oVh\2ddlmZddlmZddlmZddlmZddlm Z ddl m Z m Z m Z mZddlmZmZmZmZmZmZmZddlmZmZdd lmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&dd l'm(Z(dd l)m*Z*m+Z+m,Z,m-Z-dd l.m/Z/dd l0m1Z1ddl2m3Z3m4Z4m5Z5m6Z6ddl7m8Z8ddl9m:Z:ddl;mZ>ddl?m@Z@mAZAddlBmCZCmDZDddlEmFZFddlGmHZHmIZImJZJddlKmLZLmMZMddlNmOZOddlPmQZQddlRmSZSmTZTddlUmVZVddlWmXZXddlYmZZZm[Z[m\Z\ddl]m^Z^ddl_m`Z`ddlambZbdd lcmdZddd!lemfZfdd"lgmhZhdd#limjZjmkZkdd$llmmZmdd%lnmoZompZpdd&lqmrZrdd'lsmtZtdd(lumvZvdd)lwmxZxmyZydd*lzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZe4d+e,\ZZZGd-d.ZGd/d0eZGd1d2eZeZeZe!d3ed4eeeeeezgZed5d6eegzZd7Zd8Zd9ZGd:d;ZGd<d=eeZGd>d?ZGd@dAeZdBZdCZdDZdEZdFZdGZdHZdIZdJZdKZdLZdMZdNZdOZdPZdQZdRZdSZdTZdUZdVZdWZdXZdYZdZZd[Zd\Zd]Zd^Zd_Zeyd`ZdaZdbZdcZddZdeZdfZdgZdhZdiZdjZdkZdlZdmZdnZdoZdpZdqZdrZdsZdtZduZdvZdwZdxZdyZdzZd{Zd|Zd}Zd~ZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZeydZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZy))refine)Sum)Add)Basic)Tuple) ExprBuilder unchangedExprUnevaluatedExpr)Functionexpand WildFunction AppliedUndef DerivativediffSubs)Mul_unevaluated_Mul) NumberSymbolEzooooFloatIRationalnanIntegerNumberpi_illegal)Pow)GeLtGtLe)S)default_sort_key)SymbolsymbolsDummyWild)sympify) factorial) exp_polarexplog)sinhtanh)sqrtMax) Piecewise)tansincos) Heaviside DiracDelta)Si)gamma) integrateIntegral) FockState)apart)factorcancelPoly)together)O) FiniteSet)combsimp) gammasimp)powsimp)collectradsimp)ratsimp)simplify nsimplify)trigsimp)Indexed)meter)raisesXFAIL) abcntuxyzzf,g,hclscXeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd Zy) DummyNumbera Minimal implementation of a number that works with SymPy. If one has a Number class (e.g. Sage Integer, or some other custom class) that one wants to work well with SymPy, one has to implement at least the methods of this class DummyNumber, resp. its subclasses I5 and F1_1. Basically, one just needs to implement either __int__() or __float__() and then one needs to make sure that the class works with Python integers and with itself. cXt|ttfr||jzStSN isinstanceintfloatnumberNotImplementedselfrTs J/home/dcms/DCMS/lib/python3.12/site-packages/sympy/core/tests/test_expr.py__radd__zDummyNumber.__radd__C$ a#u &t{{? "cbt|tttfr|j|zSt Srbrdrerfr`rgrhris rk__add__zDummyNumber.__add__H' a#uk2 3;;? "rncXt|ttfr||jz StSrbrcris rk__rsub__zDummyNumber.__rsub__Mrmrncbt|tttfr|j|z St Srbrpris rk__sub__zDummyNumber.__sub__RrrrncXt|ttfr||jzStSrbrcris rk__rmul__zDummyNumber.__rmul__Wrmrncbt|tttfr|j|zSt Srbrpris rk__mul__zDummyNumber.__mul__\rrrncXt|ttfr||jz StSrbrcris rk __rtruediv__zDummyNumber.__rtruediv__armrncbt|tttfr|j|z St Srbrpris rk __truediv__zDummyNumber.__truediv__frrrncXt|ttfr||jzStSrbrcris rk__rpow__zDummyNumber.__rpow__ks% a#u & # #rncbt|tttfr|j|zSt Srbrpris rk__pow__zDummyNumber.__pow__ps( a#uk2 3;;!# #rnc|jSrbrgrjs rk__pos__zDummyNumber.__pos__u {{rnc|j Srbrrs rk__neg__zDummyNumber.__neg__xs}rnN)__name__ __module__ __qualname____doc__rlrqrtrvrxrzr|r~rrrrrnrkr`r`6sC           rnr`ceZdZdZdZy)I5c|jSrbrrs rk__int__z I5.__int__rrnN)rrrrgrrrnrkrr|s FrnrceZdZdZdZy)F1_1皙?c|jSrbrrs rk __float__zF1_1.__float__rrnN)rrrrgrrrnrkrrs Frnrz1.3rg@cBtD]}tD] }||| y)NT)all_objs)sxoyos rkdotestrs. B b"I  rnc$d}t|sJy)NcH|}|}| }||z}||z }||z}||z }||z}~yrbrrTrUrZs rkjztest_basic..jsE  B B E E aC aC qD rnr)rs rk test_basicrs  !99rnc$d}t|sJy)Nc<|}||z }|}||z}|}||z}|}||z}yrbrrs rkrztest_ibasic..ss:  Q  Q  Q  Qrnrrs rk test_ibasicrs !99rnceZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZdZdZdZdZdZdZdZdZy)NonBasicaVThis class represents an object that knows how to implement binary operations like +, -, etc with Expr but is not a subclass of Basic itself. The NonExpr subclass below does subclass Basic but not Expr. For both NonBasic and NonExpr it should be possible for them to override Expr.__add__ etc because Expr.__add__ should be returning NotImplemented for non Expr classes. Otherwise Expr.__add__ would create meaningless objects like Add(Integer(1), FiniteSet(2)) and it wouldn't be possible for other classes to override these operations when interacting with Expr. ctd||SN+ SpecialOprjothers rkrqzNonBasic.__add__dE**rnctd||Srrrs rkrlzNonBasic.__radd__eT**rnctd||SN-rrs rkrvzNonBasic.__sub__rrnctd||Srrrs rkrtzNonBasic.__rsub__rrnctd||SN*rrs rkrzzNonBasic.__mul__rrnctd||Srrrs rkrxzNonBasic.__rmul__rrnctd||SN/rrs rkr~zNonBasic.__truediv__rrnctd||Srrrs rkr|zNonBasic.__rtruediv__rrnctd||SN//rrs rk __floordiv__zNonBasic.__floordiv__tU++rnctd||Srrrs rk __rfloordiv__zNonBasic.__rfloordiv__ud++rnctd||SN%rrs rk__mod__zNonBasic.__mod__rrnctd||Srrrs rk__rmod__zNonBasic.__rmod__rrnctd||SNdivmodrrs rk __divmod__zNonBasic.__divmod__s4//rnctd||Srrrs rk __rdivmod__zNonBasic.__rdivmod__s5$//rnctd||SN**rrs rkrzNonBasic.__pow__rrnctd||Srrrs rkrzNonBasic.__rpow__rrnctd||S)Nrrs rk__gt__zNonBasic.__gt__rrnctd||S)N<=rrs rk__le__zNonBasic.__le__rrnctd||S)N>=rrs rk__ge__zNonBasic.__ge__rrnN)rrrrrqrlrvrtrzrxr~r|rrrrrrrrrrrrrrnrkrrsk ++++++++,,++00,,++,,rnrceZdZdZy)NonExprzCLike NonBasic above except this is a subclass of Basic but not ExprNrrrrrrnrkrrsMrnrceZdZdZdZy)rz>Represents the results of operations with NonBasic and NonExprcDtj|}|||f|_|Srb)object__new__args)r^oparg1arg2objs rkrzSpecialOp.__new__s#nnS!d# rnN)rrrrrrrnrkrr s HrnrceZdZdZy) NonArithmeticzGRepresents a Basic subclass that does not support arithmetic operationsNrrrnrkrrsQrnrcttjtjtjtj tj tjtdtdtdtdtdtdtdtdtdg }|D]-ttfD]}|zd|ff|zd|ff|z d|ff|z d|ff|zd|ff|zd|ff|z d|ff|z d|ff|zd|ff|zd|ff|zd |ff|zd |fft!|d |fft!|d |ff|zd |ff|zd |ff|kd |ff|kd |ff|kDd |ff|kDd |ff|kd|ff|kd|ff|k\d|ff|k\d|ffg}|D]'\}}t#|t$ur|j&|k(r'Jt)t+fD]t-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fdt-t.fd t-t.fd!t-t.fd"t-t.fd#t-t.fd$t-t.fd%t-t.fd&t-t.fd'0y())a}Tests that Expr uses binary operations cooperatively. In particular it should be possible for non-Expr classes to override binary operators like +, - etc when used with Expr instances. This should work for non-Expr classes whether they are Basic subclasses or not. Also non-Expr classes that do not define binary operators with Expr should give TypeError. ?rrZrrrrrrrrrrrrczSrbrenasrkz-test_cooperative_operations..[ q2vrnczSrbrrsrkrz-test_cooperative_operations..\ rAvrncz Srbrrsrkrz-test_cooperative_operations..]rrncz Srbrrsrkrz-test_cooperative_operations..^rrnczSrbrrsrkrz-test_cooperative_operations.._rrnczSrbrrsrkrz-test_cooperative_operations..`rrncz Srbrrsrkrz-test_cooperative_operations..arrncz Srbrrsrkrz-test_cooperative_operations..brrnczSrbrrsrkrz-test_cooperative_operations..c qBwrnczSrbrrsrkrz-test_cooperative_operations..d rQwrnczSrbrrsrkrz-test_cooperative_operations..errnczSrbrrsrkrz-test_cooperative_operations..frrnctSrbrrsrkrz-test_cooperative_operations..gs va}rnctSrbr rsrkrz-test_cooperative_operations..hs vb!}rnczSrbrrsrkrz-test_cooperative_operations..irrnczSrbrrsrkrz-test_cooperative_operations..jrrnckDSrbrrsrkrz-test_cooperative_operations..krrnckDSrbrrsrkrz-test_cooperative_operations..lrrnckSrbrrsrkrz-test_cooperative_operations..mrrnckSrbrrsrkrz-test_cooperative_operations..nrrnck\Srbrrsrkrz-test_cooperative_operations..orrnck\Srbrrsrkrz-test_cooperative_operations..prrnckSrbrrsrkrz-test_cooperative_operations..qrrnckSrbrrsrkrz-test_cooperative_operations..rrrnN)r r&ZeroOneInfinityNegativeInfinityComplexInfinityHalfrrr(rrr!rrrtyperrrrrR TypeError)exprsneresultsresrrrs @@rktest_cooperative_operationsr#s        c  s  Avc{ Avc{ Avc{ E >0:wy) CBa#r1&R#q"&a#r1&R#q"&a#r1&R#q"&a#r1&R#q"&q4Q-(b4B-(a#r1&R#q"&A2q 1221b 12q4Q-(b4B-(R#r1&a#r1&R#r1&a#r1&b4Q-(q4Q-(b4Q-(q4Q-(1G6% C TCyI-#((d2BBB C; CD!?FH- 0B 9o . 9o . 9o . 9o . 9o . 9o . 9o . 9o . 9. / 9. / 9o . 9o . 94 5 94 5 9. / 9. / 9o . 9o . 9o . 9o . 9. / 9. / 9. / 9. /3 0K>0rnc~ddlm}tdktjusJtdktjusJtdkDtj usJtdk\tj usJt dktj usJt dktj usJt dkDtjusJt dk\tjusJt dd}|dz |dz ktjusJ|ttzttzdzj|k(sJy)Nr)r#rTrealr) sympy.core.relationalr#rr&falsetruer(rZrfunc)r#r&s rktest_relationalr-us( Fqww   !G   Fqvv   !G   C!G   C1H   C!G   C1H  sA EAEMagg %% % a!eQUQY  $ $ ** *rnc|tdd}tdd}tdd}tdd }|d kt|d k(sJ|d kt|d k(sJ|d kDt|d k(sJ|d k\t |d k(sJtddd }tddd }tddd }tddd }|d kt j usJ|d kt j usJ|d kDt j usJ|d k\t j usJtdd }tdd }tdd }tdd }|d kt j usJ|d kt j usJ|d kDt j usJ|d k\t j usJtddd }tddd }tddd }tddd }|d kt jusJ|d kt jusJ|d kDt jusJ|d k\t jusJy)Nm1F) nonnegativem2positivem3) nonpositivem4)negativerT)r0r(r3r()r5r()r7r()r(r#r%r$r"r&r+r*)r/r1r4r6s rktest_relational_assumptionsr9s: % (B u %B % (B u %B Fr"ay  !G2q !! ! Fr"ay  !G2q !! ! %d 3B u4 0B %d 3B u4 0B Fqvv   !G   Fqvv   !G   t $B $ 'B t $B $ 'B Fqvv   !G   Fqvv   !G   u4 0B %d 3B u4 0B %d 3B Fqww   !G   Fqww   !G  rnctD]pttfdttfddk(r dzdk(sJttfdttfdttfdry) NcdzSN1rrsrkrz"test_basic_nostr.. #)rncdz Sr<rr>srkrz"test_basic_nostr..r?rnrr=11cdzSr<rr>srkrz"test_basic_nostr..s cCirncdz Sr<rr>srkrz"test_basic_nostr..r?rncdzSr<rr>srkrz"test_basic_nostr..s #*rn) basic_objsrRrr>s@rktest_basic_nostrrFsb.y+,y+, !89$ $$ 9/ 0y+,y,-.rnc8dtz tztzjtdddtz tdtzk(sJdtz tztzjtdddtz tzttzk(sJdtz dztzjtdddtz tdtzk(sJdtz dztzjtdddtz dzttzk(sJdtz tzjtdddtz tdtzk(sJdtz tzttzztzjtdddtz tdtzk(sJdtz tzttzztzjtdddtz tzttzk(sJyNr)rZr[seriesrErrnrk'test_series_expansion_for_uniform_orderrKs aC!GaK  1a (AaC!Aq'M 99 9 aC!GaK  1a (AaC!GadN :: : aC!GaK  1a (AaC!Aq'M 99 9 aC!GaK  1a (AaC!GadN :: : aC!G  Aq! $!a1g 55 5 aC!GacMA  % %aA .!A#!Q- ?? ? aC!GacMA  % %aA .!A#'AaD. @@ @rncddttdtdz dz zzzjtdk(sJdtdzz dztztdzzjtddk(sJdtz dztztdzzjtddk(sJtdzdtz zjtddk(sJdtdzzjtddk(sJtdzjtddk(sJttdzzjtddk(sJtdzjtddk(sJy)Nr%rrIr%rr)rZr0leadtermrrnrk test_leadtermrQs] !c!fSVma'(( ( 2 21 5 ?? ? adFQJNQT ! + +A .q 1R 77 7 aC!GaK!Q$  ( ( +A ." 44 4 qD1Q3J  #A &" ,, , 1H  q !! $ )) ) E  A q !Q && & 1H  q !! $ )) ) qD??1 a A %% %rncbddttdtdz dz zzzjtdk(sJdtdzz dztztdzzjtdtdzz k(sJdtz dztztdzzjtdtz k(sJtdzdtz zjtdtz k(sJdtdzzjtdk(sJtdzjtdk(sJttdzzjttk(sJtdzjttdzk(sJttzjttusJt t ddtztt ddztdtjzdz z dzzt ddz dtdztjzdz z}|jttd tztzk(sJdtz tdzz }dtdzdz }|jttd|z zjtdtzdtdztzz dd tdzzz k(sJttdd tzz jtd tdk(sJy) Nr%rrIc2tdzjdSNrIrZas_leading_termrrnrkrz&test_as_leading_term..sA66q9rnrid)cdir)rZr0rVrrR ValueErrorrr3r& ImaginaryUnitrsubsr[r1r2)rds rktest_as_leading_termr`s !c!fSVma'(( ( 9 9! < AA A adFQJNQT ! 2 21 51a4 ?? ? aC!GaK!Q$  / / 2ac 99 9 qD1Q3J ' ' *ac 11 1 1H % %a (A -- - E " "1 % ** * 1H % %a (A -- - qD ! !! $1 ,, , F # #A &" ,, , :9: 1HQN"T!WQ__%>BB 1a. T!W9Q__4Q6 7A  Q DG8A:a< // / A1 A T!WaA 66!Q1W  - -a 0 QDGA QtAwY/ 00 0 QAY 0 01 0 =a HH Hrncttdztdtdzztdtdzzjttdtdzdfk(sJyrH)rZr8r7rPrrnrktest_leadterm2rbs] c!fHSSV_ $s1s1v: 6 @ @ C CF OQ    rncvttztzjtttzdfk(sJy)Nr)r[r\rZrPrrnrktest_leadterm3rds+ EAI   "q1uaj 00 0rncttdztdtdzztdtdzzjttdtdzk(sJyrT)rZr8r7rVrrnrktest_as_leading_term2rfsX c!fHSSV_ $s1s1v: 6 G G J AAJ  rncdtztzjtdtzk(sJdtzttzztdzzjtdtzttzzk(sJyNr)rrZrVrrnrktest_as_leading_term3risa FQJ ' ' *a"f 44 4 aC"Q$JA  . .q 1QqS2a4Z ?? ?rnctddd}|dz d|dzzd|zzdzz |dz|dzd|zzdzz z |dz|dzz z|d|dzzd|zzdzz z ||tztzz zd|z|dzz zdz d|tztzz zd|dzz zdtz z }|jtj|dz k(sJy)NrWT)integerr3r%rrI)r(rZrVrB)rWr&s rktest_as_leading_term4rmssD40A AqAv!|a 1a4A!a#88 1a!e  !AqD&1Q3,*+ ,./1qk :<=aCQK H  qsQwK QU) $&'c *A  Q  & & (AaC // /rncGddtdtz jtdtz k(sJdjtdk(sJttfdy)Nc eZdZy)&test_as_leading_term_stub..fooNrrrrrnrkfoorp  rnrrrIcBtjtSrbrUrrsrkrz+test_as_leading_term_stub..sA(>(>q(Arn)r rZrVrRNotImplementedErrorrus@rktest_as_leading_term_stubrw se h qs8 # #A &#ac( 22 2 q6 ! !! $A .. .  ABrncttdztjtdtdzzk(sJttdztjtdk(sJt tdztjttdzdz k(sJt tdztjtttdzzk(sJtt ttjtdk(sJtt ttjtdtz jtk(sJy)Nr%rrrlrI)rrZrVr[r>r/r0rrnrk#test_as_leading_term_deriv_integralrys a1fa 0 0 3qAv == = a1fa 0 0 3q 88 8 AFA  . .q 1QT!V ;; ; AFA  . .q 1Qq!tV ;; ; c!fa 0 0 3q 88 8 c!fa 0 0 3!7L7LQ7O OO Ornc tjthk(sJdtzjttjhk(sJddt tzzjt thk(sJddt tzzjt t tjtdthk(sJdtttzzzjtdtthk(sJtjjtjhk(sJtjjt tk(sJttjttk(sJtdtjtjthk(sJtdtjtjthk(sJtttjthk(sJttttjtthk(sJtttzttjtthk(sJtttztttjttthk(sJttttzztttjtttthk(sJt t"zjt$t"hk(sJt t"zjt$t t t"zjt t$cxk(rt"t hk(sJJt't'tjt&t't'tt'thk(sJdtdtzzzt'dtzzjt(dtdtzzzt'dtzzdtzdtzhk(sJt+tttzdz}|jt,t+thk(sJ|jt,t.t+ttthk(sJ|jt.t+ttthk(sJ|jt,t t+ttdhk(sJ|jt.t tdttt+thk(sJy)NrIrrr%)rZatomsr&rr8r(rr[rsetr7rrCrr\rXrrrr/rfrr rs rk test_atomsrs 779   E==?q!%%j (( ( #a&L   'A3 .. . #a&L   /AEE1Q43C CC C q1a4yM "qtQl 22 2 66<<>affX %% % 66<< 35 (( ( r7==  %% % 1:   !&&! ,, , 1:   !%% ++ + 1:   ! $$ $ 1a=   QF ** * Aq!  " " $A .. . Aq!Q  % % 'Aq!9 44 4 AaCAq ! 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