U
    	-e                     @   s~  d dl mZ d dlmZmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ d dlmZ d dlmZ d dlmZ d dl m!Z! d dl"m#Z# d dl$m%Z% d d	l&m'Z' d d
l(m)Z) d dl*m+Z+m,Z, d dl-m.Z.m/Z/m0Z0m1Z1 d dl2m3Z3m4Z4m5Z5m6Z6m7Z7 d dl m8Z9 d dl m:Z:m;Z; d dl<m=Z=m>Z>m?Z? d dl@mAZA d dlBmCZC d dlDmEZEmFZFmGZG d dlHmIZI d dlJmKZK d dlLmMZMmNZN dd ZOdd ZPdddZQd d! ZRe3d"d# ZSd$d% ZTd&d' ZUd(d) ZVd*d+ ZWd,d- ZXdd/d0ZYe5d1d2 ZZd3d4 Z[d5d6 Z\d7d8 Z]d9d: Z^d;d< Z_d=d> Z`d?d@ ZaddAdBZbe5dCdD ZcdEdF Zde3dGdH Zee5dIdJ ZfdKdL Zge5dMdN ZhdOdP ZidQdR ZjdSdT ZkdUdV ZldWdX Zme5dYdZ Znd[d\ Zoe5d]d^ Zpe5d_d` Zqe5dadb Zre5dcdd Zse5dedf Zte5dgdh Zue5didj Zvdkdl Zwe5dmdn Zxdodp Zydqdr Zze5dsdt Z{e3dudv Z|e3dwdx Z}e3dydz Z~d{d| Zd}d~ ZdS )    )	randrange)ShiftAShiftBUnShiftAUnShiftBMeijerShiftAMeijerShiftBMeijerShiftCMeijerShiftDMeijerUnShiftAMeijerUnShiftBMeijerUnShiftCMeijerUnShiftDReduceOrderreduce_orderapply_operatorsdevise_planmake_derivative_operatorFormulahyperexpandHyper_Function
G_Functionreduce_order_meijerbuild_hypergeometric_formula)Sum)Tuple)Expr)I)S)symbols)binomial)	Piecewise)hypermeijerg)zabc)XFAILraisesslowON_CIskip)verify_numerically)Rationalpi)exp	exp_polarlog)atanh)sqrt)asincossin)besseli)erf)gamma
lowergammac                   C   s   t ttddtjftddtddft ttd  tttt	 d t d t
t	tt
t dt
t   ksztt ttdddgg tddgtddd	gtdttd
  dt
t	 tt
t t
t dttddt ttd
    ttdd ttdd kstd S )N      z1/3            r   z2/3)r   r"   r.   r   Halfr$   r;   r1   r   r/   r4   r9   AssertionErrorr#   r:    rE   rE   f/var/www/html/Darija-Ai-Train/env/lib/python3.8/site-packages/sympy/simplify/tests/test_hyperexpand.pytest_branch_bug#   s"    ,&.0 
rG   c                   C   s
  t tg g tttkstt tddgdgt t tdt ksHtt tg tjgtd  d ttksrtt ttg tdgtd  d  t	tkstt ttdtdgtdgtd t t
tksttttdttd  tdtf tstd S )NrB   r>      3/21/2r   )r   r"   r$   r0   rD   r2   r   rC   r6   r7   r5   
isinstancer   r    r%   Zdoitr   rE   rE   rE   rF   test_hyperexpand,   s    ,*0(rL   TrB   Fc              	   C   s   t t| |t}|trdS |s&dS i }|jth }|r|t|D ]\}}	t|| ||	< qBtdd t| 	|D s6q|q6ddddg\}
}}}|rdd	ddg\}
}}}t
t| |t	||tt	|t|
|||d
S )NFTc                 s   s   | ]}|j o|d kV  qdS )r   N)Z
is_Integer).0r&   rE   rE   rF   	<genexpr>E   s     zcan_do.<locals>.<genexpr>r>   r<   r=   rB   )r%   r&   r'   d)r   r"   r$   hasfree_symbols	enumeraterandcplxanyr   substnreplacer1   r0   )apbq	numericaldiv
lowerplanerreplZrandsymsnair%   r&   r'   rP   rE   rE   rF   can_do9   s0    
    rb   c                   C   s   t tjgtddgstt g dtdddgs4tt tddddgddgsRtt tddgtddtddtjdgs~tt td	dtddgtd
ddgstt td	dgtddtjgstt td	dtddgdgstd S )N	   r>   rB   r?   rH   r<   r=   rO   )rb   r   rC   r.   rD   rE   rE   rE   rF   
test_roachP   s    ,("rf   c                   C   s   t tdddgtddtjtddgs,tt tddgtdddgsLtt tddtjdgtddtddgsxtt dddgtjdgstt tjgtddtddtddgstd S )Nr<   r>   rB   rH   r=   r?   rO   )rb   r.   r   rC   rD   rE   rE   rE   rF   test_roach_fail\   s
    , ,rg   c                  C   s   ddl m}  ttg dgt| ks&tttdgdgt| ksBtttddgdgtdks`ttddt t gdt gstttdd	tdtd
  kstd S )Nr   oor<   rO   rB   re   i)r<   rB   )rO   r>   )sympy.core.numbersri   r   r"   r$   rD   rb   rT   rh   rE   rE   rF   test_polynomialg   s     rk   c                   C   s  t tdgtgtttt d  td  dt  ttd   d  tt ttd t  d ksftt tddgdgtdt dtt d  td   kstt ttj	dgt
ddgtddt d  ttttt d  kstt ttj	tj	gt
ddgtdt d d ttt d   d	t d ttt dtt
dd    ks^tt tddgt
ddgtddt d  tttttdt d  tt d    kstt tt
ddd ddgtj	dgttttt
d	d
 t
d	d  ttt dtd  dt  d	 d t  d	tt d  dtd    ksTtt tdtj	 ddgddgtdttt d d tj	  t kstt tdgtdgttt d tj	  ttd dtt  tt tt d d  ttdtt  tt  kstd S )Nr>   rB   r=   rO   r<   r?   rd   rH   rA   r@   i    #   )r   r"   r%   r$   r0   r;   rD   r2   r   rC   r.   r3   r4   r5   r&   r8   r:   rE   rE   rE   rF   test_hyperexpand_basesp   sD    8<& (
(,$*
"
0*ro   c                   C   s   t tttjt gtjgtdtt dt  d dtt dt  d  ksRtt tttddt gdt gtddt d  t d tj d dt d   kstd S )NrB   rO   r>   r<   )	r   r"   r%   r   rC   r$   r4   rD   r.   rE   rE   rE   rF   test_hyperexpand_parametric   s    .".rp   c                  C   sr   ddl m}  | ttd tdgdtdgtd   ttdt  td  tj tdt   tj ksnt	d S )Nr   simplifyrH   r>   r=   rI   )
sympy.simplify.simplifyrr   r   r$   r"   r   r7   rC   r6   rD   rq   rE   rE   rF   test_shifted_sum   s    *0rt   c                   C   s   t tdd d S )z Steer clear of integers.    
   2   )r   r   rE   rE   rE   rF   _randrat   s    rx   r<   c                 C   s   t  tt    td|    S )z+ Polys is not good with real coefficients. rB   )rx   r   )offsetrE   rE   rF   rT      s    rT   c                  C   s6  ddl m}  |  j}|D ]}||j}i }t|jD ]\}}t|||< q8||}|j	|
d}|j}t||tt|st|j|j d |
d}	t|tt|	tt|st||jdd | }
|j|j }t|
|D ]:\}}t||tt||
dtt|stqqd S )Nr   )FormulaCollectionnonrepsmallc                 S   s
   |  dS )Nr{   )rewrite)trE   rE   rF   <lambda>   s   ztest_formulae.<locals>.<lambda>)sympy.simplify.hyperexpandrz   formulaefuncr$   rS   r   rT   rV   closed_formr|   rW   rX   r1   r0   rD   CBZ	applyfuncdiffMzip)rz   r   formulahrepr`   symr   r$   clderiv1deriv2d1d2rE   rE   rF   test_formulae   s8    

 
  r   c                  C   s
  ddl m}  |  j}|D ]}|| D ]}t|jj|jj|jj|jj|j	}i }|j
D ]}t ||< qT||}|j|}|j	}t|||st|j|j d |}	t||	|st||j| }
|j|j }t|
|D ]$\}}t|||||stqq$qd S )Nr   )MeijerFormulaCollection)r   r   r   r#   r   anrY   bmrZ   r$   r   rT   rV   r   rW   rD   r   r   r   r   r   )r   r   sigr   gr   r   r   r$   r   r   r   r   r   rE   rE   rF   test_meijerg_formulae   s,     

r   c                 C   s   t | t  S N)r$   r   )frE   rE   rF   op   s    r   c               	   C   s  t tdgdtdgdtg ks$ttt  t tdgdtddt W 5 Q R X tt& t tdgdgtdgdgt W 5 Q R X tt& t tdgg ttdgg t W 5 Q R X dd tdD \} }}|dt 7 }t	| |g|gt}t	| d |f|gt}t
t|t t| d |f|gt| |f|gtt|tsDtt	| d |d f|gt}t
t|t t| d |d f|gt| |f|gtt|tstd S )	Nr   rE   rB   r>   rJ   c                 s   s   | ]}t |V  qd S r   rT   rM   r`   rE   rE   rF   rN      s     ztest_plan.<locals>.<genexpr>r=   )r   r   r$   rD   r)   
ValueErrorr   ranger   r"   rW   r   r   )a1a2b1r   h2rE   rE   rF   	test_plan   sJ    
 
$
*
*  
  r   c            
      C   s  ddt d  } }}dt d }}t| ||f||f}t| d |d |d f|d |d f}t||t}t|t|tg }t|jt}	tt|j	||	|j
 d |ttstt| |d |d f|d |d f}t||t}tt|j	||	|j
 d |tts
td S )NrB   r>   rJ   r=   z5/2r   )r   r   r   r$   r   r   r   rW   r   r   r   rD   )
r   r   a3r   b2r   r   opsr   ZderivrE   rE   rF   test_plan_derivatives   s    (($r   c            	      C   s  dd t dD \} }}t| g|gt}tddd ks:ttddd ksLttdtdd ksbtt| |f||ft}tt|||t|tstt| |d f||ft}tt|d ||t|tstt|d	 | f||ft}tt|d	 ||t|ts
t|d	 | |d f}|||f}t	t
||\}}|j| fksJt|j|fks\ttt||tt||tts~td S )
Nc                 s   s   | ]}t |V  qd S r   r   r   rE   rE   rF   rN     s     z+test_reduction_operators.<locals>.<genexpr>r=   r>   r   r<   rB   rJ   rH   )r   r"   r$   r   rD   r   rW   applyr   r   r   rY   rZ   r   )	r   r   r   r   r   rY   rZ   r   r   rE   rE   rF   test_reduction_operators  s"    "$
r   c                  C   sP  dd t dD \} }}}}t| |f|||ft}ttdd  ttdd  tt| |tt| d |f|||fttst	tt||tt| |d f|||fttst	tt
||tt| |f|d ||fttst	tt
||tt| |f||d |fttst	tt
||tt| |f|||d fttsLt	d S )Nc                 s   s   | ]}t |V  qd S r   r   r   rE   rE   rF   rN   '  s     z'test_shift_operators.<locals>.<genexpr>r?   c                   S   s   t dS )Nr   )r   rE   rE   rE   rF   r~   *      z&test_shift_operators.<locals>.<lambda>c                   S   s   t dS )NrB   )r   rE   rE   rE   rF   r~   +  r   rB   )r   r"   r$   r)   r   rW   r   r   r   rD   r   )r   r   r   r   b3r   rE   rE   rF   test_shift_operators&  s    2224r   c                  C   s  dd t dD \} }}}}t| |f|||ft}ttdd  ttdd  ttdd  ttdd  t| |f|||fd	t}t||tt| d
 |f|||fttst	t| |f|||fd
t}t||tt| |d
 f|||fttst	t
| |f|||fd	t}t||tt| |f|d
 ||ftts>t	t
| |f|||fd
t}t||tt| |f||d
 |fttst	t
| |f|||fdt}t||tt| |f|||d
 fttst	d S )Nc                 s   s   | ]}t |V  qd S r   r   r   rE   rE   rF   rN   5  s     z(test_ushift_operators.<locals>.<genexpr>r?   c                   S   s   t dddtS )NrB   rE   r   r   r$   rE   rE   rE   rF   r~   8  r   z'test_ushift_operators.<locals>.<lambda>c                   S   s   t dddtS )NrE   )r<   r   r   r$   rE   rE   rE   rF   r~   9  r   c                   S   s   t dddtS )Nr   )r   r<   rB   r   r   rE   rE   rE   rF   r~   :  r   c                   S   s   t dddtS )Nr   rB   r   r   r   rE   rE   rE   rF   r~   ;  r   r   rB   r>   )r   r"   r$   r)   r   r   rW   r   r   rD   r   )r   r   r   r   r   r   srE   rE   rF   test_ushift_operators4  s     ..00r   c                 C   s   ddl m} ddlm} tt| |||t}|tr:dS |||dddddddd}|s^dS i }tt| |||tj	th D ]\}	}
t
|	||
< q~tt| |||t|||tS )ab  
    This helper function tries to hyperexpand() the meijer g-function
    corresponding to the parameters a1, a2, b1, b2.
    It returns False if this expansion still contains g-functions.
    If numeric is True, it also tests the so-obtained formula numerically
    (at random values) and returns False if the test fails.
    Else it returns True.
    r   )expand)
unpolarifyFT)forceZ
power_baseZ	power_expmulr2   Zmultinomialbasic)Zsympy.core.functionr   $sympy.functions.elementary.complexesr   r   r#   r$   rQ   rS   rR   rT   rW   rV   )r   r   r   r   numericr   r   r^   r_   r`   ra   rE   rE   rF   can_do_meijerJ  s"    	
   $r   c               
   C   s  ddl m}  ddlm} ttg g gdgg gt ttks@tttddgg gdgdggtt	td ksptttddgg gdgdggtttd  kstttg g gt
jgdggtd d tttt kstttg g gdgt
jggtd d tttt ksttg tgtd tt
j gg s:ttg g td gt d gds^tttgtgtgttd gstttdgg g dgttdttdk fdtdt dk ftdgg g dgtdfkstttg dgdgg ttdttdk fdtdt dk ftg dgdgg tdfks4ttg g ttd  gtttd  tt
j gsfttg g tgtgdsttg t
jgtgt gsttg g ttgg sttg g ttgg sttg g ttt
j gttt
j gsttg g tt gdt
jgdsttg g ttt
j ttt
j gg s@ttt
jgg dgtt gs`ttt
jgg tgdt gdsttg tt
j gttgtt
j gdsttg tt
j gtt tt tgg dstttt
j gg tdt t tgg dsttg g g ttgstttddgg g ddgttdttdk ftddtd    d tdt dk ftddgg g ddgtdfkst| |ttdgdt gt d t d t
j gg dt d	tt ttd d t  t kstttdgg tgddgtttftd td ftttt  tt  tt ttd d  ksbttd
t
jfdftd }t|tttdtd	   kstt|ddttt ttd d  kstd S )Nr   	gammasimprq   rB   r>   FTr<   rO   )r   rE   r   )Zplace)sympy.simplify.gammasimpr   rs   rr   r   r#   r$   r0   rD   r2   r   rC   r7   r4   r/   r6   r   r%   r&   r!   absr"   r1   r   r:   )r   rr   r   rE   rE   rF   test_meijerg_expandi  s    (

$$
$$""
"
2    
("( "*,,&
0"
  &r   c                  C   s  ddl m} m} ddlm} tttgg ttgg t	t	t t
t	 tt t d  |tt t	 ksjtttdgg ddgg t	t
t	|dt	 kstttgg ttd gg stttgg td tgg stttgg td tgg sttttgg ttttj gg t	tt t	ttj   dtdtt	  |dtt	 td   dtdtt	  | dtt	      krtttgg tttj tgg t	  krtttgg ttj ttgg t	ksn tttd gg td ttdd td gg std S )Nr   )CiSi)
uppergammarB   r>   r=   )'sympy.functions.special.error_functionsr   r   'sympy.functions.special.gamma_functionsr   r   r#   r%   r&   r$   r0   r:   rD   r   r   rC   r4   r/   r6   r7   r.   )r   r   r   rE   rE   rF   test_meijerg_lookup  s*    . @"
 
 r   c                	   C   s  t g g ttj gtttd  ttd  gs0tt g g dtjgtt gsNtt g g dt tj tt tj gttj gstt g g dttj t tj gtjgstt g g tttj tgdt t gstt g g tttj tdt t gstt tjgg t tgdgstd S )Nr>   r   r=   )r   r%   r   rC   r&   rD   rE   rE   rE   rF   test_meijerg_expand_fail  s    02*(&r   c                  C   s  dd t dD \} }dd t dD \}}dd t dD \}}}}}}	t| g||g|g||gt}
tddd kszttddd kstt| |g||g|g|||gt}tt|||
t	|tstt| |g||g|g|||d	 gt}tt||d	 |
t	|tstt| |d	 g||g|g|||d gt}tt|d	 |d |
t	|tsjtt| g|||d	 g||d g||gt}tt|d |d	 |
t	|td
dst| |g}|||d	 g}|||d	 g}||d	 g}t
t||||\}}|j| fkstt|j||hks0t|j|fksBtt|j||hksZttt|
|t	t||||ttstd S )Nc                 s   s&   | ]}t |d t  |t  V  qdS r?   NrT   r   r   rE   rE   rF   rN     s     ztest_meijerg.<locals>.<genexpr>r>   c                 s   s&   | ]}t |d t  |t  V  qdS r   r   r   rE   rE   rF   rN     s     c                 s   s   | ]}t  V  qd S r   r   r   rE   rE   rF   rN     s     rA   r=   rH   rB   gư>)Ztol)r   r#   r$   r   Zmeijer_minusrD   Zmeijer_plusrW   r   r   r   r   r   setrY   r   rZ   r   )r   r   r   r   r   b4b5r   a4a5r   g2r   rZ   rY   r   Zniqr   rE   rE   rF   test_meijerg  sD      $&(*(    r   c               
   C   sx  dd t dD \
} }}}}}}}}}	t| g||g|g||gt}
tt||
tt| g||g|d g||gttszttt| |
tt| d g||g|g||gttsttt	||
tt| g||g|g|d |gttsttt
||
tt| g|d |g|g||gtts$tt| g||g|g||gdt}t||
tt| g||g|d g||gttsxtt| g||g|g||gdt}t||
tt| g||g|g|d |gttstt| g||g|g||gdt}t||
tt| d g||g|g||gtts tt| g||g|g||gdt}t||
tt| g|d |g|g||gttsttd S )Nc                 s   s   | ]}t |V  qd S r   r   r   rE   rE   rF   rN     s     z/test_meijerg_shift_operators.<locals>.<genexpr>rv   rB   r   )r   r#   r$   rW   r   r   r   rD   r   r	   r
   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   rE   rE   rF   test_meijerg_shift_operators  sT    &    

  

  

  

  r   c                  C   sV  dd } | t g ddgddgg ttt ds2t| t g ddgddgg ttd  d t ttd  tdd dszt| t g ddgddgg ttd d	 td  ttd  tdd dd
t   dst| t g ddddgddddgg tttd  d
 dst| t ddgg g ddgtdtdt  s<t| t ddgddgddgddgtt tt dt  tdt  d st| t tjgddgddgtddgtttd d dstdd }|g dgddgg st|ddgg g dgst|ddgdddgddd
gddgs,t|ddgdddgddd
gdgsRtd S )Nc                 S   s   ddl m} |||g\}}| }t| } | t|ttdk f|tdt dk f|dfks\dS | jd jd |kr| jd jd |ksdS t d }t| t|	 |t|	  	 dkrdS t| td| 	 |td| 	  	 dkrdS dS )Nr   )sympifyrB   TFrv   g|=)
Zsympy.core.sympifyr   r   r!   r   r$   argsrT   rV   r`   )mr%   r&   r   Zm_Zz0rE   rE   rF   r}     s    0(
,4z"test_meijerg_confluence.<locals>.trB   r   r=   r>   rH   r<      rA   c                 S   sJ   t | |||t}t|dd}|t r>|jr:t|jdks>dS t||tS )NT)Zallow_hyperr=   F)r#   r$   r   rQ   Zis_Piecewiselenr   rW   )r   rY   r   rZ   r   m2rE   rE   rF   u1  s
    z"test_meijerg_confluence.<locals>.ur?   )r#   r$   r2   rD   r.   r   rC   )r}   r   rE   rE   rF   test_meijerg_confluence  s8    *    & 4 <0  
>(r   c                  C   s   ddl m}  tdtddfdft}d}|ttdd  tdtddftd	dftttt   }| 	t
||  d
dstd S )Nr   )RR))g      @rB   rE   r=   r>   r   gwg      r?   g      ?g-q=)Zsympy.polys.domains.realfieldr   r#   r.   r$   r"   r1   r   r/   Zalmosteqr   r`   rD   )r   r   r%   r   rE   rE   rF   test_meijerg_with_Floats=  s
    <r   c               
   C   s  ddl m} m} ddlm} ttdtgtd gtt | tdtksJt	ttdttgtd td gttd  | tdtkst	ttdtttgtd td td gttd  | tdtkst	ttdgtgd  td gd ttd  | tdtkst	|tt
ddt gg dgt gtt t t | tdtksLt	|tt
ddt dt gg dgt t gtt t t | tdtkst	|tt
ddt dt dt gg dgt t t gtt t t | tdtkst	tttddgdgt tdt   ks&t	tttdddgddgt |dtksTt	tttddddgdddgt |dtkst	ttdtdtj gtd tjgtdt td  dtd  t | tdt  kst	tdddgddgst	tdddtd	 gddtgdd
st	tdttttd	 gtd td td tgddsTt	ddlm} tttjtjtjdgtddtddtddgtdd||dttt d  |dtj kst	d S )Nr   )lerchphipolylogr   rB   r>   r=   rv   rO   r?   )r\   Fr[   )AbsrH   )Z&sympy.functions.special.zeta_functionsr   r   r   r   r   r"   r%   r$   rD   r#   r1   r   r/   r2   r   rC   rb   r&   r   r   r.   )r   r   r   r   rE   rE   rF   test_lerchphiF  sh    .$
0
,

 


 

" 

0.2$*
&   &r   c                  C   s"  dd t dD \} }}}}t| ||g||gtg | ||||gfD ]d}t|}|j}|j||ksht|j|| }|j|j }	t	||	D ]\}
}t
|
||stqqDtd\} }}ttd| gd|g||  | d | | d  d|   t| d g|g| | | d d|   d t| g|g|  ks4tt
ttd|gd|g|td|gd|g||sjtttdgd| |g|td| |f||td| d |f| d|    ||d	  td| d |d f| d|  |   kstt
ttdgd||g|tdgd||g||std S )
Nc                 s   s   | ]}t  V  qd S r   r   )rM   _rE   rE   rF   rN   v  s     z$test_partial_simp.<locals>.<genexpr>r?   za b zr=   rB   r>   rE   rH   )r   r   r   r$   r   rD   r   r   r   r   rW   r   r   r"   )r%   r&   r'   rP   er   r   r$   r   r   Zfunc1Zfunc2rE   rE   rF   test_partial_simpt  sD    4&
  
.
  r   c                   C   s  t tttgtgdttttt t  ttt  ttt  ksJtt tttgdt t gdtdtd  tdt t  tdt  tdtd  t  kstt tttgdt t gdtdtd  tdt t  tdt  tdtd  t  kstt tdt td  gdt td  gtd gt d gdtddt  tttd  td   tdt td  td   tdt td  td   tdt td  td   kstt ttgtgddkstttgtgddkstd S )NrB   r<   r>   r   )	r   r"   r%   r&   r'   r:   rD   r#   r$   rE   rE   rE   rF   test_hyperexpand_special  s$    .>>
<B
r   c                  C   s\   ddl m}  ddlm} | ddd}|ttdgg |d gdgtt|d tksXtd S )Nr   )Symbolrq   r`   T)integerrB   )	sympy.core.symbolr   rs   rr   r   r#   r$   r;   rD   )r   rr   r`   rE   rE   rF   test_Mod1_behavior  s     r   c                   C   s   t ddt d dt d gtdddgs.tt tjtd gtddtd gddsXtt g td gsltt tgtd td gstt tgttj dt gstt tgttj dt d gstt tgttj dt d gstt tgttj dt gs
tt tgttj dt d gs.tt tgttj dt d gsRtt tjgtdt gsntt tjgtdt gstt dgdtgstt tttj gdt tdt t d gstt tttj gtjdt dt tj gs tt tgtd gddstd S )NrB   r=   r>   T)r]   )rb   r   r.   rD   r   rC   r%   r&   rE   rE   rE   rF   test_prudnikov_misc  s     .*"" $$00r   c                   C   s  t tt gtjgstt tdt gtjgs2tt tdt gtddgsPtt tdt gtjgsjtt tdt gtddgstt tdt gtddgstt tttj gdt d gstt tttj gdt gstt tttj gdt d gs
tt tttj gtjgs(tt tttj gtddgsJtt ttd d gtd gsltt dtgdgstt dtgtd gddstt tgdt gstt tgdt d gstt tgdt d gstd S )NrB   r=   r>   Fr   )rb   r%   r   rC   rD   r.   r&   rE   rE   rE   rF   test_prudnikov_1  s"    "$""r   c               
   C   s  t j} t|  |  g| gstt|  | gd|  gs8tt|  | gd|  gsRtt|  | gd|  gsltt|  dg| gst|  | fD ]}|  | dd|  dd|  dd|  df	D ]:}|  | d|  d|  d|  fD ]}t||g|gstqqdD ]"}dD ]}t||g|gstqqqd S )Nr=   r?   r@   rB   r>   rH   rB   r>   r=   rH   r   rC   rb   rD   r   pr`   r   rE   rE   rF   test_prudnikov_2  s    ( r   c                  C   s8  t rtd tj} ttddtddg| gs2tttddtddgd|  gsVtttddtddgd|  gsztttddtddg| gstttddtddgd|  gstdD ]p}|  | dd|  dd|  dd|  dd	|  f
D ]@}dd|  dd|  dd|  dfD ]}t||g|gstqqqd S )
NzToo slow for CI.rB   rH   r=   r>   r?   r   r@   rc   )r+   r,   r   rC   rb   r.   rD   r   rE   rE   rF   test_prudnikov_3  s     $$ $."r   c                  C   s   t j} d|  d|  d|  fD ]}|  | d|  d|  d|  fD ]:}d|  dd|  dd|  dfD ]}t||g|gs\tq\q<dD ]"}dD ]}t||g|gstqq|qd S )Nr=   r?   r@   r>   rH   r   )r>   r=   rH   r   r   rE   rE   rF   test_prudnikov_4  s      r   c                  C   sT  t j} dD ]H}t|dD ]8}dD ].}t|dD ]}t|  ||g||gs.tq.q qq
| dd|  dd|  dfD ]v}| d|  d|  fD ]^}| d|  d|  fD ]F}| d|  d|  fD ].}||kr||krt|  ||g||gstqqqql| dd|  dd|  dfD ]R}dD ]H}| d|  d|  fD ].}dD ]"}t|  ||g||gs"tq"qqqd S )NrB   r>   r=   rH   rB   r=   r>   r?   r   rC   r   rb   rD   )r   r   qr^   r   rE   rE   rF   test_prudnikov_5	  s"    ""r   c                  C   s8  t j} d|  d|  fD ]x}dD ]n}| ddfD ]&}dD ]}t| ||g||gs4tq4q,dD ]2}d|  d|  fD ]}t| ||g||gsltqlqXqqdD ]:}dD ]0}dD ]&}dD ]}t| ||g||gstqqqqt| | d|  gd|  d|  gstt| dd|  gd|  d|  gstt| ddgddgs4td S )Nr=   r?   r   rB   r>   )rB   r>   r   )r   r   r`   r   r   rE   rE   rF   test_prudnikov_6!  s"      $&r   c               
   C   s   t dgdgsttj} | d|  d|  d|  fD ]}t |  g|gs0tq0|  | dd|  dd|  dd|  df	D ]@}|  | d|  d|  d|  ddddf	D ]}t |g|gstqqnd S )Nr=   rA   r?   r@   rB   r>   rH   )rb   rD   r   rC   )r   r`   r   rE   rE   rF   test_prudnikov_7;  s    ((r   c               	   C   s  t j} dD ]}dD ]L}td|d D ]8}| dd|  dd|  dfD ]}t||g||gs@tq@q$qd|  d|  fD ]B}| dd|  dd|  dfD ]$}dD ]}t||g||gstqqqpq
|  | d|  d|  fD ]}dD ]B}| dd|  dd|  dfD ]$}dD ]}t||g||gstqqq| d|  d|  fD ]d}| d|  d|  dfD ]H}| dd|  dd|  dfD ](}||kr^t||g||gs^tq^qBq*qd S )Nr   rB   r=   r>   r?   r   )r   ra   ZbiciZdirE   rE   rF   test_prudnikov_8G  s(    
r   c                  C   s^   t dD ] } tg t| d d gstqt dD ]&} tg dt|  d  d gs2tq2d S )Nrc   rB   r>   r?   )r   rb   r   rD   )irE   rE   rF   test_prudnikov_9b  s    r   c               	   C   sp  t j} |  | dd|  dd|  dd|  df	D ]2}dD ](}t|dD ]}t|g||gs@tq@q2q*dD ]@}| d|  d|  d|  fD ]"}dD ]}t|g||gstqq~qbd|  d|  d|  fD ]P}| ddd|  dd|  dfD ]0}t|g| |gstt|gd|  |gstqq| ddd|  dd|  dfD ]$}td|  gd|  |gs&tq&ttddgt jt jgsltd S )	NrB   r=   r>   r?   r@   rH   r   r<   )r   rC   r   rb   rD   r.   r   r   r   r`   rE   rE   rF   test_prudnikov_10j  s     ("r   c                   C   s6  t tttj gdt tdt t gs*tt tttj gtdddt dt tj gs\tt tddtddgtjtjdgstt tddtddgtddtjdgstt tddtddgtddtdddgstt tddtddgtddtdddgstt ddgtddddgs2td S )Nr>   r=   rB   rH   r?   r@   )rb   r%   r   rC   r&   rD   r.   rE   rE   rE   rF   test_prudnikov_11  s    *2(,02r   c                   C   s  t g tttj dt gds tt g tttj dt d gdsDtt g tjtttj gs`tt g tddtttj gstt g tddtjtddgstt g tjtjdgstt g tjtdddgstt g tddtddtddgstt g ddtddgstt g ddtddgs4tt g dtddtddgsVtt g tddtddtddgs~tt g dtddtddgstd S )Nr>   FrB   r=   rH   r?   r@   )rb   r%   r   rC   rD   r.   rE   rE   rE   rF   test_prudnikov_12  s"      $ "&"(r   c                  C   sV   t j} |  | fD ]@}| d|  d|  d|  fD ]"}dD ]}t||g|gs4tq4q,qd S )Nr=   r?   r@   r   r   r   rE   rE   rF   test_prudnikov_2F1  s
    r   c                  C   s  t ttgtd gstt dtgtgs,tt ttgtt tj gsJtt ttgtt tj gshtt ttgtt tdd gstt ttgtt d d gstt ttgtt d d gstt ttgtt d gstt ttgtt d gstt ttgdt gstt ttgtjgs6tt ttgtddgsRtt tdt gtgsltt tdt gtgstt tdt gtgstt tttj gtgstt dtgtgstt dtgtddgstt tddtddgdgsttj} t | d dg| d d gs8tt | d dg| d d	 gsZtt | d dg| d d
 gs|tt | d dg| d d gstt | d dg| d d gstt | d dg| d d gstt | d dg| d d gstt | d dg| d d gs&tt | d dg| d d	 gsHtt | d d dg| d d gsntt | d d dg| d d	 gstt | d d dg| d d gstt | d d dg| d d gstt | d d dg| d d
 gstt | d d dg| d d
 gs,tt | d d dg| d d	 gsRtt | d d dg| d d gsxtt | d d dg| d d gstt | d d dg| d d gstt | d d dg| d d gstt | d d dg| d d gstt | d d dg| d d gs6tt | d d dg| d d gs\tt | d d	 dg| d d gstd S )NrB   r<   r=   r>   rH      rc   rA   r@      r?      r            )	rb   r%   r&   rD   r'   r   rC   r.   ZOne)orE   rE   rF   test_prudnikov_fail_2F1  sX    "  """"""""""&&&&&&&&&&&&&&r  c                   C   s  t tttdd ttdd gtddtddgs8tt tttdd ttdd gtddtddgsptt tttdd ttdd gtddtddgstt tttdd ttdd gttdd dt d d gstt tddtjtjgddgstt tddtjdgtddtddgs<tt tddtdddgtddtd	dgsntt tddtdddgtddtd
dgstt tddtdddgtddtddgstt tddtdddgtddtddgstt tddtdddgtddtddgs6tt tddtdddgtddtd
dgshtt tjddgtddtddgstd S )NrB   r=   r>   rH   r?   r<   r  rc   r  r  r@   r  rA   )rb   r%   r.   rD   r   rC   rE   rE   rE   rF   test_prudnikov_fail_3F2  s    888B$.222222r	  c                   C   s  t dtgtddt  t gs"tt tddgtjdgs>tt dgtjtjgsVtt tddgtjtddgsxtt tddgtddtddgstt dgtddtddgstt dgtddtddgstt dgtddtddgstt tjdgtddtddtddgs,tt tjdgtddtddtddgsZtt g tddtdgsxtt g tddtd	gstt g tddtd	gstt g tttj dt d gstd S )
NrB   r>   r<   rH   r?   r=   r@   gUUUUUU?gUUUUUU?)rb   r%   r&   rD   r.   r   rC   rE   rE   rE   rF   test_prudnikov_fail_other  s    ""&   ..r
  c                  C   s.   t ddgtgd} t| td t ks*td S )Nr<   rB   )r"   r$   r   rD   r   rE   rE   rF   test_bug  s    r  c                  C   sH   t ddd} t| tddks"tt ddd} t| tddksDtd S )N)re   rd   rn   )r  rB      )r  ire   r<   rA   )r"   r   r.   rD   r  rE   rE   rF   test_omgissue_203   s    r  N)TrB   F)r<   )T)Zsympy.core.randomr   r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   Zsympy.concrete.summationsr   Zsympy.core.containersr   Zsympy.core.exprr   rj   r   Zsympy.core.singletonr   r   r   Z(sympy.functions.combinatorial.factorialsr    Z$sympy.functions.elementary.piecewiser!   Zsympy.functions.special.hyperr"   r#   Z	sympy.abcr$   r%   r&   r'   Zsympy.testing.pytestr(   r)   r*   r+   r,   r-   rW   r.   r/   Z&sympy.functions.elementary.exponentialr0   r1   r2   Z%sympy.functions.elementary.hyperbolicr3   Z(sympy.functions.elementary.miscellaneousr4   Z(sympy.functions.elementary.trigonometricr5   r6   r7   Zsympy.functions.special.besselr8   r   r9   r   r:   r;   rG   rL   rb   rf   rg   rk   ro   rp   rt   rx   rT   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r	  r
  r  r  rE   rE   rE   rF   <module>   s   d		
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