a d d!Z?d"d#Z@d$d%ZAd&d'ZBd(d)ZCd*d+ZDd,d-ZEd.d/ZFd0d1ZGd2d3ZHd4d5ZId6d7ZJd8d9ZKd:d;ZLdd?ZNd@dAZOdBdCZPdDdEZQdFdGZRdHdIZSdJdKZTdLS)M)DifferentialOperatorHolonomicFunctionDifferentialOperators from_hyper from_meijergexpr_to_holonomic)RecurrenceOperatorsHolonomicSequence) EulerGamma)IRationalpi)S)Symbolsymbols)explog)asinhcosh)sqrt)cossin)besselj)beta)CiSierferfc)gamma)hypermeijerg)sstr)O) hyperexpand)ZZ)QQ)RRcCstd}tt|d\}}||jks*J|t|jj|jjg|ksHJ|||d|dtd||dg|ksxJ|dd|||dt|dddddd|g|ksJ|||dd||d|dd|d d |d |d |d |d|d |dks&J||d|dd|d||d}d|d|d||d|dd|d|d|dd|dd||d|dd|d|d|dd|d }||ksJdS)NxDxriii < ) rrr% old_poly_ringZderivative_operatorrbasezeroZoner'Rr(pqr=t/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/holonomic/tests/test_holonomic.pytest_DifferentialOperators800 ,&r?cCstd}tt|d\}}t|d||}td|||d|}||ksTJt||d|}t|d|}t|d|dd||d||d|}|||ksJt|||d|dd|}t|d|}td|dd|dd |dd |dd |d |d |dd|dd|d|dd|dd|dd|dd|d|d|}|||ksJt|dd|}t|d||}t|d d|dd|dd|d|dd|d|d d|dd|d d!|dd||dd|dd|dd|d|dd|d|d|dd|dd|d d!|dd|d|}|||ksJ|dd|d"}|dd |d}|||}|||}t||t||}td|dd|dd#|dd|dd$|d||dd|dd%|dd|d&|d|}||ksJdS)'Nr'r(r)r*r,i~iyiir1r0&r5(r+-i r4i'r-iv r.r/>G)rrr$r6rdiff)r'r:r(r;r<rsr=r=r>test_HolonomicFunction_addition+sl 2"@*6B4  *@2rUcCstd}tt|d\}}t||||d|}t|||||d|}td|dd|dd|ddd|d d|dd||d|dd |dd |dd|dd|d d|dd||dd|d|d|d|}|||ks,Jt|dd |}t|d |}tdd |d |d|}|||ks|Jt|dd |||}t||d d|}td|dd|dd|d d|dd|dd|dd|dd|dd|d d|dd|dd|dd|d|d|dd|d d|dd|dd|dd|d|dd|d d|dd|dd|dd||dd|d d|d|d|d|}|||ksJt||dd |}t||||}t|dd |d|||d|}|||ksJdS)Nr'r(r)r/r-r1r,rDr+r2 r*r.rKrIrFr4)rrr$r6rr'r:r(r;r<rSr=r=r>%test_HolonomicFunction_multiplicationMs\L.&TJN    &*r[cCs\td}tt|d\}}t|d|ddg}t|dd|dddg}td||d|d|dgd}|||ksJt|||d|dddg}t|d||dddg}t|d  |dd |dtdd |d|dd |tdd d||td dtd d |d|d|td d tdd |d|d|d tj|d |dgd }|||ksJt|dd |||d|ddd g}t|dd|dddg}t|d d|d d|dd d |dd|dd|||d d|d d|dd|dd |dd|dd||d|d d|dd|d |dgd}|||ksJt|d||dgd}t|d|ddg}t|d |d|d||| d|d|d|d |dgd}|||ksBJtt |}td|dd}t|dd |dd|||dd |d|dd||d|dt dddt dt d dg}|||ksJtd}tt |}tt |d|}|| |t d}|tt |t | dt |ksXJdS)Nr'r(r*rr,r))r1r,r)r1r.)r)r)rWr)r-r+$ r0r4)r1r+r\i)r,rr*)r1r*r)x0C_1)rrr%r6rr rHalfrrrrto_exprsubsr expand)r'r:r(r;r<rSrcr=r=r>test_addition_initial_conditiongsn&R& *H*&  4  L& rhcCstd}tt|d\}}t|d||d|dddg}t|dd|dddg}t|dd|dd d|||dd |dd |dd|dd ||d|dd |d|dgd}|||ksJt|d||dddg}t|d|d|dgd}t|dd|ddd |ddd|dd d|dd d|ddd|dd d|tddd|dd|dd d|dd d|dd d|dd d|d|tdd d|d|dd|dd d|dd d|ddd |dd |td!d|dd"|dd|ddd|ddd!|dd td#d |dd|dd$|dd d|dd d|d|td d td d|dd%|dd$|dd |tdd|d|dd$|ddd|ddtd d |d|dgd&}|||ksJt|d|ddg}t|dd|dddg}tdd||d|dddg}|||ksJt||ddd||dddg}t|dd"|d|||d|dddg}|||ksjJt|dd|dddg}t|dd|dgd'}td|d|dd|dd|d|d|dgd(}|||ksJtt|}td|dd)}t|d|||d|dtdtd tdg}|||ksXJtt |}tt |d|}|| }|t |t | dksJdS)*Nr'r(r)r*rr,r1rEr3r0r2rIr4)r,r1r)r,)r,r,r,r/%r.r-r+irHbRLPrW@rN)r,r,r,r]ii)r*r)r*)r*r+rErwr)ra) rrr%r6rr rrrrrer rZr=r=r>%test_multiplication_initial_conditions"D H:  : LV 8 "&2B 8  rxcCstd}tt|d\}}t|d||d|}td|d||}||ksZJt|dd||d|dd}td|dd |d d |d d |dd|dd|d|dd||d|}||ksJt|d|||d|d|dd}td|d d|d d|dd|d d|dd|dd|dd|dd|dd|dd |d|d |dd|d|dd|d||d|}||ksJt|dd|d|d}td|d|||d|}||ksHJt|dd||d|dd}t|dd |dd|d d|d d|dd|d d|dd|dd|dd |dd|dd|d d!|d d|dd||dd |dd|d d|d d|dd"|d d|dd|dd|dd |dd|d|d|}||ksJdS)#Nr'r(r*r)rWr+}rVrAr0r3r-r/r,ir1iDr.pr^rDrXr4rF0DHo6r_r2)rrr$r6r composition)r'r:r(r;rSr=r=r>"test_HolonomicFunction_compositions (D 0<  2  "(D     N   rc Cs:td}tt|d\}}tddgtddg|dd}td|d|dd||dd||d|ddtdtd d tdtd tddg}t |}||ksJt tdgtddg|dd}t| |d dd|||d|}d }t |j |ks$J|j |j ks6JdS) Nr'r(r*r,r)r1r+r/r0rNrjz?[sqrt(pi)*exp(1/4)*erf(1/2), -sqrt(pi)*exp(1/4)*erf(1/2)/2 + 1]) rrr%r6rr rrr rr!y0Z annihilator)r'r:r(r;r<rSrr=r=r>test_from_hypers l ".rc Cstd}tt|d\}}ttgtddgftjgtjdgf|}t |dtdd|d |d||d|d|d|d|ddt t ddt t ddt t g}||ksJttggfdggf|}t d||ddg}||ksJttdggftjgdgf|}t |tj|||d|dt t t dt dg}||kslJttdgdgfdggfd|d}t d|dd||d|d|dt tdd dt tdd g}||ksJdS) Nr'r(r,r)r*r1r\r)rrr%r6rr r rrdrrr rrr9r=r=r>test_from_meijergs *L(  8&NrcCsntd}tt|d\}}tddd}tt|d\}}t|d|d|||}td |d|d|dd |d d |dd ||d d d fg}||ksJt|d|d|d |d|}td |dd|d d|dd|d|dd d fg}||ks6Jt|d |dd |d|}td |dd|d |dd|||dd |d|dd d fg}||ksJtd |d |dd||||d |}td|d |dd |d d |dd |||d d |dd||dd d fg}||ksjJdS)Nr'r(nTintegerSnr)r1r*r-r,rKrrErrCr+)rrr$r6rr to_sequencer )r'r:r(r_rr;r<r=r=r>test_to_Sequences  "P *D&T6hrc Cstd}tt|d\}}tddd}tt|d\}}t|d|ddg}td |d|ddfg}||ks|Jt|d d|dddg}td|d d |d |d ddgdfg}||ksJt|d d|d ||dd d g}t||d |d d |d |dd d d td d tdd gdfg}||ksXJt|d |dd||}td|d||dd|d d||d dd fg}||ksJtd\}} } } t t d|d }t|d |d d ||d dd| gddfg}||ks2J| }t|d |d |d |dgddfg}||ksvJt t ||}td |d d ||d d |d |d |d ddd t td| gdd fg}||ksJdS)Nr'r(rTrrr*rr\r)r,r.rVr1r+C_0, C_1, C_2, C_3)rrr%r6rrrr r rrrRrrr ) r'r:r(rrrr;r<C_0rcC_2C_3r=r=r>#test_to_Sequence_Initial_Coniditonss4  0 *J"@4*Zrc Cstd}tt|d\}}t|dd|||dddgjdd}||dd|d d|d d |d d t|d}||ksJt|d||dddg}t|dd|dddg}||jdd}d|dd|ddd|ddd|ddt|d}||ks0Jtd||d||dddg}|||jdd}d||dd|ddd|ddd|d dd|ddd|d dd|ddd|d dt|d}||ksJtdd|d|dd|d|dd|d|dd|dd|d|d|dddgjd d}||ddd|dd|d d d!|dd"t|d }||ksJtdd|d|dd|d|dd|d|dd|dd|d|d|dddgjd d}dd|dd|ddd |dd#d|d d$d|dd%t|d }||ksJtt ||jdd}td&}t ||jdd}| |d'dt t |ksJtt |d|jddt |d|jddks test_seriessh*@ H"N <" H<" \":N2NP4$rcCsXtd}tt|d\}}td||d||dddg}gd}d}t|j|dd d |kshJd d tg}td D]}| |d d d tq~td D]}| |d d d tqd}t|j|dd d |ksJt|dd|dddg}d}t|j|dd d |ks&Jd g}tdD]}| |d d q4| t dd}t|j|dd d |ksJd tg}td D]}| |d d tqtdD]}| |d d q| t dttd D]}| |d d tqd}t|j|dd d |ks.Jt|dd|dddg}dg}tdD]}| |d dqV| t d}t|j|dd d |ksJd tg}td D]}| |d d tqtdD]}| |d d qtd D]}| |d d tqt|dd|dddgj|dd }d}t|d |ksTJdS)Nr'r(r*r)r 皙?g?g333333?g?g?g333333?gffffff?g?g?r*z0.699525841805253ZEuler)methodr\rr0r4z'1.07530466271334 - 0.0251200594793912*Iz*0.905546532085401 - 6.93889390390723e-18*IrEz1.08016557252834rFz*0.976882381836257 - 1.65557671738537e-16*I皙?=z-1.08140824719196r2z*0.501421652861245 - 3.88578058618805e-16*I) rrr%r6rr!evalfr rangeappendr r'r:r(r;rSrTir=r=r>test_evalf_euler>sb"                 $rcCsBtd}tt|d\}}td||d||dddg}gd}d}t||d|ksdJd d tg}td D]}| |dd d tqztd D]}| |dd d tqd }t||d d |ksJt|dd|dddg}d}t||d|ks Jd g}tdD]}| |dd q.| t dd}t||d|ksvJd tg}td D]}| |dd tqtdD]}| |dd q| t dttd D]}| |dd tqd}t||d|ks Jt|dd|dddg}dg}tdD]}| |ddqH| t d}t||d|ksJd tg}td D]}| |dd tqtdD]}| |dd qtd D]}| |dd tqt|dd|dddg|}d}t|d|ks>JdS)Nr'r(r*r)rrz0.693146363174626r\rr0r4z1.098616 + 1.36083e-7*Ir.z)0.90929463522785 + 1.52655665885959e-16*IrEz0.999999895088917rFz)1.00000003415141 + 6.11940487991086e-16*Irrz-0.999999993238714r2z*0.493152791638442 - 1.41553435639707e-15*I) rrr%r6rr!rr rrrr rr=r=r>test_evalf_rk4sb"               rc Cs" td}tt|d\}}tt||d}td|d|dd|d||d|d|d|dd dtd dg}||ksJtd d |dd}td||dd ||dd g}||ksJtt|t||t d |}td|dd |dd |d d |dd |dd |dd ||d|dd|dd|dd|dd |d|dd |dd|dd|dd|d|d|d|dd|d|dd|dd|tdd|d|dgd}||ks0Jt|t|t |d }t| d||d|d| d|d|d|d|dgd}||ksJ|t|t |d j d d|j d dksJtt d |dd }t|d|d|d|dd|d |d|dgd}||ksBJtt |d|}td|dd|dd|dd|d|d|d|dtd d|d|ddd dt dg}||ksJtt||}t|d dd|||d|d|ddd g}||ks*Jttd|}t|dd|||d|d|dddg}||ksxJttd|t|}t|d |dtj|d|dtdd||d |dd |d|d|d|d|ddd tjg}||ksJtt|d|}tdd||d|d||d|dgd}||ksrJtt|d|dd}tdd||d|d||d|dtdddtdt dtddddtdddt ddtdt dg}||ks$Jtt |dtd|dtdd}td|d||dd|d||d|dt d dtdtdddd dg}||ksJ|}t |dtd|dtdd}||ksJt|tjd d}t||tj|d d g}||ks6Jttd |d}t| |dd ||dd g}||kszJtt|td|t|td|dksJtd|dt|d|dt|ksJt|d|dd|dd|d|ddd}td |d|dd|d|d|dd|dd|dd|||dd gdi}||ksJtd |d ddd d}td|d ||d d gdi}||ksJtd}tt|||d}|t|t|k sJdS)Nr'r(r)r/r1r-r,rr*rWr4r2rIr+r.)rr*r1r\)r)r*r*r,r)r*rr))rr*rrar]lenics)r)r,r+)rrbr*rrar')rrr%r6rrrr rrrrrr rrrrdrr rersimplify)r'r:r(r;r<rr=r=r>test_expr_to_holonomics@ $ $FB> B2B@82T6:L,4((" 68F"rc CsPtd}tt|d\}}t|d|ddg}dtggd|}||ksTJttd||d|ddg}d|dd|dd|d}||ksJtd||d||dddg}|d tdd | d|}||ksJtd|||d|dddt t g}d|tt j ft ddf|d t t }||kshJttd|||d|ddd t t g}t|}|t|ksJtt|dd|||d|d|ddt j g}td|}||ks Jtt||d|||dddg}td|}||ksLJdS) Nr'r(r)rr,r*r-)r)r)r*)r,r)rW)rrr%r6rZto_hyperrr#rgrr rrdr rZrewriterr9r=r=r> test_to_hyper!s2 ($ &  ..2&  * rc Cs*td}tt|d\}}t|d|ddg}t|}||ksHJt|dd|dddg}t|}||kszJt|dd|dddg}t|}||ksJtdd|d||d||d|dddg }d|dd|d}||ksJt t |d| |d|f}t |d| |d|f}||ks^Jtd\}}}}t t d|d}|t |dd}||ksJt t d|d}|||dd}||ksJt t||}d||dtt|t|d|d|tt}||ksDJt t|dd }|t|ksjJt t|t|ksJt td|d}|td|dksJt d|ddtdd}|d|ddtddksJt t|d d|}|t|t| dks>Jt d |dd |tdd}|tddd |dd tdd}||ksJttd tjf|}ttd tjf|} td } td}||d| di| dksJddgtjdgi|_|| ks Jt |d|dks>Jt d|dd|d d|dd|dksJtd} t d|t | ||}d| |d}||ksJt d|t | ||}|| d}||ksJt d|t |}|d|ks&JdS)Nr'r(r*rr)r1rr,rarWr.rWr]D_0rr+rgffffff?g333333@)rrr$r6rrerrrrgrr integraterrRrrr r rrrrdr#rrfrr) r'r:r(r;r<rrcrrrTrrr=r=r> test_to_expr;s~    $<"$ &(("  rcCstd}tt|d\}}tt|d|dd|ddf}d}t||ksTJtt||d|f}dt |}||ksJtt||ddf}dt d}||ksJtt||dd|ddf}d }t||ksJtt|d|dd|ddf}d }t||ks&Jtt||}||t |ksRJ||ddft dkspJtt|d|}|}||||d|fksJ||ddf||ddfksJtd|dd|t |ksJt|ddt | d d|}|d d |dd |d t |ddt | }||kspJtt |d|ddgdid|}t d| t |d|}||ksJtt |d||}|tddd|dd|d|t |dtt |d|t |d}||ksLJtt |dd|}t |dd|}||dksJtd|ddgdid}td|ddd}||ksJtt |d}|||t d| t |d|ksJdS)Nr'r(r)r*rar,z0.166270406994788rz0.659329913368450z-0.423690480850035r\r-rFrXrWrrr1rr)rrr$r6rrrr!rerrrrrr rrrZr=r=r>test_integrateysT$     $$&((<.Vrc Csxtd\}}tt|d\}}t||dd|dddg}||ks^Jt|dd|dddg}||d|ksJtt |}|t ||ksJ||dksJtd\}}}}t |} ||| ksJ||d |t dd | |d ks:J||d |t dd|di| |dkstJdS) Nzx, yr(r)r*rrr\r,)rrr$r6rrRrerrrrrfr cancelr) r'yr:r(r;rrcrrr<r=r=r> test_diffs   8rc Cstd}tdtd|}|dtd|ks8Jt||dksRJtt|d\}}td|}t dd|||dd dgi}||ksJ|d|ksJt||d d ftd||d d fksJtd \}}tt ||||d }|t |||ks$J||t||| d ||ksVJtt ||||d |}t|t||||}||ksJtd }t|||}|||ksJ||||d d ksJtd\}} t|tdt|}| |d}||dtd|dksHJt|tdt|}| | d}|d|td|dksJdS)Nr'g333333?g@z0.387096774193548*sin(3.1*x)r(gݷ:>j ?gݷ:>j rr*r)zy, zrrzD_2, C_1g?) rrrrer!rrr&r6rrrf) r'r;rr(r<rzrZD_2rcr=r=r>)test_extended_domain_in_expr_to_holonomics8   0 2"$ "rcCstd}ttt|t|ks(Jttt|t|ksHJttt|t|kshJttt|t|ksJtd|dddd|dddksJttt d|ddt d|ksJt t dddfd |}t |t|ksJt t jt dft df|}tt |t|d ksZJt t d t jf|}tt d t jf|}td }td }td}t||d|d i|d ksJd dgt jd gi|_t||d ksJtt t j|dd}||t||t||t|t|d ksNJtt t j|t ddtdtttdttgid}|t t j|t t dd|d ksJdS)Nr'r1r)r,r.rr\r]r=rrrrcrr*F)Zinitcondr)rr#rrZ to_meijergrrrrrrr rrZOnergrdrrfrrerr )r'r;rTrrcrr=r=r>test_to_meijergs.   $4(&,B:rc Cstd\}}tddd}t||f}tdt| |d d|ddtt|}t|||d}t||d\}}t | |d||dd||}||ksJdS) Nzmu xsdTZpositiver)domainr(r*) rr% get_fieldrrr rrr6r) mur'rQeh1rr(h2r=r=r> test_gaussians  8(rc Cstddd\}}}||d| d|dt||}t||f}t|||d}t||d\}}t||| |dd|d|||}||ksJdS)Na b xTrr*rr(r))rrr%rrrr6r rbr'rrrrr(rr=r=r> test_betas(0rc Cstddd\}}}|| ||dt| |t|}t||f}t|||d}t||d\}}t| d|||||}||ksJdS)NrTrr*rr() rrrr%rrrr6rrr=r=r> test_gamma s, rcCsftd\}}t|}t||d\}}td|||| }t||||}||ksbJdS)Nx nr(r\rr%rrr6rr'rrrr(rrr=r=r>test_symbolic_powers   rcCsTtd}tt|d\}}td|||d}td|||}||ksPJdS)Nr'r(r\rWr))rrr%r6r)r'rr(rrr=r=r>test_negative_powers rcCsntd\}}t|}t||d\}}td||||d}t| d|||}||ksjJdS)Nrr(r\r,rrr=r=r>test_expr_in_power(s   rcCsvtddd}tt|d\}}t|d|jj|jjg|}t|dd|g|}||kr\J|jd}||krrJdS)Nr'Trr(r)r*r)rrr%r6rr7r8Z listofpoly)r'r:r(doZdo2p2r=r=r>test_DifferentialOperatorEqPoly1s   rN)UZsympy.holonomicrrrrrrZsympy.holonomic.recurrencerr Z sympy.corer Zsympy.core.numbersr r r Zsympy.core.singletonrZsympy.core.symbolrrZ&sympy.functions.elementary.exponentialrrZ%sympy.functions.elementary.hyperbolicrrZ(sympy.functions.elementary.miscellaneousrZ(sympy.functions.elementary.trigonometricrrZsympy.functions.special.besselrZ&sympy.functions.special.beta_functionsrZ'sympy.functions.special.error_functionsrrrrZ'sympy.functions.special.gamma_functionsrZsympy.functions.special.hyperrr Zsympy.printing.strr!Zsympy.series.orderr"Zsympy.simplify.hyperexpandr#Zsympy.polys.domains.integerringr$Z!sympy.polys.domains.rationalfieldr%Zsympy.polys.domains.realfieldr&r?rUr[rhrxrrrrrrrrrrrrrrrrrrrrrrr=r=r=r>s^             "#&$MNH>-