o
    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s=J 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sJ d S )N      z1/3            r   z2/3)r   r"   r.   r   Halfr$   r;   r1   r   r/   r4   r9   r#   r:    rD   rD   UD:\Projects\ConvertPro\env\Lib\site-packages\sympy/simplify/tests/test_hyperexpand.pytest_branch_bug#   s    ,&.0

rF   c                   C   s  t tg g tttksJ t tddgdgt t tdt ks$J t tg tjgtd  d ttks9J t ttg tdgtd  d  ttksQJ t ttdtdgtdgtd t t	tkslJ t
ttdttd  tdtf tsJ d S )NrB   r>      3/21/2r   )r   r"   r$   r0   r2   r   rC   r6   r7   r5   
isinstancer   r    r%   Zdoitr   rD   rD   rD   rE   test_hyperexpand,   s   ,*0(0rK   TrB   Fc              	   C   s   t t| |t}|trdS |sdS i }|jth }|r?t|D ]\}}	t|| ||	< q!tdd t| 	|D s=n|sg d\}
}}}|rQg d\}
}}}t
t| |t	||tt	|t|
|||dS )NFTc                 s   s    | ]
}|j o
|d kV  qdS )r   N)Z
is_Integer).0r&   rD   rD   rE   	<genexpr>E   s    zcan_do.<locals>.<genexpr>)r>   r<   r=   rB   )r>   r=   r<   )r%   r&   r'   d)r   r"   r$   hasfree_symbols	enumeraterandcplxanyr   substnreplacer1   r0   )apbq	numericaldiv
lowerplanerreplZrandsymsnair%   r&   r'   rO   rD   rD   rE   can_do9   s*   

ra   c                   C   s   t tjgtddgsJ t g dtdddgsJ t tddddgddgs)J t tddgtddtddtjdgs?J t td	dtddgtd
ddgsSJ t td	dgtddtjgsdJ t td	dtddgdgstJ d S )N	   r>   rB   r?   rG   r<   r=   rN   )ra   r   rC   r.   rD   rD   rD   rE   
test_roachP   s   ,("$re   c                   C   s   t tdddgtddtjtddgsJ t tddgtdddgs&J t tddtjdgtddtddgs<J t g dtjdgsHJ t tjgtddtddtddgs]J d S )	Nr<   r>   rB   rG   r=   r?   rB   r>   r=   rN   )ra   r.   r   rC   rD   rD   rD   rE   test_roach_fail\   s
   , ,.rg   c                  C   s   ddl m}  ttg dgt| u sJ ttdgdgt| u s!J ttddgdgtdks0J tddt t gdt gs@J ttdd	tdtd
  ksPJ d S )Nr   oor<   rN   rB   rd   i)r<   rB   )rN   r>   )sympy.core.numbersri   r   r"   r$   ra   rS   rh   rD   rD   rE   test_polynomialg   s    $rk   c                   C   s  t tdgtgtttt d  td  dt  ttd   d  tt ttd t  d ks3J t tddgdgtdt dtt d  td   ksQJ t ttjdgt	ddgtddt d  t
tttt d  ksvJ t ttjtjgt	ddgtdt d d ttt d   d	t d ttt dtt	dd    ksJ t tddgt	ddgtddt d  tttttdt d  tt d    ksJ t tt	ddd ddgtjdgttttt	d	d
 t	d	d  t
tt dtd  dt  d	 d t  d	tt d  dtd    ks(J t tdtj ddgddgtdttt d d tj  t ksMJ t tdgtdgttt d tj  ttd dtt  tt tt d d  ttdtt  tt  ksJ d S )Nr>   rB   r=   rN   r<   r?   rc   rG   rA   r@   i    #   )r   r"   r%   r$   r0   r;   r2   r   rC   r.   r3   r4   r5   r&   r8   r:   rD   rD   rD   rE   test_hyperexpand_basesp   sD   8<& ((,
$*
"
0*ro   c                   C   s   t tttjt gtjgtdtt dt  d dtt dt  d  ks)J t tttddt gdt gtddt d  t d tj d dt d   ksUJ d S )NrB   rN   r>   r<   )r   r"   r%   r   rC   r$   r4   r.   rD   rD   rD   rE   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s7J d S )Nr   simplifyrG   r>   r=   rH   )	sympy.simplify.simplifyrr   r   r$   r"   r   r7   rC   r6   rq   rD   rD   rE   test_shifted_sum   s   *0rt   c                   C   s   t tdd d S )z Steer clear of integers.    
   2   )r   r   rD   rD   rD   rE   _randrat   s   rx   r<   c                 C   s   t  tt    td|    S )z+ Polys is not good with real coefficients. rB   )rx   r   )offsetrD   rD   rE   rS      s   rS   c                  C   s4  ddl m}  |  j}|D ]}||j}i }t|jD ]
\}}t|||< q||}|j	|
d}|j}t||tt|sCJ |j|j d |
d}	t|tt|	tt|saJ ||jdd | }
|j|j }t|
|D ]\}}t||tt||
dtt|sJ qyqd S )Nr   )FormulaCollectionnonrepsmallc                 S   s
   |  dS )Nr{   )rewrite)trD   rD   rE   <lambda>   s    ztest_formulae.<locals>.<lambda>)sympy.simplify.hyperexpandrz   formulaefuncr$   rR   r   rS   rU   closed_formr|   rV   rW   r1   r0   CBZ	applyfuncdiffMzip)rz   r   formulahrepr_   symr   r$   clderiv1deriv2d1d2rD   rD   rE   test_formulae   s6   

r   c                  C   s
  ddl m}  |  j}|D ]v}|| D ]o}t|jj|jj|jj|jj|j	}i }|j
D ]}t ||< q*||}|j|}|j	}t|||sHJ |j|j d |}	t||	|s[J ||j| }
|j|j }t|
|D ]\}}t|||||sJ qnqqd S )Nr   )MeijerFormulaCollection)r   r   r   r#   r   anrX   bmrY   r$   r   rS   rU   r   rV   r   r   r   r   r   )r   r   sigr   gr   r   r   r$   r   r   r   r   r   rD   rD   rE   test_meijerg_formulae   s0   

r   c                 C   s   t | t  S N)r$   r   )frD   rD   rE   op   s   r   c                  C   s  t tdgdtdgdtg ksJ tt t tdgdtddt W d    n1 s.w   Y  tt t tdgdgtdgdgt W d    n1 sRw   Y  tt t tdgg ttdgg t W d    n1 svw   Y  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sJ t| d |d f|gt}t	t
|t t| d |d f|gt| |f|gtt|tsJ d S )	Nr   rD   rB   r>   rI   c                 s       | ]}t |V  qd S r   rS   rL   r_   rD   rD   rE   rM          ztest_plan.<locals>.<genexpr>r=   )r   r   r$   r)   
ValueErrorr   ranger   r"   rV   r   r   )a1a2b1r   h2rD   rD   rE   	test_plan   sF   

"
"r   c            
      C   s  ddt d} }}dt d}}t| ||f||f}t| d |d |d f|d |d f}t||t}t|t|tg }t|jt}	tt|j	||	|j
 d |ttsXJ t| |d |d f|d |d f}t||t}tt|j	||	|j
 d |ttsJ d S )NrB   r>   rI   r=   z5/2r   )r   r   r   r$   r   r   r   rV   r   r   r   )
r   r   a3r   b2r   r   opsr   ZderivrD   rD   rE   test_plan_derivatives   s   (($,r   c            	      C   sz  dd t dD \} }}t| g|gt}tddd u sJ tddd u s&J tdtdd u s1J t| |f||ft}tt|||t|tsJJ t| |d f||ft}tt|d ||t|tsgJ t|d	 | f||ft}tt|d	 ||t|tsJ |d	 | |d f}|||f}tt	||\}}|j
| fksJ |j|fksJ tt||tt||ttsJ d S )
Nc                 s   r   r   r   r   rD   rD   rE   rM     r   z+test_reduction_operators.<locals>.<genexpr>r=   r>   r   r<   rB   rI   rG   )r   r"   r$   r   r   rV   applyr   r   r   rX   rY   r   )	r   r   r   r   r   rX   rY   r   r   rD   rD   rE   test_reduction_operators  s"   ""
$r   c                  C   sL  dd t dD \} }}}}t| |f|||ft}ttdd  ttdd  tt| |tt| d |f|||ftts@J tt||tt| |d f|||fttsYJ tt	||tt| |f|d ||fttsrJ tt	||tt| |f||d |fttsJ tt	||tt| |f|||d fttsJ d S )Nc                 s   r   r   r   r   rD   rD   rE   rM   '  r   z'test_shift_operators.<locals>.<genexpr>r?   c                   S      t dS )Nr   )r   rD   rD   rD   rE   r~   *      z&test_shift_operators.<locals>.<lambda>c                   S   r   )NrB   )r   rD   rD   rD   rE   r~   +  r   rB   )
r   r"   r$   r)   r   rV   r   r   r   r   )r   r   r   r   b3r   rD   rD   rE   test_shift_operators&  s   22226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sXJ t| |f|||fd
t}t||tt| |d
 f|||ftts{J t	| |f|||fd	t}t||tt| |f|d
 ||fttsJ t	| |f|||fd
t}t||tt| |f||d
 |fttsJ t	| |f|||fdt}t||tt| |f|||d
 fttsJ d S )Nc                 s   r   r   r   r   rD   rD   rE   rM   5  r   z(test_ushift_operators.<locals>.<genexpr>r?   c                   S      t dddtS )NrB   rD   r   r   r$   rD   rD   rD   rE   r~   8      z'test_ushift_operators.<locals>.<lambda>c                   S   r   )NrD   r<   r   r   r$   rD   rD   rD   rE   r~   9  r   c                   S   r   )Nr   )r   r<   rB   r   r   rD   rD   rD   rE   r~   :  r   c                   S   r   )Nr   rB   r   r   r   rD   rD   rD   rE   r~   ;  r   r   rB   r>   )
r   r"   r$   r)   r   r   rV   r   r   r   )r   r   r   r   r   r   srD   rD   rE   test_ushift_operators4  s    ....2r   c                 C   s   ddl m} ddlm} tt| |||t}|trdS |||dddddddd}|s/dS i }tt| |||tj	th D ]
\}	}
t
|	||
< q?tt| |||t|||tS )ab  
    This helper function tries to hyperexpand() the meijer g-function
    corresponding to the parameters a1, a2, b1, b2.
    It returns False if this expansion still contains g-functions.
    If numeric is True, it also tests the so-obtained formula numerically
    (at random values) and returns False if the test fails.
    Else it returns True.
    r   )expand)
unpolarifyFT)forceZ
power_baseZ	power_expmulr2   Zmultinomialbasic)Zsympy.core.functionr   $sympy.functions.elementary.complexesr   r   r#   r$   rP   rR   rQ   rS   rV   rU   )r   r   r   r   numericr   r   r]   r^   r_   r`   rD   rD   rE   can_do_meijerJ  s   	
$$r   c               
   C   s  ddl m}  ddlm} ttg g gdgg gt ttks J ttddgg gdgdggtttd ks8J ttddgg gdgdggtttd  ksPJ ttg g gt	j
gdggtd d tttt ksmJ ttg g gdgt	j
ggtd d tttt ksJ tg tgtd tt	j
 gg sJ tg g td gt d gdsJ ttgtgtgttd gsJ ttdgg g dgttdttdk fdtdt dk ftdgg g dgtdfksJ ttg dgdgg ttdttdk fdtdt dk ftg dgdgg tdfksJ tg g ttd  gtttd  tt	j
 gs.J tg g tgtgds;J tg t	j
gtgt gsJJ tg g ttgg sVJ tg g ttgg sbJ tg g ttt	j
 gttt	j
 gsvJ tg g tt gdt	j
gdsJ tg g ttt	j
 ttt	j
 gg sJ tt	j
gg dgtt gsJ tt	j
gg tgdt gdsJ tg tt	j
 gttgtt	j
 gdsJ tg tt	j
 gtt tt tgg dsJ ttt	j
 gg tdt t tgg dsJ tg g g ttgs	J ttddgg g ddgttdttdk ftddtd    d tdt dk ftddgg g ddgtdfksDJ | |ttdgdt gt d t d t	j
 gg dt d	tt ttd d t  t ksxJ ttdgg tgddgtttftd td ftttt  tt  tt ttd d  ksJ td
t	j
fdftd }t|tttdtd	   ksJ t|ddttt ttd d  ksJ d S )Nr   	gammasimprq   rB   r>   FTr<   rN   )r   rD   r   )Zplace)sympy.simplify.gammasimpr   rs   rr   r   r#   r$   r0   r2   r   rC   r7   r4   r/   r6   r   r%   r&   r!   absr"   r1   r   r:   )r   rr   r   rD   rD   rE   test_meijerg_expandi  s   (

$$"" ""
2
("( "*,,&
0"
 &2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s5J ttdgg ddgg t	t
t	|dt	 ksMJ ttgg ttd gg s[J ttgg td tgg siJ ttgg td tgg swJ 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sJ  J ttd gg td ttdd td gg sJ d S )Nr   )CiSi)
uppergammarB   r>   r=   )'sympy.functions.special.error_functionsr   r   'sympy.functions.special.gamma_functionsr   r   r#   r%   r&   r$   r0   r:   r   r   rC   r4   r/   r6   r7   r.   )r   r   r   rD   rD   rE   test_meijerg_lookup  s*   . @"  6r   c                	   C   s  t g g ttj gtttd  ttd  gsJ t g g dtjgtt gs'J t g g dt tj tt tj gttj gs@J t g g dttj t tj gtjgsUJ t g g tttj tgdt t gsiJ t g g tttj tdt t gs|J t tjgg t tgdgsJ d S )Nr>   r   r=   )r   r%   r   rC   r&   rD   rD   rD   rE   test_meijerg_expand_fail  s   02*(&"r   c                  C   s~  dd t dD \} }dd t dD \}}dd t dD \}}}}}}	t| g||g|g||gt}
tddd u s=J tddd u sGJ t| |g||g|g|||gt}tt|||
t|tsgJ t| |g||g|g|||d	 gt}tt||d	 |
t|tsJ t| |d	 g||g|g|||d gt}tt|d	 |d |
t|tsJ t| g|||d	 g||d g||gt}tt|d |d	 |
t|td
dsJ | |g}|||d	 g}|||d	 g}||d	 g}t	t
||||\}}|j| fks	J t|j||hksJ |j|fksJ t|j||hks*J tt|
|tt||||tts=J d S )Nc                 s   s(    | ]}t |d t  |t  V  qdS r?   NrS   r   r   rD   rD   rE   rM        & ztest_meijerg.<locals>.<genexpr>r>   c                 s   s(    | ]}t |d t  |t  V  qdS r   r   r   rD   rD   rE   rM     r   c                 s       | ]}t  V  qd S r   r   r   rD   rD   rE   rM         rA   r=   rG   rB   gư>)Ztol)r   r#   r$   r   Zmeijer_minusZmeijer_plusrV   r   r   r   r   r   setrX   r   rY   r   )r   r   r   r   r   b4b5r   a4a5r   g2r   rY   rX   r   Zniqr   rD   rD   rE   test_meijerg  s8     $$(((
*r   c               
   C   sr  dd t dD \
} }}}}}}}}}	t| g||g|g||gt}
tt||
tt| g||g|d g||gtts=J tt| |
tt| d g||g|g||gttsYJ tt||
tt| g||g|g|d |gttsuJ tt	||
tt| g|d |g|g||gttsJ t
| g||g|g||gdt}t||
tt| g||g|d g||gttsJ t| g||g|g||gdt}t||
tt| g||g|g|d |gttsJ t| g||g|g||gdt}t||
tt| d g||g|g||gttsJ t| g||g|g||gdt}t||
tt| g|d |g|g||gtts7J d S )Nc                 s   r   r   r   r   rD   rD   rE   rM     r   z/test_meijerg_shift_operators.<locals>.<genexpr>rv   rB   r   )r   r#   r$   rV   r   r   r   r   r	   r
   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   rD   rD   rE   test_meijerg_shift_operators  s<   &    ***
*r   c                  C   s:  dd } | t g ddgddgg ttt dsJ | t g ddgddgg ttd  d t ttd  tdd ds=J | t g ddgddgg ttd d	 td  ttd  tdd dd
t   dshJ | t g g dg dg tttd  d
 dsJ | t ddgg g ddgtdtdt  sJ | t ddgddgddgddgtt tt dt  tdt  d sJ | t tjgddgddgtddgtttd d dsJ dd }|g dgddgg sJ |ddgg g dgsJ |ddgg dg dddgs
J |ddgg dg ddgsJ d S )Nc                 S   s   ddl m} |||g\}}| }t| } | t|ttdk f|tdt dk f|dfks.dS | jd jd |krB| jd jd |ksDdS t d }t| t|	 |t|	  	 dkradS t| td| 	 |td| 	  	 dkr}dS dS )Nr   )sympifyrB   TFrv   g|=)
Zsympy.core.sympifyr   r   r!   r   r$   argsrS   rU   r_   )mr%   r&   r   Zm_Zz0rD   rD   rE   r}     s   0(
,4z"test_meijerg_confluence.<locals>.trB   r   r=   r>   rG   r<      rA   rB   rB   rB   rB   )r   r   r   r   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$   r   rP   Zis_Piecewiselenr   rV   )r   rX   r   rY   r   m2rD   rD   rE   u1  s
   z"test_meijerg_confluence.<locals>.u)r>   r>   r?   )rB   rB   rA   )r#   r$   r2   r.   r   rC   )r}   r   rD   rD   rE   test_meijerg_confluence  s*   *(62. $<$&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sAJ d S )Nr   )RR))g      @rB   rD   r=   r>   r   gwg      r?   g      ?g-q=)Zsympy.polys.domains.realfieldr   r#   r.   r$   r"   r1   r   r/   Zalmosteqr   r_   )r   r   r%   r   rD   rD   rE   test_meijerg_with_Floats=  s
   <"r   c               
   C   s  ddl m} m} ddlm} ttdtgtd gtt | tdtks%J ttdttgtd td gttd  | tdtksBJ ttdtttgtd td td gttd  | tdtkscJ ttdgtgd  td gd ttd  | tdtksJ |tt	ddt gg dgt gt
t t t | tdtksJ |tt	ddt dt gg dgt t gt
t t t | tdtksJ |tt	ddt dt dt gg dgt t t gt
t t t | tdtksJ tttddgdgt tdt   ksJ tttg dddgt |dtks%J tttg d	g d
t |dtks;J ttdtdtj gtd tjgtdt td  dtd  t | tdt  ksgJ tg d
ddgssJ tdddtd gddtgddsJ tdttttd gtd td td tgddsJ ddlm} tttjtjtjdgtddtddtddgtdd||dt
tt d  |dtj ksJ d S )Nr   )lerchphipolylogr   rB   r>   r=   rv   )rB   rB   rB   r   )r>   r>   r>   rN   r?   )r[   FrZ   )AbsrG   )Z&sympy.functions.special.zeta_functionsr   r   r   r   r   r"   r%   r$   r#   r1   r   r/   r2   r   rC   ra   r&   r   r   r.   )r   r   r   r   rD   rD   rE   test_lerchphiF  s\   .$
0
,


"
0,,$*
&("&r   c                  C   s  dd t dD \} }}}}t| ||g||gtg | ||||gfD ]2}t|}|j}|j||ks4J |j|| }|j|j }	t||	D ]\}
}t	|
||sSJ qGq"t
d\} }}ttd| gd|g||  | d | | d  d|   t| d g|g| | | d d|   d t| g|g|  ksJ t	ttd|gd|g|td|gd|g||sJ ttdgd| |g|td| |f||td| d |f| d|    ||d	  td| d |d f| d|  |   ksJ t	ttdgd||g|tdgd||g||sJ d S )
Nc                 s   r   r   r   )rL   _rD   rD   rE   rM   v  r   z$test_partial_simp.<locals>.<genexpr>r?   za b zr=   rB   r>   rD   rG   )r   r   r   r$   r   r   r   r   r   rV   r   r   r"   )r%   r&   r'   rO   er   r   r$   r   r   Zfunc1Zfunc2rD   rD   rE   test_partial_simpt  s>   4&*.*r   c                   C   s  t tttgtgdttttt t  ttt  ttt  ks%J t tttgdt t gdtdtd  tdt t  tdt  tdtd  t  ksVJ t tttgdt t gdtdtd  tdt t  tdt  tdtd  t  ksJ t tdt td  gdt td  gtd gt d gdtddt  tttd  td   tdt td  td   tdt td  td   tdt td  td   ksJ t ttgtgddksJ ttgtgddksJ d S )NrB   r<   r>   r   )r   r"   r%   r&   r'   r:   r#   r$   rD   rD   rD   rE   test_hyperexpand_special  s$   .>><Br   c                  C   s\   ddl m}  ddlm} | ddd}|ttdgg |d gdgtt|d tks,J d S )Nr   )Symbolrq   r_   T)integerrB   )sympy.core.symbolr   rs   rr   r   r#   r$   r;   )r   rr   r_   rD   rD   rE   test_Mod1_behavior  s    r   c                   C   s  t ddt d dt d gtdddgsJ t tjtd gtddtd gdds,J t g td gs6J t tgtd td gsDJ t tgttj dt gsSJ t tgttj dt d gsdJ t tgttj dt d gsuJ t tgttj dt gsJ t tgttj dt d gsJ t tgttj dt d gsJ t tjgtdt gsJ t tjgtdt gsJ t dgdtgsJ t tttj gdt tdt t d gsJ t tttj gtjdt dt tj gsJ t tgtd gddsJ d S )NrB   r=   r>   T)r\   )ra   r   r.   r   rC   r%   r&   rD   rD   rD   rE   test_prudnikov_misc  s    .*"""".. r   c                   C   s  t tt gtjgsJ t tdt gtjgsJ t tdt gtddgs(J t tdt gtjgs5J t tdt gtddgsDJ t tdt gtddgsSJ t tttj gdt d gsdJ t tttj gdt gssJ t tttj gdt d gsJ t tttj gtjgsJ t tttj gtddgsJ t ttd d gtd gsJ t dtgdgsJ t dtgtd gddsJ t tgdt gsJ t tgdt d gsJ t tgdt d gsJ d S )NrB   r=   r>   Fr   )ra   r%   r   rC   r.   r&   rD   rD   rD   rE   test_prudnikov_1  s"   ""  r   c               
   C   s  t j} t|  |  g| gsJ t|  | gd|  gsJ t|  | gd|  gs)J t|  | gd|  gs6J t|  dg| gsAJ |  | fD ]F}|  | dd|  dd|  dd|  df	D ]}|  | d|  d|  d|  fD ]}t||g|gsvJ qjqZdD ]}dD ]}t||g|gsJ q~qzqFd S )Nr=   r?   r@   rB   r>   rG   rB   r>   r=   rG   r   rC   ra   r   pr_   r   rD   rD   rE   test_prudnikov_2  s"   ( r   c                  C   s4  t rtd tj} ttddtddg| gsJ ttddtddgd|  gs+J ttddtddgd|  gs=J ttddtddg| gsMJ ttddtddgd|  gs_J dD ]6}|  | dd|  dd|  dd|  dd	|  f
D ]}dd|  dd|  dd|  dfD ]}t||g|gsJ qqxqad S )
NzToo slow for CI.rB   rG   r=   r>   r?   r   r@   rb   )r+   r,   r   rC   ra   r.   r   rD   rD   rE   test_prudnikov_3  s    $$ $."r   c                  C   s   t j} d|  d|  d|  fD ]B}|  | d|  d|  d|  fD ]}d|  dd|  dd|  dfD ]}t||g|gs:J q.qdD ]}dD ]}t||g|gsNJ qBq>qd S )Nr=   r?   r@   r>   rG   r   )r>   r=   rG   r   r   rD   rD   rE   test_prudnikov_4  s     r   c                  C   sL  t j} dD ]$}t|dD ]}dD ]}t|dD ]}t|  ||g||gs&J qqqq| dd|  dd|  dfD ];}| d|  d|  fD ]/}| d|  d|  fD ]#}| d|  d|  fD ]}||krn||krnt|  ||g||gsnJ qWqLqAq6| dd|  dd|  dfD ]%}dD ] }| d|  d|  fD ]}dD ]}t|  ||g||gsJ qqqq~d S )Nrf   rG   rB   r=   r>   r?   r   rC   r   ra   )r   r   qr]   r   rD   rD   rE   test_prudnikov_5	  s8   r   c                  C   s4  t j} d|  d|  fD ]<}dD ]7}| ddfD ]}dD ]}t| ||g||gs(J qqdD ]}d|  d|  fD ]}t| ||g||gsDJ q6q,qqdD ]}dD ]}dD ]}dD ]}t| ||g||gsdJ qVqRqNqJt| | d|  gd|  d|  gszJ t| dd|  gd|  d|  gsJ t| ddgddgsJ d S )Nr=   r?   rf   rB   r>   )rB   r>   r   )r   r   r_   r   r   rD   rD   rE   test_prudnikov_6!  s0   $$r   c               
   C   s   t dgdgs	J tj} | d|  d|  d|  fD ]}t |  g|gs$J q|  | dd|  dd|  dd|  df	D ] }|  | d|  d|  d|  ddddf	D ]}t |g|gsVJ qKq7d S )Nr=   rA   r?   r@   rB   r>   rG   )ra   r   rC   )r   r_   r   rD   rD   rE   test_prudnikov_7;  s   ((r   c               	   C   s  t j} dD ]U}dD ]&}td|d D ]}| dd|  dd|  dfD ]}t||g||gs-J q qq	d|  d|  fD ]!}| dd|  dd|  dfD ]}dD ]}t||g||gsWJ qJqFq8q|  | d|  d|  fD ]]}dD ]!}| dd|  dd|  dfD ]}dD ]}t||g||gsJ q|qxqj| d|  d|  fD ]-}| d|  d|  dfD ] }| dd|  dd|  dfD ]}||krt||g||gsJ qqqqfd S )Nrf   rB   r=   r>   r?   r   )r   r`   ZbiciZdirD   rD   rE   test_prudnikov_8G  s@   r  c                  C   s^   t dD ]} tg t| d d gsJ qt dD ]} tg dt|  d  d gs,J qd S )Nrb   rB   r>   r?   )r   ra   r   )irD   rD   rE   test_prudnikov_9b  s
   $r  c               	   C   sj  t j} |  | dd|  dd|  dd|  df	D ]}dD ]}t|dD ]}t|g||gs,J q qqdD ] }| d|  d|  d|  fD ]}dD ]}t|g||gsOJ qCq?q1d|  d|  d|  fD ](}| ddd|  dd|  dfD ]}t|g| |gsxJ t|gd|  |gsJ qlq]| ddd|  dd|  dfD ]}td|  gd|  |gsJ qttddgt jt jgsJ d S )	NrB   r=   r>   r?   r@   rG   r   r<   )r   rC   r   ra   r.   r   r   r   r_   rD   rD   rE   test_prudnikov_10j  s*   ("r  c                   C   s2  t tttj gdt tdt t gsJ t tttj gtdddt dt tj gs.J t tddtddgtjtjdgsBJ t tddtddgtddtjdgsXJ t tddtddgtddtdddgspJ t tddtddgtddtdddgsJ t ddgtddddgsJ d S )Nr>   r=   rB   rG   r?   r@   )ra   r%   r   rC   r&   r.   rD   rD   rD   rE   test_prudnikov_11  s   *2(,00"r  c                   C   s  t g tttj dt gdsJ t g tttj dt d gds"J t g tjtttj gs0J t g tddtttj gs@J t g tddtjtddgsQJ t g tjtjdgs]J t g tjtdddgskJ t g tddtddtddgs~J t g ddtddgsJ t g ddtddgsJ t g dtddtddgsJ t g tddtddtddgsJ t g dtddtddgsJ d S )Nr>   FrB   r=   rG   r?   r@   )ra   r%   r   rC   r.   rD   rD   rD   rE   test_prudnikov_12  s   $ "& &$r  c                  C   sV   t j} |  | fD ] }| d|  d|  d|  fD ]}dD ]}t||g|gs&J qqqd S )Nr=   r?   r@   r   r   r  rD   rD   rE   test_prudnikov_2F1  s   r	  c                  C   sp  t ttgtd gsJ t dtgtgsJ t ttgtt tj gs%J t ttgtt tj gs4J t ttgtt tdd gsEJ t ttgtt d d gsUJ t ttgtt d d gseJ t ttgtt d gssJ t ttgtt d gsJ t ttgdt gsJ t ttgtjgsJ t ttgtddgsJ t tdt gtgsJ t tdt gtgsJ t tdt gtgsJ t tttj gtgsJ t dtgtgsJ t dtgtddgsJ t tddtddgdgsJ tj} t | d dg| d d gsJ t | d dg| d d	 gs"J t | d dg| d d
 gs3J t | d dg| d d gsDJ t | d dg| d d gsUJ t | d dg| d d gsfJ t | d dg| d d gswJ t | d dg| d d gsJ t | d dg| d d	 gsJ t | d d dg| d d gsJ t | d d dg| d d	 gsJ t | d d dg| d d gsJ t | d d dg| d d gsJ t | d d dg| d d
 gsJ t | d d dg| d d
 gsJ t | d d dg| d d	 gsJ t | d d dg| d d gs1J t | d d dg| d d gsDJ t | d d dg| d d gsWJ t | d d dg| d d gsjJ t | d d dg| d d gs}J t | d d dg| d d gsJ t | d d dg| d d gsJ t | d d	 dg| d d gsJ d S )NrB   r<   r=   r>   rG      rb   rA   r@      r?      r            )ra   r%   r&   r'   r   rC   r.   ZOne)orD   rD   rE   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sJ t tttdd ttdd gtddtddgs8J t tttdd ttdd gtddtddgsTJ t tttdd ttdd gttdd dt d d gsuJ t tddtjtjgddgsJ t tddtjdgtddtddgsJ t tddtdddgtddtd	dgsJ t tddtdddgtddtd
dgsJ t tddtdddgtddtddgsJ t tddtdddgtddtddgsJ t tddtdddgtddtddgsJ t tddtdddgtddtd
dgs.J t tjddgtddtddgsBJ d S )NrB   r=   r>   rG   r?   r<   r
  rb   r  r  r@   r  rA   )ra   r%   r.   r   rC   rD   rD   rD   rE   test_prudnikov_fail_3F2  s   888B",000022,r  c                   C   s  t dtgtddt  t gsJ t tddgtjdgsJ t dgtjtjgs+J t tddgtjtddgs<J t tddgtddtddgsOJ t dgtddtddgs_J t dgtddtddgsoJ t dgtddtddgsJ t tjdgtddtddtddgsJ t tjdgtddtddtddgsJ t g tddtdgsJ t g tddtd	gsJ t g tddtd	gsJ t g tttj dt d gsJ d S )
NrB   r>   r<   rG   r?   r=   r@   gUUUUUU?gUUUUUU?)ra   r%   r&   r.   r   rC   rD   rD   rD   rE   test_prudnikov_fail_other  s   ""&   ,,&r  c                  C   s.   t ddgtgd} t| td t ksJ d S )Nr<   rB   )r"   r$   r   r   rD   rD   rE   test_bug  s   r  c                  C   sH   t ddd} t| tddksJ t ddd} t| tddks"J d S )N)rd   rc   rn   )r  rB      )r  ird   r<   rA   )r"   r   r.   r  rD   rD   rE   test_omgissue_203   s   r  N)TrB   Fr   )T)Zsympy.core.randomr   r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   Zsympy.concrete.summationsr   Zsympy.core.containersr   Zsympy.core.exprr   rj   r   Zsympy.core.singletonr   r   r   Z(sympy.functions.combinatorial.factorialsr    Z$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-   rV   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;   rF   rK   ra   re   rg   rk   ro   rp   rt   rx   rS   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  rD   rD   rD   rE   <module>   s    d		
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