
    [h#                     R    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)    N)*c                      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 )N   c                 *    [        SSU -  -
  5      U -  $ )N   )cosxs    R/var/www/auris/envauris/lib/python3.13/site-packages/mpmath/tests/test_calculus.py<lambda>$test_approximation.<locals>.<lambda>   s    #a!e*Q,    r         T)errorgh㈵>
   g      @)mpdpschebyfitrangeabspolyval)fperrir
   s        r   test_approximationr      sk    BFAa!Q$/FA::2Y"H71=1Q4'(3... r   c                      S[         l        [        S S5      R                  [	        S5      S-  5      (       d   e[        S [
        5      R                  [        5      (       d   eg )Nr   c                 *    U [        U 5      -
  U S-  -  $ )N   )sinr	   s    r   r   test_limits.<locals>.<lambda>   s    Ac!fHad?r   r         c                     SSU -  -   U -  $ Nr#    )ns    r   r   r"      s    AacEA:r   )r   r   limitaempfinfer'   r   r   test_limitsr.      sO    BF*A.11#a&(;;;;%s+..q1111r   c                      [        / 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      )r   r   r0   r      T)
derivative)r2      )r   r   s    r   test_polyvalr6      sr    2q>QA3?aA3?aA1Q<31Q$':555r   c                  z   [        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#   r   r   )r#   r   r    r   c                      [        S/5      $ )Nr   )	polyrootsr'   r   r   r    test_polyroots.<locals>.<lambda>#   s
    inr   )r;   r*   sqrtjpytestraises
ValueError)r   qs     r   test_polyrootsrC      s    1R&AQ4771:::WDA44T!WQY44T!WQYaS>R
MM*45r   c            
         Sn / SQn[         R                  S5         [        R                  " [         R                  5         [        USSSU S-  S9  S S S 5        [        US	SSU S-  S9nU Vs/ s H  n[        U5      PM     nnU/ S
Q:X  d   e S S S 5        g ! , (       d  f       NM= fs  snf ! , (       d  f       g = f)N@   Al	   #!yUMDQj~U4	 r   l`<	&&
 xXD`D r   l	   #~O6dIW6ob9r   l N$UVOF>`}Dr   l	   ha0r3(|Wo9Er   lcs9lMhPc;/,3 r   l
   p~	#]ls<m r   lW)4G`Y r   l
   <g?I"GX)p@/ r   lg24Kc89z r   l
    1_bm-9w:bYj r   l	@bmDu#pO2> r   l
   J={|L	m~;` r   l`|fl?'h_K r   l
   eo.!03a7# r   l / $+-kMsf]`:r   l	   ;bfLHQLRr   l /v\ QB8%r   l	   e]r+a ;M~DMLr   l`|]B`3*0Vwk_ r   l	   J5]c<OJg1 r   l	x,a6F~E8P r   l    V'6@h>)r   l~&-ME	A"r   l   <-AGn,a;0$S r   lW?n05%Zu r   l   pbz^.qr   lcd qTT r   l   h9N$$).lF4 r   l Ns,1j	r   l   #vsKn?b; r   l`<x!ur   l   #!Oer    r0   TFr   maxstepscleanupr   	extraprec2   )@-0.999-0.996-0.991-0.983-0.973-0.961-0.946-0.93-0.911-0.889-0.866-0.841-0.813-0.784-0.753-0.72-0.685-0.649-0.611-0.572-0.531-0.489-0.446-0.402-0.357-0.311-0.265-0.217-0.17-0.121-0.073-0.02430.02430.0730.1210.170.2170.265z0.3110.3570.4020.4460.4890.5310.5720.6110.6490.6850.720.7530.7840.8130.8410.8660.8890.9110.930.9460.9610.9730.9830.9910.9960.999)r   workdpsr?   r@   NoConvergencer;   str)r(   coeffsrootsrs       r   test_polyroots_legendrer   %   s    
A FD 
A]]2++,fq$e !"& - &2t5d$!&'AQ'	B
B 
	B 
B 
,, ( 
s/   %B/BB/.B*B/
B'	#B//
B=c            
         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       N= f! , (       d  f       N= f)Nd   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   r   r   r   r   r   r   r   r   z1.0r   rK   TFrG   r0   )rH   rI   r   rJ   
roots_init   <   )matrixr   r   r   r;   r?   r@   r   maxapplyr   )
extra_precr   r   roots_exactr   r   roots1err1s           r   test_polyroots_legendre_initr   ]   s$   J FD  K LJ 
AbffH	T*+J,8 
 
r''	(&1d%&	( 
) &1d$$.FIEvk"6%=#6#6s#;;<sBBBFRT&0sOMKFvk"6&>#7#7#<<=DDD 
	 
)	(s   D!7D2!
D/2
E c                     [        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#      r   r   r   g?r9   g|=r   )
r+   r   r   r   appendpadearanger   r*   exp)	oneNakr   r   rB   r
   r   s	            r   	test_pader      s    
a&CBF
A	A	A1ac]		  a4ADAAq#AddGQ$B$ 33ttCFG$$%$  BFr   c                  .   S[         l        [        S SS/S5      u  pU S   R                  S5      (       d   eU S   R                  S[	        S	5      -  S[
        -  -  5      (       d   eU S   R                  S	[	        S	5      -  S
[
        -  -  5      (       d   eUS   S:X  d   eUS   R                  S	S[
        -  -  5      (       d   eUS   R                  S	S
[
        -  -  5      (       d   e[        X4SS/S5      R                  S5      (       d   eg )Nr   c                     U S-   $ r&   r'   r	   s    r   r   test_fourier.<locals>.<lambda>   s    QqSr   r9   r   r   g      ?r#   r    r   g?)r   r   fourierr*   r=   pi
fourierval)css     r   test_fourierr      s    BF=2q'1-DAQ4773<<<Q4772d1g:qt$%%%%Q4771T!W9ad#$$$$Q4199Q4771ad8Q4771ad8qfr1gq),,-?@@@@r   c                      S[         l        [        S SS5      R                  S[	        S[
        -  5      -  S-  5      (       d   eg )Nr   c                     U $ Nr'   ts    r   r    test_differint.<locals>.<lambda>   s    qr   r   g      r   r    )r   r   	differintr*   r=   r   r'   r   r   test_differintr      s9    BF[!T*--aQrT
l1n====r   c                     S[         l        Sn S nS nU" U 5      n[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XS	S9R                  U5      (       d   eS
n U" U 5      n[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XS	S9R                  U5      (       d   eSn S nS nU" U 5      n[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XS	S9R                  U5      (       d   eS
n U" U 5      n[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XSS9R                  U5      (       d   e[        XS	S9R                  U5      (       d   eg )Nr   g{Gz?c                     SU S-   S-  -  $ )Nr#   r   r'   r5   s    r   r   test_invlap.<locals>.<lambda>   s    1acAX:r   c                      U [        U * 5      -  $ r   )r   r   s    r   r   r      s    1S!W9r   talbot)methodstehfestdehoogcoheng      ?c                     [        U 5      U -  $ r   )logr5   s    r   r   r      s    3q6!8r   c                 (    [         * [        U 5      -
  $ r   )eulerr   r   s    r   r   r      s    E6#a&=r   )r   r   invertlaplacer*   )r   fpftftts       r   test_invlapr      s5   BFA	B	B
Q%CX.11#6666Z033C8888X.11#6666W-005555A
Q%CX.11#6666Z033C8888X.11#6666W-005555A	B	 B
Q%CX.11#6666Z033C8888X.11#6666W-005555A
Q%CX.11#6666Z033C8888X.11#6666W-005555r   )r?   mpmathr   r.   r6   rC   r   r   r   r   r   r   r'   r   r   <module>r      sB     /2
666Bp<E|
A>6r   