a
    {dI3                    @   s	  d dl Z d dlZd dlmZ d dlmZ d dlmZm	Z	m
Z
 d dl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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$Z$m%Z% d dl&m'Z'm(Z(m)Z) d dl*m+Z+ d dl,m-Z-m.Z. d dl/m0Z0 d dl1m2Z2 d dl3m4Z4m5Z5 d dl6m7Z7 d dl8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z> d dl?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZW d dlXmYZY d dlZm[Z[m\Z\ d dl]m^Z^ d dl_m`Z`maZambZb d dlcmdZdmeZe d dlfmgZgmhZhmiZimjZjmkZkmlZlmmZm d dlnmoZo d dlpmqZq d dlrmsZs d dltmuZu d d lvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~ eCeDeAeBfZd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Zd=d> Zd?d@ ZdAdB ZdCdD ZdEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZdSdT ZdUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddĄ ZddƄ ZddȄ Zddʄ Zdd̄ Zdd΄ ZddЄ Zdd҄ ZddԄ Zddք Zdd؄ Zddڄ Zdd܄ Zddބ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Z d#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Z	d5d6 Z
d7d8 Zd9d: Zd;d< Zd=d> Zd?d@ ZdAdB ZehdCdD ZdEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZeiehdQdR ZdSdT ZdUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Z dcdd Z!dedf Z"dgdh Z#didj Z$dkdl Z%dmdn Z&dodp Z'dqdr Z(dsdt Z)dudv Z*dwdx Z+dydz Z,d{d| Z-d}d~ Z.dd Z/dd Z0dd Z1ekddd Z2dd Z3dS (      N)Hashable)Add)Functiondiffexpand)EFloatIIntegerRationalnanoopi)Pow)S)Symbolsymbols)sympify)Abs)explog)MaxMinsqrt)cossintan)	integrate)PolyPurePoly)sstr)	FiniteSet)signsimpsimplify)trigsimp)
ShapeErrorMatrixErrorNonSquareMatrixErrorDeferredVector_find_reasonable_pivot_naive	_simplify)GramSchmidtImmutableMatrixImmutableSparseMatrixMatrixSparseMatrix
casoratiandiageyehessianmatrix_multiply_elementwiseones
randMatrix	rot_axis1	rot_axis2	rot_axis3	wronskianzerosMutableDenseMatrixImmutableDenseMatrixMatrixSymboldotprodsimprot_ccw_axis1rot_ccw_axis2rot_ccw_axis3)_dotprodsimp_state)TupleWild)KroneckerDelta)flattencaptureiterable)ignore_warningsSymPyDeprecationWarning)raisesXFAILslowskipskip_under_pyodidewarns_deprecated_sympywarnsQ)Array)MatPow)
Quaternion)abcdxyztc                  C   s   t tD ]\} }|dd}|jdkr:tdd |jD s>J |jdkrVt|jtu sZJ |jdkrrt|jtu svJ | d st|	 t
ttfv sJ qt| tu sJ qd S )N      )r`   ra   c                 s   s   | ]}t |tu V  qd S N)typeint.0i rh   k/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/sympy/matrices/tests/test_matrices.py	<genexpr>6       ztest_args.<locals>.<genexpr>)	enumerateclassesr;   shapeallrowsrc   rd   colsflatlisttuplerD   todokdict)nclsmrh   rh   ri   	test_args2   s    "rz   c               	   C   s   t tfD ]L} | dd}t  |j}W d    n1 s:0    Y  || ksJ qttfD ]L} | dd}t  |j}W d    n1 s0    Y  ||	 ks^J q^d S Nr`   ra   )
r.   r,   r;   rQ   Z_matrr   r/   r-   Z_smatru   )rx   ry   matZsmatrh   rh   ri   test_deprecated_mat_smat?   s    $$r}   c                  C   s8   t ddttg} | t t ddtt tt gks4J d S N   ra   )r.   r\   r]   r^   )vrh   rh   ri   test_divisionL   s    r   c                      s   t g dtttgdt dtt gg    t g ddt dt dt gdt ddt t ggkshJ t ddddgtt fdd	 d S )
Nr   ra   r`   ra   i)ra         r   ir   c                      s     S rb   rh   rh   ry   rw   rh   ri   <lambda>U   rk   ztest_sum.<locals>.<lambda>)r.   r\   r]   r^   rL   r%   rh   rh   r   ri   test_sumQ   s    &Br   c                  C   s8   t dddtg} t dddttg}t| |ks4J d S )Nr   ra   r`   )r.   r\   r   absr   rh   rh   ri   test_absW   s    r   c                  C   sH   t d} t d}| | | |  kr>t ddgddggksDn J d S )N)r   ra   r`   r   r   )r`   r   ra   r   r   r   )r.   addrX   rY   rh   rh   ri   test_addition\   s    r   c               	   C   s(  t tfD ]f} | ddtd}||d d d d f ks:J |dd d f t ddg dks^J |d d df t g dks~J |ddgd d f t g dg dgksJ |ddgdf |ddgdgf ksJ |dddgf |dgddgf ksJ |d d ddgf t ddgdd	gd
dggks*J |d dks<J |ddd d f t g dg dgksjJ |d d ddf t ddgdd	gd
dggksJ |d d ddf |ddgdf ksJ |dd d df |dddgf ksJ | ddtd}|g dd d f t g dg dg dg dg dgks>J |d d g df t g dg dg dgksJ qtd}d|d< d|d< d	|d< |ddgdgt dgdggksJ |ddgg dt g dg dgksJ |g dg dt g dg dg dg dgks$J d S )Nr`   	   r   r`   r      )r   r      r   r   r   ra   ra   r   r   r   r   r   )r   ra   r   ra   r   )r   r      )r`   r   r   r   r   )r   r   r   r   r   r   r   r   ra   r   )ra   ra   ra   r   r   r   )r   r   r   ra   )ra   r   r   r   ra   r   r   r   )r   r   r`   r   )r   r   r   r   )r.   r/   ranger;   extract)MrX   rh   rh   ri   test_fancy_index_matrixj   sZ    $ ,&&4.4((
r   c                     sR  t d t d  } | d dks(J | d dks8J | d dksHJ | d	 dksXJ | d
 dkshJ | d dksxJ ztd W n ty   Y nb0 | d dksJ | d dksJ | d dksJ | d	 dksJ | d
 dksJ | d dksJ t | }| | ksJ |d dks(J |d dks:J |d dksLJ |d	 dks^J |d
 dkspJ |d dksJ tt fdd td } t| t sJ | d t	ksJ | d dt	 ksJ | d dt	 ksJ | d	 dksJ t	 }| |ksJ d } t| t s0J | d dksBJ | d dksTJ | d dksfJ | d	 dksxJ ztd W n ty   Y nZ0 t| t sJ | d dksJ | d dksJ | d dksJ | d	 dksJ t t
dgdt
gg}|d |ksJ t t
t
gddgg}|d t ttgttggksNJ d S )N)r   r   r   r   r   r   r   r   ra   r   r   r   r   r   r      ra   r   r   z	c = a @ br   c                      s
   t  S rb   )r4   rh   r   rh   ri   r      rk   z%test_multiplication.<locals>.<lambda>r\   r`   r   
      z	c = 5 @ b)r.   evalSyntaxErrorr4   Zmultiply_elementwiserL   r%   r   
isinstancer\   r   r   )rZ   hc2r   rh   r   ri   test_multiplication   sn    
r   c               	      s  t tdd  t} tddgddgg  d d d  | dd	 | d
d	 | dd | dd gksfJ  d d d  g dksJ tg dg dg dg  d d d  g dksJ  d tdksJ  d  ksJ tdggd d dd ksJ tdd tdksJ tddgddggtd tddgddggksLJ tddgddgg  tj d d  g dksJ tddgd dgg  tj d  ksJ tddgddggtj tddgtjdggksJ tddgddggd! tddgd!dggksJ dd"lm	 tdt
gddgg tdt
 gddggksVJ ttt
gdtgg tt t
td    gdt ggksJ tt
 t
d   t
 d  t
   dt
d   gdt
 t
d   gddt
 ggsJ tt
ddgdt
dgddtgg tt
 t
d   dgdt
 dgddt ggkspJ tddgddgg  td dksJ tdgg  d td#gg  kr td  kr dksn J tg d$g d%g d&g d'g d(gt tfd)d t td*d  tg d+g d,g d-g  d. tg d-g d-g d-gks|J t t fd/d t t fd0d td	dgddgg  d. td1d2gd3d4ggksJ tg d,g d,g d,g  d. tg d,g d,g d,gksJ tg d+g d,g d,g  d. tg d,g d,g d,gksZJ td5d6d7t  tszJ td5d6d6d8t t fd9d td5d6d6d:  ttdtdtd td d gdtddtd gg d,gksJ  d  tg d,g d,g d,gks4J t t fd;d tg d,g d<g d=g  d> tg d?g d@g dAgksJ  d>  d ksJ tg d+g dBg d-g td5  d  d ksJ t tfdCd   d  ksJ tg d-g d-g d-g td5d6d6dD   ksNJ td5d6d6d:  td d d ksJ   dtdksJ   dtdksJ tg dEg dFg dGg  dH tdIdIdIksJ  t tdt dt dt ksJ tg d+g d,g d,g t t fdJd t t fdKd ttjtjgtjtjgg  tj  ksJ tddgddgg  tj ttjtjgdtj dtj ggksJ d S )LNc                   S   s   t dd S Nr   ra   r.   rh   rh   rh   ri   r      rk   ztest_power.<locals>.<lambda>ra   r`   r   r   r   ir      3   i)i  i  i,*  i7  )ra   r   r`   )r   ra   r   )r      r   )	i"  i     i  i  ip  i  i  i  r   r   d   r   i r   r   r      !      0   9   )r   ra   r   r   g      ?rw   i   )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   c                      s     tdS Nr   )_matrix_pow_by_jordan_blocksr   rh   ry   rh   ri   r     rk   c                   S   s   t ddgddggtdS )Nr   r`   )r.   r   r   rh   rh   rh   ri   r     rk   r   r   r   r   r   r   r         $@c                      s    d S N @rh   rh   Arh   ri   r     rk   c                      s    t dd S r{   r   rh   r   rh   ri   r     rk   ihiO<iv0irw   T)integer)r   negativec                      s     S rb   rh   rh   )r   rw   rh   ri   r     rk   )r   Znonnegativec                      s    t dd S r{   r   rh   r   rh   ri   r   %  rk   )r`   r   r   )r   r`   r   g      @)   H   Y   )i#        )i<  i  iI  r   r   r   c                      s     d S )N)subsdoitrh   )Anrw   rh   ri   r   -  rk   )r   positivera   r   r   )r   ra   r   r   r   ra   r   gd%%@c                      s    d S r   rh   rh   r   rh   ri   r   <  rk   c                      s    t  S rb   r	   rh   r   rh   ri   r   =  rk   )rL   r'   r   r.   r2   r
   r   Half	sympy.abcrw   rX   rY   r   Z_eval_pow_by_recursionr&   
ValueErrorr   r   rV   rF   r   r   r1   r;   r	   )Rrh   )r   r   ry   rw   ri   
test_power   s    @ 6 626J<$0&("((*,(&&r   c                  C   s   t dt dt gdt dt gg} td |   t tdt td d tdt  td d gtdt  td d tdt td d ggksJ W d    n1 s0    Y  d S )Nr   Tra   )r.   r\   r?   r   r   r   rh   rh   ri   $test_issue_17247_expression_blowup_1D  s    $
00r   c                  C   sp   t dt dt gdt dt gg} td0 |  \}}|| |  sNJ W d    n1 sb0    Y  d S Nr   T)r.   r\   r?   jordan_forminvr   PJrh   rh   ri   $test_issue_17247_expression_blowup_2K  s    $
r   c                  C   s   t dt dt gdt dt gg} td` | d t dtd  d ddtd   gddtd   dtd  d ggks~J W d    n1 s0    Y  d S )Nr   Tr   l                )r.   r\   r?   r   rh   rh   ri   $test_issue_17247_expression_blowup_3Q  s    $
r   c                  C   sP   t td} td( | d t tdks.J W d    n1 sB0    Y  d S )Na1  [
        [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64],
        [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512],
        [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64],
        [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128],
        [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16],
        [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128]]Tr   a  [
            [     7369525394972778926719607798014571861/604462909807314587353088 - 229284202061790301477392339912557559*I/151115727451828646838272,   -19704281515163975949388435612632058035/1208925819614629174706176 + 14319858347987648723768698170712102887*I/302231454903657293676544,      -3623281909451783042932142262164941211/604462909807314587353088 - 6039240602494288615094338643452320495*I/604462909807314587353088,    109260497799140408739847239685705357695/2417851639229258349412352 - 7427566006564572463236368211555511431*I/2417851639229258349412352, -16095803767674394244695716092817006641/2417851639229258349412352 + 10336681897356760057393429626719177583*I/1208925819614629174706176,    -42207883340488041844332828574359769743/2417851639229258349412352 - 182332262671671273188016400290188468499*I/4835703278458516698824704],
            [50566491050825573392726324995779608259/1208925819614629174706176 - 90047007594468146222002432884052362145*I/2417851639229258349412352,  74273703462900000967697427843983822011/1208925819614629174706176 + 265947522682943571171988741842776095421*I/1208925819614629174706176, -116900341394390200556829767923360888429/2417851639229258349412352 - 53153263356679268823910621474478756845*I/2417851639229258349412352, 195407378023867871243426523048612490249/1208925819614629174706176 - 1242417915995360200584837585002906728929*I/9671406556917033397649408,   -863597594389821970177319682495878193/302231454903657293676544 + 476936100741548328800725360758734300481*I/9671406556917033397649408, -3154451590535653853562472176601754835575/19342813113834066795298816 - 232909875490506237386836489998407329215*I/2417851639229258349412352],
            [   -1715444997702484578716037230949868543/302231454903657293676544 + 5009695651321306866158517287924120777*I/302231454903657293676544,     -30551582497996879620371947949342101301/604462909807314587353088 - 7632518367986526187139161303331519629*I/151115727451828646838272,           312680739924495153190604170938220575/18889465931478580854784 - 108664334509328818765959789219208459*I/75557863725914323419136,    -14693696966703036206178521686918865509/604462909807314587353088 + 72345386220900843930147151999899692401*I/1208925819614629174706176,  -8218872496728882299722894680635296519/1208925819614629174706176 - 16776782833358893712645864791807664983*I/1208925819614629174706176,      143237839169380078671242929143670635137/2417851639229258349412352 + 2883817094806115974748882735218469447*I/2417851639229258349412352],
            [   3087979417831061365023111800749855987/151115727451828646838272 + 34441942370802869368851419102423997089*I/604462909807314587353088, -148309181940158040917731426845476175667/604462909807314587353088 - 263987151804109387844966835369350904919*I/9671406556917033397649408,   50259518594816377378747711930008883165/1208925819614629174706176 - 95713974916869240305450001443767979653*I/2417851639229258349412352,  153466447023875527996457943521467271119/2417851639229258349412352 + 517285524891117105834922278517084871349*I/2417851639229258349412352,  -29184653615412989036678939366291205575/604462909807314587353088 - 27551322282526322041080173287022121083*I/1208925819614629174706176,   196404220110085511863671393922447671649/1208925819614629174706176 - 1204712019400186021982272049902206202145*I/9671406556917033397649408],
            [     -2632581805949645784625606590600098779/151115727451828646838272 - 589957435912868015140272627522612771*I/37778931862957161709568,     26727850893953715274702844733506310247/302231454903657293676544 - 10825791956782128799168209600694020481*I/302231454903657293676544,      -1036348763702366164044671908440791295/151115727451828646838272 + 3188624571414467767868303105288107375*I/151115727451828646838272,     -36814959939970644875593411585393242449/604462909807314587353088 - 18457555789119782404850043842902832647*I/302231454903657293676544,      12454491297984637815063964572803058647/604462909807314587353088 - 340489532842249733975074349495329171*I/302231454903657293676544,      -19547211751145597258386735573258916681/604462909807314587353088 + 87299583775782199663414539883938008933*I/1208925819614629174706176],
            [  -40281994229560039213253423262678393183/604462909807314587353088 - 2939986850065527327299273003299736641*I/604462909807314587353088, 331940684638052085845743020267462794181/2417851639229258349412352 - 284574901963624403933361315517248458969*I/1208925819614629174706176,      6453843623051745485064693628073010961/302231454903657293676544 + 36062454107479732681350914931391590957*I/604462909807314587353088,  -147665869053634695632880753646441962067/604462909807314587353088 - 305987938660447291246597544085345123927*I/9671406556917033397649408,  107821369195275772166593879711259469423/2417851639229258349412352 - 11645185518211204108659001435013326687*I/302231454903657293676544,     64121228424717666402009446088588091619/1208925819614629174706176 + 265557133337095047883844369272389762133*I/1208925819614629174706176]])r.   r   r?   r   rh   rh   ri   $test_issue_17247_expression_blowup_4X  s    
r   c                  C   s   t dddd } tdT | dttd ddt  td   dt td	   td
dks^J W d    n1 sr0    Y  d S )Nr   c                 S   s   dd| |  t   S Nr   r   r   rg   jrh   rh   ri   r     rk   z6test_issue_17247_expression_blowup_5.<locals>.<lambda>Tr\   r   $   r   ZEXdomain)r.   r?   charpolyr   r\   r	   r   rh   rh   ri   $test_issue_17247_expression_blowup_5  s    
r   c                  C   sX   t dddd tdD } td" | ddks6J W d    n1 sJ0    Y  d S )Nr   c                 S   s   g | ]}t | qS rh   r\   re   rh   rh   ri   
<listcomp>  rk   z8test_issue_17247_expression_blowup_6.<locals>.<listcomp>@   TZbareissr   r.   r   r?   detr   rh   rh   ri   $test_issue_17247_expression_blowup_6  s    
r   c                  C   sN   t dddd } td" | ddks,J W d    n1 s@0    Y  d S )Nr   c                 S   s   dd| |  t   S r   r   r   rh   rh   ri   r     rk   z6test_issue_17247_expression_blowup_7.<locals>.<lambda>T	berkowitzr   )r.   r?   r   r   rh   rh   ri   $test_issue_17247_expression_blowup_7  s    
r   c                  C   sX   t dddd tdD } td" | ddks6J W d    n1 sJ0    Y  d S )Nr   c                 S   s   g | ]}t | qS rh   r   re   rh   rh   ri   r     rk   z8test_issue_17247_expression_blowup_8.<locals>.<listcomp>r   TZlur   r   r   rh   rh   ri   $test_issue_17247_expression_blowup_8  s    
r   c                  C   s   t dddd tdD } tdX |  t g dg dg dg dg dg dg dg dgd	fkslJ W d    n1 s0    Y  d S )
Nr   c                 S   s   g | ]}t | qS rh   r   re   rh   rh   ri   r     rk   z8test_issue_17247_expression_blowup_9.<locals>.<listcomp>r   T)r   r   r   r   r   r   r   r   ra   r`   r   r   r   r   r   r   r   r   r   r   r   r   r   )r.   r   r?   rrefr   rh   rh   ri   $test_issue_17247_expression_blowup_9  s    
r   c                  C   sP   t dddd } td$ | dddks.J W d    n1 sB0    Y  d S )Nr   c                 S   s   dd| |  t   S r   r   r   rh   rh   ri   r     rk   z7test_issue_17247_expression_blowup_10.<locals>.<lambda>Tr   )r.   r?   Zcofactorr   rh   rh   ri   %test_issue_17247_expression_blowup_10  s    
r   c                  C   sZ   t dddd } td. |  t dddgd ks8J W d    n1 sL0    Y  d S )Nr   c                 S   s   dd| |  t   S r   r   r   rh   rh   ri   r     rk   z7test_issue_17247_expression_blowup_11.<locals>.<lambda>Tr   r   )r.   r?   Zcofactor_matrixr   rh   rh   ri   %test_issue_17247_expression_blowup_11  s    
r   c                  C   s\   t dddd } td0 |  dddt dddiks:J W d    n1 sN0    Y  d S )Nr   c                 S   s   dd| |  t   S r   r   r   rh   rh   ri   r     rk   z7test_issue_17247_expression_blowup_12.<locals>.<lambda>Tr   r   r   )r.   r?   Z	eigenvalsr	   r   rh   rh   ri   %test_issue_17247_expression_blowup_12  s    
r  c               	   C   s  t ddt td dt gdt td dtd gddt td dt gdddt dgg} |  }|d ddt g dgfksJ |d d ttdtd   d ksJ |d d dksJ |d d d jdddt t tdtd   d td  gdt td dt  d  td ttdtd   d  td dt  d   gt tdtd   d td  gdggks|J |d d ttdtd   d ksJ |d d dksJ |d d d jdddt t tdtd   d td  gdt td dt  d  td ttdtd   d  td dt  d   gt tdtd   d td  gdggks|J d S )	Nr   r   ra   )r   r   r   r   FT)deepZnumerr   )r.   r\   Z
eigenvectsr   r   )r   Zevrh   rh   ri   %test_issue_17247_expression_blowup_13  s0     ("P"*"P"r  c                  C   s   t dddt dt gd dt dt gd  d } td |  t td dt td dt td dt td dt gddt ddt ddt ddt gg dg dg dg dg dg dgksJ W d    n1 s0    Y  d S )Nr   r   r   Tr   r   )r.   r\   r?   Zechelon_formr   rh   rh   ri   %test_issue_17247_expression_blowup_14  s    4
2"r  c                  C   s   t dddt dt gd dt dt gd  d } td |  t td dt td dt td dt td dt ggt ddt ddt ddt ddt gggksJ W d    n1 s0    Y  d S )Nr   r   r   Tr   )r.   r\   r?   Zrowspacer   rh   rh   ri   %test_issue_17247_expression_blowup_15  s    4
r  c                  C   s   t dddt dt gd dt dt gd  d } td |  t td gdt gtd gdt gtd gdt gtd gdt ggt dt gtd gdt gtd gdt gtd gdt gtd gggksJ W d    n1 s0    Y  d S )Nr   r   r   T)r.   r\   r?   Zcolumnspacer   rh   rh   ri   %test_issue_17247_expression_blowup_16  s    4
r  c                  C   s@  t dddd tdD } td |  t dgdgdgdgdgdgdgdggt d	gd
gdgdgdgdgdgdggt dgdgdgdgdgdgdgdggt dgdgdgdgdgdgdgdggt dgdgdgdgdgdgdgdggt dgdgdgdgdgdgdgdgggksJ W d    n1 s20    Y  d S )Nr   c                 S   s   g | ]}t | qS rh   r   re   rh   rh   ri   r     rk   z9test_issue_17247_expression_blowup_17.<locals>.<listcomp>r   Tr   r   r   ra   r   r`   r   r   r   r   r   r   )r.   r   r?   Z	nullspacer   rh   rh   ri   %test_issue_17247_expression_blowup_17  s    &&&&&&r  c                  C   sl   t dddt dt gd dt dt gd  d } td |  rJJ W d    n1 s^0    Y  d S )Nr   r   r`   T)r.   r\   r?   is_nilpotentr   rh   rh   ri   %test_issue_17247_expression_blowup_18  s    4
r
  c                  C   sD   t td} td |  r"J W d    n1 s60    Y  d S )Nay  [
        [             -3/4,                     0,         1/4 + I/2,                     0],
        [                0, -177/128 - 1369*I/128,                 0, -2063/256 + 541*I/128],
        [          1/2 - I,                     0,                 0,                     0],
        [                0,                     0,                 0, -177/128 - 1369*I/128]]T)r.   r   r?   is_diagonalizabler   rh   rh   ri   %test_issue_17247_expression_blowup_19  s    
r  c                  C   s   t td dt ddgdt td dtd gddt td dgdddtd gg} td |  t dddtd td  gg dg dg dgt g dddt ddgddtd dgdddtd ggfksJ W d    n1 s0    Y  d S )	Nr   r   T)r   r   r   r   r   r   r   r   r   r   r   r   r   ra   )r.   r\   r?   diagonalizer   rh   rh   ri   %test_issue_17247_expression_blowup_20   s(    
r  c                  C   sT   t td} td, | jddt tdks2J W d    n1 sF0    Y  d S )N  [
        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
        [                0,                     0,                   0, -177/128 - 1369*I/128]]TGEmethodv  [
            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
            [0, 0, 0, -11328/952745 + 87616*I/952745]]r.   r   r?   r   r   rh   rh   ri   %test_issue_17247_expression_blowup_21  s    
r  c                  C   sT   t td} td, | jddt tdks2J W d    n1 sF0    Y  d S )Nr  TLUr  r  r  r   rh   rh   ri   %test_issue_17247_expression_blowup_22  s    
r  c                  C   sX   t td} td0 | jdd t tdks6J W d    n1 sJ0    Y  d S )Nr  TADJr  r  )r.   r   r?   r   r   r   rh   rh   ri   %test_issue_17247_expression_blowup_23,  s    
r  c                  C   sT   t td} td, | jddttdks2J W d    n1 sF0    Y  d S )Nr  TCHr  r  r/   r   r?   r   r.   r   rh   rh   ri   %test_issue_17247_expression_blowup_249  s    
r  c                  C   sT   t td} td, | jddttdks2J W d    n1 sF0    Y  d S )Nr  TLDLr  r  r  r   rh   rh   ri   %test_issue_17247_expression_blowup_25F  s    
r   c                  C   sH   t td} td  |  dks&J W d    n1 s:0    Y  d S )Na  [
        [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64,         -9/32 - I/16,      183/256 - 97*I/128],
        [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512, -219/128 + 115*I/256, 6301/4096 - 6609*I/1024],
        [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,         1/4 - 5*I/16,        65/128 + 87*I/64],
        [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,     85/256 - 33*I/16,    805/128 + 2415*I/512],
        [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,            1/4 + I/2,        -129/64 - 9*I/64],
        [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,     125/64 + 87*I/64,   -2063/256 + 541*I/128],
        [               -2,         17/4 - 13*I/2,             1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,                 -3/4,         45/32 - 37*I/16],
        [     1/4 + 13*I/4,    -825/64 - 147*I/32,          21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64,    -149/64 + 49*I/32,   -177/128 - 1369*I/128]]Tr   r.   r   r?   rankr   rh   rh   ri   %test_issue_17247_expression_blowup_26S  s    	
r#  c                  C   s   t ddt td dt gdt td dtd gddt td dt gdddt dgg} tdL |  \}}| t td ksJ |t tdksJ W d    n1 s0    Y  d S )Nr   r   Ta  [
            [    0,  4*x/(x**2 - 2*x + 1), -(-17*x**4 + 12*sqrt(2)*x**4 - 4*sqrt(2)*x**3 + 6*x**3 - 6*x - 4*sqrt(2)*x + 12*sqrt(2) + 17)/(-7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 + 8*x**3 - 2*x**2 + 8*x + 6*sqrt(2)*x - 5*sqrt(2) - 7), -(12*sqrt(2)*x**4 + 17*x**4 - 6*x**3 - 4*sqrt(2)*x**3 - 4*sqrt(2)*x + 6*x - 17 + 12*sqrt(2))/(7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 - 8*x**3 + 2*x**2 - 8*x + 6*sqrt(2)*x - 5*sqrt(2) + 7)],
            [x - 1, x/(x - 1) + 1/(x - 1),                       (-7*x**3 + 5*sqrt(2)*x**3 - x**2 + sqrt(2)*x**2 - sqrt(2)*x - x - 5*sqrt(2) - 7)/(-3*x**3 + 2*sqrt(2)*x**3 - 2*sqrt(2)*x**2 + 3*x**2 + 2*sqrt(2)*x + 3*x - 3 - 2*sqrt(2)),                       (7*x**3 + 5*sqrt(2)*x**3 + x**2 + sqrt(2)*x**2 - sqrt(2)*x + x - 5*sqrt(2) + 7)/(2*sqrt(2)*x**3 + 3*x**3 - 3*x**2 - 2*sqrt(2)*x**2 - 3*x + 2*sqrt(2)*x - 2*sqrt(2) + 3)],
            [    0,                     1,                                                                                            -(-3*x**2 + 2*sqrt(2)*x**2 + 2*x - 3 - 2*sqrt(2))/(-x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x + 1 + sqrt(2)),                                                                                            -(2*sqrt(2)*x**2 + 3*x**2 - 2*x - 2*sqrt(2) + 3)/(x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x - 1 + sqrt(2))],
            [1 - x,                     0,                                                                                                                                                                                               1,                                                                                                                                                                                             1]]a  [
            [0, 1,                       0,                       0],
            [0, 0,                       0,                       0],
            [0, 0, x - sqrt(2)*(x - 1) + 1,                       0],
            [0, 0,                       0, x + sqrt(2)*(x - 1) + 1]])r.   r\   r?   r   r   r   r   rh   rh   ri   %test_issue_17247_expression_blowup_27`  s    
r$  c                  C   sL   t td} td$ |  tdks*J W d    n1 s>0    Y  d S )Nr  Ta  [
            sqrt(14609315/131072 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2)])r.   r   r?   Zsingular_valuesr   rh   rh   ri   %test_issue_17247_expression_blowup_28s  s    
r%  c                  C   sH   t td} td  |  dks&J W d    n1 s:0    Y  d S )Na	  [
        [1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I,3/64+13/64*I,-23/32-59/256*I,15/128-3/32*I,19/256+551/1024*I],
        [21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I,119/128+143/128*I,-10879/2048+4343/4096*I,129/256-549/512*I,42533/16384+29103/8192*I],
        [-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I,3/64+13/64*I,-23/32-59/256*I],
        [1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I,119/128+143/128*I,-10879/2048+4343/4096*I],
        [-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I],
        [1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I],
        [-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I],
        [-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I],
        [0,-6,-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I],
        [1,-9/4+3*I,-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I],
        [0,-4*I,0,-6,-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I],
        [0,1/4+1/2*I,1,-9/4+3*I,-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I]]Tr   r!  r   rh   rh   ri   test_issue_16823  s    
r&  c                  C   s  t g ddtd dtd dtd td d dddddg	ddtd  ddtd  ddtd  ddtd  dddddg	d	td d dd
td  dd
td  dd
td  ddddd
g	ddtd  dtd d dtd d ddtd  dddddg	dd
td  dd
td  d	td d dd
td  ddddd
g	d	dtd  d	dtd  d	dtd  d	dtd  dddddg	dtd td d dtd dtd dddddg	g} td |  t ddddddddtdd g	ddddddddtd d g	ddddddddtdd g	ddddddddtd d g	g dddddddddtd d g	g dddddddddtd d g	gdfksJ W d    n1 s0    Y  d S )N)	r   r   r   r   r   r   r   r   r   r   ra   r   r   r  r   r   r   r`   r   r   r   T)	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   rh   rh   ri   test_issue_18531  s.    6DDDDD6

r(  c            
      C   s  t tdd  t tdd  t tdd  t t dtdd< W d    n1 sT0    Y  t tg   krtg g  krtddg ksn J t 4 td	gd
gg d	gd
ggksJ W d    n1 s0    Y  t : td	gd
ggj d	ggd
ggksJ W d    n1 s(0    Y  tdgg} t  tj| d< W d    n1 sf0    Y  tt	dgddgg}|}|j
|jksJ |j
dksJ |d d  t	dddgksJ tddt	dddg}|}|j
|jksJ |j
dksJ |d d  t	dddgks J ||ks.J t||ks@J tddtd	d}td	dtdd}t||g}|j
dksJ |jdksJ |d d  g dksJ ttdtdksJ tttdttdksJ t|| ksJ tt|t| ksJ |t|us,J tddtddd gtddd tddd gg}t|} | tg dg dg dg dg dgksJ |  |ksJ t|dd |ksJ tddd}td|g}t|td	d	gd	d	g|d |d g|d |d ggksJ t 4 t|dd dd |D ksFJ W d    n1 s\0    Y  ttdtdgttdgksJ t tdd  t tdd  td	dgddgg} t| dg}	|	td	dgddgddggksJ d S )Nc                   S   s   t ddtdS )Nr      )r.   r   rh   rh   rh   ri   r     rk   ztest_creation.<locals>.<lambda>c                   S   s   t ddg S )Nr   r   r   rh   rh   rh   ri   r     rk   c                   S   s   t dd S r   r   rh   rh   rh   ri   r     rk   r   r   r`   r   r   )ra   r   ra   r   r   	r   ra   r`   r   r   r   r   r   r   r   )r   r   ra   ra   ra   )r`   r`   r`   r   r   Fevaluater   r   r   r   c                 S   s   g | ]
}|gqS rh   rh   re   rh   rh   ri   r     rk   z!test_creation.<locals>.<listcomp>c                   S   s   t tdtddgS )Nra   r   r`   r.   r5   rh   rh   rh   ri   r     rk   c                   S   s   t tdtddgS )Nra   r`   r   r-  rh   rh   rh   ri   r     rk   )r   r   r   )rL   r   
IndexErrorr.   rQ   tolistTr   ZEmptySetr\   rq   rp   r   r2   r,   as_immutable
as_mutabler5   r>   )
r   rX   ry   rY   Zc23Zc13rZ   datr   ZM2rh   rh   ri   test_creation  s~    
*8BJ*"4D(r4  c                   C   s   t dtddtddd tddd tddd tddd tddd tddd t g dg dg d	g d
gks~J d S )Nr`   ra   r   r   r   r   r   )r   ra   ra   ra   r`   r`   )r   ra   ra   ra   r   r   )r   r   r   r   r   r   )r.   Z	irregularr5   rh   rh   rh   ri   test_irregular_block  s    &0r5  c                  C   sT   t jt jtt t jgttttd gtt j tt dgg} t| }| | ksPJ d S )Nra   r`   )	r   Oner   r\   r]   Zeror^   r.   r/  )lstry   rh   rh   ri   test_tolist  s    8r9  c                   C   s`   t dd t ddksJ t dd tt ddks<J t dd tt ddks\J d S Nr   r`   )r;   r2  r1  r,   rh   rh   rh   ri   test_as_mutable
  s     r;  c                  C   s  t d} | d dd df t dks(J | ddddf tdksHJ tdddd }|dd d f tdddksxJ |dddf tddd	ksJ tg d
g dg dg dg}|d d df tddg dksJ |dd d d f tg dg dgks
J d S )Nr   r`   ra   r   c                 S   s   | | S rb   rh   r   rh   rh   ri   r     rk   ztest_slicing.<locals>.<lambda>r   r   ra   r`   )r   r   ra   r`   )r   r   r   r   )r   r   r      )r         r   r   )r`   r   r=  r   r   )r2   r;   r.   )m0m1m2rh   rh   ri   test_slicing  s         $rC  c                  C   s   t d} td| ddddf< | tdks0J td| d dd df< | tdksXJ tddd| d d df< | tdksJ t d| d d d d f< | t dksJ g d| d d d d f< | tdksJ ddg| d ddf< | td	ksJ d S )
Nr   ra   )r   r   r   r   rD  r   r   r   r   r  r   r   ra   r`   r   r   )r   r   r   r   )ra   r   r   r   )r`   r   r   r   )r   r   r   r   rF  r   r   r   r   r   r   r=  r   r>  r?  r      ))r   ra   r`   r   )r   r   r   r   rJ  rK  )r;   r2   r.   r   rh   rh   ri   test_submatrix_assignment  s    rM  c                      s   t dddd   g dddgt ddg d	ks8J  ddgg d
t ddg dks`J  tdtd ks|J tt fdd tt fdd d S )Nr   r`   c                 S   s   | d | S Nr`   rh   r   rh   rh   ri   r   ;  rk   ztest_extract.<locals>.<lambda>)r   r   r`   r   r   ra   )r   r   r`   r   r   r   r   )r   r   ra   r   r   r=  c                      s     dgdgS )Nr   r   r   rh   r   rh   ri   r   ?  rk   c                      s     dgdgS r:  rO  rh   r   rh   ri   r   @  rk   )r.   r   r   rL   r.  rh   rh   r   ri   test_extract:  s    ((rP  c                  C   sh   t d} | ddtdddks$J tdddd }|ddtdksLJ |d	d
tdksdJ d S )Nr`   r   r   )	r   r   r   r   r   r   r   r   r   r   c                 S   s   | | S rb   rh   r   rh   rh   ri   r   F  rk   ztest_reshape.<locals>.<lambda>)r   r`   r   ra   )r`   r   ra   r   ra   r   ))r   r   ra   r`   r   ra   )r`   r   ra   r`   r   r   )r2   reshaper.   r@  rA  rh   rh   ri   test_reshapeC  s    rT  c                  C   sD   t d} | dd t dd ks&J | dd tdks@J d S )Nr`   c                 S   s   d|  S Nra   rh   r   rh   rh   ri   r   N  rk   z test_applyfunc.<locals>.<lambda>ra   c                 S   s   dS Nr   rh   r   rh   rh   ri   r   O  rk   )r2   	applyfuncr;   )r@  rh   rh   ri   test_applyfuncL  s    rX  c                  C   s"  t ttt  dgtt t t ttttt    gg} |  }|t tt td  dgttd  ttd   tt ttd   td  ggksJ tddd}t tt| gjddt t|tt|  gksJ t g dg dg d	g t d
d
t	ddgg dg dgksJ d S )Nra   r`   rX   Treal)complexr   )r   r   r   r   r   )r   r   r   r   )
r.   r\   r]   r   r   r   r	   r   r   r   )r@  rA  rX   rh   rh   ri   test_expandR  s    8F
r\  c                  C   sB  t ttd ttd gttd ttd  ttd ttd  gg} | tttt@ }|t td ttgtd tt td tt ggksJ | tttt@ }|t td tgttd  td t ggksJ | t	tt	t@ }|t td t gt td  td  t ggks>J d S rU  )
r.   r   r\   r   r]   ZrefinerT   rZ  r   r   rS  rh   rh   ri   test_refined  s    .<0r]  c                  C   s6  t dd} t dddd} | t ddddks.J t dddd} t dddd} | t ddddks`J |  }|  || ks|J td}| t dd|dksJ d	D ],}d
D ]"}t |d||d} | | jksJ qqt dddd} d}t| jd D ]4}t| jd D ] }| ||f dkr |d7 }q q|dks2J d S )Nr`   )seedr   r      T)r^  	symmetric)r`  prng)r   r=  )r   F      )r`  percentra  r   r   rb  )minrd  rc  )r6   copyr#   randomRandomr0  r   rn   )r   r   rngsizerd  Z
zero_countrg   r   rh   rh   ri   test_randomp  s,    

rk  c                     sz  t d} |  t dksJ | jddt dks4J | jddt dksLJ | jddt dksdJ | jddt dks|J | jddt dksJ tg dg d	g d
g} |  }| | t dksJ | jdd|ksJ | jdd|ksJ | jdd|ksJ | jdd|ksJ | jdd|ks4J tg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg d g d!g d"g d#g d$g}|jd%d| t |jd& ksJ t  g d'g d(g d)gt fd*d+d, D s6J t  g d'g d(g d)gt fd-d+d, D svJ d S ).Nr   r  r  r  r  r  ZQR)ra   r`   r   )r`   r   ra   )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   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   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   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   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   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   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   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   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   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   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   )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   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   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   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   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   r   r   r   r   r   ZBLOCKr   )r   1      )r   G   ^   );      A   c                 3   s    | ]}t | u V  qd S rb   rc   r   rf   srx   ry   rh   ri   rj     rk   ztest_inverse.<locals>.<genexpr>zGE ADJ LU CH LDL QRc                 3   s    | ]}t | u V  qd S rb   rs  rt  rv  rh   ri   rj     rk   )r2   r   r.   rn   r,   ro   splitr-   )r   ZAinvZAArh   rv  ri   test_inverse  sr    $"rx  c                     sX  t ddddg tt fdd t ddg d tt fdd t ddg d t ddg d	}  d
| ksvJ t ddg d  d ksJ t d
d
g d tt fdd t d
d
g d t d
d
g d}  d| ksJ t d
d
g d t d
d
g d}  d| ks J t d
d
g d t d
d
g d}  d| ksTJ d S )Nra   r   r   c                      s
     dS rU  inv_modrh   r   rh   ri   r     rk   z)test_matrix_inverse_mod.<locals>.<lambda>rG  c                      s
     dS rU  ry  rh   r   rh   ri   r     rk   rF  )r   r   r   r   r`   r   r   r   r   r*  c                      s
     dS Nr   ry  rh   r   rh   ri   r     rk   )	r   r   r`   ra   r   r   ra   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   ra   r   r   r   r   r   )	r   r   r   r   r   r   r`   ra   r   )	r   r   r`   r   r   r   r   r   r   r   )r.   rL   r'   r   rz  )ZAirh   r   ri   test_matrix_inverse_mod  s(    r}  c                  C   sB  t ddtd t dtd  tt  g} ttg}| |t dt t td gtdt t ggksfJ t ddttd td  g} | |t ddgdt td  td d td  ggksJ td t }ttg}t||t dt dt gdt dggksJ td td  }t||t dtd  dt td  gdt td  dtd  t ggksdJ tttd   }td dtd   }t ddt gdt dt gg}|t|t ttgksJ |t|t ttgjksJ t|ttf|gt ddtd  dt gdtd  dt dt gdt dt dggks>J d S )Nr   ra   r   r`   r   r   )r.   r\   r]   jacobianr3   r^   r0  )LZsymsfgansrh   rh   ri   test_jacobian_hessian  s0    (6>0>
r  c                  C   s8  t ttttgtttd ttd  ks2J t tttdt gttdt ks\J t tttgtttttt  ksJ t dttd gtdksJ dtt tt t dtt tt td   dtt tt t  tttt td   tttt td   } t tttttd gt | ksHJ t tttttd gtdd | ksvJ td  ttd  td ttd   dt ttd   dt ttd   }t tttttd gt |ksJ t tttttd gtdd |ks J t g tdks4J d S )Nra   r`   r   r   r   r   r  )r:   r   r\   r   r   r   )Zw1Zw2rh   rh   ri   test_wronskian  s&    2**J*"
R*"
r  c                  C   sv  t dtgtdggtdt ddgddggks4J t tdgtt dggtdgtdggt ddgddggksvJ t tdgtt dggtdftdfgt ddgddggksJ t tdgtt dggtdtdit ddgddggksJ t tt gjttd ttd idd	t td td  gks:J tD ]2} t dd
gd
dgg| dddks>J q>d S )Nr   r   r   ra   r   r   r   T)Zsimultaneousr   )r.   r\   r   r]   rm   r2   rx   rh   rh   ri   	test_subs  s    4(($&
r  c                  C   s   t dtgtdggtdit ddgddggks6J t tdgtt dggtdtdit ddgddggkstJ tD ]0} t ddgddgg| dddiksxJ qxd S )	Nr   r   r   ra   r   r   r   r   )r.   r\   Zxreplacer]   rm   r2   r  rh   rh   ri   test_xreplace  s    $r  c               
   C   s&  t d} td}tdt dt  ttt  t g|tt|t  |t dd|  t| t |    t gg}|  |ttt tt  dt gdt dddtt|    t|    ggksJ dt d }t|gg}|  |t|ggksJ |jtd |t|jtdggks"J d S )Nrw   r  r   ra   )Zratio)	r   r   r.   r\   r]   r   r   r#   r   )rw   r  r   eqrh   rh   ri   test_simplify"  s     :&r  c                  C   s   t g dg dg} | jt ddgddgddgddgddgddgddgd	d	gd
d
gddgg
ksbJ | jj| ksrJ | j|  ksJ d S )N)
r   ra   r`   r   r   r   r   r   r   r   r   ra   r`   r   r   r   r   r   r   r   )r.   r0  Z	transposer   rh   rh   ri   test_transpose3  s     
r  c                  C   s   t dtdgg dg} | jt ddgtdgddggks:J | jt dt dgg dgks\J | j|  ksnJ | j| jjksJ | jt ddgt dgddggksJ d S )Nr   r   )r   ra   r   r   ra   )r.   r	   r0  C	conjugateHr   rh   rh   ri   test_conjugateD  s     
r  c               	   C   s~   t tdd  tdtttgddttgdddtgg dg} | jtg dt dddgt t ddgt t tdggkszJ d S )Nc                   S   s
   t djS rN  )r2   Drh   rh   rh   ri   r   W  rk   z!test_conj_dirac.<locals>.<lambda>r   r   r  rG  r   )rL   AttributeErrorr.   r	   r  r   rh   rh   ri   test_conj_diracV  s    

r  c                  C   s.   t g dg dg dg} |  dks*J d S )Nr   r   r   )r   r   r   )r   r   r   r?  r.   tracer   rh   rh   ri   
test_traced  s
    r  c                  C   s*   t tddgdtdgg} | jdks&J d S )Nr   r<  )r.   r\   r]   rn   r   rh   rh   ri   
test_shapek  s    
r  c                  C   st  t tddgdtdgg} | ddd  | t tddgdtd dggksLJ | ddd  | t td ddgdt td dggksJ | dt td ddggksJ | d}d|d< | d	 td ksJ | dd d
f }d|d< | d	 td ksJ | d}|t td dt gks$J d|d< | d	 td ksBJ | d d df }d|d< | d	 td kspJ d S )Nr   r   c                 S   s   | | d S Nr   rh   )rr   rh   rh   ri   r   t  rk   z!test_col_row_op.<locals>.<lambda>ra   r`   c                 S   s   | t |  S rb   )r]   )rZ   r   rh   rh   ri   r   x  rk   *   r   r   )r.   r\   r]   Zrow_opZcol_oprowcol)r   Zr1Zc1rh   rh   ri   test_col_row_opq  s2    
"

r  c                  C   s   t d d D ]} | d}|dddd  || g dg dg d	gksNJ | dd }d
|d< |dddd  | || g dg dg dgksJ qd S )Nra   r`   r   r   c                 S   s   | d|  S rU  rh   r   urh   rh   ri   r     rk   z!test_zip_row_op.<locals>.<lambda>r  ra   r   r   r   r   r   c                 S   s   | d|  S rU  rh   r  rh   rh   ri   r     rk   )ra   r   r   )r   r   r   r   )rm   r2   Z
zip_row_op)rx   r   rh   rh   ri   test_zip_row_op  s    


r  c                  C   sd   t g d} t g d}t g d}| dvs0J | dvs<J | dksHJ | |ksTJ | |ks`J d S )Nr   )ra   ra   r`   rh   )r   r   r   )ry   rX   rY   rh   rh   ri   test_issue_3950  s    r  c                  C   s  G dd d} G dd d}|  }| }t g d}|| dksDJ d||< |d dks\J t g dg d	g}|||f d
ksJ |d|f d
ksJ ||df d
ksJ d|||f< |d dksJ d
|d|f< |d d
ksJ d||df< |d dksJ d S )Nc                   @   s   e Zd Zdd ZdS )ztest_issue_3981.<locals>.Index1c                 S   s   dS r  rh   selfrh   rh   ri   	__index__  s    z)test_issue_3981.<locals>.Index1.__index__N__name__
__module____qualname__r  rh   rh   rh   ri   Index1  s   r  c                   @   s   e Zd Zdd ZdS )ztest_issue_3981.<locals>.Index2c                 S   s   dS rU  rh   r  rh   rh   ri   r    s    z)test_issue_3981.<locals>.Index2.__index__Nr  rh   rh   rh   ri   Index2  s   r  r   r`   r   ra   r   r   r   r   r   r   r   r   r   )r  r  Zindex1index2ry   rh   rh   ri   test_issue_3981  s$    r  c                      sn   t tddg t fddtdD s.J t fddtdD sLJ t fddtdD sjJ d S )Nr   r   c                 3   s&   | ]}   |  |   kV  qd S rb   evalfre   rX   rh   ri   rj     rk   ztest_evalf.<locals>.<genexpr>ra   c                 3   s*   | ]"}  d |  |  d kV  qdS ra   Nr  re   r  rh   ri   rj     rk   c                 3   s*   | ]"}  d |  |  d kV  qdS r  r   re   r  rh   ri   rj     rk   )r.   r   ro   r   rh   rh   r  ri   
test_evalf  s    r  c                  C   s   t ttgttgg} |  du s$J t g dg dg} |  du sHJ t g dddtdgg} |  du spJ t dtd	gg} |  du sJ t g d
g} |  du sJ t dgtgd	gg} |  du sJ t dgdgd	gg} |  du sJ d S )NTrF  rI  Fr   r   r   r   r`   r   ra   )r.   r\   Zis_symbolicr  rh   rh   ri   test_is_symbolic  s    r  c                  C   sZ   t g dg} | jdu sJ t dgdgdgg} | jdu s>J tdd} | jdu sVJ d S )Nr   Tr   ra   r`   Fr   )r.   Zis_upperr;   r  rh   rh   ri   test_is_upper  s    
r  c                  C   sB   t g dg} | jdu sJ t dgdgdgg} | jdu s>J d S )Nr   Fr   ra   r`   T)r.   is_lowerr  rh   rh   ri   test_is_lower  s    r  c                  C   sT   t ddg d} |  sJ t ddgddgg} |  r<J t g } |  sPJ d S )Nr   )r   ra   r   r   r   r   r   ra   r   r   r   r`   r   r   r   r   r   r   r.   r	  r  rh   rh   ri   test_is_nilpotent  s    r  c                  C   s  d\} }t | |}|d dt| | }||ks6J |j|j  krNdksTn J |j|j  krldksrn J |j|j  krdksn J t dt ddksJ tdtddksJ t ddtdddgd ksJ tddtdddgd ksJ |d |t | |ksJ d S )N)r`   r   r   r`   ra   r   r   r   )r;   fillr5   rp   rq   rn   r.   )rw   ry   rX   rY   rh   rh   ri   test_zeros_ones_fill  s    

  
r  c                  C   sf   t d} | t ksJ t dd} | jdks.J | jdks<J t dd} | jdksTJ | jdksbJ d S )Nr   ra   )r;   r.   rp   rq   r  rh   rh   ri   test_empty_zeros  s    

r  c                  C   s  t td tt gttt ttt gg} | tt dt tgttttggksZJ t tt td gttdt tt  tdt  ggttt tt tgtdtggksJ t ttd t dt tt  tt gdt t	tt	ttd ggtdt g dtdtdggks(J | 
tt tddtd  ttd  d gtd tt d td tt d ggksJ d S )Nra   r   r   )r   r   r   r`   )r.   r\   r]   r   r   r   r   limitr   r   r   r   r  rh   rh   ri   test_issue_3749  s,    ,."$

 &r  c                  C   sD   t d} | dd dD ]&}| j|dd d| jdd	ksJ qd S )
Nr   r   r   )r  r  c                 S   s   | dkS rV  rh   r   rh   rh   ri   r   ,  rk   z%test_inv_iszerofunc.<locals>.<lambda>)r  
iszerofuncr  r  )r2   Zcol_swapr   )r   r  rh   rh   ri   test_inv_iszerofunc(  s    
r  c                  C   s   t d\} }t| t| | t| g}t| |g}||}|||jksRJ ||j|ksfJ ||j|jks|J |jt|jd  | }|t	}|tddgd| d ggksJ d S )Nrho,phir   r   ra   )
r   r.   r   r   r~  r0  r2   rn   rW  r$   )rhophiXYr   r  rh   rh   ri   test_jacobian_metrics0  s    

r  c                  C   s   t d\} }t| t| | t| | d g}t| |g}tt||  t| gt|| t| gd|  dgg}|||ksJ d S )Nr  ra   r   )r   r.   r   r   r~  )r  r  r  r  r   rh   rh   ri   test_jacobian2=  s    "
r  c                  C   s   t ttt t ttt t ttt t g} t tttg}tddD ]}tddD ]x}| d |d d f }|d |d d f }||}|j|ksJ |j|ksJ t|D ]}|d d |f |ksJ qqXqJd S Nr   r`   )	r.   r   r\   r]   r^   r   r~  rp   rq   )r  r  rg   r   ZX_sliceZY_slicer   krh   rh   ri   test_issue_4564I  s    2
r  c                      s   t ttt t ttt t gttt t ttt t gg tt fdd  dd d f  t ttgttggtt fdd tt fdd d S )Nc                      s     ttttgS rb   r~  r.   r\   r]   r^   rh   r  rh   ri   r   Z  rk   z(test_nonvectorJacobian.<locals>.<lambda>r   c                      s
     S rb   )r~  rh   r  r  rh   ri   r   ]  rk   c                      s     tttgttggS rb   r  rh   r  rh   ri   r   ^  rk   )r.   r   r\   r]   r^   rL   	TypeErrorrh   rh   r  ri   test_nonvectorJacobianW  s     r  c                  C   sP   t ddgddgg} |  }|jdks*J tdD ]}|| |d ks2J q2d S Nr   r`   ra   r   )r.   Zvecrq   r   )ry   Zm_vecrg   rh   rh   ri   test_veca  s
    r  c                  C   s6  t ddgddgg} |  }|jdks*J tdD ]}|| |d ks2J q2| jdd}|d dkshJ t dttt  gtt td  dgg} | jdd}|d tt td  ksJ t dttt  gtt dgg} | jddd}|d tt ksJ ttdd	  ttd
d	  ttdd	  ttdd	  d S )Nr   ra   r`   F)diagonalr   )r  Zcheck_symmetryc                   S   s   t ddgg S r  r.   vechrh   rh   rh   ri   r   z  rk   ztest_vech.<locals>.<lambda>c                   S   s   t ddgddgg S r  r  rh   rh   rh   ri   r   {  rk   c                   S   s   t ddgg S r  r  rh   rh   rh   ri   r   |  rk   c                   S   s   t ddgddgg S r  r  rh   rh   rh   ri   r   }  rk   )	r.   r  rq   r   r\   r]   rL   r%   r   )ry   Zm_vechrg   rh   rh   ri   	test_vechi  s"    ( r  c                      sZ   t g dtg dksJ dddgg tt fdd t  ddtg dksVJ d S )	Nr   r   ra   r`   c                      s   t  S rb   )r1   rh   r   rh   ri   r     rk   ztest_diag.<locals>.<lambda>F)strict)r1   r.   rL   r   rh   rh   r   ri   	test_diag  s    r  c                  C   s   t ddgddgg} t dtgtdgg}t dtdgtdtgtttgg}|  | gksZJ | |gkslJ | |gks~J d S Nr   ra   r`   )r.   r\   r]   r^   get_diag_blocksrX   rY   rZ   rh   rh   ri   test_get_diag_blocks1  s     r  c                  C   s   t ddgddgg} t dtgtdgg}t dtdgtdtgtttgg}t| || | ||gksfJ t| || | ||gksJ t| || | ||gksJ t||| |||gksJ d S r  )r.   r\   r]   r^   r1   r  r  rh   rh   ri   test_get_diag_blocks2  s     r  c               
   C   s  t ddgddgg} t dtgtdgg}t dtdgtdtgtttgg}t| ||}|jddt|  | | ks|J t| ||}|jddt|  | | ksJ t| ||}|jddt|  | | ksJ t| | || || }|jddt|  |  | |  | |  ks2J |jdddt| jdd| jdd|jdd| jdd|jdd| jddksJ d S )	Nr   ra   r`   T)try_block_diagr  )r  r  r  )r.   r\   r]   r^   r1   r   )rX   rY   rZ   r   rh   rh   ri   test_inv_block  s"     ((($r  c                   C   s   t tdd  t tdd  ttdtdks4J ttdtdksLJ t tdd  ttdtdksrJ ttdtdksJ t tdd  ttdtdtddksJ t tdd  t td	d  t td
d  dS )zg
    Check that matrix dimensions can be specified using any reasonable type
    (see issue 4614).
    c                   S   s
   t ddS )Nr`   r   r;   rh   rh   rh   ri   r     rk   z$test_creation_args.<locals>.<lambda>c                   S   s   t ddddS Nr   ra   r`   r   r  rh   rh   rh   ri   r     rk   r`   c                   S   s   t dS N      @r  rh   rh   rh   ri   r     rk   c                   S   s   t dS r  r2   rh   rh   rh   ri   r     rk   r   c                   S   s   t dS r|  r   rh   rh   rh   ri   r     rk   c                   S   s
   t ddS r~   r   rh   rh   rh   ri   r     rk   c                   S   s   t ddggS r~   r   rh   rh   rh   ri   r     rk   N)rL   r   r  r;   rd   r
   r2   r5   rh   rh   rh   ri   test_creation_args  s     r  c                  C   s^  t ddg d} |  rJ |  s(J | jdds8J t ddg d} |  sTJ tddd} |  slJ |  sxJ t ddg d} | tdddksJ t ddtdd} |  rJ |  sJ t d	} |  sJ t d
} |  sJ t dddtd dt  d ttd d ddtddg	} |  s2J | jddrDJ |  jddsZJ d S )Nra   r   r   r   r   Fr#   r{  r   r`   )	r   r   r   r   ra   r   r   r   r`   ))r   r   r   r   )r   r   r   )r   r   r   r   )r.   is_diagonalis_symmetricr1   r;   r\   r]   r   r   rh   rh   ri   test_diagonal_symmetrical  s,    6r  c                     sv  t ddt gdt dgg   s(J t ddg d   rDJ   rPJ tt fdd tddd   \} }| tdksJ | ksJ t ddg d   sJ   sJ   \} }| 	   |  |ksJ t ddg d   sJ   sJ   \} }| 	   |  |ks2J | tdksDJ | ksRJ t ddg d	   spJ   \} }| 	   |  |ksJ t ddg d
   sJ   \} }| 	   |  |ksJ | D ]}|
 d dksJ qt ddg d   sJ   s(J   \} }| 	   |  |ksNJ | t ddgddggkslJ t ddg d  drJ tt fdd   sJ   \} }| 	   |  |ksJ t ddg d   rJ tt fdd t ddg d   r J tt fdd td\}}}}t dd||||g   sdJ   srJ d S )Nr   ra   r`   r   r   r   r)  r`   r   c                      s      S rb   r  rh   r   rh   ri   r     rk   z&test_diagonalization.<locals>.<lambda>r  )r   r   r   r`   r   r   r   r   )	r   ra   r   r   r`   r   ra   r   ra   rG  r   )r   r   r   r   Tc                      s
     dS )NTr  rh   r   rh   ri   r     rk   r   r   r   r   c                      s      S rb   r  rh   r   rh   ri   r     rk   )	r   r   r   r)  r`   r   ra   r   r   c                      s      S rb   r  rh   r   rh   ri   r     rk   za b c d)r.   r	   r  r  rL   r'   r1   r  r2   r   Zas_numer_denomr  r&   r   )r   r  rg   rX   rY   rZ   r[   rh   r   ri   test_diagonalization  sl    r  c                      sv   t ddgddgg   du s$J d d<   du s<J t ddgddgg    d d< tt fdd d S )Nr   r   Tr   Fc                      s      S rb   r  rh   r  rh   ri   r   2  rk   z"test_issue_15887.<locals>.<lambda>)r<   r  r  rL   r&   rh   rh   r  ri   test_issue_15887(  s    r  c                     sD  t ddg d tt fdd t ddg d t ddg d}   \}}| |ksZJ |   d ksnJ t ddg d	 t ddg d
}   \}}| |ksJ t ddg d t ddg d}   \}}| |ksJ t ddg d t ddg d}   \}}| |ksJ t ddg d t ddg d}   \}}| |ksRJ t ddg d t ddg d}   \}}| |ksJ t ddg d   rJ t ddg d}   \}}| |ksJ t tdddtdddgtdddtdddgg   \}}| D ]"}t|tr|j	dksJ qd S )Nr`   ra   r  c                      s      S rb   )r   rh   r   rh   ri   r   8  rk   z"test_jordan_form.<locals>.<lambda>)	r   r'  r   r   ir   r   ir>  )	r   r   r   r   r   r   r   r   r   r   	r   r   r   r   r   r   r   r   ra   )	ra   r   r   r   ra   r   r   r   ra   )	ra   r   r   r   r   r   ra   r   )	r   r   r   r   r   r   r   r   r   )	r   r   ra   r   r  r`   r   r   )	r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r`   r`   ra   r   r   r   r   r   r   r   )ra   r   r   r   r   ra   r   r   r   r   ra   r   r   r   r   ra   )r   ra   r   r   ra   r   r   ra   r   r  r   r   r   r`   r   )r   r   r   r   r   ra   r   r   r   r   ra   r   r   r   r   ra   )r   r   ra   r   r   r   r   r   r   r   r`   r   r   r   r   ra   )r   r   r   r   r   ra   r   r   r   r   r   r   r   r   r   r   z1.0n   )Z	precisionz2.0z3.14159265358979323846264338327z4.0)
r.   rL   r'   r   r  r  r   valuesr   Z_prec)ZJmustr   r   Ztermrh   r   ri   test_jordan_form5  sN    
r  c                  C   s   t g dg dg dg dg} ddt  }ddt  }t |dddgd|ddgdd|dgddd|gg}t |dddgd|ddgdd|dgddd|gg}|  \}}||ks||ksJ t|| |  | ksJ d S )	N)ra   r   r   r   )r   ra   r   r   )r   r   ra   r   )r   r   r   ra   ra   r   r   r   )r.   r	   r   r#   r   )r   pqZJmust1ZJmust2r   r   rh   rh   ri   #test_jordan_form_complex_issue_9274  s(    





r  c                  C   s   t g dg dg dg dg} |  \}}|t g dg dg dg dgksTJ |t g d	g dg dg dgks|J d S )
Nr{  r  )r   r   r   r   r  r   r   r   r   rG  r  rE  r  )r.   r   r   rh   rh   ri   test_issue_10220  s"    
r  c               
   C   s   t g dg dg dg dg} |  \}}| t t t d ttd gdt ddt dgdtd d td  dtd d td  gg d	gksJ |t t dddgdt ddgddtdgdddtggksJ d S )
Nr  )r   r   r   r   )r   r   r   r   )r   r   ra   r   ra   r   r   r   r  )r.   r   r   r	   r   )r   r   r   rh   rh   ri   test_jordan_form_issue_15858  s&    .

r  c                  C   sx  t d\} }}t| |  |d ||   || ||  g|| ||  | |d ||   gg}|t}|ttd ||  ||   d| |  ||  t  || |  ||   tddksJ t|tu sJ tddgddgg}| |t  krttd t d ksn J tddgtdgg}|t}|jtksLJ | 	|jttd dt  kstJ d S )	Nz
UA K_i K_wra   zZZ(K_i,K_w,UA)r   r   r`   r   r   )
r   r.   r   r\   r   rc   r   genZas_exprr   )ZUAZK_iZK_wr   r   r  rh   rh   ri   test_Matrix_berkowitz_charpoly  s&    *$
08
r  c                  C   s   t d} td| }| tt| ggks0J td| }| tt| t| t| d gdt| t| gddt| ggksJ d S )Nlamdar   r`   ra   r   )r   r.   jordan_blockZ_eval_matrix_exp_jblockr   )lry   rh   rh   ri   test_exp_jordan_block  s    r  c                  C   s  t ddgddgg} t tddtd d dtd d  gdtdgg}|  |ks\J t| |kslJ t ddgddgg} |  t tdgdtggksJ t| t tdgdtggksJ t ddgddgg} |  t ttd t td gttd ttd ggksJ d S )	Nr`   r   r   r   r   r   r   r   )r.   r   r   r   r   )ry   Zm_exprh   rh   ri   test_exp  s    8  r  c               
      s   t d} td|    tt| ggks0J td|    tt| d|  dd| d   dd| d   gdt| d|  dd| d   gddt| d|  gdddt| ggksJ tg dg d	g d
g tt fdd d S )Nr  r   r   r   ra   r`   r   r   r   r   c                      s      S rb   )r   rh   r   rh   ri   r     rk   ztest_log.<locals>.<lambda>)r   r.   r   Z_eval_matrix_log_jblockr   rL   r&   )r  rh   r   ri   test_log  s(    *
r  c                  C   sX   t ttfdf} | tsJ | tr,J | ts:J | td} | trTJ d S )Nr<  ra   )r.   r\   r]   Zhasr^   r   r   r   rh   rh   ri   test_has  s    r  c                  C   sR   t d} tdd| t| d t| d  tjg}t|\}}}}|tjksNJ d S )Nr\   r`   r   ra   )r   r.   r   r   r   r   r)   r\   columnZpivot_offsetZ	pivot_valZpivot_assumed_nonzeroZ
simplifiedrh   rh   ri   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero1  s
    (
r  c                  C   sn   t d} tdd| t| d t| d  | d  t| d t| d  g}t|td\}}}}|dksjJ d S )Nr\   r`   r   ra   Zsimpfunc)r   r.   r   r   r)   r*   r  rh   rh   ri   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero2  s    

r
  c                  C   s   t d} tdd| t| d t| d  |  t| d t| d  g}t|td\}}}}t|dksjJ |d d dks~J |d d d|  ksJ |d d dksJ |d d dksJ d S )Nr\   r`   r   ra   r	  r   )r   r.   r   r   r)   r*   lenr  rh   rh   ri   +test_find_reasonable_pivot_naive_simplifies'  s    

r  c                      s  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t td	d  t td
d  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t td d  t td!d  t td"d  t td#d  t td$d  t td%d  t td&d  t td'd  t td(d  t td)d  td* t t fd+d tg d,gtg d-g d.g d/g t t fd0d tg d-g d.g d/g t t fd1d d S )2Nc                   S   s   t ddgdggS r~   r   rh   rh   rh   ri   r   :  rk   ztest_errors.<locals>.<lambda>c                   S   s   t ddggd S )Nr   ra   )g333333?r   r   rh   rh   rh   ri   r   ;  rk   c                   S   s   t ddggd S )Nr   ra   )r   g@r   rh   rh   rh   ri   r   <  rk   c                   S   s   t ddddS )Nr`   r   T)rZ   r`  )r6   rh   rh   rh   ri   r   =  rk   c                   S   s   t ddgddS )Nr   ra   r   r   )r.   rR  rh   rh   rh   ri   r   >  rk   c                   S   s(   t ddgddggddgt ddgS Nr   ra   r`   r   r   )r.   Zcopyin_matrixrh   rh   rh   ri   r   @  rk   c                   S   s"   t ddgddggddgt S r  )r.   Zcopyin_listsetrh   rh   rh   ri   r   A  s   c                   S   s   t g dg dg S )Nr   )ra   r`   r   r.   r   rh   rh   rh   ri   r   C  rk   c                   S   s&   t ddddgt ddgddggS r  )r.   row_joinrh   rh   rh   ri   r   E  rk   c                   S   s"   t ddgt ddgddggS r  )r.   col_joinrh   rh   rh   ri   r   G  rk   c                   S   s"   t dgdt ddgddggS r  )r.   
row_insertrh   rh   rh   ri   r   H  s   c                   S   s"   t dgdt ddgddggS r  )r.   
col_insertrh   rh   rh   ri   r   J  s   c                   S   s   t ddg S r~   r  rh   rh   rh   ri   r   L  rk   c                   S   s   t dgdS r  )r.   rW  rh   rh   rh   ri   r   M  rk   c                   S   s   t ddgddggddS Nr   ra   r`   r   r   )r.   minorrh   rh   rh   ri   r   N  rk   c                   S   s   t ddgddggddS r  )r.   Zminor_submatrixrh   rh   rh   ri   r   O  rk   c                   S   s   t g ddS Nr   r   r.   crossrh   rh   rh   ri   r   P  rk   c                   S   s   t g ddS r  r.   dotrh   rh   rh   ri   r   Q  rk   c                   S   s   t g dt ddgS )Nr   r   ra   r  rh   rh   rh   ri   r   R  rk   c                   S   s   t ddgg S r~   r  rh   rh   rh   ri   r   S  rk   c                   S   s   t ddgdS )Nr   ra   rX   r  rh   rh   rh   ri   r   T  rk   c                   S   s   t ddgg dS )Nr   ra   r   r  rh   rh   rh   ri   r   U  rk   c                   S   s   t g d S )Nr   )r.   r   rh   rh   rh   ri   r   V  rk   c                   S   s   t ddgddgg S r  )r.   
normalizedrh   rh   rh   ri   r   W  rk   c                   S   s   t ddgjddS )Nr   ra   znot a methodr  r  rh   rh   rh   ri   r   X  rk   c                   S   s   t ddg S r~   r.   Z
inverse_GErh   rh   rh   ri   r   Y  rk   c                   S   s   t ddgddgg S r~   r  rh   rh   rh   ri   r   Z  rk   c                   S   s   t ddg S r~   r.   Zinverse_ADJrh   rh   rh   ri   r   [  rk   c                   S   s   t ddgddgg S r~   r  rh   rh   rh   ri   r   \  rk   c                   S   s   t ddg S r~   )r.   Z
inverse_LUrh   rh   rh   ri   r   ]  rk   c                   S   s   t ddg S r~   r  rh   rh   rh   ri   r   ^  rk   c                   S   s   t ddg S r~   r.   r   rh   rh   rh   ri   r   _  rk   c                   S   s   t ddgddggjddS )Nr   ra   r`   r   zNot a real methodr  r  rh   rh   rh   ri   r   a  rk   c                   S   s(   t g dg dg dg dgjddS )NrF  rI  rJ  rK  zNot functionr  r  rh   rh   rh   ri   r   c  s   c                   S   s(   t g dg dg dg dgjddS )NrF  rI  rJ  rK  Fr  r  rh   rh   rh   ri   r   f  s   c                   S   s*   t tddgddggtddgddggS r  r3   r.   rh   rh   rh   ri   r   i  rk   c                   S   s   t tddgddggg S r  r   rh   rh   rh   ri   r   j  rk   c                   S   s   t tdd dS )Nr\   ra   rX   )r3   r   rh   rh   rh   ri   r   k  rk   c                   S   s   t dd S )Nr`   )r   ra   r  rh   rh   rh   ri   r   l  rk   c                   S   s   t dd S )Nr`   )ra   r   r  rh   rh   rh   ri   r   m  rk   rH  c                      s
     dS )Nzmethod=LU_decomposition())r   rh   r   rh   ri   r   o  rk   )r   r   r   r   ra   r`   r   r   c                      s     dS )Ng@)r  rh   r   Vrh   ri   r   r  rk   c                      s     dS )Ng)r  rh   r"  rh   ri   r   t  rk   )rL   r   r.  r%   r  r'   r.   rh   rh   r"  ri   test_errors9  sz    r$  c                   C   s   t t dksJ t tddggt tdgdgg  krDdksJn J t tdddd t tdddd   kr~dksn J t tg dg dgd	ksJ tdgtdggksJ t rJ t tg ksJ d S )
Nr   r   ra   c                 S   s   dS rV  rh   r   rh   rh   ri   r   y  rk   ztest_len.<locals>.<lambda>c                 S   s   dS rV  rh   r   rh   rh   ri   r   z  rk   r   r   r   )r  r.   rh   rh   rh   ri   test_lenv  s    8 
r%  c               	   C   s   t ddtftddfddtd ff} | tt tdt td d ftt dt dt fdt dt td d ffkszJ | tt tdt tt ftd d dt dt fdt dt ttd  ffksJ d S )Nr   r   ra   r   r   r`   )r.   r\   r]   r   r   rh   rh   ri   test_integrate  s    $FFr&  c                  C   sX   t ddttt ftddfddtd d ff} | tdt dtddfdfksTJ d S )	Nr   r   ra   r   r   r   )r   r   r   )r   r   r   )r.   r   r\   r]   r  r   rh   rh   ri   
test_limit  s    0r'  c                  C   sZ  t ddtftddfddtd d ff} t| tt| s@J | tt dddddt ffksfJ | tt d	ks|J t| tt dddddt ffksJ t| tt d	ksJ |  }t|tt|sJ |ttdddddt ffksJ |ttd	ksJ t|ttdddddt ffks>J t|ttd	ksVJ d S )
Nr   r   ra   r   r   r   r   r   )r   r  r   )r<   r\   r]   r   r   rc   r1  r=   )r   A_immrh   rh   ri   	test_diff  s    (&&&(r)  c               
      sv  t ttgttgg} | | tddgddggddgddgggddgddggddgddggggksfJ t| | tddgddggddgddgggddgddggddgddggggksJ |  }||tddgddggddgddgggddgddggddgddggggksJ t||tddgddggddgddgggddgddggddgddggggkshJ | tt ddgddggksJ t	tt
g}| |tddddksJ | | tddgddggddgddgggddgddggddgddggggksJ |tt
gg}|jdks,J |tdgdggdgdgggksRJ td}|ttt  tttggt t t tgksJ  tttgdft td tt ttg tt td ttg tt tt tdggks J tttt }|ttggttttt tttt gksjJ |tttffttttt tttt gksJ |tttffttt tt tttt gksJ |ttffttggttttt tt tt gtttt tttt ggksHJ  ttt tttffdd ks|J  ttt tttffdd ksJ  tttggtttfft fd	d
tttfD ksJ ttttgg}t|t	sJ |tddggks*J td tttgg}t|t	sRJ |tdtd  dggksrJ d S )Nr   r   ra   )ra   ra   r   r  r`   r   r  c                    s&   g | ]  fd dt ttfD qS )c                    s   g | ]}  | qS rh   )r   re   )fxyzr   rh   ri   r     rk   z2test_diff_by_matrix.<locals>.<listcomp>.<listcomp>)r\   r]   r^   )rf   r*  )r   ri   r     rk   z'test_diff_by_matrix.<locals>.<listcomp>)r<   r\   r]   r^   r_   r   rU   r1  rX   r=   rY   r;   rn   r   r   r   r   r.   r   )r   r(  BZdBr  exprresrh   r+  ri   test_diff_by_matrix  sF    RRTT$ T&8   :<>d44>r/  c                      sh   t ddtftddfddtd d ff tt fdd t dtt d	d
dddt ffksdJ d S )Nr   r   ra   r   r   c                      s    j S rb   )Znonexistantattributerh   r   rh   ri   r     rk   ztest_getattr.<locals>.<lambda>r   r   r   r   )r.   r\   r]   rL   r  getattrrh   rh   r   ri   test_getattr  s    (r1  c                  C   s   t g dg dg dg} | js$J | j} | js4J d| d< | jdu sJJ t g dg dg dg} | jrnJ tdd	} | jsJ d S )
N)r`   r   r   )ra   r   r   r   r   )r   r   FrQ  r   ra   )r.   Zis_upper_hessenbergr0  Zis_lower_hessenbergr;   r   rh   rh   ri   test_hessenberg  s    



r2  c                  C   s*  t tdd  t tdd  t tdd  t tdd  t tdd  tdt dfd	fjd
dttdt dgddggksJ td} | jd
d}|tddgddtd t ggksJ ||j | ksJ td} |  }||j | ksJ |jsJ |tg dg dg dgks J tddt ddt  fdt ddt fddt  dt dff} |  	 tdtddfdt ddffksJ t tdd  t tdd  t tdd  t tdd  t tdd  t
dt dfd	fjd
dttdt dgddggksJ t
d} | jd
d}|tddgddtd t ggksRJ ||j | ksfJ t
d} |  }||j | ksJ |jsJ |tg dg dg dgksJ t
ddt ddt  fdt ddt fddt  dt dff} |  tdtddfdt ddffks&J d S )Nc                   S   s   t d S Nr   r.   choleskyrh   rh   rh   ri   r     rk   ztest_cholesky.<locals>.<lambda>c                   S   s   t d S Nr   )r`   r   r4  rh   rh   rh   ri   r     rk   c                   S   s   t dt dfdf S Nr   r   r   )r.   r	   r5  rh   rh   rh   ri   r     rk   c                   S   s   t d S N)r   r   )r   r   r4  rh   rh   rh   ri   r     rk   c                   S   s   t djddS Nr7  F	hermitianr4  rh   rh   rh   ri   r     rk   r   r   r   Fr<  r   r:  ra   r   ))   r   r   )r   r   r   )r   r   r=  r  )r`   r`   r   )r   r   r`   r   r   r   r=  r   r`   c                   S   s   t d S r3  r/   r5  rh   rh   rh   ri   r      rk   c                   S   s   t d S r6  r?  rh   rh   rh   ri   r     rk   c                   S   s   t dt dfdf S r8  )r/   r	   r5  rh   rh   rh   ri   r     rk   c                   S   s   t d S r9  r?  rh   rh   rh   ri   r     rk   c                   S   s   t djddS r;  r?  rh   rh   rh   ri   r     rk   )rL   r'   r   r.   r	   r5  r   r0  r  r   r/   )r   r  rh   rh   ri   test_cholesky  sL    (
$@0*$@r@  c                  C   s  t ddd} tt| t| g}t|ddks6J |dtt| d t| d  tddkshJ tdtddgg}| td	td
d tj	ksJ |t
t|ksJ |t
 t|ksJ tddgddgg}|ddksJ |ddksJ |ddksJ tddtdd  krFdksLn J |t
dks`J tdttg| tj	t gg}|dttdddttd   td  | d  ksJ tg dddtddgg}|dttddtdd  ks J |dtju sJ |dtdd ks2J tddgddgg}tddgddgg}tdt gtdgg}tddgddgg}||||g}t ddd}dD ]}td|tju sJ |D ]B}	|D ]6}
|	||
| |	|
 | }|dksJ qʐq||||fD ]8}t|| |t|||  }|dksJ qqtdddt  dg}ttj	dt dg}tg d}tddtg}ttdtdddg}|||||g}t ddd}ddddtjtjtfD ]}|dkrtg d|tju sJ |dkrd|D ]L}	|D ]@}
|	||
| |	|
 | }t|dktju sJ qq|ddddtjtjfv r|D ]8}	t||	 |t||	|  }|dksJ qqtddg d}|ddksJ d S )Nr\   TrY  ra   r   r   r   r`   r>  r   r   r   r   Z	frobeniusfro%   )r   ra   r   r>  i  r   iI3 r   alpha)rA  ra   r   r   )r   r   r   g      Y@r   )	r   r`   r   r   r   r   r`   r   r   )r   r.   r   r   r$   normr   r   r   r   r   maxre  r2   r]   r   r   r   r7  r	   r;   r#   r
   InfinityNegativeInfinitytrue)r\   r   r   r,  r  r  r  rC  orderr  r  Zdifr   rX   rY   rZ   r[   erh   rh   ri   test_matrix_norm  s    2"2,
*

 rK  c                     s   t dddtd} d| d< tdd| d< |  d	ks:J | d
< |  tdtttddt kspJ ttt	gt	 tgg}|  t
 fddtddtjtddtd tttdd fD sJ tg  dksJ d S )Nr\   TrY  r`   r   r   r   ra   ra   r   r   c                 3   s(   | ] }t d  | V  qdS )      ?N)r   Z
epsilon_eqr   r  )rf   valZMcr\   rh   ri   rj   }  rk   z(test_condition_number.<locals>.<genexpr>r   ra   r   r   r   )r   r2   r   Zcondition_numberr   r   r   r.   r   r   ro   r   r   r   )r   r   rh   rO  ri   test_condition_numberq  s    .&*rP  c                  C   s   t d} t d}| | d d d d f ks,J | | d d d d f krHJ | |krTJ | |ks`J | dkslJ | dkrxJ td}t d}||ksJ ||krJ d S )N)r   r  r   r   r   ))r   r   r   )r   r   r   )r`   ra   r   r   )r  r   r   )r.   r/   )r   r,  r  r  rh   rh   ri   test_equality  s    rR  c                   C   s@   t dtg dgtg dg dg dg dgks<J d S )Nr`   )r   r   r   r  r   r   )r2   r  r.   rh   rh   rh   ri   test_col_join  s    rS  c                  C   s\   t g dg} tddD ]>}g d}||d ttd|| d |ksJ qd S )Nr   r   r   r   r   r  r   r`   r   )r.   r   insertrG   r2   r  r  r/  )Zr4rg   r  rh   rh   ri   test_row_insert  s
    rV  c                  C   sZ   t g d} tddD ]>}g d}||d ttd|| d |ksJ qd S )NrT  r   r   r   r   r`   r   )r.   r   rU  rG   r;   r  r  r/  )Zc4rg   r  rh   rh   ri   test_col_insert  s
    rW  c                  C   s|   t ddg t tddtddgks,J t g d t g dksLJ t g d} | jdd dt g dksxJ d S )	Nr`   r   r   r   )r   r   g0.++c                 S   s   | j dddjS )Nr   T)rw   Zchop)r  is_zeror   rh   rh   ri   r     rk   z!test_normalized.<locals>.<lambda>r  )r.   r  r   r   rh   rh   ri   test_normalized  s     
rY  c                   C   s,   t dd dksJ t dd dks(J d S )Nc                   S   s   t d S rN  r2   Zprint_nonzerorh   rh   rh   ri   r     rk   z$test_print_nonzero.<locals>.<lambda>z[X  ]
[ X ]
[  X]
c                   S   s   t ddS )Nr`   .rZ  rh   rh   rh   ri   r     rk   z[.  ]
[ . ]
[  .]
)rH   rh   rh   rh   ri   test_print_nonzero  s    

r\  c                  C   s   t dtdksJ t dtdks,J tddt dddgd ksLJ t ddgddgg} t ddgddgg}tD ]x}|d}| |ksJ | td|dksJ t||ksJ |d}||ksJ |td|dksJ t||ksxJ qxd S )Nr`   r   r   r   r   ra   r  )r.   r2   r;   r5   rm   rc   )rg   r^   rx   ry   rh   rh   ri   test_zeros_eye  s     

r]  c                  C   s
  t  jsJ t ddgddggjs&J tddjs6J tdjrDJ t tdgddggjd ksbJ ttdgddggjd ksJ ttdgddggjd ksJ ttdgddggjd ksJ t tdgddggjdksJ tddd} t | dgddggjdksJ d S )	Nr   r`   r   r   FrX   T)Znonzero)	r.   Zis_zero_matrixr;   r2   r\   r/   r,   r-   r   r  rh   rh   ri   test_is_zero  s    r^  c            
      C   s  t d } t| }t|  }t| }t|  }t| }t|  }|| td tdksZJ || td tdksvJ || td tdksJ | ddt|   ksJ | ddt|   ksJ | ddt|   ksJ tdtdksJ tdtdksJ tdtdks&J tg dt d }tg dt d }tg dt d }	tt  d |	 ks~J tt  d |	 ksJ tt  d |		 ksJ t
t 
 d |	 ksJ tt 
 d |	 ksJ tt 
 d |		 ks
J d S )Nr`   r   ra   r   r  r   r   )r   r9   r8   r7   r2   r  r   rW   Zfrom_axis_angleZto_rotation_matrixr@   rA   rB   )
thetaZr3_plusZr3_minusZr2_plusZr2_minusZr1_plusZr1_minusZq1Zq2Zq3rh   rh   ri   test_rotation_matrices  s2    


r`  c                   C   sj   t tdd dksJ ttdtdks0J ttdd  t tddksRJ ttddksfJ d S )	NZvectorr   z	vector[4]r[   c                   S   s   t dd S )Nr[   r   )r(   rh   rh   rh   ri   r   
	  rk   z%test_DeferredVector.<locals>.<lambda>testzDeferredVector('test'))strr(   r   rL   r.  reprrh   rh   rh   ri   test_DeferredVector	  s
    rd  c                   C   s   t tdrJ d S )Nr  )rI   r(   rh   rh   rh   ri    test_DeferredVector_not_iterable	  s    re  c                   C   s   t tdd  d S )Nc                   S   s   t tdS )Nr#  )r.   r(   rh   rh   rh   ri   r   	  rk   z,test_DeferredVector_Matrix.<locals>.<lambda>)rL   r  rh   rh   rh   ri   test_DeferredVector_Matrix	  s    rf  c                  C   s<  t } tddddg}tddddg}t||gtddddgtdd| dd | dd ggksdJ t|j|jgtddddgtdd| dd | dd ggksJ ttddgtddggdtdtd d tdd gttd d dtd d ggksJ ttdg}t|tdgggks8J d S )Nr   ra   r`   r   r   Tr   )r   r.   r+   r0  r   r!   )r   rA  rB  r  rh   rh   ri   test_GramSchmidt	  s    
.. rg  c                   C   s4   t g dddksJ t g dddddks0J d S )NrF  r   r   F)Zzero)r0   rh   rh   rh   ri   test_casoratian%	  s    rh  c                   C   s^   t  tdd jdksJ tddtdd tddks<J tddtdd t  ksZJ d S )Nr   r`   )r   r`   )r.   r;   rn   rh   rh   rh   ri   test_zero_dimension_multiply*	  s    "ri  c                      s   t ddtd  dd d f t ddggks2J  dd d f t ddggksTJ  d d df t ddggjksxJ  d d df t ddggjksJ tt fdd tt fdd d S )	Nra   r   r   r`   r   c                      s    dd d f S rU  rh   rh   r   rh   ri   r   6	  rk   z'test_slice_issue_2884.<locals>.<lambda>c                      s    d S )NrL  rh   rh   r   rh   ri   r   7	  rk   )r.   r   r0  rL   r.  rh   rh   r   ri   test_slice_issue_28840	  s    ""$$rj  c                   C   sJ   t ddd d df jdks J t dddd d f tddg ksFJ d S )Nr   r`   r   r   r   )r;   rn   r.   rh   rh   rh   ri   test_slice_issue_3401:	  s     rk  c                  C   s  t dd} d| d< | d d df tg dks2J | d dksBJ | dd dgksXJ d| d< | d dkspJ | ddd f tddggksJ tdd	gg| ddd f< | dd d f tg d
gksJ ddgg| ddd f< | dd d f tg dgksJ d| d< | d d d df tg dks6J g d| d< | d d df tg dksdJ tg d| d< | d d df tg dksJ tg d| d< | d d df tg dksJ d S )Nr`   r   r   r   r   r  r   r   r   )r   r   r   +   )r   r  rl     r   )rm  r   r   r   r   r   )r;   r.   r/   )ru  rh   rh   ri   test_copyin?	  s(    
 ""$&""ro  c                      s   t ddgddgg t ddgddggdfks4J ttdd  t g dtddgdtdgg t  d  jkszJ   d td	ksJ  jtd
d td	ksJ tt fdd tt fdd tt fdd d S )Nr   ra   r   )r   c                   S   s   t ddgddgg S r~   r  rh   rh   rh   ri   r   Z	  rk   z'test_invertible_check.<locals>.<lambda>)r   r   r   r   r`   r  c                      s    j ddS )Nr  r  r   rh   r   rh   ri   r   e	  rk   c                      s    j ddS )Nr  r  rp  rh   r   rh   ri   r   f	  rk   c                      s    j ddS )Nr  r  rp  rh   r   rh   ri   r   g	  rk   )	r.   r   rL   r   r\   r  rp   r2   r"   rh   rh   r   ri   test_invertible_checkV	  s    4rq  c                  C   s@   t d\} }| | }|| tg dtg d| ks<J d S )Nzx, y)r`   r   r`   )r   r   r.   )r\   r]   rJ  rh   rh   ri   test_issue_3959j	  s    rr  c                   C   s$   t tddgddggdks J d S )Nr   ra   r`   r   zMatrix([[1, 2], [3, 4]]))rb  r.   rh   rh   rh   ri   test_issue_5964p	  s    rs  c                  C   s<   t d\} }tt| d| g|d | d ggdks8J d S )Nx yra   r`   z'Matrix([
[   x,   2*y],
[y**2, x + 3]]))r   r    r.   )r\   r]   rh   rh   ri   test_issue_7604t	  s    "ru  c                	   C   s   t djsJ t d js J tdjr.J tdjr<J tg dgjrPJ tddddddjsjJ tddtdjrJ tdddddjrJ tddddddddjrJ d S )	Nr`   r  r   )r   r   rL  ra   r   )r   r   )r   r   rL  r   )r   ra   )r2   Zis_Identityr1  r;   r5   r.   r/   r   rh   rh   rh   ri   test_is_Identityz	  s    rv  c                   C   s$  t ddt dddksJ t ddg ddks:J tg dtg ddks\J tdddt gttddt gdt ksJ tdddt gjttddt gdd	dt ksJ tdddt gjttddt gd
d	dt ksJ tdddt gjttddt gd
dddt ks4J tdddt gjtddt dgd
ddddt  ksrJ tdddt gjtddt dgd
ddddt  ksJ ttdt gjttdt gddddksJ ttdt gjttdt gdddksJ ttdd  d S )Nr   r`   rn  r   r?  ra   r   Fr<  Tr>  Zphysicsr=  conjugate_conventionr   r   r   rightr   left)rx  c                   S   s    t ddgjt ddgdddS )Nr   ra   r`   r   Tra  rw  r  rh   rh   rh   ri   r   	  rk   ztest_dot.<locals>.<lambda>)r5   r  r.   r	   rL   r   rh   rh   rh   ri   test_dot	  s    "266:>>20r{  c                  C   s   t ddd\} }}}}}td|||f| d|| f| | d| f| ||  dff}td|  | | f| d|| f|| d|f||| dff}| |sJ td tdsJ |  | sJ d S )NzB_x B_y B_z E_x E_y E_zTrY  r   r`   )r   r.   Zdualequalsr2   r;   )ZB_xZB_yZB_zZE_xZE_yZE_zFZFdrh   rh   ri   	test_dual	  s$    
r~  c                  C   s   t ddg du sJ t dddtd dt  d ttd d  dtt t t t dg	} |  du slJ | jdddu sJ | jdd	 ddu sJ | d
  | d
< |  du sJ | d
  | d
< |  } | jdddu sJ d| d< |  du sJ d S )Nr   ra   Fr`   r   Tr  c                 S   s   | S rb   rh   r   rh   rh   ri   r   	  rk   z%test_anti_symmetric.<locals>.<lambda>r   r   )r.   Zis_anti_symmetricr\   r]   r   r   rh   rh   ri   test_anti_symmetric	  s    Dr  c                  C   s   t d} | jdd\}}||j |j|   kr>t|jksDn J | jddd\}}||j |j|   kr|t|jksn J || |  | ksJ d S )N)r   r   T)	normalize)r  sort)r.   r  r0  r2   rq   r   )r   r   rT   rh   rh   ri   #test_normalize_sort_diogonalization	  s    ,,r  c                   C   s   t tdd  d S )Nc                   S   s   t g dt ddg gS )Nr   r   r   r   rh   rh   rh   ri   r   	  rk   z!test_issue_5321.<locals>.<lambda>)rL   r   rh   rh   rh   ri   test_issue_5321	  s    r  c                  C   s   t tddtd t g dg dgks0J t tddtd t ddgddgddgddggkslJ t} | | td| dtd t g dg dgksJ d S )Nra   )r   r   ra   r   )r   r   r   ra   r   r   )r.   hstackr2   vstackr/   r  rh   rh   ri   test_issue_5320	  s     r  c                  C   sV   t dgg} t| }t || t ddggks2J t || t dgdggksRJ d S r  )r.   r   r  r  )r   ZAImrh   rh   ri   test_issue_11944	  s    r  c                     s   g d} g d}t g d}|j} fdd}tD ]\  | } |}|||| |||j| ||j|j| ||j|| q2ttdd  d S )Nr   r   )r   r   r   c                    s    || ksJ t |  ksJ d S rb   )rc   )r   r  r  rh   ri   ra  	  s    ztest_cross.<locals>.testc                   S   s"   t ddddgt ddddgS r~   r  rh   rh   rh   ri   r   	  s    ztest_cross.<locals>.<lambda>)r.   r0  rm   r  rL   r%   )rX   rY   r  r  ra  r   r,  rh   r  ri   
test_cross	  s    r  c                  C   sr   t dd  D ]:} | d| dh}t|dkrB| | dksJ qt d d D ]} t| dtrTJ qTd S )Nr   r   ra   )rm   r2   r  popr   r   )rx   ru  rh   rh   ri   	test_hash	  s
    $r  c                      s   t d  tt fdd d S )Nr   c                      s   t  dS r  )hashr2   rh   r  rh   ri   r   
  rk   z!test_issue_3979.<locals>.<lambda>)rm   rL   r  rh   rh   r  ri   test_issue_3979	  s    r  c                  C   sH   dt gddgg} tddgt  dgg}tD ]}|||  ks*J q*d S Nr   r   )r	   r.   rm   Zadjoint)r3  r  rx   rh   rh   ri   test_adjoint
  s    r  c                   C   s8   t tttd ttd  ggtdggks4J d S )Nra   r   )r#   r,   r   r\   r   rh   rh   rh   ri   test_simplify_immutable
  s    "
r  c                     sT   t dtd\ tddfdd} tdd fdd}| }|| ksPJ d S )NF, Gr  ra   c                    s    | | S rb   rh   r   )Grh   ri   r   
  rk   ztest_replace.<locals>.<lambda>c                    s    | | S rb   rh   r   r}  rh   ri   r   
  rk   )r   r   r.   replace)Kr   Nrh   )r}  r  ri   test_replace
  s
    r  c                     s   t dtd\ } t t tdd| d d| dif| d d| dif| d d| dif| d d| difg}W d    n1 s0    Y  tdd fdd}ttdd	 | | d
}W d    n1 s0    Y  ||ksJ d S )Nr  r  ra   r   r   c                    s    | | S rb   rh   r   r  rh   ri   r   
  rk   z"test_replace_map.<locals>.<lambda>F)Ztest_stacklevelT)r   r   rQ   r.   rR   rK   r  )r  r  r   r  rh   r  ri   test_replace_map
  s    2,$,r  c                  C   sT   t ddgtddt  gg} |  tjtdtjthks<J | tthksPJ d S r~   )r.   r\   Zatomsr   r6  ZNegativeOner   r   rh   rh   ri   
test_atoms"
  s     r  c            	         s  t ttgttgg} t| jddt|  ks4J t ddgddgddggt g d	g d
gt ttgg}|D ]d}|jdd}|| }|| }t|| |ksJ t|| |ksJ |j|ksJ |j|kspJ qp|D ]n}t|jdd}|| }|| }t|| |ksJ t|| |ks*J |j|ks:J |j|ksJ qddl	m
  | jdd}|  }tdtdtdtdi}t fddt||||D sJ d S )NZRDr  r>  h   i  r`   r   r   )r   r   r   )r=  rm     EDr   compi_ib,  i  ij  c                 3   s$   | ]\}} |  |  V  qd S rb   r   )rf   rg   r   r  rh   ri   rj   O
  s   ztest_pinv.<locals>.<genexpr>)r.   rX   rY   rZ   r[   r#   pinvr   r  sympy.core.numbersr  ro   zipr   )	A1Asr   A_pinvAApApAr  wZrepsrh   r  ri   	test_pinv(
  s:     
r  c                  C   st   t g dg dg dg dg dg dgg} | D ]<}|jdd}|| }|| }|j|ks`J |j|ks2J q2d S )	N)=   r   7   r)  rn  r   )>   `   U   r  rL  r   )E   8   rm  r   6   r   )r   r  [   )   rn  r   )r   rc  r   r   Z   r   )r   r   r   r   r   r   r  r  )r.   r  r  )r  r   r  r  r  rh   rh   ri   3test_pinv_rank_deficient_when_diagonalization_failsU
  s    	r  c                   C   sL   t ddt dd tddg ks$J t ddt dd tddg ksHJ d S r  )r5   r.   rh   rh   rh   ri   test_issue_7201k
  s    $r  c                  C   s2   t tttfD ] } | tgdggjthksJ qd S rV  )r,   r-   r.   r/   r\   Zfree_symbolsr   rh   rh   ri   test_free_symbolso
  s    r  c                      sd  zddl m  W n ty*   td Y n0 t g dtg dksLJ t g dgtg dgkspJ t g dg dgtg dg dgksJ t tttgttttgksJ tt	 fdd t dd	g d
dggtdd	gd
dggksJ t dd	gd
dggtdd	gd
dggks>J t g  g gtg ks`J dS )zSee issue 7465.r   array?NumPy must be available to test creating matrices from ndarraysr   r  c                      s(   t  ddgddggddgddgggS )	Nr   ra   r`   r   r   r   r   r   r   rh   r  rh   ri   r   
  rk   z#test_from_ndarray.<locals>.<lambda>r   ra   r`   r   N)
numpyr  ImportErrorrO   r.   r\   r]   r^   rL   NotImplementedErrorrh   rh   r  ri   test_from_ndarrays
  s      $$
62r  c                  C   s   ddl m}  zddlm}m} W n ty:   td Y n0 | |ddgddgg}|d dksdJ t|g d	ksxJ tt	( | |ddgddgg}W d    n1 s0    Y  |d dksJ t|g d	ksJ d S )
Nr   
_matrixify)r  matrixzPNumPy must be available to test indexing matrixified NumPy ndarrays and matricesr   ra   r`   r   rF  )
sympy.matrices.commonr  r  r  r  r  rO   rs   rJ   PendingDeprecationWarning)r  r  r  ry   rh   rh   ri   test_17522_numpy
  s    
6r  c                  C   sx   ddl m}  zddlm} W n ty6   td Y n0 | |ddgddgg}|d d	ks`J t|g d
kstJ d S )Nr   r  )r  zEmpmath must be available to test indexing matrixified mpmath matricesr   ra   r`   r         @)rM  g       @r  r  )r  r  Zmpmathr  r  rO   rs   )r  r  ry   rh   rh   ri   test_17522_mpmath
  s    r  c                  C   sx   ddl m}  zddlm} W n ty6   td Y n0 | |ddgddgg}|d dks`J t|g d	kstJ d S )
Nr   r  )
csr_matrixzJSciPy must be available to test indexing matrixified SciPy sparse matricesr   ra   r`   r   rF  )r  r  Zscipy.sparser  r  rO   rs   )r  r  ry   rh   rh   ri   test_17522_scipy
  s    r  c                  C   sr   t dtgt dgg} | js J dt | d< | jdu s:J t| d< | jd u sPJ | d t | d< | jdu snJ d S )Nr   ra   r   Fr   r   )r.   r	   Zis_hermitianr\   r  rh   rh   ri   test_hermitian
  s    
r  c                  C   sJ   t tttddgg} | d dt ks*J |  t dt ggksFJ d S )NFr+  r   ra   )r.   r   r\   r   r  rh   rh   ri   	test_doit
  s    r  c                     s  t g dg dg dg} | d | t g dg dgks@J t g dg dg dg}|d |t g dg dgksJ t g dg dg dg}|d |t g dg dgksJ t g dg dg dg tt fd	d
 t g dg dg dgttfdd
 t g dg dg dg} | d | t ddgddgddggks`J t g dg dg dg}|d |t ddgddgddggksJ t g dg dg dg tt fdd
 t g dg dg dgttfdd
 d S )Nr   r!  r   r   r   )r   r   r   )r   r   r=  r   c                      s
     dS r   row_delrh   r   rh   ri   r   
  rk   z+test_issue_9457_9467_9876.<locals>.<lambda>c                      s
     dS Nr   r  rh   rS   rh   ri   r   
  rk   r`   ra   r   r   c                      s
     dS r   col_delrh   r  rh   ri   r   
  rk   c                      s
     dS r  r  rh   rS   rh   ri   r   
  rk   )r.   r  rL   r.  r  )r   r  Orh   )r   rT   ri   test_issue_9457_9467_9876
  s.    



$
$r  c                  C   s   t ddd\} }t d\}}td}tdd| ||tg}||  | | | | ksTJ || | || | kspJ | | ||  ksJ || || ksJ ||  | t||  dgd||  ggksJ d S )Nrt  F)Zcommutativeza bra   r   )r   r2   r.   r^   )r\   r]   rX   rY   r   ZM1rh   rh   ri   test_issue_9422
  s    r  c            	      C   s   t g } ddgt g df}ddg|d jf}ddgt ddgdd	ggf}|||fD ]R\}}|D ]D}t| |}d
|v r~||n|d|}||krt|t|ks`J q`qTd S )Nr  r  )r   r   r`   r  r  r   ra   r`   r   joinr  )r.   r0  r0  id)	r   rX   rY   rZ   opsry   opr  newrh   rh   ri   test_issue_10770
  s    
r  c                  C   sB  t g dg dg dg} | g dg dt ddgdd	gd
dggksLJ | g dg dt dgdgd
ggksxJ | g dg dt g dgksJ | g dg dt g dg dgksJ | g dg dt ddg ksJ | g dg dt ddg ksJ | g dg dt dgdggks>J d S )Nr   r  rQ  r   )TTFr   ra   r   r   r   r   )TFF)TFT)FFFr`   r   )FTF)r.   r   r   rh   rh   ri   test_issue_10658
  s    ,&$&r  c                  C   s  t ddtd  dgdtd d d dtd d gg} |  dksLJ t ddtd t  dgdddtd t  gg} t|  d	 t ddddtd t   gd	d	gg tddksJ td
\}}}}}}}}}	}
}}t |||| || d	g|||| || d	g|||| || dg|||| || dg|	|
d|	 | |	|  d|
 | |
|  d	gg} |  dks|J d S )Nr   r   ra   r   r`   r  r   r   r   z/a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1)r.   r   r"  r	   r#   r   r;   r   )ry   axZaybxZbyZcxcyZdxZdyexZeyt0t1rh   rh   ri   !test_opportunistic_simplification
  s    <4F r  c                  C   s   t g dg dg} |  d t g dg dg  dk s@J t g dg dg d	g}t g d
g dg dg}t g dg dg d	g}| |  dk sJ | |  dk sJ d S )N)g~jth?gRM@g(\M@)gDl)@gQgp=
cG@r   )rM  r   r   )r   rM  rM  V瞯<)q7K<rM  r   )      r   r   r   )r  rM  r  )r                 @)r  r  rM  )r   r  r  )rM  r  g      )r.   r   rD  r   )mmZm_mixedZm_floatZm_invrh   rh   ri   test_partial_pivoting  s(    
r  c                  C   st   t g dg dg dg} | jdd dd }t g dg d	g d
g}|| }| dk s`J |d dkspJ dS )z When doing numerical computations, all elements that pass
    the iszerofunc test should be set to numerically zero if they
    aren't already. )?皙gɿr   )皙r  gٿr   )r  r  g333333?r   c                 S   s   t | dk S )Ng [n<)r   r   rh   rh   ri   r   *  rk   z*test_iszero_substitution.<locals>.<lambda>r  r   )rM  r   g4iҤIӿr   )r   rM  glٲer   rD  r  rL  N)r.   r   rD  )ry   Zm_rrefZ	m_correctZm_diffrh   rh   ri   test_iszero_substitution#  s    r  c            
      C   sR  ddl m}  dtttdd  tttdd td  }dtd tttdd d  d	tttdd   d
tttdd d   }| dd}| dtd }| ||}t|t| |t| g}t|| || g}tt|| t|| g}dd }	|jd|	ddksJ |jd|	ddks6J |jd|	ddksNJ d S )Nr   )Pointr   r>  -   r`   r  ra   r   r   r   c                 S   s   t |  dk S )Ng#B;)r   rw   r   rh   rh   ri   r   ?  rk   z"test_issue_11238.<locals>.<lambda>T)r#   r  )	Zsympy.geometry.pointr  r   r   r   r   r.   r#   r"  )
r  xxyyp1p2Zp0rA  rB  m3Zrh   rh   ri   test_issue_112381  s    0R

r  c                  C   sh   t ddg d} | tj }| | }tD ]<}|| \}}t|t| ksNJ t|t| ks&J q&d S )Nra   rF  )r.   r   ZImaginaryUnitrm   Zas_real_imagrs   )rA  rB  r  ZklsrX   rY   rh   rh   ri   test_as_real_imagD  s    
r  c                  C   sV   t ddg d} |  \}}|d t dddgks6J |d t ddg dksRJ d S )Nr`   r  r   ra   r   )ra   r   r   ra   )r.   Zjordan_cells)ry   r   ZJcellsrh   rh   ri   test_deprecatedN  s    r  c                  C   s\   ddl m}  tg d}tg d}| |dtg dks>J | |dtg dksXJ d S )	Nr   )Mod)r   r   ra   )r   r)  r  r`   )ra   r   ra   r   )ra   r   r   )Zsympy.core.modr  r.   )r  r   r,  rh   rh   ri   test_issue_14489Y  s
    r  c                  C   s\   zddl m}  W n ty*   td Y n0 tddgddgg}| |tdjjd	ksXJ d S )
Nr   r  r  r   ra   r`   r   )dtypefloat64)r  r  r  rO   r.   floatr  name)r  r   rh   rh   ri   test_issue_14943a  s    r  c                  C   s4   t ddd} td}| d dk}t|dks0J d S )Nry   r   rX   r   r   zm[0, 0] > 0)r>   r   rb  )ry   rX   rh   rh   ri   test_case_6913k  s    r  c                  C   s.   t ddd} td}| ||| iks*J d S )Nr   r`   rX   )r>   rE   match)r   rX   rh   rh   ri   test_issue_11948q  s    r  c                  C   s   t dtgt dt gg} t j|  t dgtggt dgt gggksJJ t dtdgt tdt gg} t j|  t dgtgdggt td gtdd gt gggksJ t dtgdt gg}| \}}||j t dksJ d S )Nr   r   ra   )r.   r	   Zorthogonalizer   ZQRdecompositionr  r2   )Zvecsr|   rT   r   rh   rh   ri   test_gramschmidt_conjugate_dotv  s     4r   c                  C   sf   t tddd} t tddd}| |}t|| d }t|| d }||d ksVJ |dksbJ d S )NrX   r`   r   rY   r   r   )r.   r>   r  r   )rX   rY   rZ   r[   rJ  rh   rh   ri   test_issue_8207  s    
r  c                     sD  ddl m}  tddgddgg  ttt tttttdt tt gdtdt ggkshJ tddgddgg t  d ttttt	dd t	d d gt	d d t	dd ggksJ t
tdd	  t
t fd
d	 tg dg dg dg dg  ttt  ks.J t
t fdd	 tddgddgg t t	ttd  ksvJ tg dg dg dg t | tdtd  ksJ tg dg dg dg dg  ttt  ksJ tg dg dg dg dg  ttt ttt t  ks@J d S )Nr   nthrootr   ra   r`   r   r   c                   S   s   t dtttS r|  )r;   analytic_funcr   r\   rh   rh   rh   ri   r     rk   ztest_func.<locals>.<lambda>c                      s    t  tt t S rb   )r\   r  r   rh   r   rh   ri   r     rk   )r   r   r   r`   )r   r   r   r   )r   r   r   r   c                      s     tttS rb   )r  r   r\   rh   r   rh   ri   r     rk   r  r   "   )r`   r'  r   )r   r   r   )r   r   r   r   )r   ra   r   r   )r   r   r`   r   )r   r   r   r`   )r   ra   r   r   )r   r   r   ra   )r   r   r   r`   rD  )sympy.simplify.simplifyr  r.   r  r   r\   r_   r   r   r   rL   r   r   r#   r   r  rh   r   ri   	test_func  s$    HT "$  r  z$Cannot create threads under pyodide.c               	   C   st   dd } t dP tj &}|| }| s4J W d    n1 sH0    Y  W d    n1 sf0    Y  d S )Nc                  S   s&   t jd ksJ tdgg} | |  } dS r   )rC   stater.   r   rh   rh   ri   r    s    ztest_issue_19809.<locals>.fT)r?   
concurrentZfuturesZThreadPoolExecutorZsubmitresult)r  executorfuturerh   rh   ri   test_issue_19809  s
    

r  c                  C   s@   t ttg} t| tddftddft tjgtjggks<J d S r  )r.   r\   r]   r   r   r   r   rh   rh   ri   test_issue_23276  s
    r  (4  rg  concurrent.futuresr	  collections.abcr   Zsympy.core.addr   Zsympy.core.functionr   r   r   r  r   r   r	   r
   r   r   r   r   Zsympy.core.powerr   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Zsympy.core.sympifyr   Z$sympy.functions.elementary.complexesr   Z&sympy.functions.elementary.exponentialr   r   Z(sympy.functions.elementary.miscellaneousr   r   r   Z(sympy.functions.elementary.trigonometricr   r   r   Zsympy.integrals.integralsr   Zsympy.polys.polytoolsr   r   Zsympy.printing.strr    Zsympy.sets.setsr!   r  r"   r#   Zsympy.simplify.trigsimpr$   Zsympy.matrices.matricesr%   r&   r'   r(   r)   r*   Zsympy.matricesr+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   Zsympy.matrices.utilitiesrC   Z
sympy.corerD   rE   Z(sympy.functions.special.tensor_functionsrF   Zsympy.utilities.iterablesrG   rH   rI   Zsympy.utilities.exceptionsrJ   rK   Zsympy.testing.pytestrL   rM   rN   rO   rP   rQ   rR   Zsympy.assumptionsrT   Zsympy.tensor.arrayrU   Zsympy.matrices.expressionsrV   Zsympy.algebrasrW   r   rX   rY   rZ   r[   r\   r]   r^   r_   rm   rz   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$  r%  r&  r(  r4  r5  r9  r;  rC  rM  rP  rT  rX  r\  r]  rk  rx  r}  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
  r  r$  r%  r&  r'  r)  r/  r1  r2  r@  rK  rP  rR  rS  rV  rW  rY  r\  r]  r^  r`  rd  re  rf  rg  rh  ri  rj  rk  ro  rq  rr  rs  ru  rv  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  r   r  r  r  r  rh   rh   rh   ri   <module>   s  ( h$(,Ma,	O			:		
	
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-


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