o
    jgS                     @   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$m%Z% d d	l&m'Z' d d
l(m)Z) d dl*m+Z+m,Z, d dl-m.Z.m/Z/m0Z0m1Z1 d dl2m3Z3m4Z4m5Z5m6Z6 d dl m7Z8 d dl m9Z9m:Z: d dl;m<Z<m=Z=m>Z> d dl?m@Z@ d dlAmBZB d dlCmDZDmEZEmFZF d dlGmHZH d dlImJZJ d dlKmLZLmMZM dd ZNdd ZOdddZPd d! ZQe3d"d# ZRd$d% ZSd&d' ZTd(d) ZUd*d+ ZVd,d- ZWdd/d0ZXe5d1d2 ZYd3d4 ZZd5d6 Z[d7d8 Z\d9d: Z]d;d< Z^d=d> Z_d?d@ Z`ddAdBZae5dCdD ZbdEdF Zce3dGdH Zde5dIdJ ZedKdL Zfe5dMdN ZgdOdP ZhdQdR ZidSdT ZjdUdV ZkdWdX Zle5dYdZ Zmd[d\ Zne5d]d^ Zod_d` Zpe6dadb Zqe5dcdd Zre5dedf Zse5dgdh Zte5didj Zue5dkdl Zvdmdn Zwe5dodp Zxdqdr Zydsdt Zze5dudv Z{e3dwdx Z|e3dydz Z}e3d{d| Z~d}d~ Zdd ZdS )    )	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tooslow)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$   r:   r0   r   r.   r3   r8   r#   r9    rC   rC   ]/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/simplify/tests/test_hyperexpand.pytest_branch_bug#   s    ,&.0

rE   c                   C   s  t tg g tttksJ t tddgdgt t tdt ks$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 )NrA   r=      3/21/2r   )r   r"   r$   r/   r1   r   rB   r5   r6   r4   
isinstancer   r    r%   doitr   rC   rC   rC   rD   test_hyperexpand,   s   ,*0(0rK   TrA   Fc              	   C   s   t t| |t}|trdS |sdS i }|jth }|r?t|D ]\}}	t|| ||	< q!tdd t| 	|D s=n|sg d\}
}}}|rQg d\}
}}}t
t| |t	||tt	|t|
|||dS )NFTc                 s   s    | ]
}|j o
|d kV  qdS )r   N)
is_Integer).0r&   rC   rC   rD   	<genexpr>E   s    zcan_do.<locals>.<genexpr>)r=   r;   r<   rA   )r=   r<   r;   )r%   r&   r'   d)r   r"   r$   hasfree_symbols	enumeraterandcplxanyr   substnreplacer0   r/   )apbq	numericaldiv
lowerplanerreplrandsymsnair%   r&   r'   rP   rC   rC   rD   can_do9   s*   

rc   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=   rA   r>   rF   r;   r<   rO   )rc   r   rB   r-   rC   rC   rC   rD   
test_roachP   s   ,("$rg   c                   C   s   t tdddgtddtjtddgsJ t tddgtdddgs&J t tddtjdgtddtddgs<J t g dtjdgsHJ t tjgtddtddtddgs]J d S )	Nr;   r=   rA   rF   r<   r>   rA   r=   r<   rO   )rc   r-   r   rB   rC   rC   rC   rD   test_roach_fail\   s
   , ,.ri   c                  C   s   ddl m}  ttg dgt| u sJ ttdgdgt| u s!J ttddgdgtdks0J tddt t gdt gs@J ttdd	tdtd
  ksPJ d S )Nr   oor;   rO   rA   rf   i)r;   rA   )rO   r=   )sympy.core.numbersrk   r   r"   r$   rc   rT   rj   rC   rC   rD   test_polynomialg   s    $rm   c                   C   s  t tdgtgtttt d  td  dt  ttd   d  tt ttd t  d ks3J t tddgdgtdt dtt d  td   ksQJ t ttjdgt	ddgtddt d  t
tttt d  ksvJ t ttjtjgt	ddgtdt d d ttt d   d	t d ttt dtt	dd    ksJ t tddgt	ddgtddt d  tttttdt d  tt d    ksJ t tt	ddd ddgtjdgttttt	d	d
 t	d	d  t
tt dtd  dt  d	 d t  d	tt d  dtd    ks(J t tdtj ddgddgtdttt d d tj  t ksMJ t tdgtdgttt d tj  ttd dtt  tt tt d d  ttdtt  tt  ksJ d S )Nr=   rA   r<   rO   r;   r>   re   rF   r@   r?   i    #   )r   r"   r%   r$   r/   r:   r1   r   rB   r-   r2   r3   r4   r&   r7   r9   rC   rC   rC   rD   test_hyperexpand_basesp   sD   8<& ((,
$*
"
0*rq   c                   C   s   t tttjt gtjgtdtt dt  d dtt dt  d  ks)J t tttddt gdt gtddt d  t d tj d dt d   ksUJ d S )NrA   rO   r=   r;   )r   r"   r%   r   rB   r$   r3   r-   rC   rC   rC   rD   test_hyperexpand_parametric   s   .".rr   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   simplifyrF   r=   r<   rG   )	sympy.simplify.simplifyrt   r   r$   r"   r   r6   rB   r5   rs   rC   rC   rD   test_shifted_sum   s   *0rv   c                   C   s   t tdd d S )z Steer clear of integers.    
   2   )r   r   rC   rC   rC   rD   _randrat   s   rz   r;   c                 C   s   t  tt    td|    S )z+ Polys is not good with real coefficients. rA   )rz   r   )offsetrC   rC   rD   rT      s   rT   c                  C   s4  ddl m}  |  j}|D ]}||j}i }t|jD ]
\}}t|||< q||}|j	|
d}|j}t||tt|sCJ |j|j d |
d}	t|tt|	tt|saJ ||jdd | }
|j|j }t|
|D ]\}}t||tt||
dtt|sJ qyqd S )Nr   )FormulaCollectionnonrepsmallc                 S   s
   |  dS )Nr}   )rewrite)trC   rC   rD   <lambda>   s    ztest_formulae.<locals>.<lambda>)sympy.simplify.hyperexpandr|   formulaefuncr$   rS   r   rT   rV   closed_formr~   rW   rX   r0   r/   CB	applyfuncdiffMzip)r|   r   formulahrepra   symr   r$   clderiv1deriv2d1d2rC   rC   rD   test_formulae   s6   

r   c                  C   s
  ddl m}  |  j}|D ]v}|| D ]o}t|jj|jj|jj|jj|j	}i }|j
D ]}t ||< q*||}|j|}|j	}t|||sHJ |j|j d |}	t||	|s[J ||j| }
|j|j }t|
|D ]\}}t|||||sJ qnqqd S )Nr   )MeijerFormulaCollection)r   r   r   r#   r   anrY   bmrZ   r$   r   rT   rV   r   rW   r   r   r   r   r   )r   r   sigr   gr   r   r   r$   r   r   r   r   r   rC   rC   rD   test_meijerg_formulae   s0   

r   c                 C   s   t | t  S N)r$   r   )frC   rC   rD   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   rC   rA   r=   rH   c                 s       | ]}t |V  qd S r   rT   rM   ra   rC   rC   rD   rN          ztest_plan.<locals>.<genexpr>r<   )r   r   r$   r)   
ValueErrorr   ranger   r"   rW   r   r   )a1a2b1r   h2rC   rC   rD   	test_plan   sF   

"
"r   c            
      C   s  ddt d} }}dt d}}t| ||f||f}t| d |d |d f|d |d f}t||t}t|t|tg }t|jt}	tt|j	||	|j
 d |ttsXJ t| |d |d f|d |d f}t||t}tt|j	||	|j
 d |ttsJ d S )NrA   r=   rH   r<   z5/2r   )r   r   r   r$   r   r   r   rW   r   r   r   )
r   r   a3r   b2r   r   opsr   derivrC   rC   rD   test_plan_derivatives   s   (($,r   c            	      C   sz  dd t dD \} }}t| g|gt}tddd u sJ tddd u s&J tdtdd u s1J t| |f||ft}tt|||t|tsJJ t| |d f||ft}tt|d ||t|tsgJ t|d	 | f||ft}tt|d	 ||t|tsJ |d	 | |d f}|||f}tt	||\}}|j
| fksJ |j|fksJ tt||tt||ttsJ d S )
Nc                 s   r   r   r   r   rC   rC   rD   rN     r   z+test_reduction_operators.<locals>.<genexpr>r<   r=   r   r;   rA   rH   rF   )r   r"   r$   r   r   rW   applyr   r   r   rY   rZ   r   )	r   r   r   r   r   rY   rZ   r   r   rC   rC   rD   test_reduction_operators  s"   ""
$r   c                  C   sL  dd t dD \} }}}}t| |f|||ft}ttdd  ttdd  tt| |tt| d |f|||ftts@J tt||tt| |d f|||fttsYJ tt	||tt| |f|d ||fttsrJ tt	||tt| |f||d |fttsJ tt	||tt| |f|||d fttsJ d S )Nc                 s   r   r   r   r   rC   rC   rD   rN   '  r   z'test_shift_operators.<locals>.<genexpr>r>   c                   S      t dS )Nr   )r   rC   rC   rC   rD   r   *      z&test_shift_operators.<locals>.<lambda>c                   S   r   )NrA   )r   rC   rC   rC   rD   r   +  r   rA   )
r   r"   r$   r)   r   rW   r   r   r   r   )r   r   r   r   b3r   rC   rC   rD   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   rC   rC   rD   rN   5  r   z(test_ushift_operators.<locals>.<genexpr>r>   c                   S      t dddtS )NrA   rC   r   r   r$   rC   rC   rC   rD   r   8      z'test_ushift_operators.<locals>.<lambda>c                   S   r   )NrC   r;   r   r   r$   rC   rC   rC   rD   r   9  r   c                   S   r   )Nr   )r   r;   rA   r   r   rC   rC   rC   rD   r   :  r   c                   S   r   )Nr   rA   r   r   r   rC   rC   rC   rD   r   ;  r   r   rA   r=   )
r   r"   r$   r)   r   r   rW   r   r   r   )r   r   r   r   r   r   srC   rC   rD   test_ushift_operators4  s    ....2r   c                 C   s   ddl m} ddlm} tt| |||t}|trdS |||dddddddd}|s/dS i }tt| |||tj	th D ]
\}	}
t
|	||
< q?tt| |||t|||tS )ab  
    This helper function tries to hyperexpand() the meijer g-function
    corresponding to the parameters a1, a2, b1, b2.
    It returns False if this expansion still contains g-functions.
    If numeric is True, it also tests the so-obtained formula numerically
    (at random values) and returns False if the test fails.
    Else it returns True.
    r   )expand)
unpolarifyFT)force
power_base	power_expmulr1   multinomialbasic)sympy.core.functionr   $sympy.functions.elementary.complexesr   r   r#   r$   rQ   rS   rR   rT   rW   rV   )r   r   r   r   numericr   r   r^   r_   ra   rb   rC   rC   rD   can_do_meijerJ  s   	
$$r   c               
   C   s  ddl m}  ddlm} ttg g gdgg gt ttks J ttddgg gdgdggtttd ks8J ttddgg gdgdggtttd  ksPJ ttg g gt	j
gdggtd d tttt ksmJ ttg g gdgt	j
ggtd d tttt ksJ tg tgtd tt	j
 gg sJ tg g td gt d gdsJ ttgtgtgttd gsJ ttdgg g dgttdttdk fdtdt dk ftdgg g dgtdfksJ ttg dgdgg ttdttdk fdtdt dk ftg dgdgg tdfksJ tg g ttd  gtttd  tt	j
 gs.J tg g tgtgds;J tg t	j
gtgt gsJJ tg g ttgg sVJ tg g ttgg sbJ tg g ttt	j
 gttt	j
 gsvJ tg g tt gdt	j
gdsJ tg g ttt	j
 ttt	j
 gg sJ tt	j
gg dgtt gsJ tt	j
gg tgdt gdsJ tg tt	j
 gttgtt	j
 gdsJ tg tt	j
 gtt tt tgg dsJ ttt	j
 gg tdt t tgg dsJ tg g g ttgs	J ttddgg g ddgttdttdk ftddtd    d tdt dk ftddgg g ddgtdfksDJ | |ttdgdt gt d t d t	j
 gg dt d	tt ttd d t  t ksxJ ttdgg tgddgtttftd td ftttt  tt  tt ttd d  ksJ td
t	j
fdftd }t|tttdtd	   ksJ t|ddttt ttd d  ksJ d S )Nr   	gammasimprs   rA   r=   FTr;   rO   )r   rC   r   )place)sympy.simplify.gammasimpr   ru   rt   r   r#   r$   r/   r1   r   rB   r6   r3   r.   r5   r   r%   r&   r!   absr"   r0   r   r9   )r   rt   r   rC   rC   rD   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)
uppergammarA   r=   r<   )'sympy.functions.special.error_functionsr   r   'sympy.functions.special.gamma_functionsr   r   r#   r%   r&   r$   r/   r9   r   r   rB   r3   r.   r5   r6   r-   )r   r   r   rC   rC   rD   test_meijerg_lookup  s*   . @"  6r   c                	   C   s  t g g ttj gtttd  ttd  gsJ t g g dtjgtt gs'J t g g dt tj tt tj gttj gs@J t g g dttj t tj gtjgsUJ t g g tttj tgdt t gsiJ t g g tttj tdt t gs|J t tjgg t tgdgsJ d S )Nr=   r   r<   )r   r%   r   rB   r&   rC   rC   rC   rD   test_meijerg_expand_fail  s   02*(&"r   c                  C   s~  dd t dD \} }dd t dD \}}dd t dD \}}}}}}	t| g||g|g||gt}
tddd u s=J tddd u sGJ t| |g||g|g|||gt}tt|||
t|tsgJ t| |g||g|g|||d	 gt}tt||d	 |
t|tsJ t| |d	 g||g|g|||d gt}tt|d	 |d |
t|tsJ t| g|||d	 g||d g||gt}tt|d |d	 |
t|td
dsJ | |g}|||d	 g}|||d	 g}||d	 g}t	t
||||\}}|j| fks	J t|j||hksJ |j|fksJ t|j||hks*J tt|
|tt||||tts=J d S )Nc                 s   s(    | ]}t |d t  |t  V  qdS r>   NrT   r   r   rC   rC   rD   rN        & ztest_meijerg.<locals>.<genexpr>r=   c                 s   s(    | ]}t |d t  |t  V  qdS r   r   r   rC   rC   rD   rN     r   c                 s       | ]}t  V  qd S r   r   r   rC   rC   rD   rN         r@   r<   rF   rA   gư>)tol)r   r#   r$   r   meijer_minusmeijer_plusrW   r   r   r   r   r   setrY   r   rZ   r   )r   r   r   r   r   b4b5r   a4a5r   g2r   rZ   rY   r   niqr   rC   rC   rD   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   rC   rC   rD   rN     r   z/test_meijerg_shift_operators.<locals>.<genexpr>rx   rA   r   )r   r#   r$   rW   r   r   r   r   r	   r
   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   rC   rC   rD   test_meijerg_shift_operators  s<   &    ***
*r   c                  C   s:  dd } | t g ddgddgg ttt dsJ | t g ddgddgg ttd  d t ttd  tdd ds=J | t g ddgddgg ttd d	 td  ttd  tdd dd
t   dshJ | t g g dg dg tttd  d
 dsJ | t ddgg g ddgtdtdt  sJ | t ddgddgddgddgtt tt dt  tdt  d sJ | t tjgddgddgtddgtttd d dsJ dd }|g dgddgg sJ |ddgg g dgsJ |ddgg dg dddgs
J |ddgg dg ddgsJ d S )Nc                 S   s   ddl m} |||g\}}| }t| } | t|ttdk f|tdt dk f|dfks.dS | jd jd |krB| jd jd |ksDdS t d }t| t|	 |t|	  	 dkradS t| td| 	 |td| 	  	 dkr}dS dS )Nr   )sympifyrA   TFrx   g|=)
sympy.core.sympifyr   r   r!   r   r$   argsrT   rV   ra   )mr%   r&   r   m_z0rC   rC   rD   r     s   0(
,4z"test_meijerg_confluence.<locals>.trA   r   r<   r=   rF   r;      r@   rA   rA   rA   rA   )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)allow_hyperr<   F)r#   r$   r   rQ   is_Piecewiselenr   rW   )r   rY   r   rZ   r   m2rC   rC   rD   u1  s
   z"test_meijerg_confluence.<locals>.u)r=   r=   r>   )rA   rA   r@   )r#   r$   r1   r-   r   rB   )r   r   rC   rC   rD   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      @rA   rC   r<   r=   r   gwg      r>   g      ?g-q=)sympy.polys.domains.realfieldr   r#   r-   r$   r"   r0   r   r.   almosteqr   ra   )r   r   r%   r   rC   rC   rD   test_meijerg_with_Floats=  s
   <"r   c               
   C   s  ddl m} m} ddlm} ttdtgtd gtt | tdtks%J ttdttgtd td gttd  | tdtksBJ ttdtttgtd td td gttd  | tdtkscJ ttdgtgd  td gd ttd  | tdtksJ |tt	ddt gg dgt gt
t t t | tdtksJ |tt	ddt dt gg dgt t gt
t t t | tdtksJ |tt	ddt dt dt gg dgt t t gt
t t t | tdtksJ tttddgdgt tdt   ksJ tttg dddgt |dtks%J tttg d	g d
t |dtks;J ttdtdtj gtd tjgtdt td  dtd  t | tdt  ksgJ tg d
ddgssJ tdddtd gddtgddsJ tdttttd gtd td td tgddsJ ddlm} tttjtjtjdgtddtddtddgtdd||dt
tt d  |dtj ksJ d S )Nr   )lerchphipolylogr   rA   r=   r<   rx   )rA   rA   rA   r   )r=   r=   r=   rO   r>   )r\   Fr[   )AbsrF   )&sympy.functions.special.zeta_functionsr   r   r   r   r   r"   r%   r$   r#   r0   r   r.   r1   r   rB   rc   r&   r   r   r-   )r   r   r   r   rC   rC   rD   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   )rM   _rC   rC   rD   rN   v  r   z$test_partial_simp.<locals>.<genexpr>r>   za b zr<   rA   r=   rC   rF   )r   r   r   r$   r   r   r   r   r   rW   r   r   r"   )r%   r&   r'   rP   er   r   r$   r   r   func1func2rC   rC   rD   test_partial_simpt  s>   4&*.*r  c                   C   s  t tttgtgdttttt t  ttt  ttt  ks%J t tttgdt t gdtdtd  tdt t  tdt  tdtd  t  ksVJ t tttgdt t gdtdtd  tdt t  tdt  tdtd  t  ksJ t tdt td  gdt td  gtd gt d gdtddt  tttd  td   tdt td  td   tdt td  td   tdt td  td   ksJ t ttgtgddksJ ttgtgddksJ d S )NrA   r;   r=   r   )r   r"   r%   r&   r'   r9   r#   r$   rC   rC   rC   rD   test_hyperexpand_special  s$   .>><Br  c                  C   s\   ddl m}  ddlm} | ddd}|ttdgg |d gdgtt|d tks,J d S )Nr   )Symbolrs   ra   T)integerrA   )sympy.core.symbolr  ru   rt   r   r#   r$   r:   )r  rt   ra   rC   rC   rD   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 )NrA   r<   r=   T)r]   )rc   r   r-   r   rB   r%   r&   rC   rC   rC   rD   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 )NrA   r<   r=   Fr   )rc   r%   r   rB   r-   r&   rC   rC   rC   rD   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?   rA   r=   rF   rA   r=   r<   rF   r   rB   rc   r   pra   r   rC   rC   rD   test_prudnikov_2  s"   ( r  c                  C   s   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s7J ttddtddg| gsGJ ttddtddgd|  gsYJ d S )NrA   rF   r<   r=   r>   )r   rB   rc   r-   r   rC   rC   rD   test_prudnikov_3  s    $$ (r  c                  C   s|   t 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s9J q-qqd S )	Nr  rA   r<   r=   r>   r?   rF   rd   r  r  rC   rC   rD   test_prudnikov_3_slow  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=   rF   r  )r=   r<   rF   r  r  rC   rC   rD   test_prudnikov_4   s     r  c                  C   sL  t j} dD ]$}t|dD ]}dD ]}t|dD ]}t|  ||g||gs&J qqqq| dd|  dd|  dfD ];}| d|  d|  fD ]/}| d|  d|  fD ]#}| d|  d|  fD ]}||krn||krnt|  ||g||gsnJ qWqLqAq6| dd|  dd|  dfD ]%}dD ] }| d|  d|  fD ]}dD ]}t|  ||g||gsJ qqqq~d S )Nrh   rF   rA   r<   r=   r>   r   rB   r   rc   )r   r  qr^   r   rC   rC   rD   test_prudnikov_5  s8   r  c                  C   s4  t j} d|  d|  fD ]<}dD ]7}| ddfD ]}dD ]}t| ||g||gs(J qqdD ]}d|  d|  fD ]}t| ||g||gsDJ q6q,qqdD ]}dD ]}dD ]}dD ]}t| ||g||gsdJ qVqRqNqJt| | d|  gd|  d|  gszJ t| dd|  gd|  d|  gsJ t| ddgddgsJ d S )Nr<   r>   rh   rA   r=   )rA   r=   r  )r   r   ra   r  r  rC   rC   rD   test_prudnikov_6$  s0   $$r  c               
   C   s   t dgdgs	J tj} | d|  d|  d|  fD ]}t |  g|gs$J q|  | dd|  dd|  dd|  df	D ] }|  | d|  d|  d|  ddddf	D ]}t |g|gsVJ qKq7d S )Nr<   r@   r>   r?   rA   r=   rF   )rc   r   rB   )r   ra   r   rC   rC   rD   test_prudnikov_7>  s   ((r  c               	   C   s  t j} dD ]U}dD ]&}td|d D ]}| dd|  dd|  dfD ]}t||g||gs-J q qq	d|  d|  fD ]!}| dd|  dd|  dfD ]}dD ]}t||g||gsWJ qJqFq8q|  | d|  d|  fD ]]}dD ]!}| dd|  dd|  dfD ]}dD ]}t||g||gsJ q|qxqj| d|  d|  fD ]-}| d|  d|  dfD ] }| dd|  dd|  dfD ]}||krt||g||gsJ qqqqfd S )Nrh   rA   r<   r=   r>   r  )r   rb   bicidirC   rC   rD   test_prudnikov_8J  s@   r  c                  C   s^   t dD ]} tg t| d d gsJ qt dD ]} tg dt|  d  d gs,J qd S )Nrd   rA   r=   r>   )r   rc   r   )irC   rC   rD   test_prudnikov_9e  s
   $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 )	NrA   r<   r=   r>   r?   rF   r  r;   )r   rB   r   rc   r-   r   r  r   ra   rC   rC   rD   test_prudnikov_10m  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<   rA   rF   r>   r?   )rc   r%   r   rB   r&   r-   rC   rC   rC   rD   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=   FrA   r<   rF   r>   r?   )rc   r%   r   rB   r-   rC   rC   rC   rD   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   rC   rC   rD   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 )NrA   r;   r<   r=   rF      rd   r@   r?      r>      r            )rc   r%   r&   r'   r   rB   r-   One)orC   rC   rD   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 )NrA   r<   r=   rF   r>   r;   r%  rd   r'  r&  r?   r*  r@   )rc   r%   r-   r   rB   rC   rC   rC   rD   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 )
NrA   r=   r;   rF   r>   r<   r?   gUUUUUU?gUUUUUU?)rc   r%   r&   r-   r   rB   rC   rC   rC   rD   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;   rA   )r"   r$   r   r  rC   rC   rD   test_bug  s   r0  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)rf   re   rp   )r1  rA      )r1  irf   r;   r@   )r"   r   r-   r  rC   rC   rD   test_omgissue_203#  s   r3  N)TrA   Fr   )T)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   sympy.concrete.summationsr   sympy.core.containersr   sympy.core.exprr   rl   r   sympy.core.singletonr   r  r   (sympy.functions.combinatorial.factorialsr    $sympy.functions.elementary.piecewiser!   sympy.functions.special.hyperr"   r#   	sympy.abcr$   r%   r&   r'   sympy.testing.pytestr(   r)   r*   r+   r,   rW   r-   r.   &sympy.functions.elementary.exponentialr/   r0   r1   %sympy.functions.elementary.hyperbolicr2   (sympy.functions.elementary.miscellaneousr3   (sympy.functions.elementary.trigonometricr4   r5   r6   sympy.functions.special.besselr7   r   r8   r   r9   r:   rE   rK   rc   rg   ri   rm   rq   rr   rv   rz   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/  r0  r3  rC   rC   rC   rD   <module>   s    d		


	

 

B

&
(	.	

	







	
6

