K iMddlmZmZddlmZmZmZmZmZm Z m Z m Z dZ dZ dZdZdZdZd Zd Zd Zd Zd ZdZdZdZdZdZy))SRational)gauss_legendregauss_laguerre gauss_hermitegauss_gen_laguerregauss_chebyshev_tgauss_chebyshev_u gauss_jacobi gauss_lobattoctdd\}}|Dcgc] }t|c}dgk(sJ|Dcgc] }t|c}dgk(sJtdd\}}|Dcgc] }t|c}ddgk(sJ|Dcgc] }t|c}ddgk(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gd k(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gdk(sJycc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}w)N02.0000000000000000z-0.57735026918962576z0.577350269189625761.0000000000000000)z-0.77459666924148338rz0.77459666924148338)0.55555555555555556z0.88888888888888889r)z-0.86113631159405258z-0.33998104358485626z0.33998104358485626z0.86113631159405258)0.347854845137453860.65214515486254614rrrstrxwrs k/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/integrals/tests/test_quadrature.py test_legendrer s !R DAq qCF 3% '' ' qCF #7"8 88 8 !R DAq qCF  " !## ## # qCF  #" "" " !R DAq qCF ## ## # qCF ## ## # !R DAq qCF ## ## #  qCF ## ## #7        s.D<E!EE 0EE?EEctdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}w)Nr()z+-0.7745966692414833770358530799564799221666rz*0.7745966692414833770358530799564799221666)*0.5555555555555555555555555555555555555556z*0.8888888888888888888888888888888888888889r#rrs rtest_legendre_preciser$,sj !R DAq qCF #: :: : qCF #: :: :   AAcztdd\}}|Dcgc] }t|c}dgk(sJ|Dcgc] }t|c}dgk(sJtdd\}}|Dcgc] }t|c}ddgk(sJ|Dcgc] }t|c}ddgk(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gd k(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gdk(sJtdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}w)Nrrrrz0.58578643762690495z3.4142135623730950z0.85355339059327376z0.14644660940672624r)z0.41577455678347908z2.2942803602790417z6.2899450829374792)z0.71109300992917302z0.27851773356924085z0.010389256501586136r)z0.32254768961939231z1.7457611011583466z4.5366202969211280z9.3950709123011331)z0.60315410434163360z0.35741869243779969z0.038887908515005384z0.00053929470556132745)z0.26356031971814091z1.4134030591065168z3.5964257710407221z7.0858100058588376z12.640800844275783)z0.52175561058280865z0.39866681108317593z0.075942449681707595z0.0036117586799220485z2.3369972385776228e-5rrrs r test_laguerrer)8s !R DAq qCF #7"8 88 8 qCF #7"8 88 8 !R DAq qCF  ! #" "" " qCF  ! !## ## # !R DAq qCF #    qCF #   !R DAq qCF #" "" "  qCF #& && & !R DAq qCF #" "" "  qCF #% %% %U          :F F!FF0FF$?F)F.F3.F8ctdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}w)Nrr")z*0.4157745567834790833115338731282744735466z)2.294280360279041719822050361359593868960z)6.289945082937479196866415765512131657493)z*0.7110930099291730154495901911425944313094z*0.2785177335692408488014448884567264810349z+0.01038925650158613574896492040067908765572r(rs rtest_laguerre_preciser,lsj !R DAq qCF #9 99 9 qCF #; ;; ;  r%cztdd\}}|Dcgc] }t|c}dgk(sJ|Dcgc] }t|c}dgk(sJtdd\}}|Dcgc] }t|c}ddgk(sJ|Dcgc] }t|c}ddgk(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gd k(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gdk(sJtdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}w)Nrrr1.7724538509055160r-0.707106781186547520.70710678118654752z0.88622692545275801r)z-1.2247448713915890rz1.2247448713915890)0.29540897515091934z1.1816359006036774r1r)z-1.6506801238857846z-0.52464762327529032z0.52464762327529032z1.6506801238857846)0.0813128354472451770.80491409000551284r3r2r')z-2.0201828704560856z-0.95857246461381851rz0.95857246461381851z2.0201828704560856)0.0199532420590459130.39361932315224116z0.94530872048294188r5r4rrrs r test_hermiter7xs  B DAq qCF 3% '' ' qCF #7"8 88 8 B DAq qCF  " !## ## # qCF  ! !## ## # B DAq qCF #" "" " qCF ## ## # B DAq qCF #" "" "  qCF #$ $$ $ B DAq qCF #" "" "  qCF #$ $$ $Q          r*ctdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}w)Nrr")z*-1.224744871391589049098642037352945695983rz)1.224744871391589049098642037352945695983)*0.2954089751509193378830279138901908637996z)1.181635900603677351532111655560763455198r9r6rs rtest_hermite_preciser:sj B DAq qCF #5 55 5 qCF #6 66 6  r%chtdtddd\}}|Dcgc] }t|c}dgk(sJ|Dcgc] }t|c}dgk(sJtdtddd\}}|Dcgc] }t|c}ddgk(sJ|Dcgc] }t|c}d d gk(sJtd tddd\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gd k(sJtdtddd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJtdtddd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJtddd\}}|Dcgc] }t|c}dgk(sJ|Dcgc] }t|c}dgk(sJtddd\}}|Dcgc] }t|c}ddgk(sJ|Dcgc] }t|c}ddgk(sJtd dd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJtddd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJtddd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}w)Nrrr0.50000000000000000r.z0.27525512860841095z2.7247448713915890z1.6098281800110257z0.16262567089449035r)z0.19016350919348813z1.7844927485432516z5.5253437422632603)z1.4492591904487850z0.31413464064571329z0.0090600198110176913r)z0.14530352150331709z1.3390972881263614z3.9269635013582872z8.5886356890120343)z1.3222940251164826z0.41560465162978376z0.034155966014826951z0.00039920814442273524r')z0.11758132021177814z1.0745620124369040z3.0859374437175500z6.4147297336620305z11.807189489971737)z1.2217252674706516z0.48027722216462937z0.067748788910962126z0.0026872914935624654z1.5280865710465241e-5z3.0000000000000000rz6.0000000000000000z1.5000000000000000)z1.5173870806774125z4.3115831337195203z9.1710297856030672)z1.0374949614904253z0.90575000470306537z0.056755033806509347)z1.2267632635003021z3.4125073586969460z6.9026926058516134z12.458036771951139)z0.72552499769865438z1.0634242919791946z0.20669613102835355z0.0043545792937974889)z1.0311091440933816z2.8372128239538217z5.6202942725987079z9.6829098376640271z15.828473921690062)z0.52091739683509184z1.0667059331592211z0.38354972366693113z0.028564233532974658z0.00026271280578124935rrrrs rtest_gen_laguerrer?sO a"a" 5DAq qCF #8"9 99 9 qCF #7"8 88 8 a"a" 5DAq qCF  ! #" "" " qCF  !## ## # a"a" 5DAq qCF #" "" " qCF #% %% % a"a" 5DAq qCF #" "" "  qCF #& && & a"a" 5DAq qCF #" "" "  qCF #% %% % aB 'DAq qCF #7"8 88 8 qCF #7"8 88 8 aB 'DAq qCF  #" "" " qCF  !## ## # aB 'DAq qCF #" "" " qCF #$ $$ $ aB 'DAq qCF #" "" "  qCF #% %% % aB 'DAq qCF #" "" "  qCF #& && &q                    svMM7MMM$1M)+M. M3M8%M=N4N#N N3NNN #N%N*3N/ctdtddd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJtddd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}wcc}wcc}w) Nrr<rr")z*0.1901635091934881328718554276203028970878z)1.784492748543251591186722461957367638500z)5.525343742263260275941422110422329464413)z)1.449259190448785048183829411195134343108z*0.3141346406457132878326231270167565378246z,0.009060019811017691281714945129254301865020)z)1.517387080677412495020323111016672547482z)4.311583133719520302881184669723530562299z)9.171029785603067202098492219259796890218)z)1.037494961490425285817554606541269153041z*0.9057500047030653669269785048806009945254z+0.05675503380650934725546688857812985243312r>rs rtest_gen_laguerre_preciserAs a"a" 5DAq qCF #9 99 9 qCF #< << < aB 'DAq qCF #9 99 9 qCF #; ;; ;    sB,B1/B6B;cztdd\}}|Dcgc] }t|c}dgk(sJ|Dcgc] }t|c}dgk(sJtdd\}}|Dcgc] }t|c}ddgk(sJ|Dcgc] }t|c}ddgk(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gd k(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gdk(sJtdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}w)Nrrr3.1415926535897932rr0r/1.5707963267948966r)0.86602540378443865r-0.86602540378443865)1.0471975511965977rGrGr)z0.92387953251128676z0.38268343236508977z-0.38268343236508977z-0.92387953251128676)0.78539816339744831rHrHrHr')z0.95105651629515357z0.58778525229247313rz-0.58778525229247313z-0.95105651629515357)0.62831853071795865rIrIrIrIr rrs rtest_chebyshev_trK.s  Q #DAq qCF 3% '' ' qCF #7"8 88 8 Q #DAq qCF  ! "#$ $$ $ qCF  #" "" " Q #DAq qCF #$ $$ $ qCF #" "" " Q #DAq qCF #$ $$ $  qCF ## ## # Q #DAq qCF #$ $$ $  qCF ## ## #Q          r*ctdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}w)Nrr")z*0.8660254037844386467637231707529361834714rz+-0.8660254037844386467637231707529361834714))1.047197551196597746154214461093167628066rMrMrJrs rtest_chebyshev_t_preciserN`sj Q #DAq qCF #; ;; ; qCF #9 99 9  r%cztdd\}}|Dcgc] }t|c}dgk(sJ|Dcgc] }t|c}dgk(sJtdd\}}|Dcgc] }t|c}ddgk(sJ|Dcgc] }t|c}ddgk(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gd k(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gdk(sJtdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}w)NrrrrDrr=-0.50000000000000000rHr)r0rr/)0.39269908169872415rHrQr)0.80901699437494742z0.30901699437494742-0.30901699437494742z-0.80901699437494742)0.217078713422705990.56831944997474231rUrTr')rEr=rrPrF)0.13089969389957472rQz0.52359877559829887rQrVr rrs rtest_chebyshev_urXls  Q #DAq qCF 3% '' ' qCF #7"8 88 8 Q #DAq qCF  ! "#$ $$ $ qCF  ! !## ## # Q #DAq qCF #$ $$ $ qCF ## ## # Q #DAq qCF #$ $$ $  qCF ## ## # Q #DAq qCF #$ $$ $  qCF ## ## #Q          r*ctdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}w)Nrr")z*0.7071067811865475244008443621048490392848rz+-0.7071067811865475244008443621048490392848)*0.3926990816987241548078304229099378605246z*0.7853981633974483096156608458198757210493rZrWrs rtest_chebyshev_u_preciser[sj Q #DAq qCF #; ;; ; qCF #: :: :  r%ctdtddtjd\}}|Dcgc] }t |c}dgk(sJ|Dcgc] }t |c}dgk(sJtdtddtjd\}}|Dcgc] }t |c}ddgk(sJ|Dcgc] }t |c}d d gk(sJtd tddtjd\}}|Dcgc] }t |c}gd k(sJ|Dcgc] }t |c}gd k(sJtdtddtjd\}}|Dcgc] }t |c}gdk(sJ|Dcgc] }t |c}gdk(sJtdtddtjd\}}|Dcgc] }t |c}gdk(sJ|Dcgc] }t |c}gdk(sJtddd d\}}|Dcgc] }t |c}dgk(sJ|Dcgc] }t |c}dgk(sJtddd d\}}|Dcgc] }t |c}ddgk(sJ|Dcgc] }t |c}ddgk(sJtd dd d\}}|Dcgc] }t |c}gdk(sJ|Dcgc] }t |c}gdk(sJtddd d\}}|Dcgc] }t |c}gdk(sJ|Dcgc] }t |c}gdk(sJtddd d\}}|Dcgc] }t |c}gdk(sJ|Dcgc] }t |c}gdk(sJycc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}w) Nrr<rrr=rCrSrRz0.86831485369082398z2.2732777998989693r)z-0.62348980185873353z0.22252093395631440z0.90096886790241913)z0.33795476356635433z1.0973322242791115z1.7063056657443274r)z-0.76604444311897804z-0.17364817766693035r=z0.93969262078590838)z0.16333179083642836z0.57690240318269103rGz1.3541609083740761r')z-0.84125353283118117z-0.41541501300188643z0.14231483827328514z0.65486073394528506z0.95949297361449739)z0.090675770007435372z0.33391416373675607z0.65248870981926643z0.94525424081394926z1.1192597692123861z0.14285714285714286z1.0666666666666667z-0.24025307335204215z0.46247529557426437z0.48514624517838660z0.58152042148828007)z-0.46115870378089762z0.10438533038323902z0.62950064612493132)z0.17937613502213266z0.61595640991147154z0.27133412173306246)z-0.59903470850824782z-0.14761105199952565z0.32554377081188859z0.72879429738819258)z0.067809641836772187z0.38956404952032481z0.47995970868024150z0.12933326662932816)z-0.69045775012676106z-0.32651993134900065z0.082337849552034905z0.47517887061283164z0.79279429464422850)z0.027410178066337099z0.21291786060364828z0.43908437944395081z0.32220656547221822z0.065047683080512268r rrHalfrrs r test_jacobir_sw 8B?AFFB 7DAq qCF #8"9 99 9 qCF #7"8 88 8 8B?AFFB 7DAq qCF  " !## ## # qCF  ! #" "" " 8B?AFFB 7DAq qCF ## ## # qCF #" "" " 8B?AFFB 7DAq qCF ## ## #  qCF #" "" " 8B?AFFB 7DAq qCF ## ## #  qCF #" "" " 1a $DAq qCF #8"9 99 9 qCF #7"8 88 8 1a $DAq qCF  " !## ## # qCF  ! !## ## # 1a $DAq qCF ## ## # qCF ## ## # 1a $DAq qCF ## ## #  qCF ## ## # 1a $DAq qCF ## ## #  qCF #$ $$ $q                    swN  N%N*5N/>N4N9'N>OO0O !OO0OO!O&!O+O02O5#O:O?ctdtddtjd\}}|Dcgc] }t |c}gdk(sJ|Dcgc] }t |c}gdk(sJtdddd\}}|Dcgc] }t |c}gdk(sJ|Dcgc] }t |c}gdk(sJycc}wcc}wcc}wcc}w) Nrr<rr")z+-0.6234898018587335305250048840042398106323z*0.2225209339563144042889025644967947594664z*0.9009688679024191262361023195074450511659)z*0.3379547635663543330553835737094171534907z)1.097332224279111467485302294320899710461z)1.706305665744327437921957515249186020246)z+-0.4611587037808976179121958105554375981274z*0.1043853303832390210914918407615869143233z*0.6295006461249313240934312425211234110769)z*0.1793761350221326596137764371503859752628z*0.6159564099114715430909548532229749439714z*0.2713341217330624639619353762933057474325r]rs rtest_jacobi_precisera s 8B?AFFB 7DAq qCF #: :: : qCF #9 99 9 1a $DAq qCF #: :: : qCF #: :: :    sB<C?CC ctdd\}}|Dcgc] }t|c}ddgk(sJ|Dcgc] }t|c}ddgk(sJtdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gd k(sJtd d\}}|Dcgc] }t|c}gd k(sJ|Dcgc] }t|c}gdk(sJycc}wcc}wcc}wcc}wcc}wcc}wcc}wcc}w)Nrr-11rrrcrrd)0.33333333333333333z1.3333333333333333rfr)rcz-0.44721359549995794z0.44721359549995794rd)0.166666666666666670.83333333333333333rhrgr')rcz-0.65465367070797714rz0.65465367070797714rd)0.100000000000000000.54444444444444444z0.71111111111111111rjrir rrs r test_lobattorl"s B DAq qCF   #   qCF  #" "" " B DAq qCF #   qCF ## ## # B DAq qCF #    qCF ## ## # B DAq qCF #    qCF ## ## #I        s.D>E#EE 2EEE!E!ctdd\}}|Dcgc] }t|c}gdk(sJ|Dcgc] }t|c}gdk(sJycc}wcc}w)Nrr"re)*0.3333333333333333333333333333333333333333z)1.333333333333333333333333333333333333333rnrkrs rtest_lobatto_preciseroPsj B DAq qCF #   qCF #: :: :  r%N) sympy.corerrsympy.integrals.quadraturerrrrr r r r r r$r)r,r7r:r?rArKrNrXr[r_rarlrorrtst"EEE !#H :1%h ;/$d 6_&D;,/#d 9/#d :_$D:,+#\ :rs