΅i2SSKrSSKrSSKrSSKrSSKJr SSKJrJrJ r SSK J r J r SSK r SSK Jr SSKJr SSKJr SSKJr SS KJrJrJr SS KJr SS KJrJr SS KJr SS K J!r! SSK"J#r# SSK$J%r% SSK&J'r' SSK(J)r) \(aSSKJ*r* \ "S\S9r+\ "S5r,/SQr-S\ R$S\.4Sjr/S\\ \,/\+4S\\ \,/\+\ R`-44Sjr1S\.S-S\.S-S\.S-4Sjr2S \ RfS!\ RfS\ Rf4S"jr4"S#S$\ Rj5r6"S%S&\ Rj5r7"S'S(\ Rj5r8"S)S*\ Rj5r9"S+S,\ Rj5r:"S-S.\65r;"S/S0\ Rj5r<"S1S2\ Rj5r="S3S4\ Rj5r>"S5S6\ Rj5r?"S7S8\ Rj5r@"S9S:\\5rA"S;S<\A\5rB"S=S>\A\5rCS?rDS@rE"SASB\ Rj5rF"SCSD\ Rj5rG"SESF\ Rj5rH"SGSH\ Rj5rI"SISJ\ Rj5rJ"SKSL\ Rj5rK"SMSN\ Rj5rL"SOSP\ Rj5rM"SQSR\ Rj5rN"SSST\ Rj5rO"SUSV\ Rj5rPSWrQ\Q"SX5rR\Q"SY5rS\Q"SZ5rT\Q"S[5rU\Q"S\5rV\Q"S]5rW\Q"S^5rX\Q"S_5rY\Q"S`5rZ\Q"Sa5r[\Q"Sb5r\\Q"Sc5r]\Q"Sd5r^\Q"Se5r_Sfr`\`"SgSh5ra\`"SiSj5rb\`"SkSl5rcg)mN)Callable) SupportsFloat TYPE_CHECKINGTypeVar) TypeVarTupleUnpack)Ssympify)Expr) Application)_torf fuzzy_andfuzzy_or) equal_valued) LatticeOp ShortCircuit)ordered)walk) PRECEDENCE)sift) TorchVersion)int_oo)Iterable_T)bound_Ts)FloorDivModularIndexingWhere PythonModModCleanDiv CeilToInt FloorToIntCeilDiv IntTrueDiv FloatTrueDivLShiftRShift!IsNonOverlappingAndDenseIndicator TruncToFloat TruncToInt RoundToInt RoundDecimalToFloatFloatPow PowByNaturalIdentityexprreturncd[U[R5=(a UR=(a} [ UR 5S:H=(a^ UR SR =(a> UR SR =(a UR SUR SL$)Nrr) isinstancesympyr is_Addlen_args is_symbol)r5s V/home/james-whalen/.local/lib/python3.13/site-packages/torch/utils/_sympy/functions.py_is_symbols_binary_summationr@\s 4$ / KK /  Oq  / JJqM # # / JJqM # #  / JJqMA . fc^[R"T5S[[S[[ R -4U4Sjj5nU$)Nargsr6c>T"U6n[SU55(a>[U[R5(d[R"[ U55nU$)Nc3V# UHn[U[R5v M! g7fN)r9r:Float.0as r? -_keep_float..inner..ns84az!U[[))4'))anyr9r:rHfloat)rDrrBs r?inner_keep_float..innerksMh 848 8 8 u{{B B  E!H%ArA) functoolswrapsrrrr:rH)rBrRs` r? _keep_floatrVhsB__QVC[R%++%5 LrAxycSX4;agX:H$rG)rWrXs r?fuzzy_eqr[xs v~ 6MrApqc^^S[RS[4SjmS[RS[4U4Sjjn[R"U"U5U"U55nX- X- p[ [ [RR[RRU555n[RRU5nUH$m[U4SjU55(dMUT-nM& U$)a Fast path for sympy.gcd, using a simple factoring strategy. We try to rewrite p and q in the form n*e*p1 + n*e*p2 and n*e*q0, where n is the greatest common integer factor and e is the largest syntactic common factor (i.e., common sub-expression) in p and q. Then the gcd returned is n*e, cancelling which we would be left with p1 + p2 and q0. Note that further factoring of p1 + p2 and q0 might be possible with sympy.factor (which uses domain-specific theories). E.g., we are unable to find that x*y + x + y + 1 is divisible by x + 1. More generally, when q is of the form q1 + q2 (instead of being already factored) it might be necessary to fall back on sympy.gcd. rWr6c[RRU5Vs/sH>n[U[[R 45(dM*[ [ U55PM@ nn[R"U5$s snfrG) r:Mul make_argsr9intIntegerabsmathprod)rWarginteger_coefficientss r?integer_coefficient0simple_floordiv_gcd..integer_coefficientsgyy**1-+ -#U]]34 CCM- + yy-.. + s )A?A?r5c>[T[RRU55n[R "[ RU5$rG)mapr:AddrarTreduceregcd)r5integer_factorsris r?integer_factor+simple_floordiv_gcd..integer_factors:), !4!4T!:* /::rAc3.># UH nTU;v M g7frGrZ)rJ base_splitrWs r?rL&simple_floordiv_gcd..s=:qJs) r:Basicrbrerolistrlr`rarmall)r\r]rqro base_splits divisor_splitrirWs @@r?simple_floordiv_gcdr{~s"/u{{/s/;U[[;S; xxq)>!+<=C 7AGq15 EII  !4!4Q!782K.3YY-@-@-CM  == = ='C JrAcB\rSrSr%SrSr\\S4\S'Sr \\S'Sr \ \S '\ S \ R4S j5r\ S \ R4S j5rS \ R"R$S \4Sjr\S\ R,S\ R,S \ RS-4Sj5rSrg)rz 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 r8.nargs# precedenceT is_integerr6c URS$NrrDselfs r?base FloorDiv.baseyy|rAc URS$Nrrrs r?divisorFloorDiv.divisorrrAprintercURUR[SS- 5nURUR[SS- 5nSUSUS3$)NAtom?(z//)) parenthesizerrrrrrrs r? _sympystrFloorDiv._sympystrsW##DIIz&/AC/GH&&t||Z5G#5MN4&7)1%%rArrNc 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$UR(a([US5(a[R"US5$X:Xa[R R$[U[R5(Ga"[U[R5(GaU[[*[R[R*4;d0U[[*[R[R*4;a[U5[U5- nU[R :Xa[$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$5(GaSn/n[R.R1U5HnXb- nSn[U[R5(am[3[R45[3S5:aGUR7[R85n [;SU 55n UR=(a U nO URnU(dMUR=U5 XG- nM [?U5S:wa&[+U[R."USS06- U5U-$[AX5n [U S5(a5[U[R.5(a[RB"X5n [U S5(d8[+[RD"X- 5[RD"X+- 55$g![RFa gf=f) Ndivision by zerorrz1.15.0c3># UHoRS:Hv M g7f)rN)r])rJrQs r?rL FloorDiv.eval..s,Iy!SSAXysevaluateF)$is_zeroZeroDivisionErrorrr:oonanr Zerorrr`Oner9NumberrPreinfisnanrcfloorrbrrDrmrar __version__atomsRationalrxappendr<r{rosimplifyPolynomialError) clsrrrQ quotientstermstermquotientquotient_is_integer rationalsall_rationals_intsros r?eval FloorDiv.evals ??#$67 7 FVGUXXy9 9g  G HH XXI J ? 99  599 599 499  <<77<<  ??|GQ77K ??|GR8899T2& & ?77;;  tU\\ * *7ELL11&%((UXXI>>vw588)DDd eGn,ADHH} txxiwAyy }}TZZ]33 dEMM * *z'5==/Q/Q==Tc'l!:; ; dH % %DIIaL$))A,*@A A gu}} - -IE ++D1> '+#h 22|%%8 *8+!)u~~ >I),,Iy,I)I&*2*=*=*TBT'*2*=*='&&LL&)I%2(5zQTEIIu$Eu$EEwO  %d4CC## 7EII(F(Fii.Q''NN4:.w}0M($$   sBT++UUrZ)__name__ __module__ __qualname____firstlineno____doc__rtuplerb__annotations__rrboolpropertyr:rvrrprinting StrPrinterstrr classmethodrcr__static_attributes__rZrAr?rrs"E5c?!JJ ekk&!:!:&s&^ ^ ^%++PTBT^^rArc \rSrSr%SrSr\\S4\S'Sr \ \S'Sr \\S '\ S \ RS \ RS \ RS \ RS-4Sj5rS \ S-4SjrSrg)r i<zC ModularIndexing(a, b, c) => (a // b) % c where % is the C modulus .rTrrrrrmodulusr6NcUS:XdUS:Xa[RR$[U[R5(aE[U[R5(a&[U[R5(aX-U-$US:waU[R "X5nUS:wa9[ [R"X- 5[R"X$- 5U5$[U[R5(Ga/nSnURHn[R "XsU-5X2-:wdM$[U[R5(aUS:d^[U[R5(aC[URS[R5(aURSS:aSn OURU5 M [U5[UR5:waU(a[ [U5X#5$[U[5(a*[ URSURSU-U5$g![Ra GNf=f)NrrTF)r:r rr9rcror rrrmrDr`rr<sumr)rrrrro new_terms all_positivers r?rModularIndexing.evalEs 191 77<<  tU]] + +7EMM227EMM22Ow. . !|ii.!8*tz2w}5 dEII & &-/I!%L 99TW#459JJ"477D1H"433&tyy|U]]CC IIaL1, (- !((." 9~TYY/L&s9~wHH dH % %"499Q<11GQ Q9$$   s AII-,I-cdURSSup[URUR5$)Nr8)rDr[is_nonnegative)rr\r]s r?_eval_is_nonnegative$ModularIndexing._eval_is_nonnegativeys,yy!}((!*:*:;;rArZ)rrrrrrrrbrrrrrr:rcrvrrrrZrAr?r r <s"E5c?!JJ1==1+0==1CH==1 t 11f%%diilDIIaL4K4Kc4QRvha  rArZN) rrrrrrrrrrrZrAr?r%r%#s%J;;!!rAr%c(\rSrSrSr\S5rSrg)r&i6TcnU[R[4;a[$U[R*[4;a[*$[U[R5(aU$[U[R 5(a3[R"[ R"[U555$grG) r:rrr9rcrrerrPrs r?rFloorToInt.eval9sz ehh' 'M uxxi( (7N femm , ,M fell + +==E&M!:; ; ,rArZNrrrrrrrrrZrAr?r&r&6sJ<.ns6  r)sympy.core.parametersrpopr"_satisfy_unique_summations_symbols frozenset_new_args_filterrzero_collapse_arguments_find_localzerosidentityr<rwr rr_argsetunique_summations_symbols)r original_args assumptionsrrrDr-objs r?rMinMaxBase.__new__js;??:/@/I/IJ6 6  77 F "  !!5!5d!;< )0..tC{C++D@K@<<  t9>:>># #ll3>>+> (A% 3  xx sDD! D!r6NcT[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. r8Nrrr-)r<r9rr@_unique_symbolsgetattr)rrDlhsrhslhs_unique_summations_symbolss r?r%-MinMaxBase._satisfy_unique_summations_symbolss< t9>$q':..!Wd1g q'47#  ,C00 ( , ,&&t, , c: & &,30$- )-8**C52OPPrA 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)setrr9r:coresymbolSymboladd)rrDr9 seen_symbolsrgelements r?r3MinMaxBase._unique_symbolssk!, 3su C99;!'5::+<+<+C+CDD, $$W- 'rAc |^^^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$s snfs snf)NrF)r9MinMaxrDfunc)airKcondirdos r?rK*MinMaxBase._collapse_arguments..do9sb3*-- U4Sjn[XSS9up#U(dU$UVs/sHn[UR5PM nn[R"U6nU(dU$[ U5nUVs/sHoU- PM n n[ U 5(a/U V s/sH n T"U SS06PM n n UR T "U SS065 T"USS06n X[UT5$rG)r9)rgothers r?GMinMaxBase._collapse_arguments..factor_minmax..Os :c5#9rAT)binaryrF)rr;rD intersectionrwrxr)rDis_other other_argsremaining_argsrgarg_setscommonnew_other_argsarg_set arg_sets_diffsother_args_diffother_args_factoredrrOs r? factor_minmax5MinMaxBase._collapse_arguments..factor_minmaxNs9H)-dT)J &J 2<<#CHH H<%%x0F !&\N=EFX'v-XMF=!!FS"Tm5!##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) r;rrFmaxrEminrr?r<nextiterrr)rvaluesoptions other_values num_valuerg other_values r?r*MinMaxBase._find_localzerossu  C}}$ #Icz$' $7 $' $7 ,{3%-@AA  %    |  !;  |  !tL12KH$)C)C'*cz|B {BA~+"9"9'*cz|B {B#rAc:[SUR55$)Nc38# UHoRv M g7frG) is_algebraicrJrJs r?rL&MinMaxBase...(HAr"rrDr\s r?rPMinMaxBase.5(H(H#HrAc:[SUR55$)Nc3:# UHnURv M g7frG)is_antihermitianrs r?rLr-A rrs r?rPru--(rAc:[SUR55$)Nc3:# UHnURv M g7frG)is_commutativers r?rLr+A rrrs r?rPrU++&rAc:[SUR55$)Nc38# UHoRv M g7frG) is_complexrs r?rLr&DV||Vr"rrs r?rPr&DQVV&D!DrAc:[SUR55$)Nc38# UHoRv M g7frG) is_compositers r?rLrrr"rrs r?rPrrrAc:[SUR55$)Nc38# UHoRv M g7frG)rrs r?rLr#>v!IIvr"rrs r?rPre#>qvv#>>rAc:[SUR55$)Nc38# UHoRv M g7frG) is_finiters r?rLrs%B6akk6r"rrs r?rPrs%B166%B BrAc:[SUR55$)Nc38# UHoRv M g7frG) is_hermitianrs r?rLrrr"rrs r?rPrrrAc:[SUR55$)Nc38# UHoRv M g7frG) is_imaginaryrs r?rLrrr"rrs r?rPrrrAc:[SUR55$)Nc38# UHoRv M g7frG) is_infiniters r?rLr'Fv! 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