K i@'dZddlmZmZddlmZddlmZddlm Z m Z ddl m Z m Z mZddlmZddlmZmZdd lmZmZdd lmZmZmZdd lmZdd lmZd ZdZ dZ!dZ"dZ#y)aO This module contains the implementation of the 2nd_hypergeometric hint for dsolve. This is an incomplete implementation of the algorithm described in [1]. The algorithm solves 2nd order linear ODEs of the form .. math:: y'' + A(x) y' + B(x) y = 0\text{,} where `A` and `B` are rational functions. The algorithm should find any solution of the form .. math:: y = P(x) _pF_q(..; ..;\frac{\alpha x^k + \beta}{\gamma x^k + \delta})\text{,} where pFq is any of 2F1, 1F1 or 0F1 and `P` is an "arbitrary function". Currently only the 2F1 case is implemented in SymPy but the other cases are described in the paper and could be implemented in future (contributions welcome!). References ========== .. [1] L. Chan, E.S. Cheb-Terrab, Non-Liouvillian solutions for second order linear ODEs, (2004). https://arxiv.org/abs/math-ph/0402063 )SPow)expand)Eq)SymbolWild)expsqrthyper)Integral)rootsgcd)cancelfactor)collectsimplify logcombine) powdenest)get_numbered_constantsc |jd}|j|}td||j||j|dg}td||j||j|dg}td||j||j|dg}||j|dz||zz||zz}t||j|d|j||gj |}|r{t d|j Ds[|j\} } t| }t||j|d|j||gj |}|r4||dk7r,t||||z } t||||z } | | gSgS)Nra3)excludeb3c3c3<K|]}|jyw)N) is_polynomial).0vals f/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/solvers/ode/hypergeometric.py z+match_2nd_hypergeometric..1s=33$$&=s) argsdiffrrmatchallvaluesas_numer_denomrr) eqfuncxdfrrrdeqrndABs r match_2nd_hypergeometricr2's ! A 1B dT499Q<1aA BB dT499Q<1aA BB dT499Q<1aA BB dii1o B &D 0C 1a$))A,- //4uSz=!((*==$$&DAqBTYYq!_diilDABHHMAQrUAX 1R52;  1R52; 1v  c `|jdtt|jdz |dzdz z|z }ttdz|zt ddz z}|j \}}t t|}t t|}fd|f}|f}|j||} t| } t tt|| dzz t ddz z | zdzz d} ttt | jt d| z zd} | jsy| j \}}t|f} |j} g}g}| D]}|jst|t ri|j#|j%d|j#t't)|j%dj+d|j#|j%d|j#t't)|j+d|j-t/| |dk(r| | |dd Sy) Nrrcddh}|D]}|jst|tr9|jdk(r#|j |jd^|k(r#|j |jd|j |j |S)Nrr6)has isinstancer as_base_expaddupdater")num_powr_power_countingr*s r r?z3equivalence_hypergeometric.._power_countingNss ;Cwwqzc3'COO,=a,@A,EHHS__.q12AXHHS__.q12KK 9: ; r3Tforce2F1)I0k sing_pointtype)r"rrr#rr'rrr<rrsubsis_rational_functionmaxr8r9rappendr:listr keyssort equivalence)r0r1r)I1J1r=dempow_numpow_demr>rDrC max_num_powdem_argsrEdem_powargr?r*s @@r equivalence_hypergeometricrX>s_ ! A qvvay{QT!V+a/0 1B q!tBw1a'( )B  "HC F3K C F3K C sg&Gsg&G NN7 D D A 8FR1W!Q$6!Q$#CDET RB yA!QK!8EF GB  " "1 %  "HCosg./KxxHJG A 771:#s#s034!!$uS__->q-A1'E'J'J'L"Ma"PQs034!!$uS!}'9'9';" eCFA&' ( SVZZ!^$ %B fT"a%"a%-#a&**4qt;<= =B r'1B r'1Brl (2,APS\a bB Ir3c |dk(r |ddggdfvryy|dk(r|gdgdddgddgfvryy|dk(r|gdddggdddgdgddgddgfvryy)Nr)rrrrBr6)r6rrr)r6r6r)rTrVs r rNrNsa 1vy) )    y)aVaV< <    y1a&)aVaS1a&1a&Q Q r3c 2|jd}ddlm}ddlm}t |d\}}|d}|d} |d} |d } d} | j d k(r@|t|| g| g|z|t|| z d z| | z d zgd| z g|z|d | z zzz} n| d k(rzttt|| zd z |z| z|dz|z z ||t|| g| g|dzz |t|| g| g|z} |t|| g| g|z|| zz} ni| |z | z j d k(rT|t|| gd |z| z| z gd |z z|t| |z | | z gd | z|z | z gd |z zd |z | |z | z zzz} | r|d }td |j|z }|| zd z|z| z j|||z}|||dz|z j|||j||zzz}||dz|z j|||dzz}tttt|d|zz |d }| j||d } | j|||dz} |j|||dz}| jsTt| dz |}tt|d }t||z ||d d zdz zz| z} t!|| } | St|||d d zdz zz| z} t!|| } | S)Nr) hyperexpand)rr)r=rZr[r\r0Fr6reTr@rD)r"sympy.simplify.hyperexpandrsympy.polys.polytoolsrr is_integerr r r rr#rGrris_zeror)r(r) match_objectr*rrC0C1rZr[r\r0soly2rGdtdx_B_Aee1s r get_sol_2F1_hypergeometricrs ! A6, #BA .FBSASASASA C||u1vsA&&E1Q3q5!A#a%.1Q3%,K)KAPQRSPSH)TT a c(ac!eHQJNQT!V#sBCT3-CJa|C002A5667;sm Jr3N)$__doc__ sympy.corerrsympy.core.functionrsympy.core.relationalrsympy.core.symbolrrsympy.functionsr r r sympy.integralsr sympy.polysr rrrrsympy.simplifyrrrsympy.simplify.powsimprsympy.solvers.ode.oderr2rXr}rNrrr3r rsP2&$*,,$"088,8.FRHV*)r3