsu  C}}$ #Icz$' $7 $' $7 ,{3%-@AA  %    |  !;  |  !tL12KH$)C)C'*cz|B {BA~+"9"9'*cz|B {B#r@c:[SUR55$)Nc38# UHoRv M g7frF) is_algebraicrKrFs r>rM&MinMaxBase...(HArrrCrXs r>rLMinMaxBase.5(H(H#Hr@c:[SUR55$)Nc38# UHoRv M g7frF)is_antihermitianr}s r>rMr~-$*qFrrrs r>rLru-$%FF-(r@c:[SUR55$)Nc38# UHoRv M g7frF)is_commutativer}s r>rMr~+"(Q&rrrs r>rLrU+"#&&+&r@c:[SUR55$)Nc38# UHoRv M g7frF) is_complexr}s r>rMr~&DV||Vrrrs r>rLr&DQVV&D!Dr@c:[SUR55$)Nc38# UHoRv M g7frF) is_compositer}s r>rMr~rrrrs r>rLrrr@c:[SUR55$)Nc38# UHoRv M g7frF)rr}s r>rMr~#>v!IIvrrrs r>rLre#>qvv#>>r@c:[SUR55$)Nc38# UHoRv M g7frF) is_finiter}s r>rMr~s%B6akk6rrrs r>rLrs%B166%B Br@c:[SUR55$)Nc38# UHoRv M g7frF) is_hermitianr}s r>rMr~rrrrs r>rLrrr@c:[SUR55$)Nc38# UHoRv M g7frF) is_imaginaryr}s r>rMr~rrrrs r>rLrrr@c:[SUR55$)Nc38# UHoRv M g7frF) is_infiniter}s r>rMr~'Fv! 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