sgKddlmZddlmZddlmZmZmZddlm Z ddl m Z ddl m Z mZmZddlmZmZmZmZmZmZddlmZmZdd lmZmZmZmZmZm Z dd l!m"Z"dd l#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;ZZ>m?Z?m@Z@mAZAmBZBdd lCmDZDdd lEmFZFmGZGmHZHmIZImJZJmKZKdZLdZMdZNdZOdZPdZQdZRdZSdZTdZUdZVdZWdZXdZYdZZdZ[dZ\dZ]d Z^d!Z_d"Z`d#Zad$Zbd%Zcd&Zdd'Zed(Zfd)Zgd*Zhd+Ziy,)-)Add)Mul)IRationalpi)evaluate)S)DummySymbolsymbols)coshcothcschsechsinhtanh)rootsqrt)coscotcscsecsintan)powsimp)LTR1TR10TR10iTR11_TR11TR12TR12iTR13TR14TR15TR16TR111TR2TR2iTR3TR4TR5TR6TR7TR8TR9TRmorrie_TR56TRpower hyper_as_trigfuprocess_common_addends trig_split as_f_sign_1)verify_numerically)abcxyzctdttzttzdt tz dt tz zk(sJy)N)rrr>rrrO/var/www/html/venv/lib/python3.12/site-packages/sympy/simplify/tests/test_fu.pytest_TR1rGs; qQx#a& !Qs1vX#a&%8 88 8rEc xtttttt tz k(sJtt tt tttz k(sJttttttt tz z dk(sJy)Nr)r)rr>rrrrDrErFtest_TR2rIss s1v;#a&Q- '' ' s1v;#a&Q- '' ' s3q6CF3q6M)* +q 00 0rEctdtzttzz dtz tzk7sJtt tt tz t tk(sJtt tt tzt tz t tt tzk(sJtdt tt tz z dt tz k(sJtdt tt tzt tz z dt tz t tz k(sJtt tdz t tdzz t tt tdzz dz k(sJtt tdz t tdzz dt tdz dz k(sJtt dt ddzz dt tjk(sJtt dt ddzz dt dk(sJtt dt ddzz dt dk(sJtt dt ddzz dt dtjzk(sJtt ddzt dz ddt tjz k(sJtt ddzt dz ddt dz k(sJtt ddzt dz ddt dz k(sJtt ddzt dz ddt dtjzz k(sJtt ddzt zt dtzzdt tjtzk(sJtt ddzt zt dtzzdt dtzk(sJtt ddzt zt dtzzdt ddzt zt dtzzk(sJtt ddzt zt dtzzdt ddzt zt dtzzk(sJtt ddztzt dt zzdt tjt zk(sJtt ddztzt dt zzdt dt zk(sJtt ddztzt dt zzdt ddztzt dt zzk(sJtt ddztzt dt zzdt ddztzt dt zzk(sJtdd}tt ddz|zt d| zzdt dtjz| zk(sJtdt ddz|zt d| zzz dt dtjz|zk(sJy) NrBrCT)halfiinteger) rr>r?r*rrrr Halfr;r )rNs rF test_TR2irRs 1a419 !A# )) ) As1v #a& (( ( As1v c!f$ %QA 66 6 3q6#a&=! "aAh .. . 3q6#a&=Q'( )Qs1vXc!f_ << < Aq#a&1*% &#a&#a&1**=a*? ?? ? Aq#a&1*%D 1S1XaZ ?? ? AA #$ /3qvv; >> > AA #$ /3q6 99 9 AA #$ /3q6 99 9 AA #$ /3qx= @@ @ Q!SV#$ /1S[= @@ @ Q!SV#$ /1SV8 ;; ; Q!SV#$ /1SV8 ;; ; Q!SV#$ /1S166]? BB B Q!r"3q619,4 8CKN JJ J Q!r"3q619,4 8CFAI EE E Q!r"3q619,4 8SVaZA2Q QQ Q CFQJ?3q6QB</0t <AaffH q@P PP PrEcttttttz zz ttttz ztzk(sJttdz tzt t k(sJtdtzdz tztt k(sJtt t tttfD]M}|ttddz}t|}t||r|j|jk7rMJtd5tdtzdz }dddjdtzrt|t tdz k(sJy#1swYBxYw) NrBF  )r+rr?r>rrrrrrrr:funcrhas)frNjeqs rFtest_TR3r_Bs/ s1q!a%y=! "c!QU)a-&8 88 8 r!tax=SVG ## # r"uQw{ Aw && &3S#s += b!Q  F!!Q'AFFaff,<<<= % 2b\ 66!B$s rFztest__TR56..Ys !a%rErUrLFrBrC raT)Trr>rr)hs rF test__TR56rmXs{A SVQYS!Q .#a&3q619*q.2I II I SVRZc1a /3q62: == = SVQYS!Q .CFAI:>A2E EE E SVQYS!Q -Q :: : SVQYS!R .CFAI:>A2E EE E SVQYS!Q -Q :: : SVacAg S!Q 5Q!A#'9J JJ JrEc:tttdzttdz dzk(sJtttdzttdzk(sJtttdzttdz dzdzk(sJyNrBrCrL)r-rr>rrDrErFtest_TR5rqey s1vqy>c!faiZ!^ ++ + s1vrz?c!frl ** * s1vqy>s1vqyj1nq0 00 0rEc:tttdzttdz dzk(sJtttdzttdzk(sJtttdzttdz dzdzk(sJyro)r.rr>rrDrErFtest_TR6rtkrrrEctttdztdtzdz tjzk(sJtttdzdztdtzdz t ddzk(sJy)NrBrCrU)r/rr>r rQrrDrErFtest_TR7rvqsg s1vqy>S1XaZ!&&0 00 0 s1vqy1} QqS!hq!n!< <<  Aq Aq> " "" " s1vc!f}SV#CF*3q61 2 B CF1HqQx{*SWRZ7#a&(B B  WRZ "%b'"* -/72 ?ADQ J JJ J s2hq!n$%q(RA->)?)BBBs2a4yRS|OT UYabcegYh hh hrEc  tj}d|z}t||k(sJttdtdzdt|zt|zk(sJttdtdz dt |zt |zk(sJtt dt dz dt |zt|zk(sJtt dt dzdt |zt|zk(sJttddt dzzdt dzztddt |zt|zzk(sJttdtdzdtdztdzzdtdztdzk(sJttdtdztdz dz tdzdtdztdzk(sJttdtdztdztdzdttjztdztt ddzk(sJttdtdtdzztdtdtdzzk(sJttt  ttt zzdt tt zdz t dz z zt tt zdz t dz zzk(sJtt t  t tt zzdt tt zdz t dz z zttt zdz t dz zzk(sJtt}t t}d D]}||f||fttttt zft tt tt zffD]}t||}t|Dcgc] }t| c}}t|}|d j|djk(r(t||jd r2|js&|dj|d jk7s||k7sJycc}w) NrUrCrBrprLrMrarW)rCrC)rC)rrC)rrrTtrig)r rQr1rrrr?r>ziprrrZr:expandis_Add) r;r<r=ssiargsaiexts rFtest_TR9rs A !A q6Q;; s1vA 1SV8CF? 22 2 s1vA 1SV8CF? 22 2 s1vA 2c!f9SV#3 33 3 s1vA 1SV8CF? 22 2 s1v#a& 1SV8+ ,A3q6#a&0H HH H s1vA3q6#a&0 1Qs1vXc!f_ DD D AQQ')CF2 3qQxA FF F s1vAQ'#a&0 1 #aff+ c!fS!Q00 11 1 s1vAs1v % &#a&3q6#a&=*@ @@ @ AwQqS! "bQqSUQqS[)9&9#ac!eack:J&J JJ J AwQqS! "aAaCEAaCK(8&8QqSUQqS[9I&I II I AA AA27a&1a&3q63qs8"4s1vs1Q3x6HI 7Ar1:D$/BsBx/0BBA! QqTYY.&r1888+>?188Q499! )bAg 77  770s5T cttttzt t t tzttttzzk(sJtt ttzt tttzt tttzzk(sJtt ttzt zt t t tzttttzzt t zt tttzt tttzztt zzk(sJttttzt zt t t tzttttzztt zt tttzt tttzzt t zz k(sJyN)rrr;r<rr=rDrErF test_TR10rsn AE Aws1v~As1v = == = AE s1vc!f}s1vc!f}< << < AEAI  a&Q#a&Q- 'Q/ QAQA &A. / // / AEAI  a&Q#a&Q- 'Q/ QAQA &A. / // /rEc ^ttdtdztdtdzztdk(sJttdtdztdtdzz tdk(sJttdtdztdtdzz tdk(sJttdtdztdtdzztdk(sJttdtdztdtdzzdztddzk(sJttdtdztdtdzztdztdtdzk(sJtdtdztdzdtdztdzztdzdtdztdzk(sJttdtdztdtdtdztdtdzzzztdk(sJtdtdztdtdtdztdtdzzzztdztdtdzz}t|t|jcxk(rtdk(sJJtt dtt zt zt dtt zt zzdt dzt ztt t dz zzk(sJttt t dz tt t dz ztt t dz dz ztt t dz dz zdt dztt t dz zzdz k(sJttt t dz tt t dz zttt dz dz zttt dz dz zt dtt t dz zzdz t dttt dz zzdz zk(sJttt t dtt zzdt dztt t dz zzzdtt zk(sJttt t dtt zzdt dztt t dz zzzdtt zzdt dztt t dz zzk(sJttdtdztdtdzztdtdztdtdzzk(sJtd d }tt dtt z|zt dtt z|zzdt dztt t dz zz|zk(sJtt }tt }tt}tt}d D]q}||z||zf||z||zffD]X}t||}t|D cgc] } t|  c} } t| } | | jd z s | jsXJstt }tt }tt dz }tt dz }d D]q}||z||zf||z||zffD]X}t||}t|D cgc] } t|  c} } t| } | | jd z s | jsXJsycc} wcc} w)NrCrUrBrLrVrMrarWAF commutativerTr) rrrrrr>rr?r rrrr) r^rr=rrlrrargsirrrrs rF test_TR10irs QAQA. /3q6 99 9 QAQA. /3q6 99 9 QAQA. /3q6 99 9 QAQA. /3q6 99 9 QAQA.2 3s1vz AA A QAQA.Q7 8CFSVO KK K 3q6#a&1SV8CF?2SV; < #a&3q6   QAQQAQA)F!GG H A   a&Q-#a& As1v As1v %' '(+A /14QA ?B 9biik* 4c!f 44 44 4 aQ!DGCFN1$44 5 $q' ! CBqDM! "" " QQ#a&a.0 F47N1 "1vd1g~a/0 145d1gIc!bd(m4KA4M NN N QQ#a&a.0 F47N1 "1vd1g~a/0 1 QA1H a$q'#a"Q$h-"7"99 :: : Q$q'#a&.(1T!W9SRT]+BB CqQx OO O Q$q'#a&.( d1gIc!bd(m #$&'Ah/ 034T!W9SRT]3J KK K QAQA. / As1v As1v % && & s&A aQ!DGCFN1$44 5 $q' #a"Q$h-! "" " AA AA AA AA2>sAaCj1Q3!*- >Er5>D$/BsBx/0Bb AQXX4X00AHH ==  >> AA AA BqD A BqD A2>sAaCj1Q3!*- >Er5>D$/BsBx/0Bb AQXX4X00AHH ==  >>00s 'b% b* c 4ttdtzdttzttzk(sJttdtzdttdz ttdzzttzttzzk(sJtttt ddzdttdz dz ttdz dzzttdz zttdz zzk(sJttdtzttdz ttdzzk(sJttdtzttdz ttdzzdzdttdzzttdzzz k(sJttdtdk(sJttt t ddzt t ddztt t ddzdz tt t ddzdzzk(sJttddtddz tddzzk(sJttddtdk(sJtttttdz z tdz dttdz zk(sJy)NrBrLrUrVra)r rr>rrrrDrErF test_TR11rsq AaC>Qs1vXc!f_ ,, , AaC>Q#a&!)c!fai!7Q ?A FG GG G Ahq!n$% & S1Xq[L3qs8Q; &AaC 0QqS 9: ;; ; AaC>c!faiZ#a&!)3 33 3 AaC> a&!)c!fai !#aA k#a&!)&;; << < A<3q6 !! ! Bx1~%&8Aq>(9 :s2hqRSnCT?UWX?X>X[^_abjklnobp_p[qst[t>t tt t A?s1vqyj3q6194 44 4 A?c!f $$ $ As1Q3x1 %3qs8 33 3rEc &tttdz tdtzzttdz zttdz ttdz zz dttdz zttdz ztdtzzk(slJtttdz tdtzzttdz zttdz ttdz zz tttdz ttdz z dttdz zk(sJtttdz ttdz z ddttdz zz k(sJttdtzttdz zttdz z tdtzdttdz zz k(sFJttdtzttdz zttdz z tttttdz z dttdz zk(sJy)NrUrBrLrarjrC)r!rr>rrDrErF test__TR11rs QqS#ac("3qs8+S1Xc!A#h->? @ #ac( 3qs8C!H$ %[%*3qs8C!H+r?r@rDrErF test_TR12rs AE AQ3q6'#a&.12DE EE E AEAI  Q3q6CF?c!fWSV^a%78 8 SVc!f_c!f $s1vgc!fnq&8 99 ; ;; ; AaC>S1X %% %rEcttdtdztd tdz tdtdz z dzk(sJttdtdzdtdtdzztdtdzzk(sJttdtdztdztd tdz tdtdz z dztdzk(sJttdtdztdztd tdz dztdtdz z tdzk(sJy)NrUrBrMrC)r$rrrDrErF test_TR13rs> As1v 3q6'#a&.3q6#a&="@1"D DD D As1v !c!fSVm"3c!fSVm"C CC C As1v c!f$ % a&Q#a&Q- '! +SV3 44 4 As1v c!f$ % a&Q! c!fSVm +SV3 44 4rEc^tttttzdk(sJyNrB)rrr>rrDrErFtest_Lrs! SVc!f_  "" "rEc  ttddztddzzttdz zt ddk(sJtt dtt zt dtt zzdt dztt tdz zzk(sJtt dzttdzz ttdzzdtt dzzz}t|tt dzdttdzzz dzk(sJttjtdt zdz z tt dzk(sJtttttttz zttttttzzzt dtttztdz zzk(sJtt dtt zdz tt dz ztt tdz zk(sJtdtdt zdzdz z ttdzz tt dzz tt dz ttdzzk(sJtttt ddzttdz k(sJtttdz ttt ddzzttt ddzzttt ddzzt dd k(sJtttt d dzttt d dzzt dttt d dzzttt d dzzz t d k(sJttdtdztdtdzk(sJttd Dcgc]}td|zc}}t|td d tdzz k(sJttt t tt dzztt t tt dzzk(sJtdtt dzzdtt zzdt dztt dzzzdt dztt zztdt zdzz d tt zdt dztt zzk(sJycc}w)N2rBrarUrLrCrWryrVrMriii#)r6rrrrrr>r?r rQr;r<rrrange)r^rNexprs rFtest_furs c"gqj3r7A:%BqD 1 2hq!n DD D d1gc!fntAws1v~- .!DG)CBqDM2I II I QSVQY Q *Qs1vqy[ 8B b6SVQY3q619,q0 00 0 affs1Q3xz! "c!fai // / c!fc!fs1vo&QQ#a&)AA B QAEBqDL!! "" " d1gc!fnQQ) *c!bd(m ;; ; a#ac(A+a-#a&!)+c!fai7 8 Q SVQY   c"Xa^#$ %RU 33 3 c"Q$iBx1~-..s2hq!n3D/EEc"XVWYZ^J[F\\ ]aijkmoap pp p  Bx2 #b!R&8"99DGC8TUWY?HZD[<[\_`bcklmoqcr`r\s>473q6AQQUXYZ[\Y\U]`aUac d #a&1T!W9SV## $$ $ /s=Wctttttz dt tk(sJtttttz dttttz k(sJy)Nc$|jSr count_opsrgs rFrhz test_objective..:s{q{{}rE)measurec&|j Srrrgs rFrhz test_objective..<s  ~rE)r6rr>rrrDrErFtest_objectiver9sd c!fSVm%< = F   c!fSVm%= > F3q6M  rEcJd}ttgdddi|dddk(sJy)NcXt|jDcgc] }||dzz c}Scc}wr)rr)r>rNs rFrhz-test_process_common_addends..Cs%31662aQqS232s')rCrBrUrLrFc |dzSrrDrgs rFrhz-test_process_common_addends..Es qsrE)key2key1ra)r7r)dos rFtest_process_common_addendsr@s9 4B !#|"De"Db  (+D EE ErEcn tttttdddttdfk(sJtdttzdttzdddttdfk(sJtttt tzttt tzt tddttdfk(sJtttt d t tzddddtt dz d fk(sJtttt tdt dddtt d z d fk(sJtttt t dt dddtt d z d fk(sJtt dttzt d t tzddt dzddtt dz d fk(sJtt d ttzt d t tzddt dzddtt dz d fk(sJtttt dz t tt dz dt ddz ddtt dz d fk(sJtt d ttzt tzt d t tzt tzddt dzt tzddtt dz d fk(sJtttt tJtttt tJtdttzt t Jtttt d t tzJtttttzt tt tzJtttttzt tt tzJtt d ttzt dt tzt tzd Jtt dt tztddJtt dttdzt dtdzdJttd tdztd t d zdJy) NrCTrBrprrU)tworaFrLrMrV) r8rr>r?rrrr@rrDrErFtest_trig_splitrHs[ c!fc!f %!Q1a)> >> > aAh3q6 *q!RAt.D DD D c!fSVmSVCF] 3 QAq!T" ## # c!ftAwhs1vo4 8 Ar1bdE" ## # c!fc!f$ / a!Q2a4' (( ( c!fs1vg4 0 a!RBqD%( )) ) d1gc!fntAwhs1vo4 @ 47Ar1bdE* ++ + tAwhs1voQxAD A DGQ1bdE* ++ + c!fT!Wnc!fT!Wn$ ? aAq!RT5) ** * tAwhs1voc!f, !WHSVOCF " . DGCF Aq!RT51 22 2 c!fc!f % -- - c!fc!f % -- - aAhQ ( 00 0 c!ftAwhs1vo . 66 6 c!fSVmSVCF] 3 ;; ; c!fSVmSVCF] 3 ;; ; tAwhs1votAws1v~c!f'<$ G     d1gd1gos1v4 8 @@ @ d1gd1aj(#a&Q-T B JJ J c!fSVmSVCF] = EE ErEc tdttdDcgc] }t|c}zdt dzt dztdztdztdzdt dzt d zz k(sJtt t k(sJtd t zd t zk(sJtt dz tt td dzztt td dzz}tt|td d k(sJttddDcgc]}td |zt zdz c}}ttt|tddk(sJtt tt d z z }t||k(sJtt d z t t d z ztt d zz}t|t d t ztt d zzd z k(sJycc}wcc}w)NrVrir{ryrMrWr|rCrUrBrLrrji) r2rrrrr>rrr0r+)rNer^s rF test_TRmorrierls AcE"I6qCF677 8 #b' #b'#a& Q'A.3q6 #a&0@A BB B A;!   AaC=AaC   BqD #b!Q'((RA->)??A x{ xA .. . uQ| 4!c!Q$r'"*o 45A s8A; HQ$6 66 6 QAaCB B<2   QqS#ac( 3q619 $B B<3qs8CFAI-a/ // /7 5s H9 H>c tdttdzz dttdzz k(sJtttdzttdz dzzdttzdz tdtzdz ztt dz tdtzdz zt ddzzk(sJt ddD]p}t tt|zttt|zsJt tt|zttt|zrpJy)NrCrBrUrLrj)r4rr>rrrr:)ks rF test_TRpowerr}s  1SVQY; 1SVQY; .. . 3q619S1Xq[( ) 3q6!c!A#hqj CF719s1Q3xz#9HQN#JK LL L 1a[A!#a&!)WSVQY-?@@@!#a&!)WSVQY-?@@@ArEc*ddlm}m}ttdzt tdzz}t |\}}|t|t dtzk(sJt tttz\}}|t|ttttzttttzdzz k(sJt}|tt|ttt|zzk(sJ|tt|ttt|zzk(sJ|tt|t!t|ztz k(sJ|t t|t#t|zk(sJ|t%t|t't|zk(sJ|t)t|t+t|ztz k(sJtt ttt$t(fD]#}|t,}||||||k(r#J|t#ttzt.ztt tt.tzzk(sJ|tttzt.ztttt.tzztz k(sJ|tttzt.ztttt.tzztz k(sJ|t!ttzt.ztttt.tzztzk(sJ|t'ttzt.ztt%tt.tzzk(sJ|t+ttzt.ztt)tt.tzztzk(sJy)Nr)_osborne _osborneirBrC)sympy.simplify.furrrr>r r5r6rr?r"r rrrrrrrrrrrr@) rrr^rr\rdrZrls rFtest_hyper_as_trigrs5 a!d1gqj B  DAq RU8tAaCy  a!e %DAq T!W:$q'DG+d1gd1go.AB BB B A DGQ 1S1X: -- - DGQ 1S1X: -- - DGQ 3qs8A: -- - DGQ 3qs8 ++ + DGQ 3qs8 ++ + DGQ 3qs8A: -- -tT4t41 H!Q+q0001 S1q\1 %a!A#g 66 6 S1q\1 %a!A#gq 88 8 S1q\1 %a!A#gq 88 8 S1q\1 %a!A#gq 88 8 S1q\1 %a!A#g 66 6 S1q\1 %a!A#gq 88 8rEctttfDcgc] }t|c}\}}}t ||z| |zdzz tttzk(sJt ||z||zdz z tttz k(sJt | |z ||zdz z tttzk(sJ||z| |zdzdzz d|zd|zz zd||zdz zz }t |j dtttzztttzzttttzdz z dz k(sJt tt tt z tt tt z k(sJ|tdz| |zdzz }t ||k(sJ||zdzdz| |zdzz }t ||k(sJ|| |zdzz }t ||k(sJ||ztdzzj dz||zdz z }t |tdzdz tttzzk(sJycc}w)NrCrBrU) r;r<r=rr#rr>rr)rNtatbtcr^s rF test_TR12irsD#$a),Q#a&,JBB "r'RCFQJ' (CAJ 66 6 "r'BrEAI& 'CAJ; 66 6 2#(RUQY' (CAJ 66 6 r'RCFQJ? "BrEAbDL 11beai= AB   3q1u: c!a%j #a&3q6/A"56q8 99 9 QA 3q6#a&= 00 0 s1v+B #B 9?? r'A+ B3r6A: &B 9?? bSVaZB 9?? Ga!e  $ $ & *BrEAI 6B 9!a%! CAJ. .. .-sI+cttdz ttdzz}ttdz }t||k(sJtd|z d|z k(sJtttdz dzttdzdzz|dzk(sJtttdz dzttdzdzz|dzttdzzk(sJtttdz dzttdzdzz|dzttdz zk(sJttdz tzttdztzz}t||k(sJttdz tzttdzz}t||k(sJt tdz dzttdzz}t||k(sJt dd}tttdz |zttdz|zz||zk(sJtttdz |zttdz|zzttdz |zk(sJttdz |dzzttdz|zz}t|ttdz ||zz|fvsJtttdz ttdzzttdz k(sJttdzttdz z}ttdz dzttdzz}dttdz zdttdzzz}t||z|ztdz zdtdz ttdzzttdzzzk(sJy) NrCrBrUrNTrOirL)rr>rr%r?rr )r^ansrNp1p2p3s rF test_TR14rs9 a&1*s1vz "B q619*C 8s?? ":3   Q!aQ!a/ 0CF :: : Q!aQ!a/ 0CFCFQJ4G GG G Q!aQ!a/ 0CFCFQJ4G GG G a&1*q#a&1*q (B 8r>> a&1*q#a&1* %B 8r>> a&1*q#a&1* %B 8r>>T"A Q!aQ!a/ 0CF :: : Q!aQ!a/ 0c!faiZ!O CC C a&1*A A Q .B 8Q!S!V+R0 00 0 Q!c!fqj) *s1vqyj 88 8 a&1*s1vz "B a&1*aQ! $B SVaZ.1c!fqj> *B 2b!a% !S1q5#a&!)*;CFAI*E%F FF FrEcRtddttdzz z ttdz k(sJt ddt tdzz z t tdz k(sJtddt tdzz z dttdzz k(sJy)NrCrB)r&rr>rr'rrr(rDrErFtest_TR15_16_17rs Ac!faiK SVQYJ .. . Ac!faiK SVQYJ .. . Qs1vqy[ !QQ] 22 2rEcttdzdtdfk(sJttdz dtdfk(sJtt dzdtdfk(sJtt dz dtdfk(sJtdtzdzdtdfk(sJtttztz ttdfk(sJtt tztzt tdfk(sJy)NrCrrB)r9r>r?rDrErFtest_as_f_sign_1rs q1u !Q ** * q1u !Q ++ + rAv 2q"+ -- - rAv 2q!* ,, , qsQw Aq!9 ,, , qsQw Aq": -- - r!tax aRBK // /rEctdd}tdd}tdttzt tz|z|zt dtz|z|zk(sJt t dt dz|z|zt d t dz t dt dz z dz|z|zk(sJdttzt tz|z|zttdzzjt dtz|z|ztdtzdz ztjdz zk(sJy) NrFrBrBrUrMrC) r r0rr>rr$rsimplifyr One)rrs rFtest_issue_25590rs"s&As&A qQxAq " #s1Q3xz!| 33 3 As1v a! "Aws1v~As1v 'E'I1&LQ&N NN N c!fHSVOA a #a&!) + 5 5 73qs8A:a<#aPQc(ST*;TWXW\W\]^W^;^ ^^ ^rEN)jsympy.core.addrsympy.core.mulrsympy.core.numbersrrrsympy.core.parametersrsympy.core.singletonr sympy.core.symbolr r r %sympy.functions.elementary.hyperbolicr rrrrr(sympy.functions.elementary.miscellaneousrr(sympy.functions.elementary.trigonometricrrrrrrsympy.simplify.powsimprrrrrrr r!r"r#r$r%r&r'r(r)r*r+r,r-r.r/r0r1r2r3rkr4r5r6r7r8r9sympy.core.randomr: sympy.abcr;r<r=r>r?r@rGrIrRr_rcrmrqrtrvr}rrrrrrrrrrrrrrrrrrrrrDrErFrs00*"66VVASS* 1&&91 !QH 29 K1 1 = i78/4>n4$0&4##$LE!FH0"A9</&G83 0 _rE