7^(hdZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z mZmZmZmZmZmZmZmZddlmZmZmZd Zd Zd Zd Zd ZdZdZ dZ!dZ"y)zETests for efficient functions for generating orthogonal polynomials. )Rational)S)symbols)Poly)raises) jacobi_polygegenbauer_polychebyshevt_polychebyshevu_poly hermite_polyhermite_prob_poly legendre_poly laguerre_polyspherical_bessel_fn)xabc ttdtdttt dt tdz tdz zdzt ztdz ztdz z t dk(sJtdttt dk(sJtdttt tdz tdz z t tdz tdz zdzzzk(sJtdttt tdzd z ttzd z z td z z tdzd z ztd z z t dztdzd z ttzd z zttd d zztdzd z zttd d zztd dzzzt tdzd z ttd d zztdzd z z ttd d zz zztjz k(sJtdttdt tdz tdz zdzt ztdz ztdz z t dk(sJy) Nc6tdtttSN)rrrr_/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/polys/tests/test_orthopolys.pyz"test_jacobi_poly..s{2q!Q7rTpolyszZZ(a,b)domainr) r ValueErrorrrrrrQrHalfrrrtest_jacobi_polyr)s- :78 q!Q .$ 1qsQAaC!A#%q3< << < q!Q "a '' ' q!Q "acAaCi!QqS1Q3Y]2C&C CC C q!Q "q!tAv!A~!';ad1f'Dqs'J'(!tQT!Vac!e^a!Qi-G!Q$q&-P-.qAwY.79:1a.A(B(BDEq!tAv,-a1gIH6891QH?AB1Q7HKEL(LOPff(U VV V q!Qd +t 1qsQAaC!A#%q0< << .*sr1a8rrTrrzZZ(a)r rr%r#r") rr&r rrrr'rr(dummy_eqrrrtest_gegenbauer_polyr.)sh :89  1at  $QqSUAg > ?? ? 1a #q (( ( 1a #qs1u ,, , 1a #rAqD!AqD&1Q3,,?'? ?? ?  1a qD!AqD&(Qq!tV+a!Qi781bAg!m;LL MM M 1aff % . .q 11 1 1at ,QqSUAg0N NN Nrc,ttdtdtdt tk(sJtdtdk(sJtdttk(sJtdtdtdzzdz k(sJtdtdtdzzdtzz k(sJtdtd tdzzd tdzzz dzk(sJtd td td zzd tdzzz d tzzk(sJtd tdtd zzdtdzzz dtdzzzdz k(sJtdtdtdtztdtztz j k(sJtdtdtdtdzzdz j k(sJtdj tsJtddt tk(sJy)Nc"tdtSr)r rrrrrz&test_chebyshevt_poly..: r15rrTrrrr%r#r" 0K%&d2)rr&r rrexpandr-rrrtest_chebyshevt_polyr?9s :56 1at ,Q 77 7 1a A %% % 1a A %% % 1a AadFQJ .. . 1a AadFQqSL 00 0 1a AadFQq!tVOa$7 77 7 1a Bq!tGbAg$5!$; ;; ; 1a Bq!tGbAg$51a4$?!$C CC C 2q !aA(>&>rST?U&UXY&Y%a%a%c cc c 3 "qQ)?)B'BQ'F&N&N&P PP P 1  & &q )) ) 1D )T!W 44 4rc8ttdtdtdt dtzk(sJtdtdk(sJtdtdtzk(sJtdtdtdzzdz k(sJtdtd tdzzdtzz k(sJtdtd tdzzd tdzzz dzk(sJtd td td zzd tdzzz dtzzk(sJtdtdtdzzdtdzzz dtdzzzdz k(sJtdj dtzsJtddt dtzk(sJy)Nc"tdtSr)r rrrrrz&test_chebyshevu_poly..Mr1rrTrrrr#r%r"r3 r2r6r5@P)rr&r rrr-rrrtest_chebyshevu_polyrFLsx :56 1at ,QqS 99 9 1a A %% % 1a AaC '' ' 1a AadFQJ .. . 1a AadFQqSL 00 0 1a Bq!tGbAg$5$9 99 9 1a Bq!tGbAg$5!$; ;; ; 1a Bq!tGbAg$51a4$?!$C CC C 1  & &qs ++ + 1D )T!A#Y 66 6rc8ttdtdtdt dtzk(sJtdtdk(sJtdtdtzk(sJtdtdtdzzdz k(sJtdtd tdzzd tzz k(sJtdtd tdzzd tdzzz d zk(sJtd tdtd zzdtdzzz dtzzk(sJtdtdtdzzdtdzzz dtdzzzdz k(sJtdj dtzsJtddt dtzk(sJy)Nc"tdtSr)r rrrrrz#test_hermite_poly..^s |B2rrTrrrr#r%r"rBr3r7r2r6xr5rCi)rr&r rrr-rrrtest_hermite_polyrL]sw :23 1D )T!A#Y 66 6 1  "" " 1 1 $$ $ 1 1a4! ++ + 1 1a4"Q$ .. . 1 AqD2ad7!2R!7 77 7 1 AqD3q!t8!3c!e!; ;; ; 1 AqD3q!t8!3c!Q$h!>!D DD D ? # #AaC (( (  &$qs) 33 3rcttdtdtdt tk(sJtdtdk(sJtdttk(sJtdttdzdz k(sJtdttdzdtzz k(sJtdttdzd tdzzz dzk(sJtd ttd zd tdzzz d tzzk(sJtd ttd zd tdzzz d tdzzzd z k(sJtdj tsJtddt tk(sJy)Nc"tdtSr)r rrrrrz(test_hermite_prob_poly..os0Q7rrTrrrr%r#r5r2 -)rr&r rrr-rrrtest_hermite_prob_polyrRnsQ :78 Q .$q' 99 9 Q "a '' ' Q "a '' ' Q "adQh .. . Q "adQqSj 00 0 Q "adQq!tVma&7 77 7 Q "adR1Wnr!t&; ;; ; Q "adR1Wnr!Q$w&>&C CC C Q  ( ( ++ + Qd +tAw 66 6rc<ttdtdtdt tdk(sJtdtdk(sJtdttk(sJtdtt d dtdzzt ddz k(sJtd tt d dtd zzt d dtzz k(sJtd tt d d td zzt dd tdzzz t d d zk(sJtd tt dd td zzt dd td zzz t dd tzzk(sJtdtt ddtdzzt ddtd zzz t ddtdzzzt d dz k(sJtdj tsJtddt tk(sJy)Nc"tdtSr)rrrrrrz$test_legendre_poly.. }R3rrTrQQr rrr%r2r##r"?FrPr5r3i;i)rr&rrrr'r-rrrtest_legendre_polyr]s :34 AT *d1T.B BB B A ! ## # A ! ## # A !Aq'!Q$,1a"8 88 8 A !Aq'!Q$,1a": :: : A !B(1a4-!B(1a4-"?!Aq'"I II I A !B(1a4-!B(1a4-"?!B(1*"L LL L A ! R#A##r 1a4#(*+C*QT/#:<=aH#E EE E   $ $Q '' ' $ '47 22 2rc:ttdtdtdt t dzdk(sJtdtdk(sJtdtt dzk(sJtdtt ddtdzzt d dtzz dzk(sJtd tt dd  td zzt d d tdzzzt d d tzz dzk(sJtd tt ddtd zzt ddtd zzz t ddtdzzzt ddtzz dzk(sJtdtt dd tdzzt ddtd zzzt ddtd zzz t ddtdzzzt ddtzz dzk(sJtd tt ddtd zzt ddtdzzz t ddtd zzzt ddtd zzz t ddtdzzzt ddtzz dzk(sJtdtt dk(sJtdtt t t zdzk(sJtdtt tdzdz t dz tzzt dzdz zt t d dzzdzk(sJtd tt td z d z t dz t d dz ztdzzzt dz dz t t ddzz d z tzzt d zd z zt dzzt t dd zzdzk(sJtdjt dzsJtddt t dzk(sJy)Nc"tdtSr)rrrrrrz$test_laguerre_poly..rUrrTrrVr rrr#r%r5 r8rEr3H`r2rJiXrK$ii` ii )rr&rrrr'rr-rrrtest_laguerre_polyrgs; :34 AT *dA26$.G GG G A ! ## # A 1"q& (( ( A !Aq'!Q$,1a":Q"> >> > A 1Q7(1a4-!Aq'!Q$,">2q!"Ka"O OO O A ! 2#!t#Bi1n#%'(RyA~#689"b ! #DFG#H HH H A 1Q9*QT/Ab#Jq!tO"Ca SGQ$G#3QT)#*,-c3KM#:<=#> >> > A !As)AqD.1R:ad?"BQsC[QRTUQUEU"UXYZ^`cXdefhieiXi"ilmnrtwlxyz|}y}l}"}ABCGILAMNOAO#ORS#S SS S Aq !Q && & Aq !aR!VaZ // / Aq !QT!VrAvqj%81a46%AAa1gI%MPQ%Q QQ Q Aq !adU1W!a 7 7 1 d0&!teAg!Aq' )A-q0&134a46&:<=qD&ACDQr1X:&NPQ&R RR R   $ $aR!V ,, , $ '4Q< 77 7rctd\}}td|d|dzz k(sJtd|d|z d|dzz zk(sJtd|d|dzz d|dzz zk(sJtd|d|z d |dzz z d |d zz zk(sJy) Nzx zrrrr%irPr#rQr\r2)rr)rzs rtest_spherical_bessel_fnrjs 5>DAq q! $!Q$ .. . q! $1qAv 55 5 q! $1a4"QT'(9 99 9 q! $!bAg AqD(@ @@ @rN)#__doc__sympy.core.numbersrr'sympy.core.singletonrsympy.core.symbolrsympy.polys.polytoolsrsympy.testing.pytestrsympy.polys.orthopolysrr r r r r rrr sympy.abcrrrr)r.r?rFrLrRr]rgrjrrrrss]K,"%&'   <" O 5&7"4"7"3$82Ar