o jgg‡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,„Zmd»d-d.„Znd/d0„Zod1d2„Zpd»d3d4„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)¼a‚ 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]]}|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©ú[/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/solvers/ode/tests/test_single.pyÚinnerŸs" õ z _add_example_keys..innerrR)rErTrRrQrSÚ_add_example_keysžs rUFcCsR|D]$}|s |ds|r|dsqt|d|dd}|ddkr&t|dƒqdS)Nr:rJT)Ú solver_flagÚ xpass_msgÚ)Ú_test_particular_exampleÚprint)Ú ode_examplesÚ run_slow_testrOÚresultrRrRrSÚ_ode_solver_testµs  €úr^cCsBttƒdg}tƒ}|D]}| d¡sd|vrq t|||ƒq dS)NÚdefaultÚ _IntegralÚseries)Úlistr1Ú_get_all_examplesÚendswithÚ_test_all_examples_for_one_hint)ÚrunxfailÚ all_hintsÚ all_examplesÚour_hintrRrRrSÚ_test_all_hints¿sýrjcs,t|ƒtkrt‡fdd„|DƒƒSˆ |¡S)Nc3s|]}ˆ |¡VqdS©N)Údummy_eq)Ú.0Úsub_dsol©Ú expected_solrRrSÚ Ës€z"_test_dummy_sol..)ÚtyperbÚanyrl)rpÚ dsolve_solrRrorSÚ_test_dummy_solÉs  rucCs*tƒ}|D] }|d|krt||ƒqdS)NrK)rcrY)rirKrhrOrRrRrSÚ_test_an_exampleÐs   €þrvc CsŒ|d}|d}|d}||dv}|d}dddœ}|d} |d } |d } |d } d } |rB|t||ƒvrBtj|||d }t|ƒ‚|t||ƒvrD||d<z| sZt||| |d}n t|ƒdkre|d}n|}Wn8ty }z,g}||d<|s|t ¡t jt |ƒ|||d|d<|r”|s”t |dƒ‚d} WYd}~nd}~ww|r6|gkr6d}t |ƒt krË|D]}| t¡rÁt||ƒ }n||v}|rÉnq³n||v}|D] }| t¡rÞt||ƒ }qÑ|rîtj||||d}t|ƒ‚dd„tt|ƒƒDƒ}t|ƒdkrd}| s6| s6t|||dd|kr6||d<d} tj||||d}|r0tj||d}t|ƒ‚d||d<| rD|rD|d||d <|S)!NrBrCrKrDrErX)ÚmsgrWrFrGrHrIT)rOrBriÚ match_list©ÚsimplifyrJérÚexception_list)ÚerJrOrBrwF)rOrBrCrtcSsg|]}d‘qS)©TrrR©rmÚirRrRrSÚ sz,_test_particular_example..r~)Úsolve_for_funcÚ unsolve_list)rJrBrCrt)rOrBzAssertionError: zis now passing for the hintrW)r/Ú hint_messageÚformatÚAssertionErrorr0ÚlenÚ ExceptionÚ tracebackÚ print_excÚ exception_msgÚstrrZrrrbÚhasr ruÚexpected_sol_messageÚranger8Údsol_incorrect_msgÚcheckodesol_msg)riÚ ode_examplerVrBrprOÚxfailrEr]rFrGrHrIÚxpassÚmessagertr}Úexpect_sol_checkÚsub_solÚexpected_checkodesolrRrRrSrY×sŽ    € €÷   ÿ€  €  rYc Csî|gkrtƒ}ggg}}}|D]?}||dv}|r|sq|r!qt||ƒ}|| dg¡7}|| dg¡7}|| dg¡7}|durP|d} | dkrPt|dƒq|durut|ƒ} t|ƒt|ƒt|ƒ} tj|| | ||d} t| ƒdSdS)NrDrxrƒr|rwrX)rJÚmatchedÚsolveÚunsolveÚ exceptions)rcrYrLrZr‡Úcheck_hint_msgr…) rirhrfrxrƒr|r’r“r]rwÚ match_countÚsolvedrRrRrSre's0   € ürecsÔtttƒ t¡ttƒtƒ}t|ƒ‰tt‡fdd„ƒtt‡fdd„ƒtt‡fdd„ƒtt‡fdd„ƒtttƒ t¡ttƒttƒttƒtƒ}t|ƒ‰tt‡fdd„ƒt|ƒ‰ˆ  ¡duscJ‚tttƒ t¡ttƒttƒtƒ}|j dks{J‚tttƒ td ¡ttƒ td ¡ttƒ td ¡ttƒtƒ}|j d ks J‚tttƒ td ¡ttƒ td ¡ttƒd ttƒtƒ}|j d ksÃJ‚tttƒ td ¡tttƒ td ¡ttƒd ttƒtƒ}|j dksèJ‚dS) Ncóˆ ¡Srk)ÚmatchesrR©rNrRrSÚFóz&test_SingleODESolver..cr rk©Úget_general_solutionrRr¢rRrSr£Gr¤cr rk)Ú_matchesrRr¢rRrSr£Hr¤cr rk)Ú_get_general_solutionrRr¢rRrSr£Ir¤cr rkr¥rRr¢rRrSr£Rr¤Fr{éééT) r5r>r;rr6r9ÚNotImplementedErrorr3r4r¡ÚorderÚ is_autonomous)ÚproblemrRr¢rSÚtest_SingleODESolverAs&*"<8<r°cCó ttƒdSrk)r^Ú)_get_examples_ode_sol_linear_coefficientsrRrRrRrSÚtest_linear_coefficientsfó r³cCs”ttƒ t¡ttƒt}t|ttƒƒ}tttƒ t¡ttƒ}t|ttƒƒ}d}d}||vr4||vs6J‚||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)Úeq1Úc1Úeq2Úc2ÚsdiÚsidrRrRrSÚtest_1st_homogeneous_coeff_odejs r¿cCsttddttdddS©NT)r\)r^r·r¸rRrRrRrSÚ,test_slow_examples_1st_homogeneous_coeff_odeys rÁcCr±rk©r^Ú;_get_examples_ode_sol_nth_linear_constant_coeff_homogeneousrRrRrRrSÚ*test_nth_linear_constant_coeff_homogeneousó rÄcCóttdddSrÀrÂrRrRrRrSÚ8test_slow_examples_nth_linear_constant_coeff_homogeneous„órÇcCr±rk)r^Ú%_get_examples_ode_sol_2nd_linear_airyrRrRrRrSÚtest_Airy_equation‰r´rÊcCr±rk)r^Ú_get_examples_ode_sol_lie_grouprRrRrRrSÚtest_lie_grouprÅrÌcCsbttƒ t¡}tttƒ|ttdttƒtdttƒdƒ}t|ƒdks+J‚ttƒdS)Nrªr{)Ú factorableÚseparable_reducedÚ lie_groupÚseparable_reduced_Integral)r>r;rr r/r^Ú'_get_examples_ode_sol_separable_reduced)ÚdfrBrRrRrSÚtest_separable_reduced’s8 rÓcCrÆrÀ)r^rÑrRrRrRrSÚ$test_slow_examples_separable_reduced›rÈrÔcCr±rk)r^Ú,_get_examples_ode_sol_2nd_2F1_hypergeometricrRrRrRrSÚtest_2nd_2F1_hypergeometric rÅrÖc Csttdttƒ td¡dtdƒdtttƒ t¡ttƒ}tttƒtttttdtdttdtƒƒdtddtƒttdtdtƒdƒttdtdtƒ dƒt tdƒddfdtƒƒ}|t |ddksyJ‚t ||ƒd ks‚J‚dS) Nr{rªéÿÿÿÿér©)r{Ú2nd_hypergeometric_Integral)rJr~) r;r>rr r ÚC1ÚC2r$rr#r0r8©rBrCrRrRrSÚ$test_2nd_2F1_hypergeometric_integral¥s,F0ÿÿÿÿÿÿÿÿþrÝcCr±rk)r^Ú8_get_examples_ode_sol_2nd_nonlinear_autonomous_conservedrRrRrRrSÚ'test_2nd_nonlinear_autonomous_conserved®rÅrßc CsÜttƒ td¡tttƒƒ}ttdttdtttƒtƒƒtttƒfƒt tƒttdttdtttƒtƒƒtttƒfƒt tƒg}t |ddd}t ||ƒD] \}}|  |¡s[J‚qPt |dd„|DƒƒddgkslJ‚dS) Nrªr{Ú+2nd_nonlinear_autonomous_conserved_IntegralF©rJrzcSsg|]}| ¡‘qSrR)Údoit)rmÚsrRrRrSr»szDtest_2nd_nonlinear_autonomous_conserved_integral..r~)r>r;rrr r$rrÚÚ_urÛr0Úziprlr8)rBÚactualrŸÚarãrRrRrSÚ0test_2nd_nonlinear_autonomous_conserved_integral³s44ÿ$rècCr±rk)r^Ú'_get_examples_ode_sol_2nd_linear_besselrRrRrRrSÚtest_2nd_linear_bessel_equation¾rÅrêcCsˆttƒttƒttƒ t¡}tttƒttƒƒtttƒttttƒƒg}t||dtƒ}|tttƒttttƒƒgks>J‚tt ƒdS©Nrª) r>r;rr rrÚrÛr2r^Ú#_get_examples_ode_sol_nth_algebraic)ÚeqnÚsolnsÚ solns_finalrRrRrSÚtest_nth_algebraicÃsÿ$ rðcCrÆrÀ©r^Ú2_get_examples_ode_sol_nth_linear_var_of_parametersrRrRrRrSÚ>test_slow_examples_nth_linear_constant_coeff_var_of_parametersÎrÈrócCr±rkrñrRrRrRrSÚ0test_nth_linear_constant_coeff_var_of_parametersÓr´rôcCs²d}ttƒ td¡dttƒ td¡ttƒ t¡dttttƒ}t|ttƒ|dd}t|ttƒ|dd}||ks?J‚t||dddd ksKJ‚t||dddd ksWJ‚dS) NÚ:nth_linear_constant_coeff_variation_of_parameters_Integralérªr«TráF©r­r‚r~)r>r;rrrr0r8)rirBÚsol_simpÚ sol_nsimprRrRrSÚ@test_nth_linear_constant_coeff_variation_of_parameters__integral×sF rúcCrÆrÀ©r^Ú_get_examples_ode_sol_1st_exactrRrRrRrSÚtest_slow_examples_1st_exactårÈrýcCr±rkrûrRrRrRrSÚtest_1st_exactêrÅrþcCsbtttƒƒttttƒƒttƒdttƒ t¡}t|ttƒddd}t||ddds/J‚dS)NrªFÚ1st_exact_Integralryr{r÷)rr>r;rrr0r8)rBÚsol_1rRrRrSÚtest_1st_exact_integralïs6rcCrÆrÀ)r^Ú)_get_examples_ode_sol_nth_order_reduciblerRrRrRrSÚ&test_slow_examples_nth_order_reducibleõrÈrcCrÆrÀ)r^Ú:_get_examples_ode_sol_nth_linear_undetermined_coefficientsrRrRrRrSÚFtest_slow_examples_nth_linear_constant_coeff_undetermined_coefficientsúrÈrcCrÆrÀ©r^Ú_get_examples_ode_sol_separablerRrRrRrSÚtest_slow_examples_separableÿrÈrcCsFttttƒtƒtttƒtjtƒ}d}|t|ƒvsJ‚tt ƒdS)NÚ3nth_linear_constant_coeff_undetermined_coefficients) r rr>r;rr ÚHalfr/r^r)rBrirRrRrSÚ8test_nth_linear_constant_coeff_undetermined_coefficientss& r cCsFdd„}t}||tttƒttƒ|ttƒtƒƒdksJ‚||tttƒttƒ|ttƒtƒƒdks4J‚|ttƒ|ttƒtƒ|ttƒtdƒƒdksMJ‚||tttƒtdƒ|ttttƒtdƒƒdksiJ‚||ttƒtdƒ|ttƒtdƒ|ttƒtdƒƒdks‡J‚||ttƒtdƒ|ttƒtdƒƒdksJ‚ttƒdS)NcSstt|ttƒtƒƒ ¡Srk)r7r5r>r;r§)rBrRrRrSr£sz*test_nth_order_reducible..Frªr«r©T)rr=r>r;r<r^r)ÚFÚDrRrRrSÚtest_nth_order_reducibles..28<, rcCr±rkrrRrRrRrSÚtest_separablerÅrcCsHtttdtƒtƒ tƒttttdtƒƒtƒ ksJ‚ttƒdSrë)r%rr>r;rr$r^Ú _get_examples_ode_sol_factorablerRrRrRrSÚtest_factorable s< rcCrÆrÀ)r^rrRrRrRrSÚtest_slow_examples_factorable&rÈrcCr±rk)r^Ú_get_examples_ode_sol_riccatirRrRrRrSÚtest_Riccati_special_minus2+r´rcCr±rk)r^Ú*_get_examples_ode_sol_1st_rational_riccatirRrRrRrSÚtest_1st_rational_riccati/rÅrcCr±rk)r^Ú_get_examples_ode_sol_bernoullirRrRrRrSÚtest_Bernoulli4r´rcCr±rk)r^Ú _get_examples_ode_sol_1st_linearrRrRrRrSÚtest_1st_linear8r´rcCr±rk)r^Ú#_get_examples_ode_sol_almost_linearrRrRrRrSÚtest_almost_linear<r´rcCsàd}ttttƒtƒtttƒtttƒttƒdtttƒtƒddttƒƒ}ttttƒtƒttttƒttƒdttttƒtƒddttƒƒ}||vsTJ‚||vsZJ‚|d|vsbJ‚|d|vsjJ‚ttƒdS)NÚ 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ttƒtttƒtƒddttƒtttƒtƒd d ttƒtttƒtƒtttƒtƒdd tttƒtƒd dtttƒttƒtttƒttd tƒ ƒtttƒttd tƒƒtttƒttƒgd œ“dtdttƒd d tdttƒtttƒtd fƒtdtttƒtd fƒd d td ttƒtttƒtƒd td tttƒtƒtttƒtd fƒdtd ttƒd dtd ttƒtttƒtd fƒtd tttƒtƒd dtttƒtttƒtƒdttƒd tttƒttd tƒt td tƒƒtttƒtttd ƒtƒt ttd ƒtƒƒgddœ“dttƒ td ¡t ttƒƒttƒ td ¡t ttƒƒtttƒtttttdtƒt tƒdƒƒtttƒtttttdtƒt tƒdƒƒtttƒttdtttdtƒt tƒƒƒtttƒttdtttdtƒt tƒƒƒgddœ“d t ttƒ t¡ƒttƒd ttdt|d ƒ|ttƒfƒttƒgd!gdœ“d"ttƒ t¡d ttƒd tttƒdtd d tttd ƒgd!gdœ“d#ttƒ t¡d ttƒtttƒtd dttd td dƒgd œ“d$ttƒ t¡d ttƒd tttƒtt tƒƒtttƒtt t ƒƒgd œ“d%ttƒ t¡d ttƒd tttƒdtd d tttd ƒgd œ“d&ttƒ t¡|td|td |td |t|d'tttƒttdt||t|td |td |tdƒtƒƒgddœ“ttd tƒttttƒƒƒƒtttƒtttttd tƒƒtƒƒtttƒttttd tƒƒtƒƒgdd(œtttƒtƒd td tttƒtd ttdd ƒdƒtttƒtd ttdd ƒdƒgd œtttƒ td ¡tttƒtttƒtt t ƒt t tƒƒgd œd)œ¥d*œS)+zß some hints are marked as xfail for examples because they missed additional algebraic solution which could be found by Factorable hint. 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ƒ}ttƒ td¡}dttƒ td¡d|ttƒ t¡ttƒt}tdƒ}tdtd}tddd \}}}}} td ƒ} d ttƒid |t|tttƒtttdƒtt tt tdd dtdtt ƒdƒgddœ“d||tttƒtttdƒtt tt tdtt ƒdƒgddœ“d|dttƒ t¡dttƒdtttƒt tdtƒt tt ƒdƒgddœ“d|dttƒ t¡dttƒdttƒtttƒt tdtƒt tt ƒdttƒƒgddœ“d|dttƒ t¡dttƒtt tƒtttƒt dƒdt dt tdtƒt tt ƒt tt tƒƒgddœ“d|dttƒ t¡dttƒt tƒtttƒt tdtƒt tt ƒt tƒddttƒdƒgddœ“d|dttƒ t¡dttƒttƒtttƒt tdtƒt tt ƒdt tƒdttƒdƒgddœ“d|dttƒ t¡dttƒddttƒdt tƒtttƒt tdtƒt tt ƒttƒt tƒddttƒddƒgddœ“d|ttƒ t¡ttƒtdtttƒdttdt t ttdƒdƒt tttdƒdƒtt dƒƒgddœ“d|dttƒ t¡dttƒd tttƒdtt ƒtttƒt ttƒdtt ƒt tdtƒt tdtƒƒgddœ“d!|dttƒ t¡dtdtƒt tƒtttƒt t tdtƒdtdtƒt tƒdtdtƒttƒdƒgddœ“d"ttƒ td¡d|ttƒtt tƒtttƒtt tƒdt t ttt ƒtttttƒƒgddœ“d#|ttƒ t¡tddttttƒt tddt tt ƒƒgddœ“d$|ttƒ t¡tt dtƒtttƒt tt dtƒdtdtƒdtddt tt ƒƒgddœ“d%|ttƒdtt tƒtttƒt tdttƒt tt tƒƒgddœ“d&|dttƒtt dtƒtttƒt tddtdtƒt td't dtƒƒgddœ“d(|dttƒ t¡ttƒtdtt ƒtttƒt tt tddtt ƒƒgddœ“id)ttƒ td¡d|dttƒ t¡ttƒdtt ƒtdtt ƒtttƒt tt tttdd*tdtt ƒƒgddœ“d+|dttƒ t¡dttƒtdtƒtdtttƒt tt ƒtddttddƒt ttdtƒtd,dƒƒgddœ“d-|dttƒ t¡dttƒttt ƒtttƒt ttƒt tdtƒdtdtt ƒd.ƒgddœ“d/|ttƒ t¡dttƒttdtƒtttƒtd0d.ƒtdt td1tƒt tdtdtƒƒgddœ“d2|ttƒt tƒtt ƒtttƒt t tƒt tdttƒtt ƒdƒgddœ“d3ttƒ td¡d|dttƒ t¡ttƒttƒtttƒt tt tttdttƒƒgddœ“d4|ttƒt jtdtƒdtttƒt jtdtƒdt t tƒt ttƒƒgddœ“d5ttƒ td¡ttƒ t¡tdtƒt jtdtƒdtttƒt t tt ƒtttƒd6t dtƒd7tdtƒd8tdtƒd9ƒgddœ“d:ttƒ td¡dttƒ td¡ttƒ t¡dtt tƒttƒtttƒt tdt tttdt tƒttttdttƒƒgddœ“d;|ttƒttƒdtdtƒdtttƒtdtƒd't ttƒt tdt tƒƒgddœ“dttƒ td¡ttƒ t¡ttƒtttƒt t tt ƒtttƒtttƒdƒgd?œ“d@ttƒ td¡dAttƒtdtƒtttƒt tdBtƒt td,tƒtdtƒdCƒgd?œ“dDttƒ td¡ttƒ t¡ttƒttƒtttƒt ttt ƒtttƒdt tdttƒƒgd?œ“dEttƒ tt¡ttƒtt tdƒtttƒt t tƒt ttƒtdttdƒdtt tdƒdƒgd?œ“dFttƒ td¡ttƒtdt tdƒtttƒt t tƒt ttƒtdttdƒdtdt tdƒdtdttdƒddtdt tdƒddtttdƒdƒgd?œ“¥ttƒ td¡ttƒttdƒtttƒt tt ƒt ttd0ƒdttƒƒgd?œttƒ td¡ttƒt tdƒdtttƒt t tƒt ttƒtttdƒddƒgd?œttƒ td¡dttƒ td¡ttƒ t¡dttt tƒtttƒt tdt tt tƒddt ttt tƒtttttƒƒgd?œt||ƒ ||¡||||ƒ |¡d||||ƒ| ƒt||ƒ||| t t| |t||dd|ƒt|ƒd|ƒt t|| t||dd|ƒt|ƒd|ƒƒg||ƒdGœt||||ƒ ||¡||||ƒ |¡||ƒ|tt | |ƒƒt||ƒt t| |t||dd|ƒt|ƒd|ƒt t|| t||dd|ƒt|ƒd|ƒ|tt | |ƒ||| dt ||| dƒg||ƒdGœttttƒtdƒdtttƒtƒttƒt tƒƒtttƒt t tttƒttƒdƒgd?œdHœ¥dIœS)JNrªr«rör&r<)ÚclszR L C E_0 alphaTr«Úomegar Úundet_01r}rXr{r•Úundet_02r2Úundet_03r©roÚundet_04r3Úundet_05r|Úundet_06Úundet_07Úundet_08r>Úundet_09Úundet_10r@Úundet_11Úundet_12Úundet_13Úundet_14Úundet_15Úundet_16rWÚundet_17Úundet_18rsÚundet_19rØÚundet_20r$Úundet_21r×r=Úundet_22Úundet_23Úundet_24Úundet_25iëÿÿÿéé‚iÚundet_26Úundet_27Úundet_28Úundet_29Úundet_30rÜÚundet_31é1iùÿÿÿr{Úundet_32Úundet_33Úundet_34rÆ)Úundet_35Úundet_36Úundet_37Úundet_38Úundet_39Úundet_40rM)rr;r>rr r'r(r rNrÚrÛrr rrrrOrr rPrr) r?Úf2r(r&r<ÚRÚLÚCÚE_0ÚalpharírRrRrSrvs 6  Pýÿ@ýù $,ýó,4ýí,Lýç(Dýá%(DýÛ+<PýÕ1 XýÏ7>FýÉ=,RýÃC*Dý½I (ý·O Lý±U.ý«[>ý¥a.,ýŸg>ÿ<ü™n4Pý’t.@ýŒz,Dý†8ýÿ8.ýù 8ýó>\ýí8ÿÿNüæ!&:ýß'ýÙ..ýÒ5$8þË:&:þÆ?,@þÁE&Nþ»J*žþ¶"P4þ&:þD Vþ>L8ÿüJ@8ÿ6þû2 *þýrcCs> tdƒ\}}d}d}d}||}tdƒ}dttƒidttƒ t¡ttƒtttƒtttƒƒgdœ“d tttƒ t¡ttƒtttƒttƒgdœ“d ttƒ t¡ttƒtttƒtt tƒƒgdœ“d ttƒd d td d ttƒ t¡tttƒt tt tƒƒƒgdœ“dttƒ t¡t tƒttƒd tttƒtt tƒd ƒgdœ“dttƒ t¡d tttƒƒd tt ttƒt ttƒƒtƒgdœ“dttƒtd ttƒ t¡ttƒdd td ttƒ t¡tttƒt t tdtttdƒttd d ƒtttƒt t tdtttdƒttd d ƒgddœ“dttƒd d d ttƒtttƒttƒ t¡tttƒt ttd dttdtd ƒ ƒtttƒt ttd dttdtd ƒƒgddœ“dtt tƒttƒ t¡t d ttƒd ƒtttƒttt t tƒƒƒƒgdddœ“dttd ƒt ttƒƒt ttƒƒttƒ t¡ttttƒt t ttƒƒd ƒd t t ttƒƒd ƒd t ttƒƒtƒgddœ“dtt ttƒƒtd tttƒƒttƒ t¡|d tttƒƒttƒ t¡tttƒttt |d  td ƒƒ d tƒtttƒttt |d  td ƒƒƒgddœ“dttƒ t¡ttƒt tƒtttƒtt tƒƒgdœ“dtd t ttƒƒttƒ t¡d ttttƒƒtttƒttttd d td td tƒƒƒtttƒtttd d td td tƒƒƒgdœ“dttƒ t¡ttƒt ttƒƒt tƒtttƒttttƒƒƒgdœ“dtttƒ t¡d ttƒd t ttƒƒtttƒt ttƒƒgdddœ“dttƒ t¡tttƒd tttƒdtttd  d ƒƒgdœ“d tttƒd ƒtd d td tttƒttƒttƒ t¡tttƒt t d ttd d tƒƒ ƒtttƒt t d ttd d tƒƒƒgdœ“ttƒ t¡ttƒtttƒttt ƒƒgdœttƒt d ttƒƒt tƒtd ttƒƒttƒ t¡tttƒtttt tƒd ƒd ƒtttƒttt tƒd ƒd ƒgdœd tttƒ t¡tttƒd tttƒttt ƒtd td ƒgdœttƒtttƒtƒtdtttƒd tttƒt dƒ t ttdtd ƒd ƒdƒtttƒt dƒt ttdtd ƒd ƒdƒgdœttƒ t¡ttttƒƒtttƒt dtttƒƒƒgd!gd"œtttƒ t¡d ttƒd tttƒt td t td ƒgdœt|ƒ |¡d d#tt|ƒtt|ƒd$tttd#|ƒd$tƒgt|ƒd%œttƒ t¡tttƒtttƒttttƒƒgdœ||||ƒd |t||ƒƒt||ƒd&ttd'|ƒƒg||ƒdd(œttƒ t¡tttƒtƒtttƒt ttƒ tttƒd ƒƒgdœd)œ ¥d*œS)+Nza,té`gš™™™™™#@gš™™™™™É?ÚvrŒÚ separable_01rÜÚ separable_02Ú separable_03Ú separable_04rªr{Ú separable_05Ú separable_06Ú separable_07r«r©Tr•Ú separable_08Ú separable_09)rBrCr:rGÚ separable_10Ú separable_11Ú separable_12Ú separable_13Ú separable_14Ú separable_15Ú separable_16r×Ú separable_17rÏrBgfffff†I@gÃXvH ”?rÆg ý‡Q|%QÀg+RÕ4JÂ?)rBrCrErG) Ú separable_18Ú separable_19Ú separable_20Ú separable_21Ú separable_22Ú separable_23Ú separable_24Ú separable_25Ú separable_26Ú separable_27rM)r r'r>r;rr rÚrrrr rrrrrrrrr=rÛrr)r&rçrÜr?rÀÚf1r rRrRrSr~s. þÿþú þõ(þð þë  þæB::ÿüá&420ÿüÚ-,üÓ40NýÌ:R0&þúÆCþ½H440þþ¸P(þ°U,ü«\$þ¤aD*(þþŸjþ<Fþ$(þ,20ÿþý &þ *ýþ"ü (þàýrcCsˆdttƒttƒtttƒƒttƒtttƒƒttƒ 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 tƒƒƒgdœtdtttƒƒttƒ t¡ttttƒƒtttƒttt t ƒtdƒ tƒtttƒttt t ƒtdƒƒgdœdœ dœS)aÔ Example 7 is an exact equation that fails under the exact engine. It is caught by first order homogeneous albeit with a much contorted solution. The exact engine fails because of a poorly simplified integral of q(0,y)dy, where q is the function multiplying f'. The solutions should be Eq(sqrt(x**2+f(x)**2)**3+y**3, C1). The equation below is equivalent, but it is so complex that checkodesol fails, and takes a long time to do so. rrªTr•r{rÏ)rBrCrDr:rG)rBrCrDr:r«F)rBrCr:rF©rBrCrFr@iåÿÿÿr)rBrCr:rHrrÜc Ss6g|]}tttƒ|tttddƒdtƒ‘qS)rªr{)r r>r;rrÚrrRrRrSrƒs6z3_get_examples_ode_sol_1st_exact..)r×r{) Ú 1st_exact_01Ú 1st_exact_02Ú 1st_exact_03Ú 1st_exact_04Ú 1st_exact_05Ú 1st_exact_06Ú 1st_exact_07Ú 1st_exact_08Ú 1st_exact_09Ú 1st_exact_10Ú 1st_exact_11rM)r>r;rrrr rrÚrrrrrrrrRrRrRrSrü2s‚4<ý@6ûD 6ü4&ý0&ü4 &ýX>ÿFÿ.þÿNüR2ÿûÿõ6þ0 þ0Rþ0Lþ·ýrücCsútt ƒ}ttƒ td¡}dttƒ td¡d|ttƒ t¡ttƒt}dttƒ|t|tttƒtttdƒtttttdddtdtt ƒdƒgdd œ||tttƒtttdƒtttttd tt ƒdƒgdd œttƒ t¡dtttƒttƒgdd œ|dttƒ t¡dttƒd tttƒttd tƒttt ƒdƒgdd œ|dttƒ t¡dttƒd ttƒtttƒttd tƒttt ƒdttƒƒgdd œ|dttƒ t¡d ttƒdtttƒdtt ƒtttƒt ttƒdtt ƒttd tƒttd tƒƒgdd œ|dttƒ t¡ttƒtdtt ƒtttƒttttdd tt ƒƒgdd œ|dttƒ t¡dttƒttt ƒtttƒtttƒttdtƒdtdtt ƒdƒgdd œttƒ td¡d|dttƒ t¡ttƒttƒtttƒttttttdttƒƒgdd œ|dttƒ t¡ttƒtt ƒttttƒtttttƒtt ƒƒgdd œ|ttƒdt tƒdt tƒtttƒttt tƒdƒdtt tƒdƒdt tƒttt tƒdƒdtt tƒdƒdt tƒƒgdd œttƒ td ¡dttttƒtttttdtdt ttƒdƒgdd œttƒ td¡dttƒ td¡ttƒ t¡dttt tƒtttƒttdttttd dtt tƒddtt tƒddtdt tƒddt tt tƒdt tt tƒt tƒt tt t td dt tt tƒddt tt tƒddt tdt tƒddtt tƒdtt tƒt tƒt tt tƒƒgdœttƒ td¡dttƒ td¡ttƒ t¡tt tƒtttƒtttttd dtdt tƒdt tƒt tt t td dt tdt tƒdt tƒt tt tƒƒgdœtttƒttƒdttƒttƒtttƒttdt dtƒdt dtƒttt tƒƒdtt tƒdƒddt tƒddt dtƒƒgdd œdœdœS)Nrªr«rörr}rXr{Tr•r2r©ror3r@r|r>r$rWrÜ)Úvar_of_parameters_01Úvar_of_parameters_02Úvar_of_parameters_03Úvar_of_parameters_04Úvar_of_parameters_05Úvar_of_parameters_06Úvar_of_parameters_07Úvar_of_parameters_08Úvar_of_parameters_09Úvar_of_parameters_10Úvar_of_parameters_11Úvar_of_parameters_12Úvar_of_parameters_13Úvar_of_parameters_14Úvar_of_parameters_15rM)rr;r>rr rNrÚrÛrrrrOrrPrr)r?rr(rRrRrSrò“sª 6 Pý@ýý$,ý,4ý>Fý.,ý.@ý8.ý*(ý"2ÿ2ÿü:ýDâÿÿÿÿÿþ<Žþ"<ÿÿ ÿü©ýròcCsþdttƒtdttƒ td¡tttƒ t¡tddttƒtttƒttdtƒttdtƒƒgdœtdttƒ td¡tttƒ t¡tddttƒtttƒttdttƒttdttƒƒgdœtdttƒ td¡tttƒ t¡tdttƒtttƒttdtƒttdtƒƒgdœtdttƒ td¡tttƒ t¡dtdt d ƒd ttƒtttƒttt d ƒd d tƒttt d ƒd d tƒƒgdœtdttƒ td¡tttƒ t¡tddttƒtttƒttd tddƒttd tddƒƒgdœtdttƒ td¡dtttƒ t¡tddttƒtttƒttt d ƒdtddƒttt d ƒdtddƒt tƒƒgdœtdttƒ td¡tttƒ t¡tdt d ƒdttƒtttƒttt d ƒdtƒttt d ƒdtƒƒgdœtdttƒ td¡d tttƒ t¡dtdttƒtttƒtdttddt tƒƒttddt tƒƒƒgdœtttƒ td¡ttƒ t¡dtd ttƒtttƒtttt d ƒdtdƒttt d ƒdtdƒƒgdœtddttƒ td¡tdttƒ t¡dtddttƒtttƒtdttd dtdƒttd dtdƒƒgdœttƒ tt¡dtttƒ t¡ttƒtttƒttt d ƒdtƒttt d ƒdtƒt tƒƒgdœtdttƒ td¡tttƒ t¡t dtdt dt dttƒtttƒttt t dƒtt t dt dƒƒttt t dƒtt t dt dƒƒƒgdœd œ dœS)NÚ2nd_linear_besselrªr©rÜéröréQr{r@r«é) Ú2nd_lin_bessel_01Ú2nd_lin_bessel_02Ú2nd_lin_bessel_03Ú2nd_lin_bessel_04Ú2nd_lin_bessel_05Ú2nd_lin_bessel_06Ú2nd_lin_bessel_07Ú2nd_lin_bessel_08Ú2nd_lin_bessel_09Ú2nd_lin_bessel_10Ú2nd_lin_bessel_11Ú2nd_lin_bessel_12rM)r>r;rr rÚr+rÛr,rr rrçr(r'rRrRrRrSréüsP<&þ<.þ8&þH>þ<6þ@NþD6þ@>þ4BþH>þ,>þP^þÈýrécCsÎdttƒttdttƒ td¡tdƒddtttƒ t¡dttƒtttƒtttdƒdttdƒdtdƒdftdƒdftƒttdtdƒ dftƒƒgdœttdttƒ td¡tdƒdtttƒ t¡ttƒtttƒtdttdƒdttdƒddftdƒdfdtƒtttdƒ dd ftdƒ dfdtƒtdtdƒdƒgdœttdttƒ td¡tdƒtdƒdtttƒ t¡ttƒtttƒtdttd ƒdttdƒddftd ƒdfdtƒtttdƒ dd ftd ƒ dfdtƒtdtd ƒdƒgdœttdƒd dttd ƒdd dttdƒddtdƒtdttƒdttdƒd tdttdƒdtdtttƒtdfƒtttƒttdƒdtttdƒdttdƒdtdƒ dftd ƒdfttdƒdƒtttdƒdtd ƒ dftdƒdfttdƒdƒttdƒddtdƒdƒgddœdœdœS)NÚ2nd_hypergeometricr{rªr«rörØ)r×rorÜror[r#éûÿÿÿr@i`þÿÿiQ ri*éÄr>é-ébr©ér6ééTTrC)Ú2nd_2F1_hyper_01Ú2nd_2F1_hyper_02Ú2nd_2F1_hyper_03Ú2nd_2F1_hyper_04rM) r>r;rr r rÚr#rÛrrRrRrRrSrÕAsJHdþ@D,ÿÿþHD,ÿÿþjÿÿÿÿ`:ÿÿûîýrÕcCs@dttƒttƒ td¡tttƒƒtttƒƒttdttdt tt ƒdt dtt ƒƒt ttƒfƒt tƒttdttdt tt ƒdt dtt ƒƒt ttƒfƒt tƒgddœttƒ td¡t ttƒƒdttƒttdƒtdtdtdt t ddƒdtt ƒƒt ttƒfƒt tƒttdƒtdtdtdt t ddƒdtt ƒƒt ttƒfƒt tƒgddœttƒ td¡t ttƒƒttdttdtt ƒƒt ttƒfƒt tƒttdttdtt ƒƒt ttƒfƒt tƒgddœttƒ td¡tttƒƒttdttdtt ƒƒt ttƒfƒt tƒttdttdtt ƒƒt ttƒfƒt tƒgddœttƒ td¡tttƒƒttdttdt tt ƒdtdt dƒƒt ttƒfƒt tƒttdttdt tt ƒdtdt dƒƒt ttƒfƒt tƒgddgd œd œd œS) NÚ"2nd_nonlinear_autonomous_conservedrªr{Fr=r«r©rà©rBrCrFrD)Ú%2nd_nonlinear_autonomous_conserved_01Ú%2nd_nonlinear_autonomous_conserved_02Ú%2nd_nonlinear_autonomous_conserved_03Ú%2nd_nonlinear_autonomous_conserved_04Ú%2nd_nonlinear_autonomous_conserved_05rM)r>r;rrrr r$rrÚrärÛrrrrrrrrRrRrRrSrÞbsF&FFþú& LLþú ..þú ..þú FFþùßýrÞc Csttƒ t¡}dttƒt|ttƒdtdttƒdtttdttƒƒdttdttƒtddƒƒdtttƒƒgddgdœttƒ t¡ttƒtd ttƒttttdttƒƒd ttdttƒtd dƒƒd tttƒƒgdd d œt|ttƒtdttƒtttdttƒƒdttdttƒdƒdtttƒƒgdd œtttƒ t¡ttƒtdttdƒdttƒddƒtdtttdƒdttƒƒdtdttd ƒdttƒddƒdtttƒƒgdd œtttƒ t¡ttƒtdtttƒddƒtttƒtdƒ tdtttƒƒdtƒtttƒtdƒtdtttƒƒdtƒgdœtttƒ t¡td ttƒdtdttƒttƒttdttƒdtd ttƒddƒtttƒtddtdƒgdœtttƒ t¡ttƒdttƒtdƒtttƒtdƒ tdtttƒƒdƒtttƒtdƒtdtttƒƒdƒgdœtttƒ t¡ttƒdttƒtttƒddƒttttƒdƒ ddtttƒƒdtttƒƒgddgdœtttƒ t¡ttƒdttƒtdƒtttƒdttddƒgdœtttƒ t¡ttƒdttƒttƒtdƒtttƒ tttƒdƒtttƒƒdttƒtƒgdgdœttƒ t¡ttƒtd ttƒttttƒtdƒ tddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒdtdƒdtdƒtddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒd tdd tdƒtdtddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒdtdƒƒdddtdƒtttƒtdƒ tddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒdtdƒdtdƒtddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒd tdd tdƒtdtddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒdtdƒƒdddtdƒtttƒtdƒtddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒdtdƒdtdƒtddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒd tdd tdƒtdtddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒdtdƒƒdddtdƒtttƒtdƒtddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒdtdƒdtdƒtddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒd tdd tdƒtdtddtddƒtdt d tƒtdt dtƒƒt d tƒtdtddƒddtddƒt d tƒtdt d tƒtdt dtƒƒt d tƒtdtddƒdtdƒƒdddtdƒgd d dœtdttƒdtt ttƒtƒtttƒdtttddƒgdœdœ dœS)NrÎr{rªr«r>FrÏrur©r3T)rBrCrFrGr=rr=rÜrBiôÿÿÿr}r@)rBrCrGr:) Úseparable_reduced_01Úseparable_reduced_02Úseparable_reduced_03Úseparable_reduced_04Úseparable_reduced_05Úseparable_reduced_06Úseparable_reduced_07Úseparable_reduced_08Úseparable_reduced_09Úseparable_reduced_10Úseparable_reduced_11Úseparable_reduced_12rM) r>r;rr rrrÚr rrr)rÒrRrRrSrÑ•s<&Hü( HüBý>^ý2.,ÿþjþ**(þþ6 8ü*þ28ý( hbÿ ÿÿ^bÿ ÿhbÿ ÿþýþûhbÿ ÿÿ^bÿ ÿhbÿ ÿþýþûfbÿ ÿÿ^bÿ þhbÿ ÿþýþûfbÿ ÿÿŠÿ ÿÿÿ ÿHÿÿbÿ ÿÿþþüîæ$"þŸýrÑcCsÎtdƒ\}}}dttƒidtttƒ t¡ttƒdttƒddttƒdtgdddœ“dtttƒ t¡ttƒdttƒddttƒdtgdd œ“d ttd tttƒtƒd td ttƒddtddttƒd dƒgdd œ“dttƒ t¡ttƒtttƒdtdttƒgdgdœ“dttƒ t¡dtttƒtƒgdgdœ“dtttƒ t¡tdttƒƒtttƒtttd ƒt dd ƒƒgdœ“dttƒ t¡|ttƒ|t|tƒtttƒt t |||tt||ƒt| tƒ||t || ƒft |tt| tƒdfƒƒgdœ“dttƒ t¡dtttƒtttd ƒtttƒttddttd ƒƒgdœ“dddtttƒ t¡ddtttƒ ƒtttƒttdtddƒƒgdœ“dtdttƒ t¡ttƒtdttdtƒtttƒtttƒtdtƒƒgdgdœ“dtdttƒdttttƒtƒtttƒdttdƒgdœ“dtttƒtƒdtttƒtttd ƒtttƒttd ƒttddƒgdœ“dtttƒtƒttƒt tƒtdtƒtttƒtt tƒ ƒtttdtƒtt tƒƒtƒƒgdœ“dtttƒtƒttƒt tƒt dtƒdtttƒttt tƒ ƒt tƒdƒgdœ“dttttƒtƒttƒtt tƒtttƒttt tƒt tƒtƒgdœ“d ttttƒtƒttƒtttƒtttƒtttttƒƒƒgdœ“d!ttƒ t¡ttƒttƒ t¡ttƒtttƒtttƒƒtttƒttt ƒƒgdœ“ttƒ t¡ttƒ t¡ttƒtttƒtttƒƒtttƒtƒgdœttƒ t¡ttƒttƒ t¡ttƒtttƒttt ƒƒtttƒtttƒƒgdœttƒ t¡ttƒ t¡ttƒtttƒtƒtttƒttt ƒƒgdœd"œ¥d#œS)$Nr@rÏÚ lie_group_01r©rªT)rBrCrHrIÚ lie_group_02r›Ú lie_group_03rØrör«rÚ lie_group_04rBÚ lie_group_05rÍÚ lie_group_06r{rÜÚ lie_group_07Ú lie_group_08Ú lie_group_09Ú lie_group_10r×Ú lie_group_11Ú lie_group_12Ú lie_group_13Ú lie_group_14Ú lie_group_15Ú lie_group_16Ú lie_group_17)Ú lie_group_18Ú lie_group_19Ú lie_group_20rM)r r>r;rr rrrÚrrrr rrr$)rçr'r(rRrRrSrË sÞ<üþ <ý÷Nýñ4ýëýå!$þß&(@ ÿÿþÚ,.(þÔ1."þÏ64"ýÊ<$þÄA.(þ¿F(:þºK,(þµP$&þ°U$þ«Z*,þ¦"`"þ*,þ"$þ—ýrËc Csºdttƒttƒ td¡tttƒtttƒtttƒtttƒƒgdœttƒ td¡dtttƒtttƒttdtdƒd tƒttdtdƒd tƒƒgdœdœdœS)NÚ2nd_linear_airyrªrÜr{r«)Ú2nd_lin_airy_01Ú2nd_lin_airy_02rM) r>r;rr rÚr)rÛr*r rRrRrRrSrÉ{ s"þFþúýrÉcCs–tddd}tddd}dd„tdƒDƒ\}}}}}d d„tdƒDƒ\}}} } } d d„tdƒDƒ\} } }}}d d„tdƒDƒ\}}}}}d d„tdƒDƒ\}}}}}td ƒ}dttƒidttƒ td¡dttƒ t¡tttƒtttdtƒƒgdœ“dttƒ td¡dttƒ t¡dttƒtttƒttttƒttƒƒgdœ“dttƒ td¡ttƒtttƒttt ƒtttƒƒgdœ“dttƒ td¡ttƒ td¡dttƒ t¡tttƒtttdtƒt tdtƒƒgddœ“ddttƒ td¡dttƒ t¡dttƒtttƒtttdƒtttt ddƒƒƒgddœ“dtttƒ td¡dttƒ t¡ttƒdƒtttƒtttdt dƒƒttt t dƒd ƒƒgddœ“d tttƒtdƒtttƒtdƒd!tttƒtƒdttƒtttƒttdtƒt tt dt dƒƒtttdt dƒƒƒgddœ“d"ttƒ td¡ttƒ td¡dttƒ td¡dttƒ t¡tttƒtttdtƒt ttƒt tdtƒƒgddœ“d#ttƒ td¡dttƒ td¡ttƒ td¡dttƒ t¡dttƒtttƒt tt ƒt ttƒttt dƒ tƒttt dƒtƒtdtƒƒgddœ“d$ttƒ td¡|dttƒtttƒttt |ƒ tƒttt |ƒtƒt t t |ƒtƒt tt |ƒtƒƒgddœ“d%ttƒ td¡d|ttƒ t¡dttƒtttƒttt|t |ddƒƒttt|t |ddƒƒƒgddœ“d&ttƒ td¡d|ttƒ t¡d'|dttƒtttƒttd(|tƒttd|tƒƒgddœ“d)ttƒ td¡tttƒtttt tdt tdƒgddœ“d*ttƒ td¡dttƒ t¡dttƒtttƒttttdtƒƒgddœ“d+dttƒ td¡dttƒ td¡ttƒ t¡ttƒtttƒttttt ƒt ttdƒƒgddœ“d,ttƒ td¡dttƒ td¡d'ttƒ t¡d-ttƒtttƒtttt ttdtƒƒgddœ“d.ttƒ td¡d|ttƒ t¡|dttƒtttƒtttt|tƒƒgddœ“id/ttƒ td¡dttƒ td¡tttƒtttt tdt tdtƒƒgddœ“d0ttƒ td¡dttƒ td¡tttƒtttt tt dƒ tƒt tt dƒtƒƒgddœ“d1ttƒ td¡dttƒ td¡dttƒ td¡d'ttƒ t¡d2ttƒtttƒttttdtƒt t ttdtƒƒgddœ“d3d2ttƒ td¡d4ttƒ td¡dttƒ t¡dttƒtttƒttt ƒttt dƒt ttdƒt ttt ddƒƒƒgddœ“d5ttƒ td¡d-ttƒ td¡d6ttƒtttƒttttdtƒt t ttdtƒƒgddœ“d7ttƒ td¡dttƒ t¡dttƒtttƒtt dtƒttdtƒttƒƒgddœ“d8ttƒ td¡ttƒ t¡ttƒtttƒtt tt dƒdƒtttt dƒdƒttdƒƒgddœ“d9ttƒ td¡dttƒ td¡dttƒtttƒtt t dƒtƒtt t dƒtƒt tt dƒtƒt tt dƒtƒƒgddœ“d:ttƒ td¡dttƒ t¡d;ttƒtttƒtt dtƒttdtƒtdtƒƒgddœ“dttƒ td¡dttƒ td¡tttƒtttt t dtƒt tdtƒƒgddœ“d?ttƒ td¡dttƒ td¡ttƒ t¡tttƒttt tt tƒt ttttƒƒgddœ“d@ttƒ td¡ttƒ td¡ttƒtttƒtt t dƒtdƒttt dƒtdƒtt dƒt t t dƒtdƒt tt dƒtdƒttdƒƒgddœ“dAttƒ td¡dttƒ td¡ttƒtttƒtt tt t dƒ dƒƒtt tt t dƒdƒƒt ttt t dƒ dƒƒt ttt t dƒdƒƒƒgddœ“dBttƒ td¡dttƒ t¡dttƒtttƒtt|tƒtt|ƒtƒtt t|ƒtƒttt|ƒtƒtt|ƒtƒt t t|ƒtƒt tt|ƒtƒƒgddCœ“dDttƒ td¡dttƒ t¡ttƒtttƒt t|tƒt t|tƒtt| tƒtt| ƒtƒtt t| ƒtƒttt| ƒtƒƒgddCœ“¥ttƒ td¡dEttƒ td¡dFttƒ t¡ttƒtttƒtt| tƒtt| tƒt t|tƒt t|tƒtt|tƒƒgddCœttƒ td¡dttƒ td¡dttƒ td¡d!ttƒ t¡dGttƒtttƒttdtƒttt|ƒtt|ƒtƒtt t|ƒtƒttt|ƒtƒtt|ƒtƒt t t|ƒtƒt tt|ƒtƒƒgddCœttƒ td!¡dttƒ td¡dttƒ td¡ttƒ td¡dttƒ td ¡ttƒtttƒttttt|ƒt t tt tt|ƒƒ tttttt|ƒƒttt|ƒƒtttt tt|ƒƒ tttttt|ƒƒttt|ƒƒƒgddCœtt dƒttƒ ttt¡ttƒ t¡dƒtttƒttt 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