Ë
    7^(hË  ã                   óJ   — d dl mZ d dlmZ d dlmZmZ d dlmZ d dl	m
Z
 d„ Zy)é    )ÚRational)Ú	fibonacci)ÚSÚsymbols)Úraises©Úlinrecc            	      ó’  ‡‡‡‡— t        ddgddgd¬«      dk(  sJ ‚t        g d¢g d¢d¬«      dk(  sJ ‚t        g d	¢d
dgd¬«      dk(  sJ ‚t        g d¢g d¢d¬«      dk(  sJ ‚t        g d¢g d¢d¬«      dk(  sJ ‚t        dgdz  g d¢z   dgdz  g d¢z   d¬«      dk(  sJ ‚t        g d¢g d¢d¬«      sJ ‚t        g d¢g d¢d¬«      sJ ‚t        d„ t        d d!«      D «       «      sJ ‚t        d"„ t        d#d$«      D «       «      sJ ‚t        j                  t        d%d&«      t        d'd(«      d)t        d*d+«      t        d%d'«      gŠdd,d*t        d'd)«      t        d%d)«      t        d,d+«      d(gŠt        d-«      \  ŠŠ} t        ‰d d' ‰d d& d.¬«      t        d/d0«      k(  sJ ‚t        ‰d d& ‰d d& d¬«      t        d1d2«      k(  sJ ‚t        ‰d%d  ‰d d% d3¬«      t        d4d5«      k(  sJ ‚t        dgd6z  t        d,d%«      t        d&d'«      gz   ‰d7¬«      t        d8d9«      k(  sJ ‚t        t        d:„ «       t        t        ˆˆfd;„«       t        t        ˆˆfd<„«       t        t        ˆˆfd=„«       t        t        ˆˆfd>„«       t        ‰‰| gg d?¢d&¬«      ‰d,z  ‰‰z  z   ‰| z  z   ‰z   | z   k(  sJ ‚t        g d@¢‰‰| gd¬«      dA‰z  dB‰z  z   dC| z  z   k(  sJ ‚t        g dD¢‰‰gdE¬«      dF‰z  dG‰z  z   k(  sJ ‚t        dgdz  g d¢z   ‰‰| gdH¬«      dI‰z  dJ‰z  z   dK| z  z   k(  sJ ‚t        g ddgd¬«      dk(  sJ ‚t        ‰‰| gg d¢d,¬«      d%k(  sJ ‚y )LNé   é   ©ÚcoeffsÚinitÚniÂ*  ©r   é   é   é   é   )r   r   r   r   é
   i  )r   r   é   é   é   é   é   l   X;GD7 )r   r   r   r   r   )r   r   r   é   é¥   ©r   r   r   é   )r   r   r   r   éF   l   Y!HcÂ"º6Þ)`ToN³R0sç(Wm…"j  r   é7   )r   r   r   r   é2   )r   r   r   i   l   »wN;ELMŽ$ÊxqK‹ «a±>Êé'  i † c              3   óX   K  — | ]"  }t        d d gdd g|¬«      t        |«      k(  –— Œ$ y­w)r   r   r   N©r	   r   ©Ú.0r   s     úc/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/discrete/tests/test_recurrences.pyú	<genexpr>ztest_linrec.<locals>.<genexpr>   s4   è ø€ ò MØ89ô ˜a ˜V¨1¨a¨&°AÔ6¼)ÀA»,ÕFñ Mùs   ‚(*é_   és   c              3   ó^   K  — | ]%  }t        d d gd d g|¬«      t        |d z   «      k(  –— Œ' y­w)r   r   Nr%   r&   s     r(   r)   ztest_linrec.<locals>.<genexpr>   s9   è ø€ ò NØ89ô ˜a ˜V¨1¨a¨&°AÔ6¼)ÀAÈÁEÓ:JÕJñ Nùs   ‚+-iS  ig  r   r   r   é   é   é   é	   r   zx y zéP   l   ua™#½o”[ò­|,VN–M,e¼*iG l	             V�vòRÂl   9g±ì‘9Z¾
¼(‡#l         krµé#   l   õ6Nn«&`^WÙ*H
UeXÕ`ƒh"l   EàW&G é<   i¸  l          Pjej~Tl   �ykØ%è+žGÒk& c                  ó&   — t        g d¢g d¢d¬«      S )Nr   r   r   r   r   © ó    r(   ú<lambda>ztest_linrec.<locals>.<lambda>,   s   € œfÒ,<Â?ÐVWÔX€ r6   c                  ó,   •— t        ‰ d d ‰d d d¬«      S )Nr   r   r#   r   r   ©ÚaÚbs   €€r(   r7   ztest_linrec.<locals>.<lambda>-   s   ø€ œf¨A¨b¨q¨E¸¸"¸1¸ÀÔG€ r6   c                  ó,   •— t        ‰ d d ‰d d d¬«      S )Nr   iðØÿÿr   r   r9   s   €€r(   r7   ztest_linrec.<locals>.<lambda>.   s   ø€ œv¨Q¨r°¨U¸¸2¸A¸À&ÔI€ r6   c                  ó    •— t        ‰‰ d¬«      S ©Nr#   )r   r   )r;   Úxs   €€r(   r7   ztest_linrec.<locals>.<lambda>/   ó   ø€ œf Q¨¨UÔ3€ r6   c                  ó    •— t        ‰ ‰d¬«      S r>   r   )r:   Úys   €€r(   r7   ztest_linrec.<locals>.<lambda>0   r@   r6   )r   r   r   )r   r   r   iæ iÿ#
 i…Õ )r   r   r   r   é   iÔã|i4.\iè  l   `7uÀ)l   <=œC•^l   x)m´ )
r	   ÚallÚranger   ÚHalfr   r   r   Ú	TypeErrorÚ
ValueError)Úzr:   r;   r?   rB   s    @@@@r(   Útest_linrecrJ      sú  û€ Ü˜!˜Q˜ q¨! f°Ô3°uÒ<Ð<Ð<Üšª|¸rÔBÀdÒJÐJÐJÜš¨r°2¨h¸"Ô=ÀÒLÐLÐLÜšªy¸BÔ?À3ÒFÐFÐFÜÒ)²ÀÔCØRòSð Sð Sä˜!˜˜R™¢,Ñ.°a°S¸±VºiÑ5GÈ4ÔPØAòBð Bð Bô Ò)²ÀÕFÐFÐFÜÒ)²ÀÕFÐFÐFäñ MÜ=BÀ2Às»^ôMô Mð Mð Mô ñ NÜ=BÀ3È»_ôNô Nð Nð Nô 
�‰”˜!˜Q“¤¨!¨Q£°´H¸QÀ³NÄHÈQÐPQÃNÐS€AØ	
ˆAˆq”(˜1˜a“.¤(¨1¨a£.´(¸1¸a³.À!ÐD€AÜ�gÓ�G€A€qˆ!ä˜˜2˜A˜ Q r¨ U¨bÔ1ÜÐQØ4ó	6ò6ð 6ð 6ô ˜˜2˜A˜ Q r¨ U¨bÔ1ÜÐ5Ð7LÓMòNð Nð Nô ˜˜1˜2˜ Q r¨ U¨bÔ1ÜÐFØ$ó	&ò&ð &ð &ô ˜!˜˜R™¤8¨A¨q£>´8¸A¸q³>Ð"BÑBÈÈdÔSÜÐ1Ð3PÓQòRð Rð Rô Œ9ÑXÔYÜ
Œ9ÔGÔHÜ
Œ:ÔIÔJÜ
Œ9Ô3Ô4Ü
Œ9Ô3Ô4ä˜!˜Q ˜ª°aÔ8Ø	ˆ1‰��!‘‰�a˜‘cÑ˜AÑ Ñ!ò"ð "ð "äš¨!¨Q°¨°bÔ9Øˆq‰�6˜!‘8Ñ˜f Q™hÑ&ò'ð 'ð 'äš¨Q°¨F°bÔ9Ø�‰
�X˜a‘ZÑò ð  ð  ä˜!˜˜R™¢)Ñ+°1°a¸°)¸tÔDØ�qÑ˜>¨!Ñ+Ñ+¨n¸QÑ.>Ñ>ò?ð ?ð ?ä˜ 1 a &¨BÔ/°1Ò4Ð4Ð4Ü˜!˜Q ˜ª°aÔ8¸AÒ=Ð=Ñ=r6   N)Úsympy.core.numbersr   Ú%sympy.functions.combinatorial.numbersr   Ú
sympy.corer   r   Úsympy.testing.pytestr   Úsympy.discrete.recurrencesr	   rJ   r5   r6   r(   ú<module>rP      s   ðÝ 'Ý ;ß !Ý 'Ý -ó4>r6   