a lº”hh‡ã @sFdZddlmZmZddlmZddlmZmZm Z m Z ddl m Z m Z ddlmZddlmZmZddlmZmZdd lmZmZmZdd lmZmZmZmZdd lm Z m!Z!dd l"m#Z#dd l$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+ddl,m-Z-m.Z.ddl/m0Z0ddl1m2Z2m3Z3ddl4m5Z5ddl6m7Z7m8Z8ddl9m:Z:m;Z;mZ>ddl?m@Z@ddlAmBZBmCZCddlDmEZEmFZFddlGmHZHmIZImJZJmKZKmLZLddlMmNZNddlOmPZPmQZQddlRZRe8dƒZSe8dƒZTedƒZUe8dƒZVe7dƒZWe7dƒZXed ƒ\ ZYZZZ[Z\Z]Z^Z_Z`ZaZbed!ƒ\ZcZdZed"Zfd#Zgd$Zhd%Zid&Zjd'Zkd(d)„Zld»d+d,„Zmd¼d-d.„Znd/d0„Zod1d2„Zpd½d3d4„Zqgdfd5d6„Zrd7d8„Zsd9d:„ZteQd;d<„ƒZueQd=d>„ƒZveQd?d@„ƒZweQdAdB„ƒZxdCdD„ZyeQdEdF„ƒZzeQdGdH„ƒZ{eQdIdJ„ƒZ|eQdKdL„ƒZ}dMdN„Z~eQdOdP„ƒZdQdR„Z€eQdSdT„ƒZeQdUdV„ƒZ‚eQdWdX„ƒZƒdYdZ„Z„eQd[d\„ƒZ…eQd]d^„ƒZ†eQd_d`„ƒZ‡dadb„ZˆeQdcdd„ƒZ‰eQdedf„ƒZŠeQdgdh„ƒZ‹eQdidj„ƒZŒdkdl„ZeQdmdn„ƒZŽeQdodp„ƒZeQdqdr„ƒZdsdt„Z‘eQdudv„ƒZ’dwdx„Z“dydz„Z”d{d|„Z•eQd}d~„ƒZ–dd€„Z—dd‚„Z˜eQdƒd„„ƒZ™eld…d†„ƒZšeld‡dˆ„ƒZ›eld‰dŠ„ƒZœeld‹dŒ„ƒZelddŽ„ƒZželdd„ƒZŸeld‘d’„ƒZ eld“d”„ƒZ¡eld•d–„ƒZ¢eld—d˜„ƒZ£eld™dš„ƒZ¤eld›dœ„ƒZ¥elddž„ƒZ¦eldŸd „ƒZ§eld¡d¢„ƒZ¨eld£d¤„ƒZ©eld¥d¦„ƒZªeld§d¨„ƒZ«eld©dª„ƒZ¬eld«d¬„ƒZ­eld­d®„ƒZ®eld¯d°„ƒZ¯eld±d²„ƒZ°eld³d´„ƒZ±eldµd¶„ƒZ²eld·d¸„ƒZ³d¹dº„Z´dS)¾a‚ This File contains test functions for the individual hints used for solving ODEs. Examples of each solver will be returned by _get_examples_ode_sol_name_of_solver. Examples should have a key 'XFAIL' which stores the list of hints if they are expected to fail for that hint. Functions that are for internal use: 1) _ode_solver_test(ode_examples) - It takes a dictionary of examples returned by _get_examples method and tests them with their respective hints. 2) _test_particular_example(our_hint, example_name) - It tests the ODE example corresponding to the hint provided. 3) _test_all_hints(runxfail=False) - It is used to test all the examples with all the hints currently implemented. It calls _test_all_examples_for_one_hint() which outputs whether the given hint functions properly if it classifies the ODE example. If runxfail flag is set to True then it will only test the examples which are expected to fail. Everytime the ODE of a particular solver is added, _test_all_hints() is to be executed to find the possible failures of different solver hints. 4) _test_all_examples_for_one_hint(our_hint, all_examples) - It takes hint as argument and checks this hint against all the ODE examples and gives output as the number of ODEs matched, number of ODEs which were solved correctly, list of ODEs which gives incorrect solution and list of ODEs which raises exception. é)Ú DerivativeÚdiff)ÚMul)ÚEÚIÚRationalÚpi)ÚEqÚNe)ÚS)ÚDummyÚsymbols)ÚimÚre)ÚLambertWÚexpÚlog)ÚasinhÚcoshÚsinhÚtanh)ÚcbrtÚsqrt)Ú Piecewise)ÚacosÚasinÚatanÚcosÚsecÚsinÚtan)ÚEiÚerfi)Úhyper)ÚIntegralÚ integrate)Úrootof)ÚFunctionÚSymbol)ÚairyaiÚairybiÚbesseljÚbesselyÚ lowergamma)ÚNonElementaryIntegral)Ú classify_odeÚdsolve)ÚallhintsÚ_remove_redundant_solutions)Ú FirstLinearÚ ODEMatchErrorÚSingleODEProblemÚSingleODESolverÚNthOrderReducible)Ú checkodesol)ÚraisesÚslowNÚxÚuÚyÚfÚgzC1:11úa b cz^Hint did not match the example {example}. The ODE is: {eq}. The expected hint was {our_hint}z•Different solution found from dsolve for example {example}. The ODE is: {eq} The expected solution was {sol} What dsolve returned is: {dsolve_sol}zFsolution found is not correct for example {example}. The ODE is: {eq}asolution returned by dsolve is incorrect when using {hint}. The ODE is: {eq} The expected solution was {sol} what dsolve returned is: {dsolve_sol} You can test this with: eq = {eq} sol = dsolve(eq, hint='{hint}') print(sol) print(checkodesol(eq, sol)) zñdsolve raised exception : {e} when using {hint} for the example {example} You can test this with: from sympy.solvers.ode.tests.test_single import _test_an_example _test_an_example('{hint}', example_name = '{example}') The ODE is: {eq} zãTested hint was : {hint} Total of {matched} examples matched with this hint. Out of which {solve} gave correct results. Examples which gave incorrect results are {unsolve}. Examples which raised exceptions are {exceptions} cs‡fdd„}|ƒS)NcsÒˆƒ}g}|dD]º}|d|d|d|d|d| dg¡|d| d|d¡||d| dd¡|d| dd ¡|d| d d¡|d| d d¡|d| d d¡|d dœ }| |¡q|S)NÚexamplesÚeqÚsolÚXFAILÚfuncr:FÚ simplify_flagTÚcheckodesol_XFAILÚdsolve_too_slowÚcheckodesol_too_slowÚhint) rBrCrDrEÚ example_namer:rFrGrHrIrJ)ÚgetÚappend)ÚsolverrAÚexampleÚtemp©rE©úQ/var/www/auris/lib/python3.9/site-packages/sympy/solvers/ode/tests/test_single.pyÚinnerŸs" õ z _add_example_keys..innerrR)rErTrRrQrSÚ_add_example_keysžs rUFcCsR|D]H}|s|ds|r"|ds"qt|d|dd}|ddkrt|dƒqdS)Nr:rJT)Ú solver_flagÚ xpass_msgÚ)Ú_test_particular_exampleÚprint)Z ode_examplesÚ run_slow_testrOÚresultrRrRrSÚ_ode_solver_testµs  r]cCsBttƒdg}tƒ}|D]$}| d¡sd|vr0qt|||ƒqdS)NÚdefaultÚ _IntegralZseries)Úlistr1Ú_get_all_examplesÚendswithÚ_test_all_examples_for_one_hint)ÚrunxfailZ all_hintsÚ all_examplesÚour_hintrRrRrSÚ_test_all_hints¿s rgcs0t|ƒtkr"t‡fdd„|DƒƒSˆ |¡SdS)Nc3s|]}ˆ |¡VqdS©N)Údummy_eq)Ú.0Zsub_dsol©Ú expected_solrRrSÚ Ëóz"_test_dummy_sol..)Útyper`Úanyri)rlÚ dsolve_solrRrkrSÚ_test_dummy_solÉs rrcCs*tƒ}|D]}|d|kr t||ƒq dS)NrK)rarY)rfrKrerOrRrRrSÚ_test_an_exampleÐs rsc Cs¤|d}|d}|d}||dv}|d}dddœ}|d} |d } |d } |d } d } |r„|t||ƒvr„tj|||d }t|ƒ‚|t||ƒvr ||d<z4| s´t||| |d}nt|ƒdkrÊ|d}n|}WnvtyF}z\g}||d<|sút ¡t jt |ƒ|||d|d<|r.|s.t |dƒ‚d} WYd}~n d}~00|r„|gkr„d}t |ƒt kr¦|D]4}| t¡rŒt||ƒ }n||v}|rnqÒqnn,||v}|D]}| t¡r²t||ƒ }q²|ròtj||||d}t|ƒ‚dd„tt|ƒƒDƒ}t|ƒdkrd}| s„| s„t|||dd|kr„||d<d} tj||||d}|rxtj||d}t|ƒ‚n d||d<| r |r |d||d <|S)!NrBrCrKrDrErX)ÚmsgrWrFrGrHrIT)rOrBrfÚ match_list©ÚsimplifyrJérÚexception_list)ÚerJrOrBrtF)rOrBrCrqcSsg|]}d‘qS)©TrrR©rjÚirRrRrSÚ rnz,_test_particular_example..r{)Úsolve_for_funcÚ unsolve_list)rJrBrCrq)rOrBzAssertionError: zis now passing for the hintrW)r/Ú hint_messageÚformatÚAssertionErrorr0ÚlenÚ ExceptionÚ tracebackÚ print_excÚ exception_msgÚstrrZror`Zhasr rrÚexpected_sol_messageÚranger8Údsol_incorrect_msgÚcheckodesol_msg)rfÚ ode_examplerVrBrlrOÚxfailrEr\rFrGrHrIZxpassÚmessagerqrzZexpect_sol_checkZsub_solZexpected_checkodesolrRrRrSrY×s‚            rYc Csê|gkrtƒ}ggg}}}|D]~}||dv}|r<|sFrnz&test_SingleODESolver..csˆ ¡Srh©Zget_general_solutionrRr—rRrSr˜Grncsˆ ¡Srh)Ú_matchesrRr—rRrSr˜Hrncsˆ ¡Srh)Z_get_general_solutionrRr—rRrSr˜Irncsˆ ¡Srhr™rRr—rRrSr˜RrnFrxéééT) r5r>r;rr6r9ÚNotImplementedErrorr3r4r–ÚorderZ is_autonomous)ÚproblemrRr—rSÚtest_SingleODESolverAs&*"<8<r¡cCs ttƒdSrh)r]Ú)_get_examples_ode_sol_linear_coefficientsrRrRrRrSÚtest_linear_coefficientsfsr£cCs”ttƒ t¡ttƒt}t|ttƒƒ}tttƒ t¡ttƒ}t|ttƒƒ}d}d}||vrh||vslJ‚||vr|||vs€J‚ttƒttƒdS)NÚ(1st_homogeneous_coeff_subs_dep_div_indepÚ(1st_homogeneous_coeff_subs_indep_div_dep)r>r;rr/r]Ú>_get_examples_ode_sol_1st_homogeneous_coeff_subs_dep_div_indepÚ0_get_examples_ode_sol_1st_homogeneous_coeff_best)Zeq1Zc1Zeq2Úc2ZsdiZsidrRrRrSÚtest_1st_homogeneous_coeff_odejsr©cCsttddttdddS©NT)r[)r]r¦r§rRrRrRrSÚ,test_slow_examples_1st_homogeneous_coeff_odeys r«cCs ttƒdSrh©r]Ú;_get_examples_ode_sol_nth_linear_constant_coeff_homogeneousrRrRrRrSÚ*test_nth_linear_constant_coeff_homogeneoussr®cCsttdddSrªr¬rRrRrRrSÚ8test_slow_examples_nth_linear_constant_coeff_homogeneous„sr¯cCs ttƒdSrh)r]Ú%_get_examples_ode_sol_2nd_linear_airyrRrRrRrSÚtest_Airy_equation‰sr±cCs ttƒdSrh)r]Ú_get_examples_ode_sol_lie_grouprRrRrRrSÚtest_lie_groupsr³cCsbttƒ t¡}tttƒ|ttdttƒtdttƒdƒ}t|ƒdksVJ‚ttƒdS)Nrœrx)Ú factorableÚseparable_reducedÚ lie_groupZseparable_reduced_Integral)r>r;rr r/r]Ú'_get_examples_ode_sol_separable_reduced)ÚdfrBrRrRrSÚtest_separable_reduced’s8r¹cCsttdddSrª)r]r·rRrRrRrSÚ$test_slow_examples_separable_reduced›srºcCs ttƒdSrh)r]Ú,_get_examples_ode_sol_2nd_2F1_hypergeometricrRrRrRrSÚtest_2nd_2F1_hypergeometric sr¼c Cs ttdttƒ td¡dtdƒdtttƒ t¡ttƒ}tttƒtttttdtdttdtƒƒdtddtƒttdtdtƒdƒttdtdtƒ dƒt tdƒddfdtƒƒ}|t |ddksòJ‚t ||ƒd ksJ‚dS) Nrxrœéÿÿÿÿér›)rxZ2nd_hypergeometric_Integral)rJr{) r;r>rr r ÚC1ÚC2r$rr#r0r8©rBrCrRrRrSÚ$test_2nd_2F1_hypergeometric_integral¥s,F0ÿÿÿÿÿÿÿÿþrÂcCs ttƒdSrh)r]Ú8_get_examples_ode_sol_2nd_nonlinear_autonomous_conservedrRrRrRrSÚ'test_2nd_nonlinear_autonomous_conserved®srÄc CsÜttƒ td¡tttƒƒ}ttdttdtttƒtƒƒtttƒfƒt tƒttdttdtttƒtƒƒtttƒfƒt tƒg}t |ddd}t ||ƒD]\}}|  |¡s J‚q t |dd„|DƒƒddgksØJ‚dS) NrœrxÚ+2nd_nonlinear_autonomous_conserved_IntegralF©rJrwcSsg|] }| ¡‘qSrR)Zdoit)rjÚsrRrRrSr~»rnzDtest_2nd_nonlinear_autonomous_conserved_integral..r{)r>r;rrr r$rr¿Ú_urÀr0Úziprir8)rBÚactualr•ÚarÇrRrRrSÚ0test_2nd_nonlinear_autonomous_conserved_integral³s44ÿrÌcCs ttƒdSrh)r]Ú'_get_examples_ode_sol_2nd_linear_besselrRrRrRrSÚtest_2nd_linear_bessel_equation¾srÎcCsˆttƒttƒttƒ t¡}tttƒttƒƒtttƒttttƒƒg}t||dtƒ}|tttƒttttƒƒgks|J‚tt ƒdS©Nrœ) r>r;rr rr¿rÀr2r]Ú#_get_examples_ode_sol_nth_algebraic)ZeqnZsolnsZ solns_finalrRrRrSÚtest_nth_algebraicÃsÿ$rÑcCsttdddSrª©r]Ú2_get_examples_ode_sol_nth_linear_var_of_parametersrRrRrRrSÚ>test_slow_examples_nth_linear_constant_coeff_var_of_parametersÎsrÔcCs ttƒdSrhrÒrRrRrRrSÚ0test_nth_linear_constant_coeff_var_of_parametersÓsrÕcCs²d}ttƒ td¡dttƒ td¡ttƒ t¡dttttƒ}t|ttƒ|dd}t|ttƒ|dd}||ks~J‚t||dddd ks–J‚t||dddd ks®J‚dS) NZ:nth_linear_constant_coeff_variation_of_parameters_IntegralérœrTrÆF©rŸrr{)r>r;rrrr0r8)rfrBZsol_simpZ sol_nsimprRrRrSÚ@test_nth_linear_constant_coeff_variation_of_parameters__integral×sF rØcCsttdddSrª©r]Ú_get_examples_ode_sol_1st_exactrRrRrRrSÚtest_slow_examples_1st_exactåsrÛcCs ttƒdSrhrÙrRrRrRrSÚtest_1st_exactêsrÜcCsbtttƒƒttttƒƒttƒdttƒ t¡}t|ttƒddd}t||ddds^J‚dS)NrœFZ1st_exact_Integralrvrxr×)rr>r;rrr0r8)rBZsol_1rRrRrSÚtest_1st_exact_integralïs6rÝcCsttdddSrª)r]Ú)_get_examples_ode_sol_nth_order_reduciblerRrRrRrSÚ&test_slow_examples_nth_order_reducibleõsrßcCsttdddSrª)r]Ú:_get_examples_ode_sol_nth_linear_undetermined_coefficientsrRrRrRrSÚFtest_slow_examples_nth_linear_constant_coeff_undetermined_coefficientsúsrácCsttdddSrª©r]Ú_get_examples_ode_sol_separablerRrRrRrSÚtest_slow_examples_separableÿsräcCsFttttƒtƒtttƒtjtƒ}d}|t|ƒvs:J‚tt ƒdS)NÚ3nth_linear_constant_coeff_undetermined_coefficients) r rr>r;rr ÚHalfr/r]rà)rBrfrRrRrSÚ8test_nth_linear_constant_coeff_undetermined_coefficientss&rçcCsJdd„}t}||tttƒttƒ|ttƒtƒƒdks:J‚||tttƒttƒ|ttƒtƒƒdkshJ‚|ttƒ|ttƒtƒ|ttƒtdƒƒdksšJ‚||tttƒtdƒ|ttttƒtdƒƒdksÒJ‚||ttƒtdƒ|ttƒtdƒ|ttƒtdƒƒdksJ‚||ttƒtdƒ|ttƒtdƒƒdks>J‚ttƒdS)NcSstt|ttƒtƒƒ ¡Srh)r7r5r>r;rš)rBrRrRrSr˜rnz*test_nth_order_reducible..Frœrr›T)rr=r>r;r<r]rÞ)ÚFÚDrRrRrSÚtest_nth_order_reducibles..28>.rêcCs ttƒdSrhrârRrRrRrSÚtest_separablesrëcCsHtttdtƒtƒ tƒttttdtƒƒtƒ ksr;rr$r]Ú _get_examples_ode_sol_factorablerRrRrRrSÚtest_factorable s<rícCsttdddSrª)r]rìrRrRrRrSÚtest_slow_examples_factorable&srîcCs ttƒdSrh)r]Ú_get_examples_ode_sol_riccatirRrRrRrSÚtest_Riccati_special_minus2+srðcCs ttƒdSrh)r]Ú*_get_examples_ode_sol_1st_rational_riccatirRrRrRrSÚtest_1st_rational_riccati/sròcCs ttƒdSrh)r]Ú_get_examples_ode_sol_bernoullirRrRrRrSÚtest_Bernoulli4srôcCs ttƒdSrh)r]Ú _get_examples_ode_sol_1st_linearrRrRrRrSÚtest_1st_linear8sröcCs ttƒdSrh)r]Ú#_get_examples_ode_sol_almost_linearrRrRrRrSÚtest_almost_linear<srøcCsàd}ttttƒtƒtttƒtttƒttƒdtttƒtƒddttƒƒ}ttttƒtƒttttƒttƒdttttƒtƒddttƒƒ}||vs¨J‚||vs´J‚|d|vsÄJ‚|d|vsÔJ‚ttƒdS)NÚ Liouvillerœr_)r/rr>r;r]Ú_get_examples_ode_sol_liouville)rJZnot_Liouville1Znot_Liouville2rRrRrSÚtest_Liouville_ODE@s .ÿÿ&ÿÿ  rûcCsÈtdƒ\}}}}}tdƒ}d}tt|ƒ|dƒ|ddtt|ƒ|dƒ|ddt|ƒ}|t|ƒvsnJ‚|||ƒ||t||ƒ|ƒ||dt||ƒ|dƒ}|t|ƒvs¼J‚ttƒdS)Nz x t a b cr=Únth_linear_euler_eq_homogeneousr›é rœé$)r r'rr>r/r]Ú'_get_examples_ode_sol_euler_homogeneous)r;ÚtrËÚbÚcr=rfrBrRrRrSÚ*test_nth_order_linear_euler_eq_homogeneousOs@>rcCsêtdƒ\}}tddd\}}}}d}|dtt|ƒ|dƒd|dtt|ƒ|dƒd t|ƒ|}|t|t|ƒƒvs~J‚||dtt|ƒ|dƒ||tt|ƒ|ƒ|t|ƒ|t|ƒ}|t|t|ƒƒvsÞJ‚ttƒdS) Nzx tza b c dT©ÚintegerÚr/rr]Ú._get_examples_ode_sol_euler_undetermined_coeff©r;rrËrrÚdrfrBrRrRrSÚGtest_nth_order_linear_euler_eq_nonhomogeneous_undetermined_coefficients]s DJr cCstdƒ\}}tddd\}}}}d}t|dtt|ƒ|dƒd|tt|ƒ|ƒdt|ƒ|dƒ}|t|t|ƒƒvs~J‚t||d tt|ƒ|d ƒ||dtt|ƒ|dƒ||tt|ƒ|ƒ|t|ƒ|t|ƒƒ}|t|t|ƒƒvsüJ‚ttƒdS) Nzx, tz a, b, c, 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ttƒƒttƒ t¡ttttƒt t ttƒƒd ƒdt t ttƒƒd ƒdt ttƒƒtƒgd d œtt ttƒƒtdtttƒƒttƒ t¡|dtttƒƒttƒ t¡tttƒttt |d tdƒƒ dtƒtttƒttt |d tdƒƒƒgd d œttƒ t¡ttƒt tƒtttƒtt tƒƒgdœtd t ttƒƒttƒ t¡dttttƒƒtttƒttttddtd tdtƒƒƒtttƒtttddtd tdtƒƒƒgdœttƒ t¡ttƒt ttƒƒt tƒtttƒttttƒƒƒgdœtttƒ t¡d ttƒdt ttƒƒtttƒt ttƒƒgd d dœttƒ t¡tttƒd tttƒdtttd dƒƒgdœtttƒdƒtddtd tttƒttƒttƒ t¡tttƒt t d ttddtƒƒ ƒtttƒt t d ttddtƒƒƒgdœttƒ t¡ttƒtttƒttt ƒƒgdœttƒt dttƒƒt tƒtdttƒƒttƒ t¡tttƒtttt tƒdƒdƒtttƒttt tƒdƒdƒgdœd tttƒ t¡tttƒd tttƒttt ƒtd td ƒgdœttƒtttƒtƒtd tttƒdtttƒt d ƒ t ttd tdƒd ƒd ƒtttƒt d ƒt ttd tdƒd ƒd ƒgdœttƒ t¡ttttƒƒtttƒt dtttƒƒƒgdgdœtttƒ t¡d ttƒdtttƒt tdt tdƒgdœt|ƒ |¡d dtt|ƒtt|ƒdtttd|ƒdtƒgt|ƒdœttƒ t¡tttƒtttƒttttƒƒgdœ||||ƒd|t||ƒƒt||ƒdttd|ƒƒg||ƒd dœttƒ t¡tttƒtƒtttƒt ttƒ tttƒd ƒƒgdœdœdœS)Nza,té`gš™™™™™#@gš™™™™™É?Úvr=rÁrœrxrr›TrA)rBrCr:rGr½r¶rgfffff†I@gÃXvH ”?rKg ý‡Q|%QÀg+RÕ4JÂ?)rBrCrErG)Z separable_01Z separable_02Z separable_03Z separable_04Z separable_05Z separable_06Z separable_07Z separable_08Z separable_09Z separable_10Z separable_11Z separable_12Z separable_13Z separable_14Z separable_15Z separable_16Z separable_17Z separable_18Z separable_19Z separable_20Z separable_21Z separable_22Z separable_23Z separable_24Z separable_25Z separable_26Z separable_27r)r r'r>r;rr r¿rrrr rrrrrrrrr=rÀrr)rrËrNr?rJÚf1r\rRrRrSrã~sè þþþ(þ þ  þB::ÿü420ÿü,ü0NýR0&þú þ440þþ (þ,ü$þD*(þþ þ<Fþ$(þ,20ÿþý &þ *ýþ"ü (þ€áýrãcCsˆdttƒttƒtttƒƒttƒtttƒƒttƒ t¡tttƒttttƒƒ dtƒtttƒttttƒƒƒgddœdtttƒdttƒttƒtttƒdttƒ t¡tttƒt ttdt t t t tdƒƒƒƒgdgdddœdtttƒttƒdttƒttƒtttƒƒttƒ t¡tttƒttƒtttƒƒtdttƒdtƒgdgddœtttƒƒttttƒƒttƒdttƒ t¡tttttƒƒttƒd d tƒgddœdtttƒtdttƒdttƒ t¡ttdttƒttƒd d tƒgdd d œtttƒƒttttƒƒttƒdttƒ t¡tttttƒƒttƒd d tƒgd d œtt tdttƒdƒtdttƒttƒt tdttƒdƒttƒ t¡tt tƒtd t dttƒdtdƒt ttƒtƒdttƒtdt dttƒdtdƒd t dttƒdtdƒt dt dttƒdtdƒttƒtdttƒdtdƒdttƒtdt dttƒdtdƒd t ttƒtƒttƒtdttƒtdt dttƒdtdƒd ttƒt dt dttƒdtdƒttƒtdttƒdtdƒtdttƒtdt dttƒdtdƒƒgdddœttdttƒ t¡d tttƒttƒtdƒtttƒtttƒtd ƒgdœttƒtdttƒtdtttƒ t¡dd„dDƒdœtttƒdttƒ t¡tdtttƒtttƒtt ttddt tƒƒƒtttƒtt ttddt 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