gdZddlmZddlmZddlmZddlm Z ddl m Z ddl m Z mZmZmZmZmZmZmZmZddlmZmZmZd Zd Zd Zd Zd ZdZdZ dZ!dZ"dS)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 dksJtdttt dksJtdttt tdz tdz z t tdz tdz zdzzzksJtdttt 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 zztj z ksJtdttdt tdz tdz zdzt ztdz ztdz z t dksJdS) NcDtdtttSN)rrrr]/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/polys/tests/test_orthopolys.pyz"test_jacobi_poly..s{2q!Q77rTpolyszZZ(a,b)domainr) r ValueErrorrrrrrQrHalfrrrtest_jacobi_polyr)s :77888 q!Q . . .$ 1qsQAaC!A#%q3<3<3< < < < < q!Q " "a ' ' ' ' q!Q " "acAaCi!QqS1Q3Y]2C&C C C C C q!Q " "q!tAv!A~!';ad1f'Dqs'J'(!tQT!Vac!e^a!Qi-G!Q$q&-P-.qAwwY.79:1a.A(B(BDEq!tAv,-a1ggIH6891QH?AB1Q77HKEL(LOPf(U V V V V q!Qd + + +t 1qsQAaC!A#%q0<0<0< < < < < < .*sr1a88rrTrrzZZ(a)r rr%r#r") rr&r rrrr'rr(dummy_eqrrrtest_gegenbauer_polyr.)s :88999  1at    $QqSUAg > > > ? ? ? ? 1a # #q ( ( ( ( 1a # #qs1u , , , , 1a # #rAqD!AqD&1Q3,,?'? ? ? ? ?  1a  qD!AqD&(Qq!tV+a!Qi781bAg!m;LL M M M M 1af % % . .q 1 1111 1at , , ,QqSUAg0N0N0N N N N N N Nrc(ttdtdtdt tksJtdtdksJtdttksJtdtdtdzzdz ksJtdtdtdzzdtzz ksJtdtd tdzzd tdzzz dzksJtd td td zzd tdzzz d tzzksJtd tdtd zzdtdzzz dtdzzzdz ksJtdtdtdtztdtztz ksJtdtdtdtdzzdz ksJtdtsJtddt tksJdS)Nc,tdtSr)r rrrrrz&test_chebyshevt_poly..:r155rrTrrrr%r#r" 0K%&d2)rr&r rrexpandr-rrrtest_chebyshevt_polyr?9sK :55666 1at , , ,Q 7 7 7 7 1a A % % % % 1a A % % % % 1a AadFQJ . . . . 1a AadFQqSL 0 0 0 0 1a AadFQq!tVOa$7 7 7 7 7 1a Bq!tGbAg$5!$; ; ; ; ; 1a Bq!tGbAg$51a4$?!$C C C C C 2q ! !aA(>(>&>rST?U?U&UXY&Y%a%a%c%c c c c c 3 " "qQ)?)?)B'BQ'F&N&N&P&P P P P P 1   & &q ) )))) 1D ) ) )T!WW 4 4 4 4 4 4rcttdtdtdt dtzksJtdtdksJtdtdtzksJtdtdtdzzdz ksJtdtd tdzzdtzz ksJtdtd tdzzd tdzzz dzksJtd td td zzd tdzzz dtzzksJtdtdtdzzdtdzzz dtdzzzdz ksJtddtzsJtddt dtzksJdS)Nc,tdtSr)r rrrrrz&test_chebyshevu_poly..Mr1rrTrrrr#r%r"r3 r2r6r5@P)rr&r rrr-rrrtest_chebyshevu_polyrFLs :55666 1at , , ,QqS 9 9 9 9 1a A % % % % 1a AaC ' ' ' ' 1a AadFQJ . . . . 1a AadFQqSL 0 0 0 0 1a Bq!tGbAg$5$9 9 9 9 9 1a Bq!tGbAg$5!$; ; ; ; ; 1a Bq!tGbAg$51a4$?!$C C C C C 1   & &qs + ++++ 1D ) ) )T!A#YY 6 6 6 6 6 6rcttdtdtdt dtzksJtdtdksJtdtdtzksJtdtdtdzzdz ksJtdtd tdzzd tzz ksJtdtd tdzzd tdzzz d zksJtd tdtd zzdtdzzz dtzzksJtdtdtdzzdtdzzz dtdzzzdz ksJtddtzsJtddt dtzksJdS)Nc,tdtSr)r rrrrrz#test_hermite_poly..^s|B22rrTrrrr#r%r"rBr3r7r2r6xr5rCi)rr&r rrr-rrrtest_hermite_polyrL]s :22333 1D ) ) )T!A#YY 6 6 6 6 1   " " " " 1  1 $ $ $ $ 1  1a4! + + + + 1  1a4"Q$ . . . . 1  AqD2ad7!2R!7 7 7 7 7 1  AqD3q!t8!3c!e!; ; ; ; ; 1  AqD3q!t8!3c!Q$h!>!D D D D D ?? # #AaC ( ((((  & & &$qs)) 3 3 3 3 3 3rcttdtdtdt tksJtdtdksJtdttksJtdttdzdz ksJtdttdzdtzz ksJtdttdzd tdzzz dzksJtd ttd zd tdzzz d tzzksJtd ttd zd tdzzz d tdzzzd z ksJtdtsJtddt tksJdS)Nc,tdtSr)r rrrrrz(test_hermite_prob_poly..os0Q77rrTrrrr%r#r5r2 -)rr&r rrr-rrrtest_hermite_prob_polyrRns :77888 Q . . .$q'' 9 9 9 9 Q " "a ' ' ' ' Q " "a ' ' ' ' Q " "adQh . . . . Q " "adQqSj 0 0 0 0 Q " "adQq!tVma&7 7 7 7 7 Q " "adR1Wnr!t&; ; ; ; ; Q " "adR1Wnr!Q$w&>&C C C C C Q   ( ( + ++++ Qd + + +tAww 6 6 6 6 6 6rc`ttdtdtdt tdksJtdtdksJtdttksJtdtt d dtdzzt ddz ksJtd tt d dtd zzt d dtzz ksJtd tt d d td zzt dd tdzzz t d d zksJtd tt dd td zzt dd td zzz t dd tzzksJtdtt ddtdzzt ddtd zzz t ddtdzzzt d dz ksJtdtsJtddt tksJdS)Nc,tdtSr)rrrrrrz$test_legendre_poly..}R33rrTrQQr rrr%r2r##r"?FrPr5r3i;i)rr&rrrr'r-rrrtest_legendre_polyr]s\ :33444 AT * * *d1T.B.B.B B B B B A  ! # # # # A  ! # # # # A  !Aq''!Q$,1a"8 8 8 8 8 A  !Aq''!Q$,1a": : : : : A  !B((1a4-!B((1a4-"?!Aq''"I I I I I A  !B((1a4-!B((1a4-"?!B((1*"L L L L L A  ! R##A##r 1a4#(*+C**QT/#:<=aHH#E E E E E    $ $Q ' '''' $ ' ' '477 2 2 2 2 2 2rc ttdtdtdt t dzdksJtdtdksJtdtt dzksJtdtt ddtdzzt d dtzz dzksJtd tt dd  td zzt d d tdzzzt d d tzz dzksJtd tt ddtd zzt ddtd zzz t ddtdzzzt ddtzz dzksJtdtt dd tdzzt ddtd zzzt ddtd zzz t ddtdzzzt ddtzz dzksJtd tt ddtd zzt ddtdzzz t ddtd zzzt ddtd zzz t ddtdzzzt ddtzz dzksJtdtt dksJtdtt t t zdzksJtdtt tdzdz t dz tzzt dzdz zt t d dzzdzksJtd 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 zzdzksJtdt dzsJtddt t dzksJdS)Nc,tdtSr)rrrrrrz$test_laguerre_poly..rUrrTrrVr rrr#r%r5 r8rEr3H`r2rJiXrK$ii` ii )rr&rrrr'rr-rrrtest_laguerre_polyrgs :33444 AT * * *dA26$.G.G.G G G G G A  ! # # # # A  1"q& ( ( ( ( A  !Aq''!Q$,1a":Q"> > > > > A  1Q77(1a4-!Aq''!Q$,">2q!"Ka"O O O O O A  ! 2##!t#Bii1n#%'(RyyA~#689"b ! #DFG#H H H H H A  1Q99*QT/Ab#JJq!tO"Ca SGGQ$G#3QT)#*,-c3KKM#:<=#> > > > > A  !As))AqD.1R::ad?"BQsC[[QRTUQUEU"UXYZ^`cXdXdefhieiXi"ilmnrtwlxlxyz|}y}l}"}ABCGILAMAMNOAO#ORS#S S S S S Aq ! !Q & & & & Aq ! !aR!VaZ / / / / Aq ! !QT!VrAvqj%81a46%AAa1ggI%MPQ%Q Q Q Q Q Aq ! !adU1W!a 7 7 7 1 d0&!teAg!Aq'' )A-q0&134a46&:<=qD&ACDQr1XX:&NPQ&R R R R R    $ $aR!V , ,,,, $ ' ' '4Q<< 7 7 7 7 7 7rcFtd\}}td|d|dzz ksJtd|d|z d|dzz zksJtd|d|dzz d|dzz zksJtd|d|z d |dzz z d |d zz zksJdS) Nzx zrrrr%irPr#rQr\r2)rr)rzs rtest_spherical_bessel_fnrjs 5>>DAq q! $ $!Q$ . . . . q! $ $1qAv 5 5 5 5 q! $ $1a4"QT'(9 9 9 9 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]rgrjrrrrssKK,,,,,,""""""%%%%%%&&&&&&''''''                      <<<" O O O 555&777"444"777"333$8882AAAAAr