U
    L?hAs                 	   @   sh  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l3m4Z4 d dl5m6Z6m7Z7 d dl8m9Z9 d dl:m;Z;m<Z<m=Z= d dl>m?Z? d dl@mAZA d dlBmCZC d dlDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\ d dlBm]Z] d dl^m_Z_m`Z` d dlambZb d dlcmdZdmeZemfZf d dlgmhZh d dlimjZjmkZkmlZlmmZmmnZnmoZo d d lpmqZq d d!lrmsZs d d"ltmuZu d d#lvmwZw d d$lxmyZy d d%lzm{Z{m|Z|m}Z}m~Z~mZmZmZmZ eHeIeFeGfZd d&lmZmZ d d'lmZmZ eo  G d(d) d)eeeZW 5 Q R X eo  G d*d+ d+eeeZW 5 Q R X d,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zd|d} Zd~d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddÄ Zddń ZddǄ ZddɄ Zdd˄ Zdd̈́ Zddτ Zddф Zddӄ ZddՄ Zddׄ Zddل Zddۄ Zdd݄ Zdd߄ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d Zdd Zdd Zdd Zdd	 Zd
d Zdd Zdd Zdd Zdd Zdd Z dd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$d% Zd&d' Z	d(d) Z
d*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU Z ekdVdW Z!dXdY Z"dZd[ Z#d\d] Z$d^d_ Z%d`da Z&eldbdc Z'ddde Z(dfdg Z)dhdi Z*djdk Z+dldm Z,dndo Z-dpdq Z.drds Z/dtdu Z0dvdw Z1dxdy Z2dzd{ Z3d|d} Z4d~d Z5dd Z6dd Z7dd Z8dd Z9dd Z:dd Z;dd Z<dd Z=dd Z>dd Z?dd Z@enddd ZAdd ZBdd ZCdd ZDdd ZEdd ZFdd ZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPd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)RootOf)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)raisesXFAILslowskipskip_under_pyodidewarns_deprecated_sympyQ)Array)ArrayDerivative)MatPow)
Quaternion)abcdxyzt)_MinimalMatrix_CastableMatrix)MatrixSubspacesMatrixReductionsc                   @   s   e Zd ZdS )SubspaceOnlyMatrixN__name__
__module____qualname__ rj   rj   T/var/www/html/venv/lib/python3.8/site-packages/sympy/matrices/tests/test_matrices.pyre   C   s   re   c                   @   s   e Zd ZdS )ReductionsOnlyMatrixNrf   rj   rj   rj   rk   rl   H   s   rl   c                 C   s   t | | dd S )Nc                 S   s   t | |kS N)intijrj   rj   rk   <lambda>M       z eye_Reductions.<locals>.<lambda>rl   nrj   rj   rk   eye_ReductionsL   s    rw   c                 C   s   t | | dd S )Nc                 S   s   dS Nr   rj   ro   rj   rj   rk   rr   Q   rs   z"zeros_Reductions.<locals>.<lambda>rt   ru   rj   rj   rk   zeros_ReductionsP   s    ry   c                  C   s   t tD ]\} }|dd}|jdkr:tdd |jD s>t|jdkrVt|jtksZt|j	dkrrt|j	tksvt| d st|
 tttfkstqt| tkstqd S )N      )rz   r{   c                 s   s   | ]}t |tkV  qd S rm   )typern   .0rp   rj   rj   rk   	<genexpr>X   s     ztest_args.<locals>.<genexpr>)	enumerateclassesr=   shapeallAssertionErrorrowsr|   rn   colsflatlisttuplerF   todokdict)rv   clsmrj   rj   rk   	test_argsT   s    "r   c               
   C   s   t tfD ]8} | dd}t  |j}W 5 Q R X || kstqttfD ]8} | dd}t  |j	}W 5 Q R X ||
 ksJtqJd S Nrz   r{   )r0   r.   r=   rR   Z_matr   r   r1   r/   Z_smatr   )r   r   matZsmatrj   rj   rk   test_deprecated_mat_smata   s    r   c                  C   s8   t ddttg} | t t ddtt tt gks4td S N   r{   )r0   r]   r^   r_   r   )vrj   rj   rk   test_divisionn   s    r   c                      s   t dddgtttgdt dtt gg    t dddgdt dt dt gdt ddt t ggksltt ddddgtt fdd	 d S )
Nr   r{   rz   i      ic                      s     S rm   rj   rj   r   rv   rj   rk   rr   w   rs   ztest_sum.<locals>.<lambda>)r0   r]   r^   r_   r   rM   r&   rj   rj   r   rk   test_sums   s    (Dr   c                  C   s8   t dddtg} t dddttg}t| |ks4td S )Nr   r{   rz   )r0   r]   r   absr   r   rj   rj   rk   test_absy   s    r   c                  C   sH   t d} t d}| | | |  kr>t ddgddggksDn td S )N)r   r{   rz   r   r   )rz   r   r{   r   r   r   )r0   addr   rY   rZ   rj   rj   rk   test_addition~   s    r   c               
   C   sz  t tfD ]} | ddtd}||d d d d f ks:t|dd d f t dddddgks`t|d d df t dddgkst|ddgd d f t dddgdddggkst|ddgdf |ddgdgf kst|dddgf |dgddgf kst|d d ddgf t ddgddgd	dggks2t|d
 dksDt|ddd d f t dddgdddggksvt|d d ddf t ddgddgd	dggkst|d d ddf |ddgdf kst|dd d df |dddgf kst| ddtd}|dddddgd d f t dddgd	ddgdddgd	ddgdddggksZt|d d dddddgf t dddddgdddddgd	ddddggkstqtd}d|d< d|d< d|d< |ddgdgt dgdggkst|ddgdddgt dddgdddggks$t|ddddgddddgt ddddgddddgddddgddddggksvtd S )Nrz   	   r   r         r   r{   r   r   r      r   r   r   r{   r   )r0   r1   ranger   r=   extract)MrY   rj   rj   rk   test_fancy_index_matrix   sZ    &"0&&424((




r   c                     sV  t d t d  } | d dks(t| d dks8t| d dksHt| d	 dksXt| d
 dksht| d dksxtztd W n tk
r   Y nbX | d dkst| d dkst| d dkst| d	 dkst| d
 dkst| d dkstt | }| | kst|d dks*t|d dks<t|d dksNt|d	 dks`t|d
 dksrt|d dksttt fdd td } t	| t st| d t
kst| d dt
 kst| d dt
 kst| d	 dkstt
 }| |kstd } t	| t s2t| d dksDt| d dksVt| d dksht| d	 dksztztd W n tk
r   Y nZX t	| t st| d dkst| d dkst| d dkst| d	 dkstt tdgdtgg}|d |kstt ttgddgg}|d t ttgttggksRtd S )N)r   r   r   r   r   r   r   r   r{   r   r   r   r   r   r      r{   r   r   z	c = a @ br   c                      s
   t  S rm   )r6   rj   r   rj   rk   rr      rs   z%test_multiplication.<locals>.<lambda>r]   rz   r   
      z	c = 5 @ b)r0   r   evalSyntaxErrorr6   Zmultiply_elementwiserM   r&   r   
isinstancer]   r   r   )r[   hc2r   rj   r   rk   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sft d d d  ddddgksttdddgdddgdddgg  d d d  dddddddddg	kst d tdkst d  ksttdggd d dd ksttdd  tdks0ttddgddggtd td!d"gd#d$ggksfttd%d&gd'd(gg  tj d d  dddd!gksttddgd)dgg  tj d  ksttddgddggtj tddgtjdggks ttddgddggd* tddgd*dggks2tdd+l	m
 tdtgddgg tdt gddggkstttttgdtgg tt ttd    gdt ggksttt td   t d  t   dtd   gdt td   gddt ggs,t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sttddgdd!gg  td dksttdgg  d" td,gg  kr td"  kr d"ksn ttdddddgdddddgdddddgdddddgdddddggt tfd-d t td.d  tdddgdddgdddgg  d/ tdddgdddgdddggkstt t fd0d t t fd1d td	dgddgg  d/ td2d3gd4d5ggksttdddgdddgdddgg  d/ tdddgdddgdddggkslttdddgdddgdddgg  d/ tdddgdddgdddggksttd6d7d8t  tsttd6d7d7d9t t fd:d td6d7d7d;  ttdtdtd td d gdtddtd gdddggksjt d  tdddgdddgdddggkstt t fd<d tdddgdddgdddgg  d= td>d?d@gdAdBdCgdDdEdFggkst d=  d ksttdddgd)ddgdddgg td6  d  d ks`tt tfdGd   d  ksttdddgdddgdddgg td6d7d7dH   ksttd6d7d7d;  td d d kst  dtdks t  dtdks>ttdddgdddgdddgg  dI tdJdJdJksxt t tdt dt dt ksttdddgdddgdddgg t t fdKd t t fdLd ttjtjgtjtjgg  tj  k	st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	sZtd S )MNc                   S   s   t dd S Nr   r{   r0   rj   rj   rj   rk   rr     rs   ztest_power.<locals>.<lambda>r{   rz   r   r   r   ir      3   ii  i  i,*  i7  r   r      i"  i     i  i  ip  i  i  i  r   d   r   i r   r   r      !      0   9   g      ?ru   i   c                      s     tdS Nr   )_matrix_pow_by_jordan_blocksr   rj   r   rj   rk   rr   /  rs   c                   S   s   t ddgddggtdS )Nr   rz   )r0   r   r   rj   rj   rj   rk   rr   2  rs         $@c                      s    d S N @rj   rj   Arj   rk   rr   5  rs   c                      s    t dd S r   r   rj   r   rj   rk   rr   6  rs   ihiO<iv0irv   T)integer)r   negativec                      s     S rm   rj   rj   )r   rv   rj   rk   rr   @  rs   )r   Znonnegativec                      s    t dd S r   r   rj   r   rj   rk   rr   G  rs   g      @   H   Y   i#        i<  i  iI  c                      s     d S )N)subsdoitrj   )Anrv   rj   rk   rr   O  rs   )r   positiver   gd%%@c                      s    d S r   rj   rj   r   rj   rk   rr   ^  rs   c                      s    t  S rm   r	   rj   r   rj   rk   rr   _  rs   )rM   r(   r   r0   r   r4   r
   r   Half	sympy.abcrv   rY   rZ   r   Z_eval_pow_by_recursionr'   
ValueErrorr   r   rW   rH   r   r   r3   r=   r	   )Rrj   )r   r   r   rv   rk   
test_power  s    @  *"6$626J<$0D ." . .*2 .  & & 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stW 5 Q R X d S )Nr   Tr{   )r0   r]   rA   r   r   r   r   rj   rj   rk   $test_issue_17247_expression_blowup_1f  s    $
00r   c               	   C   s\   t dt dt gdt dt gg} td& |  \}}|| |  sNtW 5 Q R X d S Nr   T)r0   r]   rA   jordan_forminvr   r   PJrj   rj   rk   $test_issue_17247_expression_blowup_2m  s    $
r   c               	   C   s   t dt dt gdt dt gg} tdV | d t dtd  d ddtd   gddtd   dtd  d ggks~tW 5 Q R X d S )Nr   Tr   l                )r0   r]   rA   r   r   rj   rj   rk   $test_issue_17247_expression_blowup_3s  s    $
r   c               	   C   s<   t td} td | d t tdks.tW 5 Q R X 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]])r0   r   rA   r   r   rj   rj   rk   $test_issue_17247_expression_blowup_4z  s    
r   c               	   C   sl   t dddd } tdJ | dttd ddt  td   dt td	   td
dks^tW 5 Q R X d S )Nr   c                 S   s   dd| |  t   S Nr   r   r   ro   rj   rj   rk   rr     rs   z6test_issue_17247_expression_blowup_5.<locals>.<lambda>Tr]   r   $   r   ZEXdomain)r0   rA   charpolyr   r]   r	   r   r   rj   rj   rk   $test_issue_17247_expression_blowup_5  s    
r   c               	   C   sD   t dddd tdD } td | ddks6tW 5 Q R X d S )Nr   c                 S   s   g | ]}t | qS rj   r]   r}   rj   rj   rk   
<listcomp>  s     z8test_issue_17247_expression_blowup_6.<locals>.<listcomp>@   TZbareissr   r0   r   rA   detr   r   rj   rj   rk   $test_issue_17247_expression_blowup_6  s    
r   c               	   C   s:   t dddd } td | ddks,tW 5 Q R X d S )Nr   c                 S   s   dd| |  t   S r   r   ro   rj   rj   rk   rr     rs   z6test_issue_17247_expression_blowup_7.<locals>.<lambda>T	berkowitzr   )r0   rA   r   r   r   rj   rj   rk   $test_issue_17247_expression_blowup_7  s    
r   c               	   C   sD   t dddd tdD } td | ddks6tW 5 Q R X d S )Nr   c                 S   s   g | ]}t | qS rj   r   r}   rj   rj   rk   r     s     z8test_issue_17247_expression_blowup_8.<locals>.<listcomp>r   TZlur   r   r   rj   rj   rk   $test_issue_17247_expression_blowup_8  s    
r   c                  C   s   t dddd tdD } td |  t dddd	d
dddgddddddddgddddddddgddddddddgddddddddgddddddddgddddddddgddddddddggdfkstW 5 Q R X d S )Nr   c                 S   s   g | ]}t | qS rj   r   r}   rj   rj   rk   r     s     z8test_issue_17247_expression_blowup_9.<locals>.<listcomp>r   Tr   r   r   r   r   r   r{   rz   r   r   r   r   r   )r0   r   rA   rrefr   r   rj   rj   rk   $test_issue_17247_expression_blowup_9  s    
r  c               	   C   s<   t dddd } td | dddks.tW 5 Q R X d S )Nr   c                 S   s   dd| |  t   S r   r   ro   rj   rj   rk   rr     rs   z7test_issue_17247_expression_blowup_10.<locals>.<lambda>Tr   )r0   rA   Zcofactorr   r   rj   rj   rk   %test_issue_17247_expression_blowup_10  s    
r  c               	   C   sF   t dddd } td$ |  t dddgd ks8tW 5 Q R X d S )Nr   c                 S   s   dd| |  t   S r   r   ro   rj   rj   rk   rr     rs   z7test_issue_17247_expression_blowup_11.<locals>.<lambda>Tr   r   )r0   rA   Zcofactor_matrixr   r   rj   rj   rk   %test_issue_17247_expression_blowup_11  s    
r  c               	   C   sH   t dddd } td& |  dddt dddiks:tW 5 Q R X d S )Nr   c                 S   s   dd| |  t   S r   r   ro   rj   rj   rk   rr     rs   z7test_issue_17247_expression_blowup_12.<locals>.<lambda>Tr   r   r   )r0   rA   Z	eigenvalsr	   r   r   rj   rj   rk   %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 ddddggfkst|d d ttdtd   d kst|d d dkst|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st|d d ttdtd   d kst|d d dkst|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std S )	Nr   r   r{   r   FT)deepZnumerr   )r0   r]   Z
eigenvectsr   r   r   )r   Zevrj   rj   rk   %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ddddddddgddddddddgddddddddgddddddddgddddddddgddddddddggkstW 5 Q R X d S Nr   r   r   Tr   )r0   r]   rA   echelon_formr   r   rj   rj   rk   %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v |  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stW 5 Q R X d S r  )r0   r]   rA   rowspacer   r   rj   rj   rk   %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stW 5 Q R X d S )Nr   r   r   T)r0   r]   rA   columnspacer   r   rj   rj   rk   %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tW 5 Q R X d S )Nr   c                 S   s   g | ]}t | qS rj   r   r}   rj   rj   rk   r   
  s     z9test_issue_17247_expression_blowup_17.<locals>.<listcomp>r   Tr   r   r   r{   r   rz   r   r   r   r   r   r   )r0   r   rA   	nullspacer   r   rj   rj   rk   %test_issue_17247_expression_blowup_17	  s    
&&&&&&r  c               	   C   sX   t dddt dt gd dt dt gd  d } td |  rJtW 5 Q R X d S )Nr   r   rz   T)r0   r]   rA   is_nilpotentr   r   rj   rj   rk   %test_issue_17247_expression_blowup_18  s    4
r  c               	   C   s0   t td} td |  r"tW 5 Q R X 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)r0   r   rA   is_diagonalizabler   r   rj   rj   rk   %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ddddgddddgddddggt ddddgddt ddgddtd dgdddtd ggfkstW 5 Q R X d S )Nr   r   Tr   r{   )r0   r]   rA   diagonalizer   r   rj   rj   rk   %test_issue_17247_expression_blowup_20"  s(    




r  c               	   C   s@   t td} td" | jddt tdks2tW 5 Q R X 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]]r0   r   rA   r   r   r   rj   rj   rk   %test_issue_17247_expression_blowup_214  s    
r  c               	   C   s@   t td} td" | jddt tdks2tW 5 Q R X d S )Nr  TLUr  r  r  r   rj   rj   rk   %test_issue_17247_expression_blowup_22A  s    
r   c               	   C   sD   t td} td& | jdd t tdks6tW 5 Q R X d S )Nr  TADJr  r  )r0   r   rA   r   r   r   r   rj   rj   rk   %test_issue_17247_expression_blowup_23N  s    
r"  c               	   C   s@   t td} td" | jddttdks2tW 5 Q R X d S )Nr  TCHr  r  r1   r   rA   r   r0   r   r   rj   rj   rk   %test_issue_17247_expression_blowup_24[  s    
r%  c               	   C   s@   t td} td" | jddttdks2tW 5 Q R X d S )Nr  TLDLr  r  r$  r   rj   rj   rk   %test_issue_17247_expression_blowup_25h  s    
r'  c               	   C   s4   t td} td |  dks&tW 5 Q R X 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   r0   r   rA   rankr   r   rj   rj   rk   %test_issue_17247_expression_blowup_26u  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B |  \}}| t td kst|t tdkstW 5 Q R X 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]])r0   r]   rA   r   r   r   r   r   rj   rj   rk   %test_issue_17247_expression_blowup_27  s    
r+  c               	   C   s8   t td} td |  tdks*tW 5 Q R X 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)])r0   r   rA   Zsingular_valuesr   r   rj   rj   rk   %test_issue_17247_expression_blowup_28  s    
r,  c               	   C   s4   t td} td |  dks&tW 5 Q R X 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   rj   rj   rk   test_issue_16823  s    
r-  c                  C   s  t dddddddddg	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	dddddddddg	ddddddddtd d g	dddddddddg	ddddddddtd d g	gdfkstW 5 Q R X d S )Nr   r   r{   r   r   r  r   r   rz   r   r   r   T)r   r   r{   rz   r   r   r   r   )r0   r   rA   r  r   r   r   rj   rj   rk   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 5 Q R X t tg   krltddg ksrn ttg gtd	dg ksttg g gtd
dg kstt * td	gdgg d	gdggkstW 5 Q R X t 0 td	gdggj d	ggdggkstW 5 Q R X tdgg} t  tj	| d< W 5 Q R X tt
dgddgg}|}|j|jkslt|jd
ks|t|d d  t
dddgksttd
d
t
dddg}|}|j|jkst|jd
kst|d d  t
dddgkst||ks tt||ksttd
dtd	d}td	dtdd}t||g}|jdksRt|jdksbt|d d  d	d
dddddddg	kstttd
td
ksttttd
ttd
kstt|| ksttt|t| kst|t|k	sttdd
tddd
 gtd
dd td
d
d gg}t|} | td	d	d
d
d
gd	d	d
d
d
gd	d	d
d
d
gdddddgdddddggkst|  |kstt|dd |ksttdd
d
}td
|g}t|td	d	gd	d	g|d |d g|d |d ggkstt * t|dd dd |D ksDtW 5 Q R X ttd
tdgttd
gksvt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std S )Nc                   S   s   t ddtdS )Nr      )r0   r   rj   rj   rj   rk   rr     rs   ztest_creation.<locals>.<lambda>c                   S   s   t ddg S )Nr   r   r   rj   rj   rj   rk   rr     rs   c                   S   s   t dd S r   r   rj   rj   rj   rk   rr     rs   r   r   rz   r   r   r{   )r{   r   r   r   r   r   r   r   Fevaluater   r   r   r   c                 S   s   g | ]
}|gqS rj   rj   r}   rj   rj   rk   r     s     z!test_creation.<locals>.<listcomp>c                   S   s   t tdtddgS )Nr{   r   rz   r0   r7   rj   rj   rj   rk   rr     rs   c                   S   s   t tdtddgS )Nr{   rz   r   r3  rj   rj   rj   rk   rr     rs   )r   r   )rM   r   
IndexErrorr0   r   rR   tolistTr   ZEmptySetr]   r   r   r   r4   r.   as_immutable
as_mutabler7   r@   )
r   rY   r   rZ   Zc23Zc13r[   datr   M2rj   rj   rk   test_creation  s    
(.4("4.(r;  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 ddddddgddddddgddddddgddddddggkstd S )Nrz   r{   r   r   r   r   r   )r0   Z	irregularr7   r   rj   rj   rj   rk   test_irregular_block   s    &   r<  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sPt	d S )Nr{   rz   )
r   Oner   r]   r^   Zeror_   r0   r5  r   )lstr   rj   rj   rk   test_tolist)  s    8r@  c                   C   s`   t dd t ddkstt dd tt ddks<tt dd tt ddks\td S Nr   rz   )r=   r8  r   r7  r.   rj   rj   rj   rk   test_as_mutable/  s     rB  c                  C   s*  t d} | d dd df t dks(t| ddddf tdksHttdddd }|dd d f tdddksxt|dddf tddd	ksttddddgdd
ddgddddgddddgg}|d d df tddddddgkst|dd d d f tddddgddddggks&td S )Nr   rz   r{   r   c                 S   s   | | S rm   rj   ro   rj   rj   rk   rr   :  rs   ztest_slicing.<locals>.<lambda>r   r   r   r{   r{   rz   r   r   r   r   r   r      r         r   r   r   )r4   r   r=   r0   )m0m1m2rj   rj   rk   test_slicing5  s        0(rK  c                  C   s   t d} td| ddddf< | tdks0ttd| d dd df< | tdksXttddd| d d df< | tdkstt d| d d d d f< | t dkstddd	d
g| d d d d f< | tdkstddg| d ddf< | tdkstd S )Nr   r{   )r   r   r   r   rL  )r   r   r   r   )r   r   r   r   r   r   r{   rz   r   r   ))r   r   r   r   )r{   r   r   r   )rz   r   r   r   )r   r   r   r   r   r   r   r   r   r   rE  r   rF  rG  r      rM  rN  rO  rP  ))r   r{   rz   r   )r   r   r   r   rO  rP  )r=   r4   r0   r   r   rj   rj   rk   test_submatrix_assignmentC  s    rS  c                
      s   t dddd   dddgddgt dddddddd	gksBt ddgdddgt dddddddd
gkstt tdtd ksttt fdd tt fdd d S )Nr   rz   c                 S   s   | d | S Nrz   rj   ro   rj   rj   rk   rr   `  rs   ztest_extract.<locals>.<lambda>r   r   r{   r   r   rE  c                      s     dgdgS )Nr   r   r   rj   r   rj   rk   rr   d  rs   c                      s     dgdgS rA  rU  rj   r   rj   rk   rr   e  rs   )r0   r   r   r   rM   r4  rj   rj   r   rk   test_extract_  s    22rV  c                  C   sh   t d} | ddtdddks$ttdddd }|ddtdksLt|d	d
tdksdtd S )Nrz   r   r   )	r   r   r   r   r   r   r   r   r   r   c                 S   s   | | S rm   rj   ro   rj   rj   rk   rr   k  rs   ztest_reshape.<locals>.<lambda>)rC  )rz   r   r{   )rz   r   r{   )rz   r   r   r{   r   ))r   r   r{   rz   r   r{   )rz   r   r{   rz   r   r   )r4   reshaper0   r   rH  rI  rj   rj   rk   test_reshapeh  s     rY  c                  C   sD   t d} | dd t dd ks&t| dd tdks@td S )Nrz   c                 S   s   d|  S Nr{   rj   r   rj   rj   rk   rr   s  rs   z test_applyfunc.<locals>.<lambda>r{   c                 S   s   dS rx   rj   r   rj   rj   rk   rr   t  rs   )r4   	applyfuncr   r=   )rH  rj   rj   rk   test_applyfuncq  s    r\  c                  C   s,  t ttt  dgtt t t ttttt    gg} |  }|t tt td  dgttd  ttd   tt ttd   td  ggksttddd}t tt| gjddt t|tt	|  gkstt dddgddd	gdddgg t ddt
ddgddd	gdddggks(td S )
Nr{   rz   rY   Treal)complexr   r   r   )r0   r]   r^   r   r   r   r   r	   r   r   r   )rH  rI  rY   rj   rj   rk   test_expandw  s    8F
$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st| t	tt	t@ }|t td tgttd  td t ggkst| t
tt
t@ }|t td t gt td  td  t ggks>td S rZ  )r0   r   r]   r   r^   ZrefinerT   r^  r   r   r   rX  rj   rj   rk   test_refine  s    .<0ra  c                  C   s6  t dd} t dddd} | t ddddks.tt dddd} t dddd} | t ddddks`t|  }|  || ks|ttd}| t dd|dkstd	D ],}d
D ]"}t |d||d} | | jkst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s2td S )Nrz   )seedr   r      T)rb  	symmetric)rd  prng)r   rE  )r   F      )rd  percentre  r   r   rf  )minrh  rg  )	r8   r   copyr$   randomRandomr6  r   r   )r   r   rngsizerh  Z
zero_countrp   rq   rj   rj   rk   test_random  s,    

ro  c               2      s
  t d} |  t dkst| jddt dks4t| jddt dksLt| jddt dksdt| jddt dks|t| jddt dksttdd	d
gd	ddgdd	dgg} |  }| | t d	kst| jdd|kst| jdd|kst| jdd|kst| jdd|ks$t| jdd|ks:ttdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgdddddddddddddddddddddddddgg}|jdd| t |jd ksztt  dddgdddgdddggt fddd D stt  dddgdddgdddggt fddd D std S )Nr   r  r  r!  r#  r&  ZQRr{   rz   r   r   r   r   r   ZBLOCKr   1      r   G   ^   ;      A   c                 3   s    | ]}t | kV  qd S rm   r|   r   r~   sr   r   rj   rk   r     s     ztest_inverse.<locals>.<genexpr>zGE ADJ LU CH LDL QRc                 3   s    | ]}t | kV  qd S rm   rw  rx  rz  rj   rk   r     s     )	r4   r   r   r0   r   r.   r   splitr/   )r   ZAinvZAArj   rz  rk   test_inverse  sr    
6444444444444444444444444$
"
r|  c                  C   sB  t ddtd t dtd  tt  g} ttg}| |t dt t td gtdt t ggksftt ddttd td  g} | |t ddgdt td  td d td  ggksttd t }ttg}t||t dt dt gdt dggksttd td  }t||t dtd  dt td  gdt td  dtd  t ggksdttttd   }td dtd   }t ddt gdt dt gg}|t|t ttgkst|t|t ttgjkstt|ttf|gt ddtd  dt gdtd  dt dt gdt dt dggks>td S )Nr   r{   r   rz   r   r   )r0   r]   r^   jacobianr   r5   r_   r6  )LZsymsfgansrj   rj   rk   test_jacobian_hessian  s0    (6>0>
r  c                  C   s8  t ttttgtttd ttd  ks2tt tttdt gttdt ks\tt tttgtttttt  kstt dttd gtdkstdtt tt t dtt tt td   dtt tt t  tttt td   tttt td   } t tttttd gt | ksHtt tttttd gtdd | ksvttd  ttd  td ttd   dt ttd   dt ttd   }t tttttd gt |kstt tttttd gtdd |ks tt g tdks4td S )Nr{   rz   r   r   r   r   r  )r<   r   r]   r   r   r   r   )Zw1Zw2rj   rj   rk   test_wronskian	  s&    2**J*"
R*"
r  c                  C   sv  t dtgtdggtdt ddgddggks4tt tdgtt dggtdgtdggt ddgddggksvtt tdgtt dggtdftdfgt ddgddggkstt tdgtt dggtdtdit ddgddggkstt tt gjttd ttd idd	t td td  gks:ttD ]2} t dd
gd
dgg| dddks>tq>d S )Nr   r   r   r{   r   r   r   T)Zsimultaneousr   )r0   r]   r   r   r^   r   r4   r   rj   rj   rk   	test_subs  s    4(($&
r  c                  C   s   t dtgtdggtdit ddgddggks6tt tdgtt dggtdtdit ddgddggkstttD ]0} t ddgddgg| dddiksxtqxd S )	Nr   r   r   r{   r   r   r   r   )r0   r]   xreplacer   r^   r   r4   r  rj   rj   rk   test_xreplace(  s    $r  c               
   C   s&  t d} td}tdt dt  ttt  t g|tt|t  |t dd|  t| t |    t gg}|  |ttt tt  dt gdt dddtt|    t|    ggkstdt d }t|gg}|  |t|ggkst|jt	d |t|jt	dggks"td S )Nrv   r  r   r{   )ratio)
r   r   r0   r]   r^   r   r   r$   r   r   )rv   r  r   eqrj   rj   rk   test_simplify0  s     :&r  c                  C   s   t ddddddddd	d
g
ddddddddd	d
g
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st| jj| kst| j|  kstd S )Nr   r{   rz   r   r   r   r   r   r   r   )r0   r6  r   	transposer   rj   rj   rk   test_transposeA  s     
r  c                  C   s   t dtdgdddgg} | jt ddgtdgddggks<t| jt dt dgdddggks`t| j|  ksrt| j| jjkst| jt ddgt dgddggkstd S )Nr   r   r   r{   )r0   r	   r6  r   C	conjugateHr   rj   rj   rk   test_conjugateR  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ddddgg} | jtddddgt dddgt t ddgt t tdggkstd S )Nc                   S   s
   t djS rT  )r4   Drj   rj   rj   rk   rr   e  rs   z!test_conj_dirac.<locals>.<lambda>r   r   r   )rM   AttributeErrorr0   r	   r  r   r   rj   rj   rk   test_conj_diracd  s    


r  c                  C   s4   t dddgdddgdddgg} |  dks0td S )Nr   r   r   r   rG  )r0   tracer   r   rj   rj   rk   
test_tracer  s
    
r  c                  C   s*   t tddgdtdgg} | jdks&td S )Nr   rD  )r0   r]   r^   r   r   r   rj   rj   rk   
test_shapey  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sLt| ddd  | t td ddgdt td dggkst| dt td ddggkst| d}d|d< | d	 td kst| dd d
f }d|d< | d	 td kst| d}|t td dt gks$td|d< | d	 td ksBt| d d df }d|d< | d	 td ksptd S )Nr   r   c                 S   s   | | d S Nr   rj   )rrq   rj   rj   rk   rr     rs   z!test_col_row_op.<locals>.<lambda>r{   rz   c                 S   s   | t |  S rm   )r^   )r[   rq   rj   rj   rk   rr     rs   *   r   r   )r0   r]   r^   Zrow_opr   Zcol_oprowcol)r   r1c1rj   rj   rk   test_col_row_op  s2    
"

r  c                  C   sX   t dddgdddgg} | dd | d dks4t| d	 dksDt| d
 dksTtd S )Nr   r{   rz   r   r   r   r   r   r   r   r   )r0   Zrow_multr   r   rj   rj   rk   test_row_mult  s    
r  c                  C   sb   t dddgdddgdddgg} | ddd | d dks>t| d	 dksNt| d
 dks^td S )Nr   r{   rz   r   r   r   r   r   r   r   r{   r   )r0   Zrow_addr   r   rj   rj   rk   test_row_add  s    
r  c                  C   s   t d d D ]} | d}|dddd  || dddgdddgdddggksTt| dd }d|d< |ddd	d  | || dddgd
ddgdddggkstqd S )Nr{   rz   r   r   c                 S   s   | d|  S rZ  rj   r   urj   rj   rk   rr     rs   z!test_zip_row_op.<locals>.<lambda>r   r   c                 S   s   | d|  S rZ  rj   r  rj   rj   rk   rr     rs   r   )r   r4   Z
zip_row_opr   )r   r   rj   rj   rk   test_zip_row_op  s    
 r  c                  C   sj   t dddg} t dddg}t dddg}| dks6t| dksBt| dksNt| |ksZt| |ksftd S )Nr   r{   rz   rj   )r   r0   r   )r   rY   rZ   rj   rj   rk   test_issue_3950  s    r  c                  C   s  G dd d} G dd d}|  }| }t dddg}|| dksFtd||< |d dks^tt dddgd	dd
gg}|||f d
kst|d|f d
kst||df d
kstd	|||f< |d d	kstd
|d|f< |d d
kstd||df< |d dkstd S )Nc                   @   s   e Zd Zdd ZdS )ztest_issue_3981.<locals>.Index1c                 S   s   dS r  rj   selfrj   rj   rk   	__index__  s    z)test_issue_3981.<locals>.Index1.__index__Nrg   rh   ri   r  rj   rj   rj   rk   Index1  s   r  c                   @   s   e Zd Zdd ZdS )ztest_issue_3981.<locals>.Index2c                 S   s   dS rZ  rj   r  rj   rj   rk   r    s    z)test_issue_3981.<locals>.Index2.__index__Nr  rj   rj   rj   rk   Index2  s   r  r   r{   rz   r   r   r   r   r   r  )r  r  Zindex1index2r   rj   rj   rk   test_issue_3981  s$    r  c                      sn   t tddg t fddtdD s.tt fddtdD sLtt fddtdD sjtd S )Nr   r   c                 3   s&   | ]}   |  |   kV  qd S rm   evalfr}   rY   rj   rk   r     s     ztest_evalf.<locals>.<genexpr>r{   c                 3   s*   | ]"}  d |  |  d kV  qdS r{   Nr  r}   r  rj   rk   r     s     c                 3   s*   | ]"}  d |  |  d kV  qdS r  ru   r}   r  rj   rk   r     s     )r0   r   r   r   r   rj   rj   r  rk   
test_evalf  s    r  c                  C   s
  t ttgttgg} |  dks$tt ddddgdddd	gg} |  d
ksPtt ddddgddtd	gg} |  dks|tt dtdgg} |  dkstt dddgg} |  d
kstt dgtgdgg} |  dkstt dgdgdgg} |  d
kstd S )NTr   r{   rz   r   r   r   r   r   F)r0   r]   Zis_symbolicr   r  rj   rj   rk   test_is_symbolic  s    r  c                  C   s\   t dddgg} | jdkstt dgdgdgg} | jdks@ttdd} | jdksXtd S )Nr   r{   rz   TFr   )r0   Zis_upperr   r=   r  rj   rj   rk   test_is_upper   s    
r  c                  C   sD   t dddgg} | jdkstt dgdgdgg} | jdks@td S )Nr   r{   rz   FT)r0   is_lowerr   r  rj   rj   rk   test_is_lower	  s    r  c                  C   sp   t ddddddddddddddddddg} |  s8tt ddgddgg} |  rXtt g } |  sltd S )Nr   r   r{   r   r   rz   )r0   r  r   r  rj   rj   rk   test_is_nilpotent  s    ,r  c                  C   s  d\} }t | |}|d dt| | }||ks6t|j|j  krNdksTn t|j|j  krldksrn t|j|j  krdksn tt dt ddksttdtddkstt ddtdddgd ksttddtdddgd kst|d |t | |kstd S )N)rz   r   r   rz   r{   r   r   r   )r=   fillr7   r   r   r   r   r0   )rv   r   rY   rZ   rj   rj   rk   test_zeros_ones_fill  s    

  
r  c                  C   sf   t d} | t kstt dd} | jdks.t| jdks<tt dd} | jdksTt| jdksbtd S )Nr   r{   )r=   r0   r   r   r   r  rj   rj   rk   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sZt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st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 dddgt	dtdggks*t| 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std S )Nr{   r   r   rz   )r0   r]   r^   r   r   r   r   r   limitr   r   r   r   r  rj   rj   rk   test_issue_37499  s0    ,." $ 

 &r  c                  C   sD   t d} | dd dD ]&}| j|dd d| jdd	kstqd S )
Nr   r   r   )r  r  c                 S   s   | dkS rx   rj   r   rj   rj   rk   rr   M  rs   z%test_inv_iszerofunc.<locals>.<lambda>)r  
iszerofuncr!  r  )r4   Zcol_swapr   r   )r   r  rj   rj   rk   test_inv_iszerofuncI  s    
r  c                  C   s   t d\} }t| t| | t| g}t| |g}||}|||jksRt||j|ksft||j|jks|t|jt|jd  | }|	t
}|tddgd| d ggkstd S )Nrho,phir   r   r{   )r   r0   r   r   r}  r6  r   r4   r   r[  r%   )rhophiXYr   r  rj   rj   rk   test_jacobian_metricsQ  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std S )Nr  r{   r   )r   r0   r   r   r}  r   )r  r  r  r  r   rj   rj   rk   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st|j	|kstt|D ]}|d d |f |kstqqXqJd S Nr   rz   )
r0   r   r]   r^   r_   r   r}  r   r   r   )r  r  rp   rq   ZX_sliceZY_slicer   krj   rj   rk   test_issue_4564j  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 rm   r}  r0   r]   r^   r_   rj   r  rj   rk   rr   {  rs   z(test_nonvectorJacobian.<locals>.<lambda>r   c                      s
     S rm   )r}  rj   r  r  rj   rk   rr   ~  rs   c                      s     tttgttggS rm   r  rj   r  rj   rk   rr     rs   )r0   r   r]   r^   r_   rM   	TypeErrorrj   rj   r  rk   test_nonvectorJacobianx  s     r  c                  C   sP   t ddgddgg} |  }|jdks*ttdD ]}|| |d ks2tq2d S Nr   rz   r{   r   )r0   Zvecr   r   r   )r   Zm_vecrp   rj   rj   rk   test_vec  s
    r  c                  C   s6  t ddgddgg} |  }|jdks*ttdD ]}|| |d ks2tq2| jdd}|d dkshtt dttt  gtt td  dgg} | jdd}|d tt td  kstt dttt  gtt dgg} | jddd}|d tt kstttdd	  tt	d
d	  ttdd	  tt	dd	  d S )Nr   r{   rz   F)diagonalr   )r  Zcheck_symmetryc                   S   s   t ddgg S r  r0   vechrj   rj   rj   rk   rr     rs   ztest_vech.<locals>.<lambda>c                   S   s   t ddgddgg S r  r  rj   rj   rj   rk   rr     rs   c                   S   s   t ddgg S r  r  rj   rj   rj   rk   rr     rs   c                   S   s   t ddgddgg S r  r  rj   rj   rj   rk   rr     rs   )
r0   r  r   r   r   r]   r^   rM   r&   r   )r   Zm_vechrp   rj   rj   rk   	test_vech  s"    ( r  c                      s`   t dddgtdddgks tdddgg tt fdd t  ddtdddgks\td S )Nr   r{   rz   c                      s   t  S rm   )r3   rj   r   rj   rk   rr     rs   ztest_diag.<locals>.<lambda>F)strict)r3   r0   r   rM   r   rj   rj   r   rk   	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sZt| |gkslt| |gks~td S Nr   r{   rz   )r0   r]   r^   r_   get_diag_blocksr   rY   rZ   r[   rj   rj   rk   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sftt| || | ||gkstt| || | ||gkstt||| |||gkstd S r  )r0   r]   r^   r_   r3   r  r   r  rj   rj   rk   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|tt| ||}|jddt|  | | kstt| ||}|jddt|  | | kstt| | || || }|jddt|  |  | |  | |  ks2t|jdddt| jdd| jdd|jdd| jdd|jdd| jddkstd S )	Nr   r{   rz   T)try_block_diagr!  )r  r  r  )r0   r]   r^   r_   r3   r   r   )rY   rZ   r[   r   rj   rj   rk   test_inv_block  s4     (((     
 
 

 
 
r  c                   C   s   t tdd  t tdd  ttdtdks4tttdtdksLtt tdd  ttdtdksrtttdtdkstt tdd  ttdtdtddkst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 )Nrz   r   r=   rj   rj   rj   rk   rr     rs   z$test_creation_args.<locals>.<lambda>c                   S   s   t ddddS Nr   r{   rz   r   r  rj   rj   rj   rk   rr     rs   rz   c                   S   s   t dS N      @r  rj   rj   rj   rk   rr     rs   c                   S   s   t dS r  r4   rj   rj   rj   rk   rr     rs   r   c                   S   s   t dS Nr   r   rj   rj   rj   rk   rr     rs   c                   S   s
   t ddS r   r   rj   rj   rj   rk   rr     rs   c                   S   s   t ddggS r   r   rj   rj   rj   rk   rr     rs   N)	rM   r   r  r=   rn   r   r
   r4   r7   rj   rj   rj   rk   test_creation_args  s     r  c                  C   sv  t ddddddg} |  r t|  s,t| jdds<tt ddddddg} |  s\ttddd} |  stt|  stt dddddddddddg	} | tdddkstt ddtdd} |  rt|  stt d} |  stt d} |  stt dddtd dt  d ttd d ddtddg	} |  sJt| jddr\t|  jddsrtd S )	Nr{   r   r   Fr$   rz   ))r   r   r   r   ))r   r   r   )r   r   r   )	r0   is_diagonalr   is_symmetricr3   r=   r]   r^   r   r   rj   rj   rk   test_diagonal_symmetrical  s,    6r  c                     s  t ddt gdt dgg   s(tt ddddddddg   rLt  rXttt fdd tddd   \} }| t	dkst| kstt ddd	ddd	g   st  st  \} }| 
   |  |kstt dddd	d	dg   st  st  \} }| 
   |  |ksDt| t	dksVt| ksdtt ddddd	d	g   st  \} }| 
   |  |kstt ddddd	d	dd	dd
dg	   st  \} }| 
   |  |kst| D ]}| d dkstqt dddd	d	d	g   sBt  sPt  \} }| 
   |  |ksvt| t d	dgdd	ggkstt ddd	ddd	g  drttt fdd   st  \} }| 
   |  |kstt ddd	dd	d	g   r ttt fdd t dddddddddddg	   r^ttt fdd td\}}}}t dd||||g   st  std S )Nr   r{   rz   r   r0  r   c                      s      S rm   r  rj   r   rj   rk   rr     rs   z&test_diagonalization.<locals>.<lambda>r   r   r   Tc                      s
     dS )NTr  rj   r   rj   rk   rr   4  rs   c                      s      S rm   r  rj   r   rj   rk   rr   <  rs   r   r   c                      s      S rm   r  rj   r   rj   rk   rr   @  rs   a b c d)r0   r	   r  r   r  rM   r(   r3   r  r4   r   Zas_numer_denomr  r'   r   )r   r  rp   rY   rZ   r[   r\   rj   r   rk   test_diagonalization  sl    r  c                      sv   t ddgddgg   dks$td d<   dks<tt ddgddgg    d d< tt fdd d S )Nr   r   Tr   Fc                      s      S rm   r  rj   r  rj   rk   rr   S  rs   z"test_issue_15887.<locals>.<lambda>)r>   r  r   r  rM   r'   rj   rj   r  rk   test_issue_15887I  s    r  c                     sf  t ddddddddg tt fdd t ddd	d
dddddddg	 t dddddddddddg	}   \}}| |ks~t|   d kstt dddddddddddg	 t dddddddddddg	}   \}}| |kstt dddddddddddg	 t dddddddddddg	}   \}}| |ks<tt dddddddddddg	 t dddddddddddg	}   \}}| |kstt ddddddddddddddddddg t ddddddddddddddddddg}   \}}| |kstt ddddddddddddddddddg t ddddddddddddddddddg}   \}}| |ksvtt ddddddddddddddddddg   rtt ddddddddddddddddddg}   \}}| |kstt tdddtd ddgtd!ddtd"ddgg   \}}| D ]"}t	|tr>|j
dks>tq>d S )#Nrz   r{   r   r   r0  r   c                      s      S rm   )r   rj   r   rj   rk   rr   Y  rs   z"test_jordan_form.<locals>.<lambda>r   r.  r   ir   irF  r   r   r   r   r   r   r   r   r  r   z1.0n   )	precisionz2.0z3.14159265358979323846264338327z4.0)r0   rM   r(   r   r   r  r  r   valuesr   Z_prec)ZJmustr   r   termrj   r   rk   test_jordan_formV  s    
,         ,         ,,r  c                  C   s   t ddddgddddgddddgddddgg} ddt  }ddt  }t |dddgd|ddgdd|dgddd|gg}t |dddgd|ddgdd|dgddd|gg}|  \}}||ks||kstt|| |  | kstd S )Nr{   r   r   r   r   )r0   r	   r   r   r$   r   )r   pqZJmust1ZJmust2r   r   rj   rj   rk   #test_jordan_form_complex_issue_9274  s(    








r  c               	   C   s   t ddddgddddgddddgddddgg} |  \}}|t ddddgddddgddddgddddggkstt|t ddddgddddgddddgddddggkstd S )Nr   r   )r0   r   r   r   rj   rj   rk   test_issue_10220  s"    









r  c               
   C   s   t ddddgddddgddddgddddg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ddddggkst|t t dddgdt ddgddtdgdddtggkstd S )Nr   r   r   r   r{   )r0   r   r   r	   r   r   )r   r   r   rj   rj   rk   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stt|tksttddgddgg}| |t  krttd t d ksn ttddgtdgg}|t}|jtksLt|	 
|jttd dt  ksttd S )	Nz
UA K_i K_wr{   zZZ(K_i,K_w,UA)r   r   rz   r   r   )r   r0   r   r]   r   r   r|   r   genZas_exprr   )ZUAZK_iZK_wr   r   r  rj   rj   rk   test_Matrix_berkowitz_charpoly  s(    *$
0 8
r  c                  C   s   t d} td| }| tt| ggks0ttd| }| tt| t| t| d gdt| t| gddt| ggkstd S )Nlamdar   rz   r{   r   )r   r0   jordan_blockZ_eval_matrix_exp_jblockr   r   )lr   rj   rj   rk   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\tt| |ksltt ddgddgg} |  t tdgdtggkstt| t tdgdtggkst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td S )	Nrz   r   r   r   r   r   r   r   )r0   r   r   r   r   r   )r   Zm_exprj   rj   rk   test_exp  s    8  r   c               
      s   t d} td|    tt| ggks0t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sttdddgdddgdddgg tt fdd	 d S )
Nr  r   r   r   r{   rz   r   c                      s      S rm   )r   rj   r   rj   rk   rr      rs   ztest_log.<locals>.<lambda>)r   r0   r  Z_eval_matrix_log_jblockr   r   rM   r'   )r  rj   r   rk   test_log
  s(    *
r  c                  C   sX   t ttfdf} | tst| tr,t| ts:t| td} | trTtd S )NrD  r{   )r0   r]   r^   hasr   r_   r   r   r   rj   rj   rk   test_has#  s    r  c                  C   sR   t d} tdd| t| d t| d  tjg}t|\}}}}|tjksNtd S )Nr]   rz   r   r{   )r   r0   r   r   r   r   r+   r   r]   columnZpivot_offsetZ	pivot_valZpivot_assumed_nonzeroZ
simplifiedrj   rj   rk   :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sjtd S )Nr]   rz   r   r{   Zsimpfunc)r   r0   r   r   r+   r,   r   r  rj   rj   rk   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero29  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sjt|d d dks~t|d d d|  kst|d d dkst|d d dkstd S )Nr]   rz   r   r{   r  r   )r   r0   r   r   r+   r,   lenr   r  rj   rj   rk   +test_find_reasonable_pivot_naive_simplifiesH  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d,d,d,ggtd-d.d/gd.d/d0gd/d0d1gg t t fd2d td-d.d/gd.d/d0gd/d0d1gg t t fd3d d S )4Nc                   S   s   t ddgdggS r   r   rj   rj   rj   rk   rr   [  rs   ztest_errors.<locals>.<lambda>c                   S   s   t ddggd S )Nr   r{   )g333333?r   r   rj   rj   rj   rk   rr   \  rs   c                   S   s   t ddggd S )Nr   r{   )r   g@r   rj   rj   rj   rk   rr   ]  rs   c                   S   s   t ddddS )Nrz   r   T)r[   rd  )r8   rj   rj   rj   rk   rr   ^  rs   c                   S   s   t ddgddS )Nr   r{   r   r   )r0   rW  rj   rj   rj   rk   rr   _  rs   c                   S   s(   t ddgddggddgt ddgS Nr   r{   rz   r   r   )r0   Zcopyin_matrixrj   rj   rj   rk   rr   a  rs   c                   S   s"   t ddgddggddgt S r  )r0   Zcopyin_listsetrj   rj   rj   rk   rr   b  s   c                   S   s   t dddgdddgg S Nr   r{   rz   r   r0   r   rj   rj   rj   rk   rr   d  rs   c                   S   s&   t ddddgt ddgddggS r  )r0   row_joinrj   rj   rj   rk   rr   f  rs   c                   S   s"   t ddgt ddgddggS r  )r0   col_joinrj   rj   rj   rk   rr   h  rs   c                   S   s"   t dgdt ddgddggS r  )r0   
row_insertrj   rj   rj   rk   rr   i  s   c                   S   s"   t dgdt ddgddggS r  )r0   
col_insertrj   rj   rj   rk   rr   k  s   c                   S   s   t ddg S r   )r0   r  rj   rj   rj   rk   rr   m  rs   c                   S   s   t dgdS r  )r0   r[  rj   rj   rj   rk   rr   n  rs   c                   S   s   t ddgddggddS Nr   r{   rz   r   r   )r0   minorrj   rj   rj   rk   rr   o  rs   c                   S   s   t ddgddggddS r  )r0   Zminor_submatrixrj   rj   rj   rk   rr   p  rs   c                   S   s   t dddgdS r  r0   crossrj   rj   rj   rk   rr   q  rs   c                   S   s   t dddgdS r  r0   dotrj   rj   rj   rk   rr   r  rs   c                   S   s   t dddgt ddgS r  r  rj   rj   rj   rk   rr   s  rs   c                   S   s   t ddgg S r   r  rj   rj   rj   rk   rr   t  rs   c                   S   s   t ddgdS )Nr   r{   rY   r  rj   rj   rj   rk   rr   u  rs   c                   S   s   t ddgdddgS r  r  rj   rj   rj   rk   rr   v  rs   c                   S   s   t dddg S r  )r0   r   rj   rj   rj   rk   rr   w  rs   c                   S   s   t ddgddgg S r  )r0   
normalizedrj   rj   rj   rk   rr   x  rs   c                   S   s   t ddgjddS )Nr   r{   znot a methodr  r  rj   rj   rj   rk   rr   y  rs   c                   S   s   t ddg S r   r0   Z
inverse_GErj   rj   rj   rk   rr   z  rs   c                   S   s   t ddgddgg S r   r  rj   rj   rj   rk   rr   {  rs   c                   S   s   t ddg S r   r0   Zinverse_ADJrj   rj   rj   rk   rr   |  rs   c                   S   s   t ddgddgg S r   r  rj   rj   rj   rk   rr   }  rs   c                   S   s   t ddg S r   )r0   Z
inverse_LUrj   rj   rj   rk   rr   ~  rs   c                   S   s   t ddg S r   )r0   r  rj   rj   rj   rk   rr     rs   c                   S   s   t ddg S r   r0   r   rj   rj   rj   rk   rr     rs   c                   S   s   t ddgddggjddS )Nr   r{   rz   r   zNot a real methodr  r  rj   rj   rj   rk   rr     rs   c                   S   s8   t ddddgddddgd	d
ddgddddggjddS )Nr   r{   rz   r   r   r   r   r   r   r   rE  r   rF  rG  r   rQ  zNot functionr  r  rj   rj   rj   rk   rr     s
   
 
c                   S   s8   t ddddgddddgd	d
ddgddddggjddS )Nr   r{   rz   r   r   r   r   r   r   r   rE  r   rF  rG  r   rQ  Fr  r  rj   rj   rj   rk   rr     s
   
 
c                   S   s*   t tddgddggtddgddggS r  r5   r0   rj   rj   rj   rk   rr     rs   c                   S   s   t tddgddggg S r  r  rj   rj   rj   rk   rr     rs   c                   S   s   t tdd dS )Nr]   r{   rY   )r5   r   rj   rj   rj   rk   rr     rs   c                   S   s   t dd S )Nrz   )r   r{   r  rj   rj   rj   rk   rr     rs   c                   S   s   t dd S )Nrz   )r{   r   r  rj   rj   rj   rk   rr     rs   rR  c                      s
     dS )Nzmethod=LU_decomposition())r   rj   r   rj   rk   rr     rs   r   r   r{   rz   r   r   c                      s     dS )Ng@)r  rj   r   Vrj   rk   rr     rs   c                      s     dS )Ng)r  rj   r  rj   rk   rr     rs   )rM   r   r4  r&   r  r(   r0   rj   rj   r  rk   test_errorsZ  s|       r!  c                   C   s   t t dkstt tddggt tdgdgg  krDdksJn tt tdddd t tdddd   kr~dksn tt tdddgddd	ggd
ksttdgtdggkstt rtt tg kstd S )Nr   r   r{   c                 S   s   dS rx   rj   ro   rj   rj   rk   rr     rs   ztest_len.<locals>.<lambda>c                 S   s   dS rx   rj   ro   rj   rj   rk   rr     rs   rz   r   r   r   )r	  r0   r   rj   rj   rj   rk   test_len  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szt| 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std S )Nr   r   r{   r   r   rz   )r0   r]   r^   r   r   r   rj   rj   rk   test_integrate  s    $FFr#  c                  C   sX   t ddttt ftddfddtd d ff} | tdt dtddfdfksTtd S )	Nr   r   r{   r   r   r   )r   r   r   )r   r   r   )r0   r   r]   r^   r  r   r   rj   rj   rk   
test_limit  s    0r$  c                  C   s  t ddtftddfddtd d ff} t| tt| s@t| tt dddddt ffksft| tt d	ks|tt| tt dddddt ffkstt| tt d	kst|  }t|tt|st|ttdddddt ffkst|ttd	kstt|ttdddddt ffks>tt|ttd	ksVt| jtd
dt	| td
dksxtt| td
dt	| td
dkstd S )Nr   r   r{   r   r   r   r   r   r   r   r   r   )r&  r   r   r   r&  Fr1  )
r>   r]   r^   r   r   r|   r   r7  r?   rV   )r   A_immrj   rj   rk   	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sft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st|  }||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t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sht| t	t ddgddggkstt
t	tg}| |tddddkst| | 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t|t	tgg}|jdks,t|tdgdggdgdgggksRttd}|ttt  tttggt t t tgkst 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 ttttt }|ttggttttt tttt gksjt|tttffttttt tttt gkst|tttffttt tt tttt gkst|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sHt ttt tttffdd ks|t ttt tttffdd kst tttggtttfft fd	d
tttfD kstttttgg}t|t
st|tddggks*ttd tttgg}t|t
sRt|tdtd  dggksrtd S )Nr   r   r{   )r{   r{   r   r  rz   r   r   r   )r{   r   r   c                    s&   g | ]  fd dt ttfD qS )c                    s   g | ]}  | qS rj   )r   r}   )fxyzrq   rj   rk   r     s     z2test_diff_by_matrix.<locals>.<listcomp>.<listcomp>)r]   r^   r_   )r~   r+  )rq   rk   r     s     z'test_diff_by_matrix.<locals>.<listcomp>)r>   r]   r^   r_   r`   r   rU   r   r7  rY   r?   rZ   r=   r   r   r   r   r   r0   r   )r   r(  BZdBr  exprresrj   r,  rk   test_diff_by_matrix  sF    RRTT$ T&8   :<>d44>r0  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sdtd S )Nr   r   r{   r   r   c                      s    j S rm   )Znonexistantattributerj   r   rj   rk   rr     rs   ztest_getattr.<locals>.<lambda>r   r%  r&  r   )r0   r]   r^   rM   r  getattrr   rj   rj   r   rk   test_getattr  s    (r2  c                  C   s   t dddgdddgdddgg} | js*t| j} | js:td| d< | jdksPtt dddgdddgdddgg} | jrzttdd} | jstd S )	Nrz   r   r   r{   r   r   )r   r   F)r0   Zis_upper_hessenbergr   r6  Zis_lower_hessenbergr=   r   rj   rj   rk   test_hessenberg  s     

 

r3  c                  C   s6  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sttd} | jd
d}|tddgddtd t ggkst||j | ksttd} |  }||j | kst|j	st|tdddgdddgdddggks&t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st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ttd} | jd
d}|tddgddtd t ggksXt||j | kslttd} |  }||j | kst|j	st|tdddgdddgdddggkst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s2td S )Nc                   S   s   t d S Nr   r0   choleskyrj   rj   rj   rk   rr     rs   ztest_cholesky.<locals>.<lambda>c                   S   s   t d S Nr   )rz   r   r5  rj   rj   rj   rk   rr     rs   c                   S   s   t dt dfdf S Nr   r   r   )r0   r	   r6  rj   rj   rj   rk   rr     rs   c                   S   s   t d S N)r   r   )r   r   r5  rj   rj   rj   rk   rr     rs   c                   S   s   t djddS Nr8  F	hermitianr5  rj   rj   rj   rk   rr     rs   r   r   r   Fr=  r   r;  r{   r   ))   r   r   )r   r   r   )r   r   rE  rz   r   r   r   rE  )r{   r   r   c                   S   s   t d S r4  r1   r6  rj   rj   rj   rk   rr   $  rs   c                   S   s   t d S r7  r@  rj   rj   rj   rk   rr   %  rs   c                   S   s   t dt dfdf S r9  )r1   r	   r6  rj   rj   rj   rk   rr   &  rs   c                   S   s   t d S r:  r@  rj   rj   rj   rk   rr   '  rs   c                   S   s   t djddS r<  r@  rj   rj   rj   rk   rr   (  rs   )rM   r(   r   r0   r	   r6  r   r   r6  r  r   r1   )r   r~  rj   rj   rk   test_cholesky  sP     (
*@0 **@rA  c                  C   s  t ddd} tt| t| g}t|ddks6t|dtt| d t| d  tddkshttdtddgg}| td	td
d t	j
kst|tt|kst|t t|ksttddgddgg}|ddkst|ddkst|ddksttddtdd  krFdksLn t|tdks`ttdttg| t	j
t gg}|dttdddttd   td  | d  ksttdddgddtddgg}|dttddtdd  kst|dt	jkst|dtdd ks4t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kst|D ]B}	|D ]6}
|	||
| |	|
 | }|dkstq̐q||||fD ]8}t|| |t|||  }|dkstqqtdddt  dg}tt	j
dt dg}tdddg}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dddg|t	jkst|dkrj|D ]L}	|D ]@}
|	||
| |	|
 | }t|dkt	jks$tq$q|ddddt	jt	jfkr|D ]8}	t||	 |t||	|  }|dkstqqtdddddddddd
dg	}|ddkstd S )Nr]   Tr]  r{   r   r   r   rz   r?  r   r   r   r   Z	frobeniusfro%   r   rF  i  r   iI3 r   alpha)rB  r{   r   g      Y@r   )r   r0   r   r   r%   normr   r   r   r   r   r   maxri  r4   r^   r   r   r   r>  r	   r=   r$   r
   InfinityNegativeInfinitytrue)r]   r   r   r-  r  r  r~  rD  orderr  r  Zdifr   rY   rZ   r[   r\   erj   rj   rk   test_matrix_norm8  s    2"2,
*
 
 rL  c                     s   t dddtd} d| d< tdd| d< |  d	ks:t| d
< |  tdtttddt kspt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 sttg  dkstd S )Nr]   Tr]  rz   r   r   r   r{   r{   r   r   c                 3   s(   | ] }t d  | V  qdS )      ?N)r   Z
epsilon_eqr   r  )r~   valZMcr]   rj   rk   r     s     z(test_condition_number.<locals>.<genexpr>r   r{   r   r   r   )r   r4   r   Zcondition_numberr   r   r   r   r0   r   r   r   r   r   r   )r   r   rj   rP  rk   test_condition_number  s    .&*rQ  c                  C   s   t d} t d}| | d d d d f ks,t| | d d d d f krHt| |krTt| |ks`t| dkslt| dkrxttd}t d}||kst||krtd S )N))r   r{   rz   )r   r   r   )r   r   r   ))r   r   r   )r   r   r   )rz   r{   r   r   )r'  r*  r%  )r0   r   r1   )r   r-  r  r  rj   rj   rk   test_equality  s    rR  c                   C   sJ   t dtdddggtdddgdddgdddgdddggksFtd S )Nrz   r   r   r   )r4   r  r0   r   rj   rj   rj   rk   test_col_join  s    
rS  c                  C   s`   t dddgg} tddD ]@}dddg}||d ttd|| d |kstqd S )Nr   r   r   r   r   rz   )	r0   r   insertrI   r4   r  r  r5  r   )Zr4rp   r  rj   rj   rk   test_row_insert  s
    
rU  c                  C   s^   t dddg} tddD ]@}dddg}||d ttd|| d |kstqd S )Nr   r   r   r   rz   )	r0   r   rT  rI   r=   r  r  r5  r   )Zc4rp   r  rj   rj   rk   test_col_insert  s
    
rV  c                  C   s   t ddg t tddtddgks,tt dddg t dddgksPtt dddg} | jdd dt dddgkstd S )	Nrz   r   r   r   g0.++c                 S   s   | j dddjS )Nr   T)rv   Zchop)r  is_zeror   rj   rj   rk   rr     rs   z!test_normalized.<locals>.<lambda>r  )r0   r  r   r   r   rj   rj   rk   test_normalized  s    $rX  c                   C   s,   t dd dkstt dd dks(td S )Nc                   S   s   t d S rT  r4   Zprint_nonzerorj   rj   rj   rk   rr     rs   z$test_print_nonzero.<locals>.<lambda>z[X  ]
[ X ]
[  X]
c                   S   s   t ddS )Nrz   .rY  rj   rj   rj   rk   rr     rs   z[.  ]
[ . ]
[  .]
)rJ   r   rj   rj   rj   rk   test_print_nonzero  s    

r[  c                  C   s   t dtdkstt dtdks,ttddt dddgd ksLtt ddgddgg} t ddgddgg}tD ]x}|d}| |kst| td|dkstt||kst|d}||kst|td|dkstt||ksxtqxd S )Nrz   r   r   r   r   r{   r  )r0   r4   r   r=   r7   r   r|   )rp   r_   r   r   rj   rj   rk   test_zeros_eye  s     

r\  c                  C   s
  t  jstt ddgddggjs&ttddjs6ttdjrDtt tdgddggjd ksbtttdgddggjd kstttdgddggjd kstttdgddggjd kstt tdgddggjdkstt	ddd} t | dgddggjdkstd S )	Nr   rz   r   r   FrY   T)Znonzero)
r0   Zis_zero_matrixr   r=   r4   r]   r1   r.   r/   r   r  rj   rj   rk   test_is_zero  s    r]  c            
      C   s  t d } t| }t|  }t| }t|  }t| }t|  }|| td tdksZt|| td tdksvt|| td tdkst| ddt|   kst| ddt|   kst| ddt|   ksttdtdksttdtdksttdtdks&tt	dddgt d }t	dddgt d }t	dddgt d }	tt  d |
 ksttt  d |
 ksttt  d |	
 ksttt 
 d |
 ksttt 
 d |
 ksttt 
 d |	
 kstd S )Nrz   r   r{   r   )r   r;   r:   r9   r4   r   r  r   rX   Zfrom_axis_angleZto_rotation_matrixrB   rC   rD   )
thetaZr3_plusZr3_minusZr2_plusZr2_minusZr1_plusZr1_minusq1q2Zq3rj   rj   rk   test_rotation_matrices	  s2    


ra  c                   C   sj   t tdd dkstttdtdks0tttdd  t tddksRtttddksftd S )	NZvectorr   z	vector[4]r\   c                   S   s   t dd S )Nr\   r   r)   rj   rj   rj   rk   rr   .	  rs   z%test_DeferredVector.<locals>.<lambda>testzDeferredVector('test'))strr*   r   r   rM   r4  reprrj   rj   rj   rk   test_DeferredVector+	  s
    re  c                   C   s   t tdrtd S )Nr  )rK   r*   r   rj   rj   rj   rk    test_DeferredVector_not_iterable2	  s    rf  c                   C   s   t tdd  d S )Nc                   S   s   t tdS )Nr   )r0   r*   rj   rj   rj   rk   rr   6	  rs   z,test_DeferredVector_Matrix.<locals>.<lambda>)rM   r  rj   rj   rj   rk   test_DeferredVector_Matrix5	  s    rg  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sdtt|j|jgtddddgtdd| dd | dd ggkst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tttdg}t|tdgggks8td S )Nr   r{   rz   r   r   Tr   )r   r0   r-   r   r6  r   r"   )r   rI  rJ  r~  rj   rj   rk   test_GramSchmidt8	  s    
.. rh  c                   C   s<   t ddddgddkstt ddddgddddks8td S )Nr   r{   rz   r   r   F)zero)r2   r   rj   rj   rj   rk   test_casoratianI	  s    rj  c                   C   s^   t  tdd jdksttddtdd tddks<ttddtdd t  ksZtd S )Nr   rz   )r   rz   )r0   r=   r   r   rj   rj   rj   rk   test_zero_dimension_multiplyN	  s    "rk  c                      s   t ddtd  dd d f t ddggks2t dd d f t ddggksTt d d df t ddggjksxt d d df t ddggjksttt fdd tt fdd d S )	Nr{   r   r   rz   r   c                      s    dd d f S rZ  rj   rj   r   rj   rk   rr   Z	  rs   z'test_slice_issue_2884.<locals>.<lambda>c                      s    d S )NrM  rj   rj   r   rj   rk   rr   [	  rs   )r0   r   r   r6  rM   r4  rj   rj   r   rk   test_slice_issue_2884T	  s    ""$$rl  c                   C   sJ   t ddd d df jdks tt dddd d f tddg ksFtd S )Nr   rz   r   r   r   )r=   r   r   r0   rj   rj   rj   rk   test_slice_issue_3401^	  s     rm  c                  C   s  t dd} d| d< | d d df tdddgks4t| d dksDt| dd dgksZtd| d< | d dksrt| ddd f tddggksttddgg| ddd f< | dd d f tdddggkstdd	gg| ddd f< | dd d f tddd	ggkstd
| d< | d d d df td
ddgks>tdddg| d< | d d df tdddgkspttdddg| d< | d d df tdddgksttdddg| d< | d d df tdddgkstd S )Nrz   r   r   r   r  r   r   r   +      r   )r=   r0   r   r1   )ry  rj   rj   rk   test_copyinc	  s(    
""$&($$rp  c                      s   t ddgddgg t ddgddggdfks4tttdd  t dddgtddgdtdgg t  d  jks|t  d tdkst jt	d	d tdksttt fd
d tt fdd tt fdd d S )Nr   r{   r   )r   c                   S   s   t ddgddgg S r   r  rj   rj   rj   rk   rr   ~	  rs   z'test_invertible_check.<locals>.<lambda>r   rz   r  c                      s    j ddS )Nr!  r  r   rj   r   rj   rk   rr   	  rs   c                      s    j ddS )Nr  r  rq  rj   r   rj   rk   rr   	  rs   c                      s    j ddS )Nr  r  rq  rj   r   rj   rk   rr   	  rs   )
r0   r  r   rM   r   r]   r	  r   r4   r#   rj   rj   r   rk   test_invertible_checkz	  s    4rr  c                  C   sD   t d\} }| | }|| tdddgtdddg| ks@td S )Nzx, yrz   r   )r   r   r0   r   )r]   r^   rK  rj   rj   rk   test_issue_3959	  s    rs  c                   C   s$   t tddgddggdks td S )Nr   r{   rz   r   zMatrix([[1, 2], [3, 4]]))rc  r0   r   rj   rj   rj   rk   test_issue_5964	  s    rt  c                  C   s<   t d\} }tt| d| g|d | d ggdks8td S )Nx yr{   rz   z'Matrix([
[   x,   2*y],
[y**2, x + 3]]))r   r!   r0   r   )r]   r^   rj   rj   rk   test_issue_7604	  s    "rv  c                	   C   s   t djstt d js ttdjr.ttdjr<ttdddggjrRttddddddjslttddtdjrttdddddjrttddddddddjrtd S )	Nrz   r   r   )r   r   rM  r{   r   )r   r   )r   r   rM  r   r  )	r4   Zis_Identityr   r7  r=   r7   r0   r1   r   rj   rj   rj   rk   test_is_Identity	  s    rw  c                   C   s,  t ddt dddkstt dddddgdks<ttdddgtdddgdksbttdddt gttddt gdt ksttdddt gjttddt gdddt ksttdddt gjttddt gddd	t ksttdddt gjttddt gdd
dd	t ks<ttdddt gjtddt dgdddddt  kszttdddt gjtddt dgdddddt  kstttdt gjttdt gddddkstttdt gjttdt gdddkstttdd  d S )Nr   rz   r{   rG  r   Fr=  TrF  Zphysicsr>  conjugate_conventionr   r   r   rightr   left)ry  c                   S   s    t ddgjt ddgdddS )Nr   r{   rz   r   Trb  rx  r  rj   rj   rj   rk   rr   	  rs   ztest_dot.<locals>.<lambda>)r7   r  r   r0   r	   rM   r   rj   rj   rj   rk   test_dot	  s    &268:>>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}| |sttd tdst|  | std S )NzB_x B_y B_z E_x E_y E_zTr]  r   rz   )r   r0   Zdualequalsr   r4   r=   )ZB_xZB_yZB_zZE_xZE_yZE_zFZFdrj   rj   rk   	test_dual	  s&     
r  c                  C   s   t ddg dkstt dddtd dt  d ttd d  dtt t t t dg	} |  dkslt| jddd kst| jdd	 dd kst| d
  | d
< |  d kst| d
  | d
< |  } | jdddkstd| d< |  dkstd S )Nr   r{   Frz   r   Tr  c                 S   s   | S rm   rj   r   rj   rj   rk   rr   	  rs   z%test_anti_symmetric.<locals>.<lambda>r   r   )r0   is_anti_symmetricr   r]   r^   r   r   rj   rj   rk   test_anti_symmetric	  s    Dr  c                  C   s   t d} | jdd\}}||j |j|   kr>t|jksDn t| jddd\}}||j |j|   kr|t|jksn t|| |  | kstd S )N)r   r   T)	normalize)r  sort)r0   r  r6  r4   r   r   r   )r   r   rT   rj   rj   rk   #test_normalize_sort_diogonalization	  s    ,,r  c                   C   s   t tdd  d S )Nc                   S   s   t dddgt ddg gS r  r   rj   rj   rj   rk   rr   	  rs   z!test_issue_5321.<locals>.<lambda>)rM   r   rj   rj   rj   rk   test_issue_5321	  s    r  c                  C   s   t tddtd t ddddgddddggks8tt tddtd t ddgddgddgddggksttt} | | td| dtd t ddddgddddggkstd S )Nr{   r   r   )r0   hstackr4   r   vstackr1   r  rj   rj   rk   test_issue_5320	  s    

 

r  c                  C   sV   t dgg} t| }t || t ddggks2tt || t dgdggksRtd S r  )r0   r   r  r   r  )r   ZAImrj   rj   rk   test_issue_11944 
  s    r  c                     s   dddg} dddg}t dddg}|j} fdd}tD ]\  | } |}|||| |||j| ||j|j| ||j|| q8ttd	d
  d S )Nr   r{   rz   r   r   r   c                    s    || kst t|  kst d S rm   )r   r|   )r   r  r  rj   rk   rb  
  s    ztest_cross.<locals>.testc                   S   s"   t ddddgt ddddgS r   r  rj   rj   rj   rk   rr   
  s    ztest_cross.<locals>.<lambda>)r0   r6  r   r  rM   r&   )rY   rZ   r  r  rb  r   r-  rj   r  rk   
test_cross
  s    

r  c                  C   s^   t tttg} t tttg}|  | | |ks6t	|  
 sFt	|   | ksZt	d S rm   )r0   r]   r^   r_   rY   rZ   r[   Zhatr  r   r  Zvee)Zv1Zv2rj   rj   rk   test_hat_vee
  s
    r  c                  C   sr   t dd  D ]:} | d| dh}t|dkrB| | dkstqt d d D ]} t| dtrTtqTd S )Nr   r   r{   )r   r4   r	  popr   r   r   )r   ry  rj   rj   rk   	test_hash 
  s
    $r  c                      s   t d  tt fdd d S )Nr   c                      s   t  dS r  )hashr4   rj   r  rj   rk   rr   .
  rs   z!test_issue_3979.<locals>.<lambda>)r   rM   r  rj   rj   r  rk   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*tq*d S Nr   r   )r	   r0   r   Zadjointr   )r9  r  r   rj   rj   rk   test_adjoint1
  s    r  c                   C   s8   t tttd ttd  ggtdggks4td S )Nr{   r   )r$   r.   r   r]   r   r   rj   rj   rj   rk   test_simplify_immutable7
  s    "
r  c                     sT   t dtd\ tddfdd} tdd fdd}| }|| ksPtd S )NzF, Gr  r{   c                    s    | | S rm   rj   ro   )Grj   rk   rr   =
  rs   ztest_replace.<locals>.<lambda>c                    s    | | S rm   rj   ro   )r~  rj   rk   rr   >
  rs   )r   r   r0   replacer   )Kr   Nrj   )r~  r  rk   test_replace;
  s
    r  c                  C   sT   t ddgtddt  gg} |  tjtdtjthks<t| tthksPtd S r   )r0   r]   atomsr   r=  ZNegativeOner   r   r   rj   rj   rk   
test_atomsC
  s     r  c            	         s  t ttgttgg} t| jddt|  ks4tt ddgddgddggt d	d
dgdddggt ttgg}|D ]d}|jdd}|| }|| }t|| |kstt|| |kst|j	|kst|j	|ksttqt|D ]n}t|jdd}|| }|| }t|| |kstt|| |ks.t|j	|ks>t|j	|kstqddl
m  | jdd}|  }tdtdtdtdi}t fddt||||D std S )NZRDr  rF  h   i  rz   r   r   r   r   r   rE  ro     EDr   compi_ib,  i  ij  c                 3   s$   | ]\}} |  |  V  qd S rm   ru   )r~   rp   rq   r  rj   rk   r   p
  s   ztest_pinv.<locals>.<genexpr>)r0   rY   rZ   r[   r\   r$   pinvr   r   r  sympy.core.numbersr  r   zipr   )	A1Asr   A_pinvAApApAr  wZrepsrj   r  rk   	test_pinvI
  s:     
r  c                  C   s   t ddddddgddd	d	d
dgddddddgddddddgddddddgddddddggg} | D ]F}|jdd}|| }|| }|j|kstdd }||j|sbtqbd S )N=   r   7   r0  rr  r   >   `   U   rQ  E   8   ro  r   6   r   [   )   r   rg  r   Z   r  r  c                 S   s<   |  t}dd |D }| | | }tdd |D S )Nc                 S   s   i | ]}||  qS rj   r  )r~   r  rj   rj   rk   
<dictcomp>
  s      zYtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose.<locals>.<dictcomp>c                 s   s   | ]}t |d k V  qdS )g|=Nr   r~   rK  rj   rj   rk   r   
  s     zXtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose.<locals>.<genexpr>)r  r    r  r  r   )M1r:  ZrootofsZrootofs_approxZdiff_approxrj   rj   rk   allclose
  s    
zEtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose)r0   r  r  r   )r  r   r  r  r  r  rj   rj   rk   3test_pinv_rank_deficient_when_diagonalization_failsv
  s     	r  c                   C   sL   t ddt dd tddg ks$tt ddt dd tddg ksHtd S r  )r7   r0   r   rj   rj   rj   rk   test_issue_7201
  s    $r  c                  C   s2   t tttfD ] } | tgdggjthkstqd S rx   )r.   r/   r0   r1   r]   Zfree_symbolsr   r   rj   rj   rk   test_free_symbols
  s    r  c                      s  zddl m  W n tk
r,   td Y nX t dddgtdddgksRtt dddggtdddggksztt dddgddd	ggtdddgddd	ggkstt tttgttttgkstt	t
 fd
d t ddg ddggtddgddggkstt ddgddggtddgddggksPtt g  g gtddg   krtddg ksn tdS )zSee issue 7465.r   array?NumPy must be available to test creating matrices from ndarraysr   r{   rz   r   r   r   c                      s(   t  ddgddggddgddgggS )	Nr   r{   rz   r   r   r   r   r   r   rj   r  rj   rk   rr   
  rs   z#test_from_ndarray.<locals>.<lambda>N)numpyr  ImportErrorrP   r0   r   r]   r^   r_   rM   NotImplementedErrorrj   rj   r  rk   test_from_ndarray
  s     $($
62r  c               	   C   s   ddl m}  zddlm}m} W n tk
r<   td Y nX | |ddgddgg}|d dksftt|ddddgks~tt	t
 | |ddgddgg}W 5 Q R X |d dkstt|ddddgkstd S )	Nr   
_matrixify)r  matrixzPNumPy must be available to test indexing matrixified NumPy ndarrays and matricesr   r{   rz   r   )sympy.matrices.commonr  r  r  r  r  rP   r   r   rL   PendingDeprecationWarning)r  r  r  r   rj   rj   rk   test_17522_numpy
  s    
"r  c                  C   s~   ddl m}  zddlm} W n tk
r8   td Y nX | |ddgddgg}|d d	ksbtt|d
ddd	gksztd S )Nr   r  )r  zEmpmath must be available to test indexing matrixified mpmath matricesr   r{   rz   r         @rN  g       @r  )r  r  Zmpmathr  r  rP   r   r   )r  r  r   rj   rj   rk   test_17522_mpmath
  s    r  c                  C   s~   ddl m}  zddlm} W n tk
r8   td Y nX | |ddgddgg}|d dksbtt|ddddgksztd S )	Nr   r  )
csr_matrixzJSciPy must be available to test indexing matrixified SciPy sparse matricesr   r{   rz   r   )r  r  Zscipy.sparser  r  rP   r   r   )r  r  r   rj   rj   rk   test_17522_scipy
  s    r  c                  C   sr   t dtgt dgg} | js tdt | d< | jdks:tt| d< | jd ksPt| d t | d< | jdksntd S )Nr   r{   r   Fr   r   )r0   r	   Zis_hermitianr   r]   r  rj   rj   rk   test_hermitian
  s    
r  c                  C   sJ   t tttddgg} | d dt ks*t|  t dt ggksFtd S )NFr1  r   r{   )r0   r   r]   r   r   r  rj   rj   rk   	test_doit
  s    r  c                     sF  t dddgdddgdddgg} | d | t dddgdddggksJtt dddgdddgdddgg}|d |t dddgdddggkstt dddgdddgd	d
dgg}|d |t dddgdddggkstt dddgdddgdddgg tt fdd t dddgdddgdddggttfdd t dddgdddgdddgg} | d | t ddgddgddggkstt dddgdddgdddgg}|d |t ddgddgddggkstt dddgdddgdddgg tt fdd t dddgdddgdddggttfdd d S )Nr   r{   rz   r   r   r   r   r   r   r   rE  r   c                      s
     dS r   row_delrj   r   rj   rk   rr   
  rs   z+test_issue_9457_9467_9876.<locals>.<lambda>c                      s
     dS Nr   r  rj   rS   rj   rk   rr   
  rs   c                      s
     dS r   col_delrj   r  rj   rk   rr     rs   c                      s
     dS r  r  rj   rS   rj   rk   rr     rs   )r0   r  r   rM   r4  r  )r   r  Orj   )r   rT   rk   test_issue_9457_9467_9876
  s.     
  
  
    
$ 
$  r  c                  C   s   t ddd\} }t d\}}td}tdd| ||tg}||  | | | | ksTt|| | || | kspt| | ||  kst|| || kst||  | t||  dgd||  ggkstd S )Nru  F)Zcommutativeza br{   r   )r   r4   r0   r_   r   )r]   r^   rY   rZ   r   r  rj   rj   rk   test_issue_9422  s    r  c            	      C   s   t g } ddgt dddgf}ddg|d jf}ddgt dd	gdd
ggf}|||fD ]R\}}|D ]D}t| |}d|kr||n|d|}||krt|t|ksbtqbqVd S )Nr  r  r   r   rz   r  r  r   r{   r   joinr  )r0   r6  r1  idr   )	r   rY   rZ   r[   Zopsr   opr  newrj   rj   rk   test_issue_10770  s    
r  c                  C   sl  t dddgdddgddd	gg} | d
ddgdddgt ddgddgddggksVt| d
ddgdddgt dgdgdggkst| dddgd
ddgt dddggkst| dddgd
ddgt dddgddd	ggkst| d
ddgdddgt dd
g kst| dddgd
ddgt d
dg ks:t| dddgdddgt dgdggkshtd S )Nr   r{   rz   r   r   r   r   r   r   r   TF)r0   r   r   r   rj   rj   rk   test_issue_10658  s     0,**r  c                  C   s  t ddtd  dgdtd d d dtd d gg} |  dksLtt ddtd t  dgdddtd t  gg} t|  d	 t ddddtd t   gd	d	gg tddksttd
\}}}}}}}}}	}
}}t |||| || d	g|||| || d	g|||| || dg|||| || dg|	|
d|	 | |	|  d|
 | |
|  d	gg} |  dks|td S )Nr   r   r{   r   rz   r  r   r   r   /a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1)	r0   r   r)  r   r	   r$   r  r=   r   )r   axaybxbycxcydxdyexeyt0t1rj   rj   rk   !test_opportunistic_simplification,  s    <4F r  c                  C   s   t dddgdddgg} |  d t ddd	gdddgg  d
k sHtt 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g}t dddgdddgdddgg}| |  d
k st| |  d
k std S )Ng~jth?gRM@g(\M@gDl)@gQgp=
cG@r   rN  r   V瞯<gq7K<r   g      r   r   r  g        g       @g      )r0   r  rE  r   r   )mmZm_mixedZm_floatZm_invrj   rj   rk   test_partial_pivoting<  s(    



r  c                  C   s   t ddddgddddgddddgg} | jdd	 d
d }t ddddgddddgddddgg}|| }| dk sxt|d dkst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. g?ggɿr   ggٿg333333?c                 S   s   t | dk S )Ng [n<r  r   rj   rj   rk   rr   [  rs   z*test_iszero_substitution.<locals>.<lambda>r  rN  g4iҤIӿglٲer  rM  N)r0   r  rE  r   )r   Zm_rrefZ	m_correctZm_diffrj   rj   rk   test_iszero_substitutionT  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t	|jd|	ddks6t	|jd|	ddksNt	d S )Nr   )Pointr   rF  -   rz   r  r{   r   r   r   c                 S   s   t |  dk S )Ng#B;)r   rv   r   rj   rj   rk   rr   p  rs   z"test_issue_11238.<locals>.<lambda>T)r$   r  )
Zsympy.geometry.pointr  r   r   r   r   r0   r$   r)  r   )
r  Zxxyyp1Zp2p0rI  rJ  m3Zrj   rj   rk   test_issue_11238b  s    0R

r  c                  C   sl   t ddddddg} | tj }| | }tD ]<}|| \}}t|t| ksRtt|t| ks*tq*d S )Nr{   r   rz   r   )r0   r   ZImaginaryUnitr   Zas_real_imagr   r   )rI  rJ  r  ZklsrY   rZ   rj   rj   rk   test_as_real_imagu  s    
r  c                  C   sh   t dddddddddddg	} |  \}}|d t dddgksDt|d t ddddddgksdtd S )Nrz   r   r   r   r   r   r{   )r0   Zjordan_cellsr   )r   r   ZJcellsrj   rj   rk   test_deprecated  s    r  c                  C   sd   ddl m}  tdddg}tdddg}| |d	tdddgksDt| |d
tdddgks`td S )Nr   )Modr   r   r{   r   r0  r  rz   r   )Zsympy.core.modr  r0   r   )r  r   r-  rj   rj   rk   test_issue_14489  s
    r  c                  C   s^   zddl m}  W n tk
r,   td Y nX tddgddgg}| |tdjjd	ksZtd S )
Nr   r  r  r   r{   rz   r   )dtypeZfloat64)	r  r  r  rP   r0   floatr  namer   )r  r   rj   rj   rk   test_issue_14943  s    r  c                  C   s4   t ddd} td}| d dk}t|dks0td S )Nr   r   rY   r   r   zm[0, 0] > 0)r@   r   rc  r   )r   rY   rj   rj   rk   test_case_6913  s    r   c                  C   s.   t ddd} td}| ||| iks*td S )Nr   rz   rY   )r@   rG   matchr   )r   rY   rj   rj   rk   test_issue_11948  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sJt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stt dtgdt gg}| \}}||j t dkstd S )Nr   r   r{   )r0   r	   Zorthogonalizer   r   ZQRdecompositionr  r4   )Zvecsr   rT   r   rj   rj   rk   test_gramschmidt_conjugate_dot  s     4r  c                  C   sf   t tddd} t tddd}| |}t|| d }t|| d }||d ksVt|dksbtd S )NrY   rz   r   rZ   r   r   )r0   r@   r  r   r   )rY   rZ   r[   r\   rK  rj   rj   rk   test_issue_8207  s    
r  c                     sz  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sht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stttdd	  tt fd
d	 tddddgddddgddddgddddgg  ttt  ks>ttt fdd	 tddgddgg t t
ttd  ksttdddgdddgdddgg t | tdtd  ksttddddgddddgddddgddddgg  ttt  ksttddddgddddgddddgddddgg  ttt ttt t  ksvtd S )Nr   nthrootr   r{   rz   r   r   c                   S   s   t dtttS r  )r=   analytic_funcr   r]   rj   rj   rj   rk   rr     rs   ztest_func.<locals>.<lambda>c                      s    t  tt t S rm   )r]   r  r   rj   r   rj   rk   rr     rs   r   r   c                      s     tttS rm   )r  r   r]   rj   r   rj   rk   rr     rs   r  r   "   r.  r   )sympy.simplify.simplifyr  r0   r  r   r]   r`   r   r   r   r   rM   r   r   r$   r   r  rj   r   rk   	test_func  s$    HT0" $00r
  z$Cannot create threads under pyodide.c               
   C   sL   dd } t d2 tj }|| }| s4tW 5 Q R X W 5 Q R X d S )Nc                  S   s&   t jd ksttdgg} | |  } dS r   )rE   stater   r0   r   rj   rj   rk   r    s    ztest_issue_19809.<locals>.fT)rA   
concurrentZfuturesZThreadPoolExecutorZsubmitresultr   )r  executorfuturerj   rj   rk   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<td S r  )r0   r]   r^   r   r   r   r   r   rj   rj   rk   test_issue_23276  s
    r  c               	   C   s   t dddddgdddddgdd	d
ddgd
ddddgg} |  }|d tdddd
gks\t|d tddd	dgksxt|d tddddgkstt|d
ksttj| f|  |kstd S Nr   r{   r   r   r   r   r   r  r   rz   r   r   r  )re   r  r0   r   r	  r  r   Zbasisrj   rj   rk   test_columnspace_one  s    r  c               	   C   s   t dddddgdddddgdd	d
ddgd
ddddgg} |  }|d tdddddggks`t|d tdddd
dggkst|d tdddddggkstt|d
kstd S r  )re   r  r0   r   r	  r  rj   rj   rk   test_rowspace  s       r  c               	   C   s   t dddddgdddddgdd	d
ddgd
ddddgg} |  }|d tdddddgks^t|d tdddddgks|ttdd | |d  D sttdd | |d  D std S )Nr   r{   r   r   r   r   r   r  r   rz   r   r   r  c                 s   s   | ]}|j V  qd S rm   rW  r  rj   rj   rk   r     s     z%test_nullspace_one.<locals>.<genexpr>c                 s   s   | ]}|j V  qd S rm   r  r  rj   rj   rk   r     s     )re   r  r0   r   r   r  rj   rj   rk   test_nullspace_one  s    r  c                     s  t d tt fdd tt fdd tt fdd tt fdd tt fdd tt fdd tt fd	d tt fd
d tt fdd tt fdd tt fdd tt fdd tt fdd  dddtdddgdddgdddggks&t dddtdddgdddgdddggksZt jddddtdddgdddgdddggkst jddddtdddgdddgdddggkst dddtdddgdddgdddggkst jddddtdddgdddgdddggks0t jddddtdddgdddgdddggksft ddddtdddgdddgdddggkst jdddddtdddgdddgdddggkst jdddddtdddgdddgdddggksttdddgd } | dddtdddgd ksDt| dddtdddgd ksjt| ddddtdddgd kstd S )Nrz   c                      s
     dS Nabcelementary_row_oprj   rK  rj   rk   rr   !  rs   ztest_row_op.<locals>.<lambda>c                      s      S rm   r  rj   r  rj   rk   rr   "  rs   c                      s    j ddddS )Nn->knr   r  r  r  rj   r  rj   rk   rr   #  rs   c                      s    j ddddS )Nr  r   r   r  r  rj   r  rj   rk   rr   $  rs   c                      s    j ddddS )Nn<->mr   r   row1row2r  rj   r  rj   rk   rr   %  rs   c                      s    j ddddS )Nr  r   r   r   r  rj   r  rj   rk   rr   &  rs   c                      s    j ddddS )Nr  r   r   r   r  rj   r  rj   rk   rr   '  rs   c                      s    j ddddS )Nr  r   r   r   r  rj   r  rj   rk   rr   (  rs   c                      s    j dddddS Nn->n+kmr   r   r!  r"  r  r  rj   r  rj   rk   rr   )  rs   c                      s    j dddddS )Nr$  r   r   r%  r  rj   r  rj   rk   rr   *  rs   c                      s    j dddddS )Nr$  r   r   r   r%  r  rj   r  rj   rk   rr   +  rs   c                      s    j dddddS )Nr$  r   r   r   r%  r  rj   r  rj   rk   rr   ,  rs   c                      s    j dddddS r#  r  rj   r  rj   rk   rr   -  rs   r  r   r   r   r  )r!  r  r  r   )r  r"  r$  )r  r  r"  )r!  r  r"  r{   r   )rw   rM   r   r  r0   r   rl   r  rj   r  rk   test_row_op  s8    4466466688&&r&  c                     s  t d tt fdd tt fdd tt fdd tt fdd tt fdd tt fdd tt fd	d tt fd
d tt fdd tt fdd tt fdd tt fdd tt fdd  dddtdddgdddgdddggks&t dddtdddgdddgdddggksZt jddddtdddgdddgdddggkst jddddtdddgdddgdddggkst dddtdddgdddgdddggkst jddddtdddgdddgdddggks0t jddddtdddgdddgdddggksft ddddtdddgdddgdddggkst jdddddtdddgdddgdddggkst jdddddtdddgdddgdddggksttdddgd } | dddtdddgd ksDt| dddtdddgd ksjt| ddddtdddgd kstd S )Nrz   c                      s
     dS r  elementary_col_oprj   r  rj   rk   rr   E  rs   ztest_col_op.<locals>.<lambda>c                      s      S rm   r'  rj   r  rj   rk   rr   F  rs   c                      s    j ddddS )Nr  r   r  r  r'  rj   r  rj   rk   rr   G  rs   c                      s    j ddddS )Nr  r   r   r)  r'  rj   r  rj   rk   rr   H  rs   c                      s    j ddddS )Nr  r   r   col1col2r'  rj   r  rj   rk   rr   I  rs   c                      s    j ddddS )Nr  r   r   r*  r'  rj   r  rj   rk   rr   J  rs   c                      s    j ddddS )Nr  r   r   r*  r'  rj   r  rj   rk   rr   K  rs   c                      s    j ddddS )Nr  r   r   r*  r'  rj   r  rj   rk   rr   L  rs   c                      s    j dddddS Nr$  r   r   r+  r,  r  r'  rj   r  rj   rk   rr   M  rs   c                      s    j dddddS )Nr$  r   r   r.  r'  rj   r  rj   rk   rr   N  rs   c                      s    j dddddS )Nr$  r   r   r   r.  r'  rj   r  rj   rk   rr   O  rs   c                      s    j dddddS )Nr$  r   r   r   r.  r'  rj   r  rj   rk   rr   P  rs   c                      s    j dddddS r-  r'  rj   r  rj   rk   rr   Q  rs   r  r   r   r   r)  )r+  r  r  r*  )r  r,  r$  )r  r  r,  )r+  r  r,  r{   r   )rw   rM   r   r(  r0   r   rl   r  rj   r  rk   test_col_opB  s8    4466466688&&r/  c                  C   s   t d} td}| jst|js$ttddg }|js:ttddddddddg}|js\ttddddddddg}|jr~ttd}tdd|ddg}|jsttdd||dg}|jrttdddddddddddg	}|jrtd S )Nrz   r   r{   r   r   r]   )ry   rw   
is_echelonr   rl   r   )ZzroidentrY   r]   rj   rj   rk   test_is_echelonf  s"    






r2  c                     s  t d td}    ks t|  | ks0ttddg     ksLttdddg    ksjtfdd}tdddddddd	d
ddg	 tdgdgdggg} fddt jD }  jst| || tdddddddd	d
ddg	 g } fddt jD }  js.t| || tdddddddddddg	 tt	ddgdgdggtt	ddgdgdggg} fddt jD }  jst| || tdddddddddddg	 tdgdgdggg} fddt jD }  js$t| || tdddddddddddg	 tdgdgdggtdgdgdggg} fddt jD }  jst| || tddddddddg tdgdgdggg} fddt jD }  jst| || d S )Nrz   r   r   r   c                    sb   |D ]}t dd  | D stq|D ]4}t dd |D s(t dd  |  D r(tq(d S )Nc                 s   s   | ]}|j V  qd S rm   r  r~   r`   rj   rj   rk   r     s     zCtest_echelon_form.<locals>.verify_row_null_space.<locals>.<genexpr>c                 s   s   | ]}|j V  qd S rm   r  r3  rj   rj   rk   r     s     c                 s   s   | ]}|j V  qd S rm   r  r3  rj   rj   rk   r     s     )r   r   r  )r   r   nullsr   )	a_echelonrj   rk   verify_row_null_space  s
    z0test_echelon_form.<locals>.verify_row_null_spacer{   r   r   r   r   r   r   c                    s   g | ]} |d d f qS rm   rj   r}   r  rj   rk   r     s     z%test_echelon_form.<locals>.<listcomp>c                    s   g | ]} |d d f qS rm   rj   r}   r  rj   rk   r     s     r   r   c                    s   g | ]} |d d f qS rm   rj   r}   r  rj   rk   r     s     c                    s   g | ]} |d d f qS rm   rj   r}   r  rj   rk   r     s     c                    s   g | ]} |d d f qS rm   rj   r}   r  rj   rk   r     s     c                    s   g | ]} |d d f qS rm   rj   r}   r  rj   rk   r     s     )
ry   rw   r	  r   rl   r0   r   r   r0  r   )rK  r6  r4  r   rj   )rY   r5  rk   test_echelon_form  s    


r7  c                  C   s  t ddg } | jdd| ks tt dddg} t dddg}| jdd|jdd  kr`| ksfn tt dddddg}|jddtdgdgdggkstt dddddg}|jddtdddggkstt dddddddd	d
ddg	}|jddtdddgdddgdddggkstt dddddddddddg	}t dddddddddddg	}t dddddddddddg	}t dddddddddddg	}|jdd|jdd  kr|jdd  kr|jdd  kr|ksn ttd} td}| jdd| kst|jdd|ks(tt dddddddgdddddddgdddddddgdddddddgg}| \}}|tdddddddgdddddddgdddddddgdddddddggkst|dkstt tddtddddgddd	d
gddddgddddgg}|jddtdddtddgdddtddgdddtddgddddggkslttd}t dd|ddt||dg}t	|jddddt|| d  |tdd  |  dddt|| d  gD ]\}	}
t
|	|
 jstqd S )Nr   F)pivotsr   r   rz   r{   r   r   r   r   r   r   r   r  r   r   )r   r{   rz   r  r   rE  r   rF  rG  r   i      r]   )rl   r  r   r0   rw   ry   r   r   r   r  r$   rW  )rK  rY   rZ   r[   r\   r_   r   Zpivot_offsetsr]   rp   rq   rj   rj   rk   	test_rref  s    *$ 










(  r;  c                  C   s   t d\} }}}tddgddgddgddgg}t| |||g}||tddgddgddgddggtd| | gd| d |d  g| g|ggfkstd S )Nr  r   r   r{   rz   r   r   )r   r0   Zrref_rhsr   )rY   rZ   r[   r\   r   r-  rj   rj   rk   test_rref_rhs!  s      
r<  c               
      s"  t ddddgddddgdd	ddgd	ddd
gddddgddddgg  jdd	dd}  jddddd} jddd	d}| dd d f t dd	ddggkst|dd d f t ddddggkst|dd d f t ddddggksttt fdd tt fdd tt fdd d S )Nrz   r   r   r   r   r   r   r   r{   r   r   r   r   r   r  r   r   r$  r   r%  r  r  rG  rQ  rg  c                      s    j ddddS )Nr  r{   r   r   r  rj   r  rj   rk   rr   A  rs   z"test_issue_17827.<locals>.<lambda>c                      s    j ddddS )Nr  r   r{   r  r  rj   r=  rj   rk   rr   B  rs   c                      s    j dddddS )Nr$  r   r   r{   r%  r  rj   r=  rj   rk   rr   C  rs   )r0   r  r   rM   r   )r  r   r~  rj   r=  rk   test_issue_178270  s"    





	&&&r>  c                  C   sj   t ddgtddt  gg} |  dks,tt ddtdd}| dksNttd}| dksftd S )Nr   r{   rz   r   r   )r0   r]   r)  r   r   r=   )r   rv   r  rj   rj   rk   	test_rankE  s    r?  c                  C   s   t d\} }}}}}}}}}	}
}t| || |
 ||
 dg||||
 ||
 dg||||
 ||
 dg||||
 ||
 dg||	d| | ||
  d|	 | |	|
  dgg}| dkstd S )Nr  r   r   r{   r   )r   r0   r)  r   )r  r  r  r  r  r  r  r  r  r  r  r  r   rj   rj   rk   test_issue_11434M  s    ,r@  c               	   C   s   t d\} }td|  dddgd|  d|  d ddgdd|  d|  | d dgdd| | dgg}tdddd| d | |    gdddd| | |    gdddd| |   gddddgg}d	}| \}}t|| t|j kst||kstd S )
Nz
nu, lambdar   r   r   rz   r   r{   r   rC  )r   r0   r  r$   r=   r   r   )nuZlambr   Zexpected_reducedZexpected_pivotsZreducedr8  rj   rj   rk   test_rank_regression_from_soW  s    
rB  c                  C   s~   t ddddgddddgddddgddddgg} | t dt  }| dksRt|d  dksft|d  dksztd S )Nr   r   r   r   r{   r   rz   )r0   r4   r	   r)  r   )r   r-  rj   rj   rk   test_issue_15872k  s
    0rC  (Q  rk  concurrent.futuresr  collections.abcr   Zsympy.core.addr   Zsympy.core.functionr   r   r   r  r   r   r	   r
   r   r   r   r   Zsympy.core.powerr   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Zsympy.core.sympifyr   Z$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.polys.rootoftoolsr    Zsympy.printing.strr!   Zsympy.sets.setsr"   r	  r#   r$   Zsympy.simplify.trigsimpr%   Zsympy.matrices.exceptionsr&   r'   r(   Zsympy.matrices.matrixbaser*   Zsympy.matrices.determinantr+   Zsympy.matrices.utilitiesr,   Zsympy.matricesr-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   Z
sympy.corerF   rG   Z(sympy.functions.special.tensor_functionsrH   Zsympy.utilities.iterablesrI   rJ   rK   Zsympy.utilities.exceptionsrL   Zsympy.testing.pytestrM   rN   rO   rP   rQ   rR   Zsympy.assumptionsrT   Zsympy.tensor.arrayrU   Z$sympy.tensor.array.array_derivativesrV   Zsympy.matrices.expressionsrW   Zsympy.algebrasrX   r   rY   rZ   r[   r\   r]   r^   r_   r`   r   r  ra   rb   Zsympy.matrices.matricesrc   rd   re   rl   rw   ry   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r
  r  r  r  r  r  r  r  r   r"  r%  r'  r*  r+  r,  r-  r/  r;  r<  r@  rB  rK  rS  rV  rY  r\  r`  ra  ro  r|  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r
  r!  r"  r#  r$  r)  r0  r2  r3  rA  rL  rQ  rR  rS  rU  rV  rX  r[  r\  r]  ra  re  rf  rg  rh  rj  rk  rl  rm  rp  rr  rs  rt  rv  rw  r|  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r
  r  r  r  r  r  r&  r/  r2  r7  r;  r<  r>  r?  r@  rB  rC  rj   rj   rj   rk   <module>   s  (h (,Ma,	R			:	
		
	
 HK
=7(]%
		-%


	$$_A
