ó
    �È¦jã#  ã                   óR   • S SK r S SK7  S rS rS rS rS rS rS	 rS
 r	S r
S rg)é    N)Ú*c                  óÊ   • S[         l        S n [        U SS/SSS9u  pUS:  d   e[        S	5       H.  nSUS
-  -   n[	        [        X5      U " U5      -
  5      U:  a  M.   e   g )Né   c                 ó*   • [        SSU -  -
  5      U -  $ )Né   )Úcos©Úxs    Ú¨C:\Users\johnn\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\mpmath/tests/test_calculus.pyÚ<lambda>Ú$test_approximation.<locals>.<lambda>   s   € ”#�a˜˜!™‘e“*˜Q’,ó    r   é   é   T)Úerrorgñhãˆµøä>é
   g      @)ÚmpÚdpsÚchebyfitÚrangeÚabsÚpolyval)ÚfÚpÚerrÚir
   s        r   Útest_approximationr      sk   € Ø„B„FÙ€AÜ�a˜!˜Q˜ ¨$Ñ/�F€AØ�‹:Ðˆ:Ü�2ŽYˆØ��"‘‰HˆÜ”7˜1“=¡1 Q£4Ñ'Ó(¨3Õ.Ð.Ð.ò r   c                  óÎ   • S[         l        [        S S5      R                  [	        S5      S-  5      (       d   e[        S [
        5      R                  [        5      (       d   eg )Nr   c                 ó*   • U [        U 5      -
  U S-  -  $ )Né   )Úsinr	   s    r   r   Útest_limits.<locals>.<lambda>   s   € ˜Aœc !›f™H a¨¡dš?r   r   é   é   c                 ó   • SSU -  -   U -  $ ©Nr#   © )Úns    r   r   r"      s   € ˜A˜a ™c™E Aš:r   )r   r   ÚlimitÚaeÚmpfÚinfÚer'   r   r   Útest_limitsr.      sO   € Ø„B„FÜÑ*¨AÓ.×1Ñ1´#°a³&¸±(×;Ñ;Ð;Ð;ÜÑ%¤sÓ+×.Ñ.¬q×1Ñ1Ð1Ñ1r   c                  óÂ   • [        / S5      S:X  d   e[        S/S5      S:X  d   e[        S/S5      S:X  d   e/ SQn [        U S5      S:X  d   e[        U SSS9S	:X  d   eg )
Nr    r   é   )r   r   éþÿÿÿr0   r   éý   T)Ú
derivative)r2   é¾   )r   ©r   s    r   Útest_polyvalr6      sr   € Ü�2�q‹>˜QÓÐÐÜ�A�3˜‹?˜aÓÐÐÜ�A�3˜‹?˜aÓÐÐâ€AÜ�1�Q‹<˜3ÓÐÐÜ�1�Q $Ñ'¨:Ó5Ð5Ñ5r   c                  óz  • [        SS/5      n U S   R                  S5      (       d   e[        / SQ5      u  pU R                  S[        S5      [        -  -
  5      (       d   eUR                  S[        S5      [        -  -   5      (       d   e[        S/5      / :X  d   e[        R
                  " [        S 5        g )	Nr#   éüÿÿÿr   r   )r#   r   r    éÿÿÿÿr   c                  ó   • [        S/5      $ )Nr   )Ú	polyrootsr'   r   r   r   Ú test_polyroots.<locals>.<lambda>#   s
   € ¤i°°¤nr   )r;   r*   ÚsqrtÚjÚpytestÚraisesÚ
ValueError)r   Úqs     r   Útest_polyrootsrC      s—   € Ü�1�R�&Ó€AØˆQ‰4�7‰7�1�:‰:Ðˆ:Ü’WÓ�D€AØ�4‰4�”T˜!“WœQ‘Y‘×ÑÐÐØ�4‰4�”T˜!“WœQ‘Y‘×ÑÐÐä�a�S‹>˜RÓÐÐÜ
‡M‚M”*Ñ4Õ5r   c            
      ó€  • Sn / SQn[         R                  S5         [        R                  " [         R                  5         [        USSSU S-  S9  S S S 5        [        US	SSU S-  S9nU Vs/ s H  n[        U5      PM     nnU/ S
Q:X  d   e S S S 5        g ! , (       d  f       NM= fs  snf ! , (       d  f       g = f)Né@   ©Al	   #!”¤yÓUMDQj~U4	 r   l÷ÿÿÿ`<²	&&
 xXD`D� r   l	   Ð#~O6dI�W6o²¡b9r   l÷ÿÿÿ NÚ$‡U­VOF>³`…}Dr   l	   ha0¦rÌ3(|Wo9Er   löÿÿÿàcs9�l™MhPc;/,3 r   l
   pâ~	#ð]¤‚lùs<m r   löÿÿÿ Wß)ç4“G‡°`ŸY r   l
   Ô<¥gó?IŒ"GX)p@/ r   löÿÿÿàög24ú¸Kc�89z… r   l
   Ð 1_âbm-ƒ9w:øbYj r   löÿÿÿ 	Œ@bmÏDu#Ép‹O2‡> r   l
   ØJ=Ð{|L	mã~È;` r   löÿÿÿ`|½fl?Ñ'ÕhØ_ÖÖK¥ r   l
   ðeŒoÔ.!03aÉ—7Í# r   l÷ÿÿÿ /Ç $+È-kMsf]¤`û:r   l	   ’þ;bfL†HQLRr   l÷ÿÿÿ /�¦vÍ\ Q¼B‘8¢%Œr   l	   ðe¤]r+…a ;M~ÕDML³r   l÷ÿÿÿ`|]€B`3*0Vwk£_ r   l	   ØJ5]c<üO¤JÖg¢1 r   l÷ÿÿÿ 	”x,a6ƒF~E8P r   l   Ð ‰VÉ'6@âhË>ˆ)r   løÿÿÿà~&-ME³	A"r   l   Ô<-A»Gn,a;Ã0À$S r   løÿÿÿ W?nÀ05õ%Zu½ r   l   pbŽzÐ^.qr   lùÿÿÿàcd qT¿Tõ r   l   h9N$$).ÁlF4 r   lúÿÿÿ NÂs,�1j	r   l   Ð#vsKn?b; r   lûÿÿÿ`<xŽ!£ur   l   #!°Oä»er    r0   TFr   ©ÚmaxstepsÚcleanupr   Ú	extraprecé2   )@ú-0.999ú-0.996ú-0.991ú-0.983ú-0.973ú-0.961ú-0.946ú-0.93ú-0.911ú-0.889ú-0.866ú-0.841ú-0.813ú-0.784ú-0.753ú-0.72ú-0.685ú-0.649ú-0.611ú-0.572ú-0.531ú-0.489ú-0.446ú-0.402ú-0.357ú-0.311ú-0.265ú-0.217ú-0.17ú-0.121ú-0.073ú-0.0243ú0.0243ú0.073ú0.121ú0.17ú0.217ú0.265z0.311ú0.357ú0.402ú0.446ú0.489ú0.531ú0.572ú0.611ú0.649ú0.685ú0.72ú0.753ú0.784ú0.813ú0.841ú0.866ú0.889ú0.911ú0.93ú0.946ú0.961ú0.973ú0.983ú0.991ú0.996ú0.999)r   Úworkdpsr?   r@   ÚNoConvergencer;   Ústr)r(   ÚcoeffsÚrootsÚrs       r   Útest_polyroots_legendrer‘   %   s²   € Ø
€Aò €FôD 
�‰�A�Ü�]Š]œ2×+Ñ+Õ,Ü�f q°$¸eØ ! "¡ò&÷ -ô ˜&¨2°tÀ5Ø ™dñ$ˆá!&Ó'¢˜A”�Q–¡ˆÐ'Øò	Bó
Bð 
	Bñ 
B÷ 
ˆß,Õ,üò (÷ 
�ús/   œ%B/ÁBÁB/Á.B*ÂB/Â
B'	Â#B/Â/
B=c            
      ó†  • Sn / SQn[        / SQ5      n[        R                  S[        R                  -  5         [	        USSSSU -  S9nS S S 5        [
        R                  " [        R                  5         [	        US	SSU S9  S S S 5        [	        US	SSXS
9u  pE[        [        W5      [        U5      R                  [        5      -
  5      U:  d   e[	        USSSXS S S
9u  pg[        [        U5      [        U5      R                  [        5      -
  5      U:  d   eg ! , (       d  f       NÜ= f! , (       d  f       N³= f)Néd   rF   )ArL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   z 0.311rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r€   r�   r‚   rƒ   r„   r…   r†   r‡   rˆ   r‰   rŠ   z1.0r   rK   TFrG   r0   )rH   rI   r   rJ   Ú
roots_inité   é<   )Úmatrixr   r‹   r   r;   r?   r@   rŒ   ÚmaxÚapplyr   )Ú
extra_precrŽ   r”   Úroots_exactr�   r   Úroots1Úerr1s           r   Útest_polyroots_legendre_initrž   ]   s$  € Ø€Jò €FôD ò Kó L€Jô 
�‰�A”b—f‘f‘HÕ	Ü °¸TÈØ*+¨J©,ñ8ˆ÷ 
ô 
�Š”r×'Ñ'Õ	(Ü�& 1¨d¸%Ø&ò	(÷ 
)ô ˜&¨1°dÀ$Ø$.ñF�I€EäŒv�kÓ"¤6¨%£=×#6Ñ#6´sÓ#;Ñ;Ó<¸sÓBÐBÐBÜ˜F¨R¸ÀTØ&0ÀsÈ¸OñM�K€FäŒv�kÓ"¤6¨&£>×#7Ñ#7¼Ó#<Ñ<Ó=ÀÓDÐDÑD÷ 
Õ	ú÷ 
)Õ	(ús   ºD!Á7D2Ä!
D/Ä2
E c                  óŒ  • [        S5      n S[        l        SnU /nSn[        SUS-   5       H  nX4-  nUR	                  X-  5        M     [        X!S-  US-  5      u  pV[        SSS5       HJ  n[        US S S2   U5      [        US S S2   U5      -  nUR                  [        U5      S5      (       a  MJ   e   S	[        l        g )
Nr#   é   r   r   r   gš™™™™™¹?r9   g»½×Ùß|Û=r   )
r+   r   r   r   ÚappendÚpadeÚaranger   r*   Úexp)	ÚoneÚNÚaÚkr   r   rB   r
   r�   s	            r   Ú	test_pader©   ›   sÂ   € Ü
ˆa‹&€CØ„B„FØ
€AØ	ˆ€AØ	€AÜ�1�a˜‘cŽ]ˆØ	‰ˆØ	�‰�‘Žñ ô ��a‘4˜˜A™Ó�D€AÜ�A�q˜#ÖˆÜ�A‘d˜�d‘G˜QÓ¤¨©$¨B¨$©°Ó 3Ñ3ˆØ�t‰t”C˜“F˜G×$Ó$Ð%Ð$ñ ð „B…Fr   c                  ó.  • S[         l        [        S SS/S5      u  pU S   R                  S5      (       d   eU S   R                  S[	        S	5      -  S[
        -  -  5      (       d   eU S   R                  S	[	        S	5      -  S
[
        -  -  5      (       d   eUS   S:X  d   eUS   R                  S	S[
        -  -  5      (       d   eUS   R                  S	S
[
        -  -  5      (       d   e[        X4SS/S5      R                  S5      (       d   eg )Nr   c                 ó   • U S-   $ r&   r'   r	   s    r   r   Útest_fourier.<locals>.<lambda>¬   s   € ˜Q˜qšSr   r9   r   r   g      ø?r#   éýÿÿÿr    r   gè–¯®�þ?)r   r   Úfourierr*   r=   ÚpiÚ
fourierval)ÚcÚss     r   Útest_fourierr³   ª   s   € Ø„B„FÜ‘= 2 q '¨1Ó-�D€AàˆQ‰4�7‰7�3�<‰<Ðˆ<ØˆQ‰4�7‰7�2”d˜1“g‘:˜q¤™tÑ$×%Ñ%Ð%Ð%ØˆQ‰4�7‰7�1”T˜!“W‘9˜a¤™dÑ#×$Ñ$Ð$Ð$ØˆQ‰4�1‹9Ðˆ9ØˆQ‰4�7‰7�1�aœ‘d‘8×ÑÐÐØˆQ‰4�7‰7�1�aœ‘d‘8×ÑÐÐÜ�q�f˜r 1˜g qÓ)×,Ñ,Ð-?×@Ñ@Ð@Ñ@r   c                  óŽ   • S[         l        [        S SS5      R                  S[	        S[
        -  5      -  S-  5      (       d   eg )Nr   c                 ó   • U $ ©Nr'   ©Úts    r   r   Ú test_differint.<locals>.<lambda>¸   s   € ™qr   r   g      à¿r   r    )r   r   Ú	differintr*   r=   r¯   r'   r   r   Útest_differintr»   ¶   s9   € Ø„B„FÜ‘[ ! TÓ*×-Ñ-¨a´°Q´r±T³
©l¸1©n×=Ñ=Ð=Ñ=r   c                  ó‚  • S[         l        Sn S nS nU" U 5      n[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XS	S9R                  U5      (       d   eS
n U" U 5      n[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XS	S9R                  U5      (       d   eSn S nS nU" U 5      n[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XS	S9R                  U5      (       d   eS
n U" U 5      n[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XS	S9R                  U5      (       d   eg )Nr   g{®Gáz„?c                 ó   • SU S-   S-  -  $ )Nr#   r   r'   r5   s    r   r   Útest_invlap.<locals>.<lambda>½   s   € �1�a˜‘c˜A‘X’:r   c                 ó    • U [        U * 5      -  $ r¶   )r¤   r·   s    r   r   r¾   ¾   s   € �1”S˜!˜“W’9r   Útalbot)ÚmethodÚstehfestÚdehoogÚcoheng      ð?c                 ó   • [        U 5      U -  $ r¶   )Úlogr5   s    r   r   r¾   Ì   s   € ”3�q“6˜!’8r   c                 ó(   • [         * [        U 5      -
  $ r¶   )ÚeulerrÆ   r·   s    r   r   r¾   Í   s   € ”E�6œ#˜a›&’=r   )r   r   Úinvertlaplacer*   )r¸   ÚfpÚftÚftts       r   Útest_invlaprÍ   º   s5  € Ø„B„FØ€AÙ	€BÙ	€BÙ
ˆQ‹%€CÜ˜ XÑ.×1Ñ1°#×6Ñ6Ð6Ð6Ü˜ ZÑ0×3Ñ3°C×8Ñ8Ð8Ð8Ü˜ XÑ.×1Ñ1°#×6Ñ6Ð6Ð6Ü˜ WÑ-×0Ñ0°×5Ñ5Ð5Ð5Ø€AÙ
ˆQ‹%€CÜ˜ XÑ.×1Ñ1°#×6Ñ6Ð6Ð6Ü˜ ZÑ0×3Ñ3°C×8Ñ8Ð8Ð8Ü˜ XÑ.×1Ñ1°#×6Ñ6Ð6Ð6Ü˜ WÑ-×0Ñ0°×5Ñ5Ð5Ð5à€AÙ	€BÙ	 €BÙ
ˆQ‹%€CÜ˜ XÑ.×1Ñ1°#×6Ñ6Ð6Ð6Ü˜ ZÑ0×3Ñ3°C×8Ñ8Ð8Ð8Ü˜ XÑ.×1Ñ1°#×6Ñ6Ð6Ð6Ü˜ WÑ-×0Ñ0°×5Ñ5Ð5Ð5Ø€AÙ
ˆQ‹%€CÜ˜ XÑ.×1Ñ1°#×6Ñ6Ð6Ð6Ü˜ ZÑ0×3Ñ3°C×8Ñ8Ð8Ð8Ü˜ XÑ.×1Ñ1°#×6Ñ6Ð6Ð6Ü˜ WÑ-×0Ñ0°×5Ñ5Ð5Ñ5r   )r?   Úmpmathr   r.   r6   rC   r‘   rž   r©   r³   r»   rÍ   r'   r   r   Ú<module>rÏ      sB   ðÛ Ü ò/ò2ò
6ò6ò6Bòp<Eò|ò
Aò>ó6r   