o
    *ήck4                    @   s	  d dl Z d dlZd dlmZ d dlmZ d dlmZm	Z	m
Z
 d dlmZmZmZmZmZmZmZmZ d dlmZ d dlmZ d dlmZmZ d d	lmZ d d
lmZ d dlm Z m!Z! d dl"m#Z#m$Z$m%Z% d dl&m'Z'm(Z(m)Z) d dl*m+Z+ d dl,m-Z-m.Z. d dl/m0Z0 d dl1m2Z2 d dl3m4Z4m5Z5 d dl6m7Z7 d dl8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z> d dl?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZT d dlUmVZV d dlWmXZXmYZY d dlZm[Z[ d dl\m]Z]m^Z^m_Z_ d dl`maZambZb d dlcmdZdmeZemfZfmgZgmhZhmiZi d dljmkZk d dllmmZm d dlnmoZo d dlpmqZq d d lrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZz eqd!Z{eCeDeAeBfZ|d"d# Z}d$d% Z~d&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zd|d} Zd~d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddÄ Zddń ZddǄ ZddɄ Zdd˄ Zdd̈́ Zddτ Zddф Zddӄ ZddՄ Zddׄ Zddل Zddۄ Zdd݄ Zdd߄ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d Zdd Zdd Zdd Zdd	 Zd
d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$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eedDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZefeedRdS ZdTdU ZdVdW ZdXdY ZdZ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&dvdw Z'dxdy Z(dzd{ Z)d|d} Z*d~d Z+dd Z,dd Z-dd Z.dd Z/dd Z0dd Z1dS (      N)Hashable)Add)Functiondiffexpand)EFloatIIntegerRationalnanoopi)Pow)S)Symbolsymbols)sympify)Abs)explog)MaxMinsqrt)cossintan)	integrate)PolyPurePoly)sstr)	FiniteSet)signsimpsimplify)trigsimp)
ShapeErrorMatrixErrorNonSquareMatrixErrorDeferredVector_find_reasonable_pivot_naive	_simplify)GramSchmidtImmutableMatrixImmutableSparseMatrixMatrixSparseMatrix
casoratiandiageyehessianmatrix_multiply_elementwiseones
randMatrix	rot_axis1	rot_axis2	rot_axis3	wronskianzerosMutableDenseMatrixImmutableDenseMatrixMatrixSymboldotprodsimp)_dotprodsimp_state)TupleWild)KroneckerDelta)flattencaptureiterable)ignore_warningsSymPyDeprecationWarning)raisesXFAILslowskipwarns_deprecated_sympywarnsQ)Array)MatPow)import_module)abcdxyzt
pyodide_jsc                  C   s   t tD ]S\} }|dd}|jdkrtdd |jD sJ |jdkr+t|jtu s-J |jdkr9t|jtu s;J | d sMt|	 t
ttfv sLJ qt| tu sWJ qd S )N      )r]   r^   c                 s   s    | ]	}t |tu V  qd S N)typeint.0i re   I/tmp/pip-target-vg8gfxp4/lib/python/sympy/matrices/tests/test_matrices.py	<genexpr>7   s    ztest_args.<locals>.<genexpr>)	enumerateclassesr;   shapeallrowsr`   ra   colsflatlisttuplerA   todokdict)nclsmre   re   rf   	test_args3   s   "rv   c               	   C   s   t tfD ]&} | dd}t  |j}W d    n1 sw   Y  || ks*J qttfD ]&} | dd}t  |j}W d    n1 sHw   Y  ||	 ksUJ q/d S Nr]   r^   )
r.   r,   r;   rM   _matrn   r/   r-   _smatrq   )rt   ru   matsmatre   re   rf   test_deprecated_mat_smat@   s   r|   c                  C   s8   t ddttg} | t t ddtt tt gksJ d S N   r^   )r.   rX   rY   rZ   )vre   re   rf   test_divisionM   s   (r   c                      s   t g dtttgdt dtt gg    t g ddt dt dt gdt ddt t ggks4J t ddddgtt fdd	 d S )
Nr~   r^   r]   r^   i)r^         r   ir~   c                      s     S r_   re   re   ru   rs   re   rf   <lambda>V       ztest_sum.<locals>.<lambda>)r.   rX   rY   rZ   rI   r%   re   re   r   rf   test_sumR   s   &Br   c                  C   s8   t dddtg} t dddttg}t| |ksJ d S )Nr~   r^   r]   )r.   rX   r   absr   re   re   rf   test_absX   s   r   c                  C   sJ   t d} t d}| | | |  kr t ddgddggks#J  J d S )N)r~   r^   r]   r~   r   )r]   r   r^   r   r   r~   )r.   addrT   rU   re   re   rf   test_addition]   s   :r   c               	   C   s  t tfD ].} | ddtd}||d d d d f ksJ |dd d f t ddg dks/J |d d df t g dks?J |ddgd d f t g dg dgksUJ |ddgdf |ddgdgf kshJ |dddgf |dgddgf ks{J |d d ddgf t ddgdd	gd
dggksJ |d dksJ |ddd d f t g dg dgksJ |d d ddf t ddgdd	gd
dggksJ |d d ddf |ddgdf ksJ |dd d df |dddgf ksJ | ddtd}|g dd d f t g dg dg dg dg dgksJ |d d g df t g dg dg dgks3J qtd}d|d< d|d< d	|d< |ddgdgt dgdggksYJ |ddgg dt g dg dgkspJ |g dg dt g dg dg dg dgksJ d S )Nr]   	   r~   r]   r      )r~   r      r   r   r~   r^   r^   r   r   r   r   r   )r   r^   r~   r^   r~   )r   r      )r]   r   r   r   r   )r   r   r   r   r   r   r   r~   r^   r   )r^   r^   r^   r   r   r   )r~   r   r~   r^   )r^   r   r~   r   r^   r   r   r   )r   r   r]   r   )r   r   r   r   )r.   r/   ranger;   extract)MrT   re   re   rf   test_fancy_index_matrixk   sZ   $ ,&&2,2&&
r   c                     s8  t d t d  } | d dksJ | d dksJ | d dks$J | d	 dks,J | d
 dks4J | d dks<J ztd W n	 tyK   Y n1w | d dksTJ | d dks\J | d dksdJ | d	 dkslJ | d
 dkstJ | d dks|J t | }| | ksJ |d dksJ |d dksJ |d dksJ |d	 dksJ |d
 dksJ |d dksJ tt fdd td } t| t sJ | d t	ksJ | d dt	 ksJ | d dt	 ksJ | d	 dksJ t	 }| |ksJ d } t| t sJ | d dksJ | d dksJ | d dks&J | d	 dks/J ztd W n
 ty?   Y n-w t| t sHJ | d dksQJ | d dksZJ | d dkscJ | d	 dkslJ t t
dgdt
gg}|d |ksJ t t
t
gddgg}|d t ttgttggksJ 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 r_   )r4   re   r   re   rf   r         
 z%test_multiplication.<locals>.<lambda>rX   r]   r   
      z	c = 5 @ b)r.   evalSyntaxErrorr4   multiply_elementwiserI   r%   r   
isinstancerX   r   r   )rV   hc2r   re   r   rf   test_multiplication   sr   
&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s3J  d d d  g dksAJ tg dg dg dg  d d d  g dks\J  d tdksfJ  d  ksnJ tdggd d dd ks~J tdd tdksJ tddgddggtd tddgddggksJ tddgddgg  tj d d  g dksJ tddgd dgg  tj d  ksJ tddgddggtj tddgtjdggksJ tddgddggd! td"dgd!d"ggksJ dd#lm	 tdt
gddgg tdt
 gddggks&J ttt
gdtgg tt t
td    gdt ggksKJ tt
 t
d   t
 d  t
   dt
d   gdt
 t
d   gddt
 ggsJ 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sJ tddgddgg  td dksJ tdgg  d td$gg  kr td  kr dksJ  J tg d%g d&g d'g d(g d)gt tfd*d t td+d  tg d,g d-g d.g  d/ tg d.g d.g d.gks:J t t fd0d t t fd1d td	dgddgg  d/ td2d3gd4d5ggksgJ tg d-g d-g d-g  d/ tg d-g d-g d-gksJ tg d,g d-g d-g  d/ tg d-g d-g d-gksJ td6d7d8t  tsJ 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g d-gks J  d  tg d-g d-g d-gksJ t t fd<d tg d-g d=g d>g  d? tg d@g dAg dBgks@J  d?  d ksKJ tg d,g dCg d.g td6  d  d ksoJ t tfdDd   d  ksJ tg d.g d.g d.g td6d7d7dE   ksJ td6d7d7d;  td d d ksJ   dtdksJ   dtdksJ tg dFg dGg dHg  dI tdJdJdJksJ  t tdt dt dt ksJ tg d,g d-g d-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?J 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scJ d S )MNc                   S   s   t dd S Nr   r^   r.   re   re   re   rf   r          ztest_power.<locals>.<lambda>r^   r]   r   r   r   ir      3   i)i  i  i,*  i7  )r^   r~   r]   )r   r^   r   )r      r~   )	i"  i     i  i  ip  i  i  i  r   r~   d   r   i r   r   r      !      0   9   )r   r^   r   r         ?      ?rs   i   )r]   r   r   r   r   )r   r   r   r   r]   )r   r]   r   r]   r   )r   r   r]   r   r]   )r]   r   r   r]   r   c                      s     tdS Nr   )_matrix_pow_by_jordan_blocksr   re   ru   re   rf   r         c                   S   s   t ddgddggtdS )Nr~   r]   )r.   r   r   re   re   re   rf   r     s    r   r~   r   r   r   r~   r         $@c                          d S N @re   re   Are   rf   r     r   c                          t dd S rw   r   re   r   re   rf   r     r   ihiO<iv0irs   T)integer)r   negativec                      s     S r_   re   re   )r   rs   re   rf   r     r   )r   nonnegativec                      r   rw   r   re   r   re   rf   r   &  r   )r]   r   r~   )r   r]   r~   g      @)   H   Y   )i#        )i<  i  iI  r   r   r   c                      s     d S )N)subsdoitre   )Anrs   re   rf   r   .      )r   positiver^   r   r   )r   r^   r   r   r   r^   r   gd%%@c                      r   r   re   re   r   re   rf   r   =  r   c                      s    t  S r_   r	   re   r   re   rf   r   >  r   )rI   r'   r   r.   r2   r
   r   Half	sympy.abcrs   rT   rU   r   _eval_pow_by_recursionr&   
ValueErrorr   r   rR   rC   r   r   r1   r;   r	   )Rre   )r   r   ru   rs   rf   
test_power   s   @ 4426J<$0&("((*,(&&8r   c                  C   s   t dt dt gdt dt gg} tdE |   t tdt td d tdt  td d gtdt  td d tdt td d ggksSJ W d    d S 1 s^w   Y  d S )Nr~   Tr^   )r.   rX   r?   r   r   r   re   re   rf   $test_issue_17247_expression_blowup_1E  s   $
00"r   c                  C   sr   t dt dt gdt dt gg} td |  \}}|| |  s'J W d    d S 1 s2w   Y  d S Nr~   T)r.   rX   r?   jordan_forminvr   PJre   re   rf   $test_issue_17247_expression_blowup_2L  s
   $
"r   c                  C   s   t dt dt gdt dt gg} td1 | d t dtd  d ddtd   gddtd   dtd  d ggks?J W d    d S 1 sJw   Y  d S )Nr~   Tr   l                )r.   rX   r?   r   re   re   rf   $test_issue_17247_expression_blowup_3R  s   $
"r   c                  C   sR   t td} td | d t tdksJ W d    d S 1 s"w   Y  d S )Na1  [
        [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64],
        [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512],
        [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64],
        [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128],
        [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16],
        [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128]]Tr   a  [
            [     7369525394972778926719607798014571861/604462909807314587353088 - 229284202061790301477392339912557559*I/151115727451828646838272,   -19704281515163975949388435612632058035/1208925819614629174706176 + 14319858347987648723768698170712102887*I/302231454903657293676544,      -3623281909451783042932142262164941211/604462909807314587353088 - 6039240602494288615094338643452320495*I/604462909807314587353088,    109260497799140408739847239685705357695/2417851639229258349412352 - 7427566006564572463236368211555511431*I/2417851639229258349412352, -16095803767674394244695716092817006641/2417851639229258349412352 + 10336681897356760057393429626719177583*I/1208925819614629174706176,    -42207883340488041844332828574359769743/2417851639229258349412352 - 182332262671671273188016400290188468499*I/4835703278458516698824704],
            [50566491050825573392726324995779608259/1208925819614629174706176 - 90047007594468146222002432884052362145*I/2417851639229258349412352,  74273703462900000967697427843983822011/1208925819614629174706176 + 265947522682943571171988741842776095421*I/1208925819614629174706176, -116900341394390200556829767923360888429/2417851639229258349412352 - 53153263356679268823910621474478756845*I/2417851639229258349412352, 195407378023867871243426523048612490249/1208925819614629174706176 - 1242417915995360200584837585002906728929*I/9671406556917033397649408,   -863597594389821970177319682495878193/302231454903657293676544 + 476936100741548328800725360758734300481*I/9671406556917033397649408, -3154451590535653853562472176601754835575/19342813113834066795298816 - 232909875490506237386836489998407329215*I/2417851639229258349412352],
            [   -1715444997702484578716037230949868543/302231454903657293676544 + 5009695651321306866158517287924120777*I/302231454903657293676544,     -30551582497996879620371947949342101301/604462909807314587353088 - 7632518367986526187139161303331519629*I/151115727451828646838272,           312680739924495153190604170938220575/18889465931478580854784 - 108664334509328818765959789219208459*I/75557863725914323419136,    -14693696966703036206178521686918865509/604462909807314587353088 + 72345386220900843930147151999899692401*I/1208925819614629174706176,  -8218872496728882299722894680635296519/1208925819614629174706176 - 16776782833358893712645864791807664983*I/1208925819614629174706176,      143237839169380078671242929143670635137/2417851639229258349412352 + 2883817094806115974748882735218469447*I/2417851639229258349412352],
            [   3087979417831061365023111800749855987/151115727451828646838272 + 34441942370802869368851419102423997089*I/604462909807314587353088, -148309181940158040917731426845476175667/604462909807314587353088 - 263987151804109387844966835369350904919*I/9671406556917033397649408,   50259518594816377378747711930008883165/1208925819614629174706176 - 95713974916869240305450001443767979653*I/2417851639229258349412352,  153466447023875527996457943521467271119/2417851639229258349412352 + 517285524891117105834922278517084871349*I/2417851639229258349412352,  -29184653615412989036678939366291205575/604462909807314587353088 - 27551322282526322041080173287022121083*I/1208925819614629174706176,   196404220110085511863671393922447671649/1208925819614629174706176 - 1204712019400186021982272049902206202145*I/9671406556917033397649408],
            [     -2632581805949645784625606590600098779/151115727451828646838272 - 589957435912868015140272627522612771*I/37778931862957161709568,     26727850893953715274702844733506310247/302231454903657293676544 - 10825791956782128799168209600694020481*I/302231454903657293676544,      -1036348763702366164044671908440791295/151115727451828646838272 + 3188624571414467767868303105288107375*I/151115727451828646838272,     -36814959939970644875593411585393242449/604462909807314587353088 - 18457555789119782404850043842902832647*I/302231454903657293676544,      12454491297984637815063964572803058647/604462909807314587353088 - 340489532842249733975074349495329171*I/302231454903657293676544,      -19547211751145597258386735573258916681/604462909807314587353088 + 87299583775782199663414539883938008933*I/1208925819614629174706176],
            [  -40281994229560039213253423262678393183/604462909807314587353088 - 2939986850065527327299273003299736641*I/604462909807314587353088, 331940684638052085845743020267462794181/2417851639229258349412352 - 284574901963624403933361315517248458969*I/1208925819614629174706176,      6453843623051745485064693628073010961/302231454903657293676544 + 36062454107479732681350914931391590957*I/604462909807314587353088,  -147665869053634695632880753646441962067/604462909807314587353088 - 305987938660447291246597544085345123927*I/9671406556917033397649408,  107821369195275772166593879711259469423/2417851639229258349412352 - 11645185518211204108659001435013326687*I/302231454903657293676544,     64121228424717666402009446088588091619/1208925819614629174706176 + 265557133337095047883844369272389762133*I/1208925819614629174706176]])r.   r   r?   r   re   re   rf   $test_issue_17247_expression_blowup_4Y  s   
"r   c                  C   s   t dddd } td+ | dttd ddt  td   dt td	   td
dks/J W d    d S 1 s:w   Y  d S )Nr   c                 S      dd| |  t   S Nr~   r   r   rd   jre   re   rf   r         z6test_issue_17247_expression_blowup_5.<locals>.<lambda>TrX   r   $   r   EXdomain)r.   r?   charpolyr   rX   r	   r   re   re   rf   $test_issue_17247_expression_blowup_5  s   
F"r   c                  C   Z   t dddd tdD } td | ddksJ W d    d S 1 s&w   Y  d S )Nr   c                 S      g | ]}t | qS re   rX   rb   re   re   rf   
<listcomp>  r   z8test_issue_17247_expression_blowup_6.<locals>.<listcomp>@   Tbareissr   r.   r   r?   detr   re   re   rf   $test_issue_17247_expression_blowup_6     
"r  c                  C   sP   t dddd } td | ddksJ W d    d S 1 s!w   Y  d S )Nr   c                 S   r   r   r   r   re   re   rf   r     r   z6test_issue_17247_expression_blowup_7.<locals>.<lambda>T	berkowitzr   )r.   r?   r  r   re   re   rf   $test_issue_17247_expression_blowup_7  s   
"r	  c                  C   r   )Nr   c                 S   r   re   r   rb   re   re   rf   r    r   z8test_issue_17247_expression_blowup_8.<locals>.<listcomp>r  Tlur   r  r   re   re   rf   $test_issue_17247_expression_blowup_8  r  r  c                  C   s   t dddd tdD } td- |  t g dg dg dg dg dg dg dg dgd	fks6J W d    d S 1 sAw   Y  d S )
Nr   c                 S   r   re   r   rb   re   re   rf   r    r   z8test_issue_17247_expression_blowup_9.<locals>.<listcomp>r  T)r~   r   r   r   r   r   r   r~   r^   r]   r   r   r   r   r   r   r   r   r   r   r   r   r   )r.   r   r?   rrefr   re   re   rf   $test_issue_17247_expression_blowup_9  s   
"r  c                  C   sR   t dddd } td | dddksJ W d    d S 1 s"w   Y  d S )Nr   c                 S   r   r   r   r   re   re   rf   r     r   z7test_issue_17247_expression_blowup_10.<locals>.<lambda>Tr   )r.   r?   cofactorr   re   re   rf   %test_issue_17247_expression_blowup_10  s   
"r  c                  C   s\   t dddd } td |  t dddgd ksJ W d    d S 1 s'w   Y  d S )Nr   c                 S   r   r   r   r   re   re   rf   r     r   z7test_issue_17247_expression_blowup_11.<locals>.<lambda>Tr   r   )r.   r?   cofactor_matrixr   re   re   rf   %test_issue_17247_expression_blowup_11  s   
 "r  c                  C   s^   t dddd } td |  dddt dddiksJ W d    d S 1 s(w   Y  d S )Nr   c                 S   r   r   r   r   re   re   rf   r     r   z7test_issue_17247_expression_blowup_12.<locals>.<lambda>Tr~   r   r   )r.   r?   	eigenvalsr	   r   re   re   rf   %test_issue_17247_expression_blowup_12  s   
""r  c               	   C   sz  t ddt td dt gdt td dtd gddt td dt gdddt dgg} |  }|d ddt g dgfks@J |d d ttdtd   d ksTJ |d d dks^J |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sJ |d d ttdtd   d ksJ |d d dksJ |d d d jdddt t tdtd   d td  gdt td dt  d  td ttdtd   d  td dt  d   gt tdtd   d td  gdggks;J d S )	Nr   r~   r^   )r   r   r   r~   FT)deepnumerr  )r.   rX   
eigenvectsr   r   )r   evre   re   rf   %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O |  t td dt td dt td dt td dt gddt ddt ddt ddt gg dg dg dg dg dg dgkseJ W d    d S 1 spw   Y  d S )Nr   r~   r   Tr   r  )r.   rX   r?   echelon_formr   re   re   rf   %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A |  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sWJ W d    d S 1 sbw   Y  d S )Nr   r~   r   Tr   )r.   rX   r?   rowspacer   re   re   rf   %test_issue_17247_expression_blowup_15  s   4
r"r   c                  C   s   t dddt dt gd dt dt gd  d } tdW |  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smJ W d    d S 1 sxw   Y  d S )Nr   r~   r   T)r.   rX   r?   columnspacer   re   re   rf   %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sJ W d    d S 1 sw   Y  d S )Nr   c                 S   r   re   r   rb   re   re   rf   r    r   z9test_issue_17247_expression_blowup_17.<locals>.<listcomp>r  Tr~   r   r   r^   r   r]   r  r   r  r   r   r   )r.   r   r?   	nullspacer   re   re   rf   %test_issue_17247_expression_blowup_17  s   
&&&&&&"r%  c                  C   sn   t dddt dt gd dt dt gd  d } td |  r%J W d    d S 1 s0w   Y  d S )Nr   r~   r]   T)r.   rX   r?   is_nilpotentr   re   re   rf   %test_issue_17247_expression_blowup_18  s   4
"r'  c                  C   sF   t td} td |  rJ W d    d S 1 sw   Y  d S )Nay  [
        [             -3/4,                     0,         1/4 + I/2,                     0],
        [                0, -177/128 - 1369*I/128,                 0, -2063/256 + 541*I/128],
        [          1/2 - I,                     0,                 0,                     0],
        [                0,                     0,                 0, -177/128 - 1369*I/128]]T)r.   r   r?   is_diagonalizabler   re   re   rf   %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C |  t dddtd td  gg dg dg dgt g dddt ddgddtd dgdddtd ggfksgJ W d    d S 1 srw   Y  d S )	Nr~   r   T)r~   r   r   r   r~   r~   r~   r   r   r   r   r~   r   r^   )r.   rX   r?   diagonalizer   re   re   rf   %test_issue_17247_expression_blowup_20  s*   
"r-  c                  C   V   t td} td | jddt tdksJ W d    d S 1 s$w   Y  d S )N  [
        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
        [                0,                     0,                   0, -177/128 - 1369*I/128]]TGEmethodv  [
            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
            [0, 0, 0, -11328/952745 + 87616*I/952745]]r.   r   r?   r   r   re   re   rf   %test_issue_17247_expression_blowup_21     
"r5  c                  C   r.  )Nr/  TLUr1  r3  r4  r   re   re   rf   %test_issue_17247_expression_blowup_22   r6  r8  c                  C   sZ   t td} td | jdd t tdksJ W d    d S 1 s&w   Y  d S )Nr/  TADJr1  r3  )r.   r   r?   r   r   r   re   re   rf   %test_issue_17247_expression_blowup_23-  s   
""r:  c                  C   V   t td} td | jddttdksJ W d    d S 1 s$w   Y  d S )Nr/  TCHr1  r3  r/   r   r?   r   r.   r   re   re   rf   %test_issue_17247_expression_blowup_24:  r6  r>  c                  C   r;  )Nr/  TLDLr1  r3  r=  r   re   re   rf   %test_issue_17247_expression_blowup_25G  r6  r@  c                  C   J   t td} td |  dksJ W d    d S 1 sw   Y  d S )Na  [
        [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64,         -9/32 - I/16,      183/256 - 97*I/128],
        [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512, -219/128 + 115*I/256, 6301/4096 - 6609*I/1024],
        [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,         1/4 - 5*I/16,        65/128 + 87*I/64],
        [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,     85/256 - 33*I/16,    805/128 + 2415*I/512],
        [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,            1/4 + I/2,        -129/64 - 9*I/64],
        [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,     125/64 + 87*I/64,   -2063/256 + 541*I/128],
        [               -2,         17/4 - 13*I/2,             1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,                 -3/4,         45/32 - 37*I/16],
        [     1/4 + 13*I/4,    -825/64 - 147*I/32,          21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64,    -149/64 + 49*I/32,   -177/128 - 1369*I/128]]Tr   r.   r   r?   rankr   re   re   rf   %test_issue_17247_expression_blowup_26T  s   
	"rD  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' |  \}}| t td ksEJ |t tdksOJ W d    d S 1 sZw   Y  d S )Nr   r~   Ta  [
            [    0,  4*x/(x**2 - 2*x + 1), -(-17*x**4 + 12*sqrt(2)*x**4 - 4*sqrt(2)*x**3 + 6*x**3 - 6*x - 4*sqrt(2)*x + 12*sqrt(2) + 17)/(-7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 + 8*x**3 - 2*x**2 + 8*x + 6*sqrt(2)*x - 5*sqrt(2) - 7), -(12*sqrt(2)*x**4 + 17*x**4 - 6*x**3 - 4*sqrt(2)*x**3 - 4*sqrt(2)*x + 6*x - 17 + 12*sqrt(2))/(7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 - 8*x**3 + 2*x**2 - 8*x + 6*sqrt(2)*x - 5*sqrt(2) + 7)],
            [x - 1, x/(x - 1) + 1/(x - 1),                       (-7*x**3 + 5*sqrt(2)*x**3 - x**2 + sqrt(2)*x**2 - sqrt(2)*x - x - 5*sqrt(2) - 7)/(-3*x**3 + 2*sqrt(2)*x**3 - 2*sqrt(2)*x**2 + 3*x**2 + 2*sqrt(2)*x + 3*x - 3 - 2*sqrt(2)),                       (7*x**3 + 5*sqrt(2)*x**3 + x**2 + sqrt(2)*x**2 - sqrt(2)*x + x - 5*sqrt(2) + 7)/(2*sqrt(2)*x**3 + 3*x**3 - 3*x**2 - 2*sqrt(2)*x**2 - 3*x + 2*sqrt(2)*x - 2*sqrt(2) + 3)],
            [    0,                     1,                                                                                            -(-3*x**2 + 2*sqrt(2)*x**2 + 2*x - 3 - 2*sqrt(2))/(-x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x + 1 + sqrt(2)),                                                                                            -(2*sqrt(2)*x**2 + 3*x**2 - 2*x - 2*sqrt(2) + 3)/(x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x - 1 + sqrt(2))],
            [1 - x,                     0,                                                                                                                                                                                               1,                                                                                                                                                                                             1]]a  [
            [0, 1,                       0,                       0],
            [0, 0,                       0,                       0],
            [0, 0, x - sqrt(2)*(x - 1) + 1,                       0],
            [0, 0,                       0, x + sqrt(2)*(x - 1) + 1]])r.   rX   r?   r   r   r   r   re   re   rf   %test_issue_17247_expression_blowup_27a  s   
"rE  c                  C   sN   t td} td |  tdksJ W d    d S 1 s w   Y  d S )Nr/  Ta  [
            sqrt(14609315/131072 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2)])r.   r   r?   singular_valuesr   re   re   rf   %test_issue_17247_expression_blowup_28t  s   
"rG  c                  C   rA  )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   rB  r   re   re   rf   test_issue_16823  s   
"rH  c                  C   sH  t g ddtd dtd dtd td d dddddg	ddtd  ddtd  ddtd  ddtd  dddddg	d	td d dd
td  dd
td  dd
td  ddddd
g	ddtd  dtd d dtd d ddtd  dddddg	dd
td  dd
td  d	td d dd
td  ddddd
g	d	dtd  d	dtd  d	dtd  d	dtd  dddddg	dtd td d dtd dtd dddddg	g} td. |  t g dg dg dg dg dg dg dg dgdfksJ W d    d S 1 sw   Y  d S )N)	r~   r~   r~   r~   r~   r   r~   r   r   r~   r^   r   r  r#  r   r   r   r]   r   r   r   T)	r~   r   r   r   r   r   r   r   r   )	r   r~   r   r   r   r   r   r         )	r   r   r~   r   r   r   r   r   r   )	r   r   r   r~   r   r   r   r   rJ  )	r   r   r   r   r~   r   r   r   r   )	r   r   r   r   r   r~   r   r   rJ  )	r   r   r   r   r   r   r~   r   r   )	r   r   r   r   r   r   r   r~   rJ  r  )r.   r   r?   r  r   re   re   rf   test_issue_18531  s0   6DDDDD6

$rK  c            
      C   s  t tdd  t tdd  t tdd  t t dtdd< W d    n1 s*w   Y  t tg   krItg g  krItddg ksLJ  J t  td	gd
gg d	gd
ggksbJ W d    n1 slw   Y  t  td	gd
ggj d	ggd
ggksJ W d    n1 sw   Y  tdgg} t  tj| d< W d    n1 sw   Y  tt	dgddgg}|}|j
|jksJ |j
dksJ |d d  t	dddgksJ tddt	dddg}|}|j
|jksJ |j
dksJ |d d  t	dddgks	J ||ksJ t||ksJ tddtd	d}td	dtdd}t||g}|j
dks9J |jdksAJ |d d  g dksNJ ttdtdks[J tttdttdkslJ t|| kswJ tt|t| ksJ |t|usJ tddtddd gtddd tddd gg}t|} | tg dg dg dg dg dgksJ |  |ksJ t|dd |ksJ tddd}td|g}t|td	d	gd	d	g|d |d g|d |d ggksJ t  t|dd dd |D ksJ W d    n	1 s'w   Y  ttdtdgttdgks@J 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spJ d S )Nc                   S   s   t ddtdS )Nr      )r.   r   re   re   re   rf   r     r   ztest_creation.<locals>.<lambda>c                   S   s   t ddg S )Nr   r   r   re   re   re   rf   r     r   c                   S      t dd S r   r   re   re   re   rf   r     r   r   r   r]   r   r~   )r^   r   r^   r   r   	r~   r^   r]   r   r   r   r   r   r   r   )r~   r~   r^   r^   r^   )r]   r]   r]   r   r   Fevaluater   r   r   r   c                 S   s   g | ]}|gqS re   re   rb   re   re   rf   r        z!test_creation.<locals>.<listcomp>c                   S      t tdtddgS )Nr^   r   r]   r.   r5   re   re   re   rf   r         c                   S   rR  )Nr^   r]   r   rS  re   re   re   rf   r     rT  )r   r   r   )rI   r   
IndexErrorr.   rM   tolistTr   EmptySetrX   rm   rl   r   r2   r,   as_immutable
as_mutabler5   r>   )
r   rT   ru   rU   c23c13rV   datr   M2re   re   rf   test_creation  s   
:&*"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 g dg dg d	g d
gks?J d S )Nr]   r^   r~   r   r   r   r   )r~   r^   r^   r^   r]   r]   )r   r^   r^   r^   r   r   )r   r   r   r   r   r   )r.   	irregularr5   re   re   re   rf   test_irregular_block  s   &0ra  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s(J d S )Nr^   r]   )	r   Oner   rX   rY   ZerorZ   r.   rV  )lstru   re   re   rf   test_tolist  s   8re  c                   C   s`   t dd t ddksJ t dd tt ddksJ t dd tt ddks.J d S Nr   r]   )r;   rZ  rY  r,   re   re   re   rf   test_as_mutable  s    $rg  c                  C   s  t d} | d dd df t dksJ | ddddf tdks$J tdddd }|dd d f tdddks<J |dddf tddd	ksLJ tg d
g dg dg dg}|d d df tddg dksnJ |dd d d f tg dg dgksJ d S )Nr   r]   r^   r   c                 S      | | S r_   re   r   re   re   rf   r     r   ztest_slicing.<locals>.<lambda>r~   r   r^   r]   )r   r~   r^   r]   )r   r   r   r   )r   r   r      )r         r   r   )r]   r   rj  r   r   )r2   r;   r.   )m0m1m2re   re   rf   test_slicing  s        $0rp  c                  C   s   t d} td| ddddf< | tdksJ td| d dd df< | tdks,J tddd| d d df< | tdks@J t d| d d d d f< | t dksTJ g d| d d d d f< | tdkshJ ddg| d ddf< | td	kszJ d S )
Nr   r^   )r   r   r   r   rq  r   r   r~   r   r+  r~   r~   r^   r]   r   r   )r~   r   r   r   )r^   r~   r   r   )r]   r   r~   r   )r   r   r   r~   rs  r   r   r   r   r   r   rj  r   rk  rl  r      ))r   r^   r]   r   )r   r   r   r   rw  rx  )r;   r2   r.   r   re   re   rf   test_submatrix_assignment  s   rz  c                      s   t dddd   g dddgt ddg d	ksJ  ddgg d
t ddg dks0J  tdtd ks>J tt fdd tt fdd d S )Nr   r]   c                 S   s   | d | S Nr]   re   r   re   re   rf   r   <  r   ztest_extract.<locals>.<lambda>)r   r~   r]   r   r~   r^   )r   r~   r]   r   r   r   r   )r   r   r^   r   r   rj  c                           dgdgS )Nr   r   r   re   r   re   rf   r   @  r   c                      r|  rf  r}  re   r   re   rf   r   A  r   )r.   r   r   rI   rU  re   re   r   rf   test_extract;  s   ((r~  c                  C   sh   t d} | ddtdddksJ tdddd }|ddtdks&J |d	d
tdks2J d S )Nr]   r~   r   )	r~   r   r   r   r~   r   r   r   r~   r   c                 S   rh  r_   re   r   re   re   rf   r   G  r   ztest_reshape.<locals>.<lambda>)r   r]   r~   r^   )r]   r   r^   r   r^   r   ))r   r~   r^   r]   r~   r^   )r]   r   r^   r]   r   r   )r2   reshaper.   rm  rn  re   re   rf   test_reshapeD  s   r  c                  C   sD   t d} | dd t dd ksJ | dd tdks J d S )Nr]   c                 S   s   d|  S Nr^   re   r   re   re   rf   r   O  r   z test_applyfunc.<locals>.<lambda>r^   c                 S      dS Nr   re   r   re   re   rf   r   P      )r2   	applyfuncr;   )rm  re   re   rf   test_applyfuncM  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sJJ tddd}t tt| gjddt t|tt|  gkslJ t g dg dg d	g t d
d
t	ddgg dg dgksJ d S )Nr^   r]   rT   Treal)complexr   )r   r   r   r   r~   )r   r~   r   r   )
r.   rX   rY   r   r   r   r	   r   r   r   )rm  rn  rT   re   re   rf   test_expandS  s   8F
r  c                  C   s@  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sQJ | tttt@ }|t td tgttd  td t ggksvJ | t	tt	t@ }|t td t gt td  td  t ggksJ d S r  )
r.   r   rX   r   rY   refinerP   r  r   r   r  re   re   rf   test_refinee  s   .<0:r  c                  C   s0  t dd} t dddd} | t ddddksJ t dddd} t dddd} | t ddddks0J |  }|  || ks>J td}| t dd|dksNJ d	D ]}d
D ]}t |d||d} | | jkseJ qTqPt dddd} d}t| jd D ]}t| jd D ]}| ||f dkr|d7 }qqw|dksJ d S )Nr]   )seedr   r      T)r  	symmetric)r  prng)r   rj  )r   F      )r  percentr  r   r~   r  )minr  r  )r6   copyr#   randomRandomrW  r   rj   )r   r   rngsizer  
zero_countrd   r   re   re   rf   test_randomq  s2   

r  c                     sr  t d} |  t dksJ | jddt dksJ | jddt dks&J | jddt dks2J | jddt dks>J | jddt dksJJ tg dg d	g d
g} |  }| | t dkseJ | jdd|ksoJ | jdd|ksyJ | jdd|ksJ | jdd|ksJ | jdd|ksJ tg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg d g d!g d"g d#g d$g}|jd%d| t |jd& ksJ t  g d'g d(g d)gt fd*d+d, D sJ t  g d'g d(g d)gt fd-d+d, D s7J d S ).Nr   r7  r1  r9  r<  r?  QR)r^   r]   r   )r]   r   r^   )r   r]   r   r]   )r   r   r   r   r~   r   r   r~   r   r~   r~   r~   r   r   r   r~   r~   r   r   r   r   r~   r~   r   r   )r~   r   r~   r   r   r~   r   r   r~   r   r~   r   r~   r~   r~   r   r~   r~   r   r   r   r   r   r~   r   )r~   r~   r~   r~   r   r~   r   r   r~   r~   r   r   r   r~   r~   r~   r~   r   r   r~   r~   r   r   r~   r~   )r~   r   r   r   r   r   r~   r~   r   r   r~   r~   r~   r   r   r   r   r   r   r~   r   r   r~   r   r   )r~   r   r   r~   r~   r~   r   r~   r   r   r~   r   r   r~   r~   r~   r   r~   r   r   r   r~   r   r   r   )r~   r   r   r   r   r   r   r   r~   r~   r~   r   r~   r   r~   r~   r~   r~   r   r   r   r~   r~   r   r~   )r   r~   r~   r~   r   r   r   r   r~   r~   r~   r   r~   r   r~   r   r~   r   r~   r   r~   r   r   r~   r   )r~   r~   r   r   r   r~   r~   r   r   r~   r~   r   r~   r~   r   r~   r~   r   r~   r   r~   r~   r   r~   r~   )r   r   r~   r~   r~   r   r   r~   r~   r   r~   r~   r   r~   r   r   r   r   r   r   r~   r   r~   r   r~   )r~   r   r~   r~   r~   r   r~   r   r   r~   r~   r   r~   r~   r   r~   r~   r~   r~   r   r~   r~   r~   r   r   )r   r~   r~   r   r   r   r   r~   r~   r   r~   r   r~   r   r~   r~   r   r   r~   r   r   r   r~   r~   r   )r~   r   r   r~   r   r~   r   r~   r~   r   r   r~   r   r~   r   r~   r   r~   r   r~   r   r~   r~   r   r   )r   r~   r~   r   r   r~   r~   r   r   r~   r~   r   r~   r   r   r   r~   r   r   r~   r   r~   r~   r   r~   )r~   r~   r~   r   r~   r   r   r~   r   r   r~   r   r~   r~   r   r   r~   r~   r~   r   r~   r   r~   r~   r   )r   r~   r   r   r   r   r~   r~   r   r~   r~   r   r   r   r   r~   r   r~   r~   r~   r   r   r~   r   r   )r~   r~   r~   r~   r   r~   r~   r~   r~   r~   r~   r   r   r   r~   r   r~   r   r~   r   r   r~   r   r   r   )r   r   r   r~   r   r~   r~   r   r~   r   r   r   r   r   r~   r   r~   r~   r   r~   r   r~   r~   r   r~   )r   r~   r   r~   r   r   r   r   r~   r~   r~   r   r   r~   r~   r~   r   r   r~   r   r~   r~   r   r~   r~   )r~   r   r~   r~   r   r~   r   r~   r~   r   r~   r~   r~   r   r~   r   r   r   r   r~   r   r   r~   r   r~   )r   r   r   r~   r   r   r~   r~   r   r~   r~   r   r~   r   r~   r~   r   r   r   r   r   r   r   r   r   )r~   r   r   r   r   r~   r   r~   r   r   r~   r~   r   r~   r   r~   r~   r~   r~   r   r~   r~   r~   r~   r~   )r   r   r~   r~   r   r~   r   r   r   r~   r   r   r~   r   r   r~   r   r   r   r~   r   r~   r   r~   r~   )r   r   r   r   r   r~   r~   r~   r   r~   r~   r~   r   r   r   r~   r   r~   r~   r   r~   r~   r   r   r   )r   r   r~   r   r~   r~   r   r~   r~   r~   r   r   r~   r   r~   r   r   r~   r   r~   r   r   r   r   r   )r   r   r   r~   r~   r   r~   r~   r~   r   r   r~   r   r~   r   r~   r~   r   r~   r~   r~   r   r   r~   r   BLOCKr   )r   1      )r   G   ^   );      A   c                 3   "    | ]}t | u V  qd S r_   r`   r   rc   srt   ru   re   rf   rg          ztest_inverse.<locals>.<genexpr>zGE ADJ LU CH LDL QRc                 3   r  r_   r  r  r  re   rf   rg     r  )r2   r   r.   rj   r,   rk   splitr-   )r   AinvAAre   r  rf   test_inverse  sr   ""&r  c                     sT  t ddddg tt fdd t ddg d tt fdd t ddg d t ddg d	}  d
| ks;J t ddg d  d ksLJ t d
d
g d tt fdd t d
d
g d t d
d
g d}  d| ksvJ t d
d
g d t d
d
g d}  d| ksJ t d
d
g d t d
d
g d}  d| ksJ d S )Nr^   r~   r   c                      
     dS r  inv_modre   r   re   rf   r     r   z)test_matrix_inverse_mod.<locals>.<lambda>rt  c                      r  r  r  re   r   re   rf   r     r   rs  )r~   r~   r   r~   r]   r~   r   r   r~   rN  c                      r  Nr   r  re   r   re   rf   r     r   )	r   r~   r]   r^   r   r   r^   r~   r~   )	r   r   r   r~   r   r   r   r   r   r   )	r~   r   r   r   r~   r  r]   r  r   )	r   r]   r]   r~   r^   r   r~   r   r~   r   )	r~   r   r~   r   r~   r   r]   r^   r   )	r   r   r]   r   r   r   r~   r   r~   r   )r.   rI   r'   r   r  )Aire   r   rf   test_matrix_inverse_mod  s(   r  c                  C   s:  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s3J 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s`J td t }ttg}t||t dt dt gdt dggksJ 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sJ tttd   }td dtd   }t ddt gdt dt gg}|t|t ttgksJ |t|t ttgjksJ t|ttf|gt ddtd  dt gdtd  dt dt gdt dt dggksJ d S )Nr~   r^   r   r]   r   r   )r.   rX   rY   jacobianr3   rZ   rW  )Lsymsfgansre   re   rf   test_jacobian_hessian  s0   (6>.>r  c                  C   s2  t ttttgtttd ttd  ksJ t tttdt gttdt ks.J t tttgtttttt  ksCJ t dttd gtdksQJ 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sJ t tttttd gtdd | ksJ td  ttd  td ttd   dt ttd   dt ttd   }t tttttd gt |ksJ t tttttd gtdd |ksJ t g tdksJ d S )Nr^   r]   r~   r   r   r  r1  )r:   r   rX   r   r   r   )w1w2re   re   rf   test_wronskian  s&   2**J("R("
r  c                  C   sp  t dtgtdggtdt ddgddggksJ 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s;J 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s\J t tdgtt dggtdtdit ddgddggks{J t tt gjttd ttd idd	t td td  gksJ tD ]} t dd
gd
dgg| dddksJ qd S )Nr~   r   r   r^   r   r   r   T)simultaneousr   )r.   rX   r   rY   ri   r2   rt   re   re   rf   	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sJ t tdgtt dggtdtdit ddgddggks:J tD ]} t ddgddgg| dddiksTJ q<d S )	Nr~   r   r   r^   r   r   r   r   )r.   rX   xreplacerY   ri   r2   r  re   re   rf   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sbJ dt d }t|gg}|  |t|ggks|J |jtd |t|jtdggksJ d S )Nrs   r  r~   r^   )ratio)	r   r   r.   rX   rY   r   r   r#   r   )rs   r  r   eqre   re   rf   test_simplify#  s    :& r  c                  C   s   t g dg dg} | jt ddgddgddgddgddgddgddgd	d	gd
d
gddgg
ks1J | jj| ks9J | j|  ksBJ d S )N)
r~   r^   r]   r   r   r   r   r   r   r   r~   r^   r]   r   r   r   r   r   r   r   )r.   rW  	transposer   re   re   rf   test_transpose4  s    
r  c                  C   s   t dtdgg dg} | jt ddgtdgddggksJ | jt dt dgg dgks.J | j|  ks7J | j| jjks@J | jt ddgt dgddggksSJ d S )Nr   r   )r~   r^   r   r~   r^   )r.   r	   rW  C	conjugateHr   re   re   rf   test_conjugateE  s    
r  c               	   C   s~   t tdd  tdtttgddttgdddtgg dg} | jtg dt dddgt t ddgt t tdggks=J d S )Nc                   S   s
   t djS r{  )r2   Dre   re   re   rf   r   X  r   z!test_conj_dirac.<locals>.<lambda>r~   r   r+  rt  r   )rI   AttributeErrorr.   r	   r  r   re   re   rf   test_conj_diracW  s   

r  c                  C   s.   t g dg dg dg} |  dksJ d S )Nr~   r   r   )r   r   r   )r   r   r   rl  r.   tracer   re   re   rf   
test_tracee  s
   r  c                  C   s*   t tddgdtdgg} | jdksJ d S )Nr   ri  )r.   rX   rY   rj   r   re   re   rf   
test_shapel  s   
r  c                  C   sn  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s&J | ddd  | t td ddgdt td dggksDJ | dt td ddggksUJ | d}d|d< | d	 td kshJ | dd d
f }d|d< | d	 td ks~J | d}|t td dt gksJ d|d< | d	 td ksJ | d d df }d|d< | d	 td ksJ d S )Nr   r~   c                 S   s   | | d S Nr~   re   )rr   re   re   rf   r   u  r   z!test_col_row_op.<locals>.<lambda>r^   r]   c                 S   s   | t |  S r_   )rY   )rV   r   re   re   rf   r   y  r   *   r   r   )r.   rX   rY   row_opcol_oprowcol)r   r1c1re   re   rf   test_col_row_opr  s2   
"

r  c                  C   s   t d d D ]H} | d}|dddd  || g dg dg d	gks'J | dd }d
|d< |dddd  | || g dg dg dgksNJ qd S )Nr^   r]   r~   r   c                 S      | d|  S r  re   r   ure   re   rf   r     r   z!test_zip_row_op.<locals>.<lambda>r  r^   r~   r   r   r   r   c                 S   r  r  re   r  re   re   rf   r     r   )r^   r   r   )r   r   r   r   )ri   r2   
zip_row_op)rt   r   re   re   rf   test_zip_row_op  s   


r  c                  C   sd   t g d} t g d}t g d}| dvsJ | dvsJ | dks$J | |ks*J | |ks0J d S )Nr   )r^   r^   r]   re   )r~   r~   r   )ru   rT   rU   re   re   rf   test_issue_3950  s   r  c                  C   s  G dd d} G dd d}|  }| }t g d}|| dks"J d||< |d dks.J t g dg d	g}|||f d
ksBJ |d|f d
ksLJ ||df d
ksVJ d|||f< |d dksdJ d
|d|f< |d d
ksrJ d||df< |d dksJ d S )Nc                   @      e Zd Zdd ZdS )ztest_issue_3981.<locals>.Index1c                 S   r  r  re   selfre   re   rf   	__index__     z)test_issue_3981.<locals>.Index1.__index__N__name__
__module____qualname__r  re   re   re   rf   Index1      r  c                   @   r  )ztest_issue_3981.<locals>.Index2c                 S   r  r  re   r  re   re   rf   r    r  z)test_issue_3981.<locals>.Index2.__index__Nr  re   re   re   rf   Index2  r  r  r   r]   r   r^   r   r   r   r   r~   r   r   r   r   )r  r  index1index2ru   re   re   rf   test_issue_3981  s$   r  c                      sn   t tddg t fddtdD sJ t fddtdD s&J t fddtdD s5J d S )Nr   r   c                 3   s(    | ]}   |  |   kV  qd S r_   evalfrb   rT   re   rf   rg     s   & ztest_evalf.<locals>.<genexpr>r^   c                 3   ,    | ]}  d |  |  d kV  qdS r^   Nr  rb   r  re   rf   rg        * c                 3   r  r  r   rb   r  re   rf   rg     r  )r.   r   rk   r   re   re   r  rf   
test_evalf  s   "r  c                  C   s   t ttgttgg} |  du sJ t g dg dg} |  du s$J t g dddtdgg} |  du s8J t dtd	gg} |  du sHJ t g d
g} |  du sWJ t dgtgd	gg} |  du siJ t dgdgd	gg} |  du s{J d S )NTrs  rv  Fr   r   r   r~   r]   r   r^   )r.   rX   is_symbolicr  re   re   rf   test_is_symbolic  s   r  c                  C   sZ   t g dg} | jdu sJ t dgdgdgg} | jdu sJ tdd} | jdu s+J d S )Nr   Tr~   r^   r]   Fr   )r.   is_upperr;   r  re   re   rf   test_is_upper  s   
r  c                  C   sB   t g dg} | jdu sJ t dgdgdgg} | jdu sJ d S )Nr   Fr~   r^   r]   T)r.   is_lowerr  re   re   rf   test_is_lower  s   r  c                  C   sT   t ddg d} |  sJ t ddgddgg} |  rJ t g } |  s(J d S )Nr   )r   r^   r~   r   r   r   r~   r^   r   r   r   r]   r   r   r   r   r~   r   r.   r&  r  re   re   rf   test_is_nilpotent  s   r  c                  C   s"  d\} }t | |}|d dt| | }||ksJ |j|j  kr(dks+J  J |j|j  kr8dks;J  J |j|j  krHdksKJ  J t dt ddksVJ tdtddksaJ t ddtdddgd ksqJ tddtdddgd ksJ |d |t | |ksJ d S )N)r]   r   r   r]   r^   r   r   r~   )r;   fillr5   rl   rm   rj   r.   )rs   ru   rT   rU   re   re   rf   test_zeros_ones_fill  s   

     
r	  c                  C   sf   t d} | t ksJ t dd} | jdksJ | jdksJ t dd} | jdks*J | jdks1J d S )Nr   r^   )r;   r.   rl   rm   r  re   re   rf   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s-J 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s\J t ttd t dt tt  tt gdt t	tt	ttd ggtdt g dtdtdggksJ | 
tt tddtd  ttd  d gtd tt d td tt d ggksJ d S )Nr^   r~   r   )r~   r   r~   r]   )r.   rX   rY   r   r   r   r   limitr   r   r   r   r  re   re   rf   test_issue_3749  s(   ,."$
 &r  c                  C   sD   t d} | dd dD ]}| j|dd d| jdd	ksJ qd S )
Nr   r   r~   )r0  r7  c                 S   s   | dkS r  re   r   re   re   rf   r   -  r   z%test_inv_iszerofunc.<locals>.<lambda>)r2  
iszerofuncr9  r1  )r2   col_swapr   )r   r2  re   re   rf   test_inv_iszerofunc)  s   

r  c                  C   s   t d\} }t| t| | t| g}t| |g}||}|||jks)J ||j|ks3J ||j|jks>J |jt|jd  | }|t	}|tddgd| d ggks_J d S )Nrho,phir   r~   r^   )
r   r.   r   r   r  rW  r2   rj   r  r$   )rhophiXYr   r  re   re   rf   test_jacobian_metrics1  s   

$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sBJ d S )Nr  r^   r   )r   r.   r   r   r  )r  r  r  r  r   re   re   rf   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 ]D}tddD ]<}| d |d d f }|d |d d f }||}|j|ksNJ |j|ksUJ t|D ]}|d d |f |ksgJ qYq,q%d S Nr~   r]   )	r.   r   rX   rY   rZ   r   r  rl   rm   )r  r  rd   r   X_sliceY_slicer   kre   re   rf   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 r_   r  r.   rX   rY   rZ   re   r  re   rf   r   [  r   z(test_nonvectorJacobian.<locals>.<lambda>r   c                      s
     S r_   )r  re   r  r  re   rf   r   ^  r   c                      s     tttgttggS r_   r  re   r  re   rf   r   _      )r.   r   rX   rY   rZ   rI   	TypeErrorre   re   r  rf   test_nonvectorJacobianX  s    r!  c                  C   sP   t ddgddgg} |  }|jdksJ tdD ]}|| |d ks%J qd S Nr~   r]   r^   r   )r.   vecrm   r   )ru   m_vecrd   re   re   rf   test_vecb  s   r%  c                  C   s6  t ddgddgg} |  }|jdksJ tdD ]}|| |d ks%J q| jdd}|d dks4J t dttt  gtt td  dgg} | jdd}|d tt td  ks\J t dttt  gtt dgg} | jddd}|d tt ks}J ttdd	  ttd
d	  ttdd	  ttdd	  d S )Nr~   r^   r]   F)diagonalr   )r&  check_symmetryc                   S      t ddgg S r  r.   vechre   re   re   rf   r   {  rQ  ztest_vech.<locals>.<lambda>c                   S      t ddgddgg S r"  r)  re   re   re   rf   r   |      c                   S   r(  r  r)  re   re   re   rf   r   }  rQ  c                   S   r+  r"  r)  re   re   re   rf   r   ~  r,  )	r.   r*  rm   r   rX   rY   rI   r%   r   )ru   m_vechrd   re   re   rf   	test_vechj  s"   ( r.  c                      sZ   t g dtg dksJ dddgg tt fdd t  ddtg dks+J d S )	Nr   r~   r^   r]   c                      s   t  S r_   )r1   re   r   re   rf   r     r   ztest_diag.<locals>.<lambda>F)strict)r1   r.   rI   r   re   re   r   rf   	test_diag  s    r0  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s-J | |gks6J | |gks?J d S Nr~   r^   r]   )r.   rX   rY   rZ   get_diag_blocksrT   rU   rV   re   re   rf   test_get_diag_blocks1  s    r4  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s3J t| || | ||gksBJ t| || | ||gksQJ t||| |||gks`J d S r1  )r.   rX   rY   rZ   r1   r2  r3  re   re   rf   test_get_diag_blocks2  s    "r5  c               
   C   s  t ddgddgg} t dtgtdgg}t dtdgtdtgtttgg}t| ||}|jddt|  | | ks>J t| ||}|jddt|  | | ksXJ t| ||}|jddt|  | | ksrJ t| | || || }|jddt|  |  | |  | |  ksJ |jdddt| jdd| jdd|jdd| jdd|jdd| jddksJ d S )	Nr~   r^   r]   T)try_block_diagr9  )r6  r2  r1  )r.   rX   rY   rZ   r1   r   )rT   rU   rV   r   re   re   rf   test_inv_block  s"    ((($
r7  c                   C   s   t tdd  t tdd  ttdtdksJ ttdtdks&J t tdd  ttdtdks9J ttdtdksEJ t tdd  ttdtdtddks\J t tdd  t td	d  t td
d  dS )zg
    Check that matrix dimensions can be specified using any reasonable type
    (see issue 4614).
    c                   S   
   t ddS )Nr]   r   r;   re   re   re   rf   r     r   z$test_creation_args.<locals>.<lambda>c                   S   s   t ddddS Nr~   r^   r]   r   r9  re   re   re   rf   r     r   r]   c                   S      t dS Ng      @r9  re   re   re   rf   r     r   c                   S   r;  r<  r2   re   re   re   rf   r     r   r   c                   S   r;  r  r   re   re   re   rf   r     r   c                   S   r8  r}   r   re   re   re   rf   r     r   c                   S   s   t ddggS r}   r   re   re   re   rf   r     r   N)rI   r   r   r;   ra   r
   r2   r5   re   re   re   rf   test_creation_args  s    r>  c                  C   sX  t ddg d} |  rJ |  sJ | jddsJ t ddg d} |  s*J tddd} |  s6J |  s<J t ddg d} | tdddksNJ t ddtdd} |  r]J |  scJ t d	} |  smJ t d
} |  swJ t dddtd dt  d ttd d ddtddg	} |  sJ | jddrJ |  jddsJ d S )Nr^   r   r~   r~   r   Fr#   r  r~   r]   )	r~   r   r   r   r^   r   r   r   r]   ))r   r   r   r   )r   r   r   )r   r   r   r   )r.   is_diagonalis_symmetricr1   r;   rX   rY   r   r   re   re   rf   test_diagonal_symmetrical  s,   6rD  c                     sb  t ddt gdt dgg   sJ t ddg d   r"J   r(J tt fdd tddd   \} }| tdksEJ | ksKJ t ddg d   sYJ   s_J   \} }| 	   |  |ksqJ t ddg d   sJ   sJ   \} }| 	   |  |ksJ | tdksJ | ksJ t ddg d	   sJ   \} }| 	   |  |ksJ t ddg d
   sJ   \} }| 	   |  |ksJ | D ]}|
 d dksJ qt ddg d   sJ   s
J   \} }| 	   |  |ksJ | t ddgddggks,J t ddg d  dr<J tt fdd   sLJ   \} }| 	   |  |ks_J t ddg d   rnJ tt fdd t ddg d   rJ tt fdd td\}}}}t dd||||g   sJ   sJ d S )Nr~   r^   r]   r   r~   r   rL  r]   r   c                            S r_   r,  re   r   re   rf   r     r   z&test_diagonalization.<locals>.<lambda>r?  )r~   r   r   r]   r~   r~   r   r   )	r~   r^   r   r   r]   r   r^   r  r^   rt  r   )r   r~   r   r   Tc                      r  )NTrG  re   r   re   rf   r     r   r   r~   r   r   c                      rF  r_   rG  re   r   re   rf   r     r   )	r   r~   r   rL  r]   r   r^   r   r   c                      rF  r_   rG  re   r   re   rf   r      r   za b c d)r.   r	   r(  rC  rI   r'   r1   r,  r2   r   as_numer_denomrB  r&   r   )r   r  rd   rT   rU   rV   rW   re   r   rf   test_diagonalization  sl   rK  c                      s   t ddgddgg   du sJ d d<   du sJ t ddgddgg    d d< tt fdd t   jdd W d    n1 sMw   Y  t   jdd	 W d    d S 1 sgw   Y  d S )
Nr   r~   Tr   Fc                      rF  r_   rG  re   r  re   rf   r   3  r   z"test_issue_15887.<locals>.<lambda>)clear_cache)clear_subproducts)r<   r(  r,  rI   r&   rM   re   re   r  rf   test_issue_15887)  s   "rN  c                     s:  t ddg d tt fdd t ddg d t ddg d}   \}}| |ks-J |   d ks7J t ddg d	 t ddg d
}   \}}| |ksSJ t ddg d t ddg d}   \}}| |ksoJ t ddg d t ddg d}   \}}| |ksJ t ddg d t ddg d}   \}}| |ksJ t ddg d t ddg d}   \}}| |ksJ t ddg d   rJ t ddg d}   \}}| |ksJ t tdddtdddgtdddtdddgg   \}}| D ]}t|tr|j	dksJ q	d S )Nr]   r^   rE  c                      rF  r_   )r   re   r   re   rf   r   @  r   z"test_jordan_form.<locals>.<lambda>)	r   rI  r   r   ir   r   irk  )	r   r   r   r   r~   r   r   r   r~   r~   	r   r~   r   r  r   r   r   r~   r^   )	r^   r~   r   r   r^   r   r   r   r^   )	r^   r   r~   r~   r  r~   r^   r   )	r   r~   r   r   r   r   r   r   r   )	r   r  r^   r   r#  r]   r   r   )	r   r~   r   r   r   r   r   r   r~   r   )r   r   r   r   r   r   r]   r]   r^   r~   r   r   r   r~   r   r   )r^   r~   r   r   r   r^   r   r   r   r   r^   r~   r   r   r   r^   )r   r^   r   r   r^   r   r   r^   r   rR  r   r   r   r]   r   )r   r   r   r   r   r^   r~   r   r   r   r^   r   r   r   r   r^   )r   r   r^   r~   r   r~   r   r   r   r   r]   r   r~   r~   r   r^   )r~   r   r   r   r   r^   r   r   r   r   r   r~   r   r   r   r   z1.0n   )	precisionz2.0z3.14159265358979323846264338327z4.0)
r.   rI   r'   r   r,  r(  r   valuesr   _prec)Jmustr   r   termre   r   rf   test_jordan_form=  sR   
rY  c                  C   s   t g dg dg dg dg} ddt  }ddt  }t |dddgd|ddgdd|dgddd|gg}t |dddgd|ddgdd|dgddd|gg}|  \}}||ks\||ks\J t|| |  | ksjJ d S )	N)r^   r   r~   r   )r  r^   r   r~   )r   r   r^   r   )r   r   r  r^   r^   r   r~   r   )r.   r	   r   r#   r   )r   pqJmust1Jmust2r   r   re   re   rf   #test_jordan_form_complex_issue_9274  s(   





 r^  c                  C   s   t g dg dg dg dg} |  \}}|t g dg dg dg dgks*J |t g d	g dg dg dgks>J d S )
Nr  r?  )r   r   r~   r~   r+  r   r~   r   r~   rt  rI  rr  rH  )r.   r   r   re   re   rf   test_issue_10220  s"   
r`  c               
   C   s   t g dg dg dg dg} |  \}}| t t t d ttd gdt ddt dgdtd d td  dtd d td  gg d	gksNJ |t t dddgdt ddgddtdgdddtggkslJ d S )
Nr*  )r   r   r   r   )r   r   r   r   )r   r   r^   r~   r^   r   r   r~   r_  )r.   r   r   r	   r   )r   r   r   re   re   rf   test_jordan_form_issue_15858  s&   .

ra  c                  C   sr  t d\} }}t| |  |d ||   || ||  g|| ||  | |d ||   gg}|t}|ttd ||  ||   d| |  ||  t  || |  ||   tddksaJ t|tu siJ tddgddgg}| |t  krttd t d ksJ  J tddgtdgg}|t}|jtksJ | 	|jttd dt  ksJ d S )	Nz
UA K_i K_wr^   zZZ(K_i,K_w,UA)r   r~   r]   r   r   )
r   r.   r   rX   r   r`   r   genas_exprr   )UAK_iK_wr   r   rZ  re   re   rf   test_Matrix_berkowitz_charpoly  s&   *$
06
*rg  c                  C   s   t d} td| }| tt| ggksJ td| }| tt| t| t| d gdt| t| gddt| ggksBJ d S )Nlamdar~   r]   r^   r   )r   r.   jordan_block_eval_matrix_exp_jblockr   )lru   re   re   rf   test_exp_jordan_block  s   rl  c                  C   s  t ddgddgg} t tddtd d dtd d  gdtdgg}|  |ks.J t| |ks6J t ddgddgg} |  t tdgdtggksPJ t| t tdgdtggks`J 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sJ d S )	Nr]   r   r   r   r  r   r~   r   )r.   r   r   r   r   )ru   m_expre   re   rf   test_exp  s   8  Frn  c               
      s   t d} td|    tt| ggksJ 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s\J tg dg d	g d
g tt fdd d S )Nrh  r~   r   r   r^   r]   r   r   r   r   c                      rF  r_   )r   re   r   re   rf   r     r   ztest_log.<locals>.<lambda>)r   r.   ri  _eval_matrix_log_jblockr   rI   r&   )rk  re   r   rf   test_log  s(   *
rp  c                  C   sX   t ttfdf} | tsJ | trJ | tsJ | td} | tr*J d S )Nri  r^   )r.   rX   rY   hasrZ   r   r   r   re   re   rf   test_has
  s   rr  c                  C   sR   t d} tdd| t| d t| d  tjg}t|\}}}}|tjks'J d S )NrX   r]   r~   r^   )r   r.   r   r   r   r   r)   rX   columnpivot_offset	pivot_valpivot_assumed_nonzero
simplifiedre   re   rf   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero1  s
   (
ry  c                  C   sn   t d} tdd| t| d t| d  | d  t| d t| d  g}t|td\}}}}|dks5J d S )NrX   r]   r~   r^   simpfunc)r   r.   r   r   r)   r*   rs  re   re   rf   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero2   s   

r|  c                  C   s   t d} tdd| t| d t| d  |  t| d t| d  g}t|td\}}}}t|dks5J |d d dks?J |d d d|  ksKJ |d d dksUJ |d d dks_J d S )NrX   r]   r~   r^   rz  r   )r   r.   r   r   r)   r*   lenrs  re   re   rf   +test_find_reasonable_pivot_naive_simplifies/  s   

r~  c                      s  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t td	d  t td
d  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t  tddgddggtddgddgg W d    n1 sw   Y  t tdd  t tdd  t tdd  t tdd  t tdd  t td d  t td!d  t td"d  t td#d  t td$d  t td%d  t td&d  t td'd  t td(d  t td)d  t td*d  t td+d  t td,d  t td-d  td. t t fd/d tg d0gtg d1g d2g d3g t t fd4d tg d1g d2g d3g t t fd5d d S )6Nc                   S   s   t ddgdggS r}   r   re   re   re   rf   r   B  rQ  ztest_errors.<locals>.<lambda>c                   S      t ddggd S )Nr~   r^   )g333333?r   r   re   re   re   rf   r   C  rQ  c                   S   r  )Nr~   r^   )r~   g@r   re   re   re   rf   r   D  rQ  c                   S   s   t ddddS )Nr]   r   T)rV   r  )r6   re   re   re   rf   r   E  r   c                   S   s   t ddgddS )Nr~   r^   r   r   )r.   r  re   re   re   rf   r   F  r   c                   S   s(   t ddgddggddgt ddgS Nr~   r^   r]   r   r   )r.   copyin_matrixre   re   re   rf   r   H     ( c                   S   s"   t ddgddggddgt S r  )r.   copyin_listsetre   re   re   rf   r   I  s
    c                   S   s   t g dg dg S )Nr   )r^   r]   r   r.   r   re   re   re   rf   r   K  r,  c                   S   s&   t ddddgt ddgddggS r:  )r.   row_joinre   re   re   rf   r   M     & c                   S   s"   t ddgt ddgddggS r:  )r.   col_joinre   re   re   rf   r   O  s   " c                   S   "   t dgdt ddgddggS r:  )r.   
row_insertre   re   re   rf   r   P  
    c                   S   r  r:  )r.   
col_insertre   re   re   rf   r   R  r  c                   S      t ddg S r}   r  re   re   re   rf   r   T  r   c                   S   s   t dgdS r  )r.   r  re   re   re   rf   r   U  r   c                   S      t ddgddggddS Nr~   r^   r]   r   r   )r.   minorre   re   re   rf   r   V      c                   S   r  r  )r.   minor_submatrixre   re   re   rf   r   W  r  c                   S      t g ddS Nr   r~   r.   crossre   re   re   rf   r   X  rQ  c                   S   r  r  r.   dotre   re   re   rf   r   Y  rQ  c                   S   s   t g dt ddgS )Nr   r~   r^   r  re   re   re   rf   r   Z  r  c                   S   s   t ddgg S r}   r  re   re   re   rf   r   [  rQ  c                   S   s   t ddgdS )Nr~   r^   rT   r  re   re   re   rf   r   \  rQ  r~   r^   r]   r   c                   S   s   t ddgg dS )Nr~   r^   r   r  re   re   re   rf   r   _  rT  c                   S   s   t g d S )Nr   )r.   r   re   re   re   rf   r   `  r   c                   S   r+  r:  )r.   
normalizedre   re   re   rf   r   a  r,  c                   S   s   t ddgjddS )Nr~   r^   znot a methodr1  r  re   re   re   rf   r   b  r   c                   S   r  r}   r.   
inverse_GEre   re   re   rf   r   c  r   c                   S      t ddgddgg S r}   r  re   re   re   rf   r   d  r,  c                   S   r  r}   r.   inverse_ADJre   re   re   rf   r   e  r   c                   S   r  r}   r  re   re   re   rf   r   f  r,  c                   S   r  r}   )r.   
inverse_LUre   re   re   rf   r   g  r   c                   S   r  r}   r  re   re   re   rf   r   h  r   c                   S   r  r}   r.   r  re   re   re   rf   r   i  r   c                   S   s   t ddgddggjddS )Nr~   r^   r]   r   zNot a real methodr1  r  re   re   re   rf   r   k  r  c                   S   (   t g dg dg dg dgjddS )Nrs  rv  rw  rx  zNot functionr  r  re   re   re   rf   r   m  
    c                   S   r  )Nrs  rv  rw  rx  Fr  r  re   re   re   rf   r   p  r  c                   S   s*   t tddgddggtddgddggS r:  r3   r.   re   re   re   rf   r   s  s   * c                   S   s   t tddgddggg S r:  r  re   re   re   rf   r   t  r  c                   S   s   t tdd dS )NrX   r^   rT   )r3   r   re   re   re   rf   r   u  rQ  c                   S   rM  )Nr]   )r   r^   r=  re   re   re   rf   r   v  r   c                   S   rM  )Nr]   )r^   r   r=  re   re   re   rf   r   w  r   ru  c                      r  )Nzmethod=LU_decomposition())r  re   r   re   rf   r   y  r   )r   r   r   r   r^   r]   r   r   c                           dS )Ng@)r  re   r   Vre   rf   r   |  r   c                      r  )Ng)r  re   r  re   rf   r   ~  r   )	rI   r   rU  r%   r   r'   rM   r.   r  re   re   r  rf   test_errorsA  s   ,r  c                   C   s   t t dks	J t tddggt tdgdgg  kr#dks&J  J t tdddd t tdddd   krAdksDJ  J t tg dg dgd	ksTJ tdgtdggksaJ t rfJ t tg ksoJ d S )
Nr   r~   r^   c                 S   r  r  re   r   re   re   rf   r     r  ztest_len.<locals>.<lambda>c                 S   r  r  re   r   re   re   rf   r     r  r   r   r   )r}  r.   re   re   re   rf   test_len  s   : 
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s=J | 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shJ d S )Nr~   r   r^   r   r   r]   r.   rX   rY   r   r   re   re   rf   test_integrate  s   $FFr  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s*J d S )	Nr~   r   r^   r   r   r   )r~   r   r~   )r   r   r~   )r.   r   rX   rY   r  r   re   re   rf   
test_limit  s   0(r  c                  C   sT  t ddtftddfddtd d ff} t| tt| s J | tt dddddt ffks3J | tt d	ks>J t| tt dddddt ffksQJ t| tt d	ks\J |  }t|tt|slJ |ttdddddt ffksJ |ttd	ksJ t|ttdddddt ffksJ t|ttd	ksJ d S )
Nr~   r   r^   r   r   r   r   r   )r   r  r   )r<   rX   rY   r   r   r`   rY  r=   )r   A_immre   re   rf   	test_diff  s   (&&&&r  c               
      sn  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s3J 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s\J |  }||tddgddggddgddgggddgddggddgddggggksJ t||tddgddggddgddgggddgddggddgddggggksJ | tt ddgddggksJ t	tt
g}| |tddddksJ | | tddgddggddgddgggddgddggddgddggggksJ |tt
gg}|jdksJ |tdgdggdgdgggks%J td}|ttt  tttggt t t tgksKJ  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sJ tttt }|ttggttttt tttt gksJ |tttffttttt tttt gksJ |tttffttt tt tttt gksJ |ttffttggttttt tt tt gtttt tttt ggks J  ttt tttffdd ks:J  ttt tttffdd ksTJ  tttggtttfft fd	d
tttfD kssJ ttttgg}t|t	sJ |tddggksJ td tttgg}t|t	sJ |tdtd  dggksJ d S )Nr~   r   r^   )r^   r^   r~   r  r]   r   r  c                    s&   g | ]  fd dt ttfD qS )c                    s   g | ]
}  | qS re   )r   rb   )fxyzr   re   rf   r    r  z2test_diff_by_matrix.<locals>.<listcomp>.<listcomp>)rX   rY   rZ   )rc   r  )r   rf   r    r  z'test_diff_by_matrix.<locals>.<listcomp>)r<   rX   rY   rZ   r[   r   rQ   rY  rT   r=   rU   r;   rj   r   r   r   r   r.   r   )r   r  BdBr  exprresre   r  rf   test_diff_by_matrix  sF   RRRR"T&8   :<>d44>$r  c                      sh   t ddtftddfddtd d ff tt fdd t dtt d	d
dddt ffks2J d S )Nr~   r   r^   r   r   c                      s    j S r_   )nonexistantattributere   r   re   rf   r     s    ztest_getattr.<locals>.<lambda>r   r   r   r   )r.   rX   rY   rI   r  getattrre   re   r   rf   test_getattr  s   (.r  c                  C   s   t g dg dg dg} | jsJ | j} | jsJ d| d< | jdu s%J t g dg dg dg} | jr7J tdd	} | jsAJ d S )
N)r]   r   r~   )r^   r   r   r   r~   )r   r   Fr  r   r^   )r.   is_upper_hessenbergrW  is_lower_hessenbergr;   r   re   re   rf   test_hessenberg  s   



r  c                  C   s&  t tdd  t tdd  t tdd  t tdd  t tdd  tdt dfd	fjd
dttdt dgddggksAJ td} | jd
d}|tddgddtd t ggks_J ||j | kshJ td} |  }||j | ksyJ |js~J |tg dg dg dgksJ tddt ddt  fdt ddt fddt  dt dff} |  	 tdtddfdt ddffksJ t tdd  t tdd  t tdd  t tdd  t tdd  t
dt dfd	fjd
dttdt dgddggksJ t
d} | jd
d}|tddgddtd t ggks'J ||j | ks1J t
d} |  }||j | ksCJ |jsIJ |tg dg dg dgks[J t
ddt ddt  fdt ddt fddt  dt dff} |  tdtddfdt ddffksJ d S )Nc                   S      t d S Nr   r.   choleskyre   re   re   rf   r     r   ztest_cholesky.<locals>.<lambda>c                   S   r  Nr   )r]   r   r  re   re   re   rf   r     r   c                   S      t dt dfdf S Nr   r   r   )r.   r	   r  re   re   re   rf   r     r,  c                   S   r  N)r~   r   )r   r~   r  re   re   re   rf   r     r   c                   S      t djddS Nr  F	hermitianr  re   re   re   rf   r     r   r   r   r   Fr  r~   r  r^   r   ))   r   r  )r   r   r   )r  r   rj  rA  )r]   r]   r   )r   r~   r]   r   r   r   rj  r   r]   c                   S   r  r  r/   r  re   re   re   rf   r   
  r   c                   S   r  r  r  re   re   re   rf   r     r   c                   S   r  r  )r/   r	   r  re   re   re   rf   r     r,  c                   S   r  r  r  re   re   re   rf   r     r   c                   S   r  r  r  re   re   re   rf   r     r   )rI   r'   r   r.   r	   r  r   rW  r  r   r/   )r   r  re   re   rf   test_cholesky  sL   (
"@.*$@0r  c                  C   s  t ddd} tt| t| g}t|ddksJ |dtt| d t| d  tddks4J tdtddgg}| td	td
d tj	ksOJ |t
t|ksZJ |t
 t|ksfJ tddgddgg}|ddksyJ |ddksJ |ddksJ tddtdd  krdksJ  J |t
dksJ tdttg| tj	t gg}|dttdddttd   td  | d  ksJ tg dddtddgg}|dttddtdd  ksJ |dtju sJ |dtdd ksJ tddgddgg}tddgddgg}tdt gtdgg}tddgddgg}||||g}t ddd}dD ]W}td|tju sYJ |D ]!}	|D ]}
|	||
| |	|
 | }|dksyJ q_q[||||fD ]}t|| |t|||  }|dksJ qqJtdddt  dg}ttj	dt dg}tg d}tddtg}ttdtdddg}|||||g}t ddd}ddddtjtjtfD ]q}|dkrtg d|tju sJ |dkr,|D ]&}	|D ] }
|	||
| |	|
 | }t|dktju s(J q	q|ddddtjtjfv rX|D ]}	t||	 |t||	|  }|dksVJ q;qtddg d}|ddkslJ d S )NrX   Tr  r^   r~   r   r   r]   r  r   r   r   r   	frobeniusfro%   )r~   r^   r   rk  i  r   iI3 r   alpha)r  r^   r   r   )r   r   r   g      Y@r   )	r~   r]   r   r   r   r   r]   r   r   )r   r.   r   r   r$   normr   r   r   r   r   maxr  r2   rY   r   r   r   rc  r	   r;   r#   r
   InfinityNegativeInfinitytrue)rX   r   r   r  r  r  r  r  orderr  r  difr   rT   rU   rV   rW   ere   re   rf   test_matrix_norm  s   2"0,(

r  c                     s   t dddtd} d| d< tdd| d< |  d	ksJ | d
< |  tdtttddt ks8J 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 sqJ tg  dks{J d S )NrX   Tr  r]   r   r   r~   r^   r^   r   r   c                 3   s*    | ]}t d  | V  qdS )r   N)r   
epsilon_eqr   r  )rc   valMcrX   re   rf   rg     s   ( z(test_condition_number.<locals>.<genexpr>r   r^   r   r   r   )r   r2   r   condition_numberr   r   r   r.   r   r   rk   r   r   r   )r   r   re   r  rf   test_condition_number{  s   .&*r  c                  C   s   t d} t d}| | d d d d f ksJ | | d d d d f kr$J | |kr*J | |ks0J | dks6J | dkr<J td}t d}||ksJJ ||krPJ d S )N)r   r  r   r   r   ))r   r   r   )r   r   r   )r]   r^   r~   r   )r  r   r   )r.   r/   )r   r  r  r  re   re   rf   test_equality  s   r  c                   C   s@   t dtg dgtg dg dg dg dgksJ d S )Nr]   )r   r   r   r  r   r   )r2   r  r.   re   re   re   rf   test_col_join  s   r  c                  C   s\   t g dg} tddD ]}g d}||d ttd|| d |ks+J qd S )Nr   r   r   r  r   r  r   r]   r   )r.   r   insertrD   r2   r  r  rV  )r4rd   rk  re   re   rf   test_row_insert  s   (r  c                  C   sZ   t g d} tddD ]}g d}||d ttd|| d |ks*J qd S )Nr  r  r   r   r   r]   r   )r.   r   r  rD   r;   r  r  rV  )c4rd   rk  re   re   rf   test_col_insert  s   (r  c                  C   s|   t ddg t tddtddgksJ t g d t g dks&J t g d} | jdd dt g dks<J d S )	Nr]   r   r   r   )r   r   g0.++c                 S   s   | j dddjS )Nr   T)rs   chop)r  is_zeror   re   re   rf   r     r   z!test_normalized.<locals>.<lambda>r  )r.   r  r   r   re   re   rf   test_normalized  s    
r  c                   C   s,   t dd dks
J t dd dksJ d S )Nc                   S   r  r{  r2   print_nonzerore   re   re   rf   r     r   z$test_print_nonzero.<locals>.<lambda>z[X  ]
[ X ]
[  X]
c                   S   s   t ddS )Nr]   .r  re   re   re   rf   r     r   z[.  ]
[ . ]
[  .]
)rE   re   re   re   rf   test_print_nonzero  s   

r  c                  C   s   t dtdksJ t dtdksJ tddt dddgd ks&J t ddgddgg} t ddgddgg}tD ]<}|d}| |ksIJ | td|dksSJ t||ks[J |d}||ksfJ |td|dkspJ t||ksxJ q<d S )Nr]   r   r~   r   r   r^   r  )r.   r2   r;   r5   ri   r`   )rd   rZ   rt   ru   re   re   rf   test_zeros_eye  s    

r  c                  C   s  t  jsJ t ddgddggjsJ tddjsJ tdjr"J t tdgddggjd ks1J ttdgddggjd ks@J ttdgddggjd ksOJ ttdgddggjd ks^J t tdgddggjdksmJ tddd} t | dgddggjdksJ d S )	Nr   r]   r   r~   FrT   T)nonzero)	r.   is_zero_matrixr;   r2   rX   r/   r,   r-   r   r  re   re   rf   test_is_zero  s   "r  c                  C   s&  t d } t| }t|  }t| }t|  }t| }t|  }|| td tdks-J || td tdks;J || td tdksIJ | ddt|   ksWJ | ddt|   kseJ | ddt|   kssJ tdtdks}J tdtdksJ tdtdksJ d S )Nr]   r~   r^   r   )r   r9   r8   r7   r2   r  r   )thetar3_plusr3_minusr2_plusr2_minusr1_plusr1_minusre   re   rf   test_rotation_matrices  s    


r  c                   C   sj   t tdd dksJ ttdtdksJ ttdd  t tddks)J ttddks3J d S )	Nvectorr   z	vector[4]rW   c                   S   rM  )NrW   r   )r(   re   re   re   rf   r   	  r   z%test_DeferredVector.<locals>.<lambda>testzDeferredVector('test'))strr(   r   rI   rU  reprre   re   re   rf   test_DeferredVector	  s
   r  c                   C   s   t tdrJ d S )Nr  )rF   r(   re   re   re   rf    test_DeferredVector_not_iterable	  s   r  c                   C      t tdd  d S )Nc                   S   s   t tdS )Nr  )r.   r(   re   re   re   rf   r   	  r   z,test_DeferredVector_Matrix.<locals>.<lambda>)rI   r   re   re   re   rf   test_DeferredVector_Matrix	     r  c                  C   s8  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s2J t|j|jgtddddgtdd| dd | dd ggksTJ 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sJ ttdg}t|tdgggksJ d S )Nr~   r^   r]   r   r   Tr   )r   r.   r+   rW  r   r!   )r   rn  ro  r  re   re   rf   test_GramSchmidt	  s   
.. 
r  c                   C   s4   t g dddksJ t g dddddksJ d S )Nrs  r~   r   F)zero)r0   re   re   re   rf   test_casoratian"	  s   r	  c                   C   s^   t  tdd jdksJ tddtdd tddksJ tddtdd t  ks-J d S )Nr   r]   )r   r]   )r.   r;   rj   re   re   re   rf   test_zero_dimension_multiply'	  s   ""r
  c                      s   t ddtd  dd d f t ddggksJ  dd d f t ddggks*J  d d df t ddggjks<J  d d df t ddggjksNJ tt fdd tt fdd d S )	Nr^   r   r~   r]   r   c                      s    dd d f S r  re   re   r   re   rf   r   3	  r   z'test_slice_issue_2884.<locals>.<lambda>c                      s    d S )Nr  re   re   r   re   rf   r   4	  r   )r.   r   rW  rI   rU  re   re   r   rf   test_slice_issue_2884-	  s   ""$$r  c                   C   sJ   t ddd d df jdksJ t dddd d f tddg ks#J d S )Nr   r]   r   r   r~   )r;   rj   r.   re   re   re   rf   test_slice_issue_34017	  s    *r  c                  C   s  t dd} d| d< | d d df tg dksJ | d dks!J | dd dgks,J d| d< | d dks8J | ddd f tddggksIJ tdd	gg| ddd f< | dd d f tg d
gksgJ ddgg| ddd f< | dd d f tg dgksJ d| d< | d d d df tg dksJ g d| d< | d d df tg dksJ tg d| d< | d d df tg dksJ tg d| d< | d d df tg dksJ d S )Nr]   r~   r   r   r   r  r   r   r   )r~   r   r   +   )r~   r  r     r   )r  r~   r   r~   r~   r~   )r;   r.   r/   )r  re   re   rf   test_copyin<	  s(   
 """$  $r  c                      s   t ddgddgg t ddgddggdfksJ ttdd  t g dtddgdtdgg t  d  jks=J   d td	ksIJ  jtd
d td	ksWJ tt fdd tt fdd tt fdd d S )Nr~   r^   r   )r   c                   S   r  r}   r  re   re   re   rf   r   W	  r,  z'test_invertible_check.<locals>.<lambda>)r   r   r   r   r]   r@  c                          j ddS )Nr9  r1  r   re   r   re   rf   r   b	  r   c                      r  )Nr0  r1  r  re   r   re   rf   r   c	  r   c                      r  )Nr7  r1  r  re   r   re   rf   r   d	  r   )	r.   r  rI   r   rX   r}  rl   r2   r"   re   re   r   rf   test_invertible_checkS	  s   4r  c                  C   s@   t d\} }| | }|| tg dtg d| ksJ d S )Nzx, y)r]   r   r]   )r   r   r.   )rX   rY   r  re   re   rf   test_issue_3959g	  s   ,r  c                   C   s$   t tddgddggdksJ d S )Nr~   r^   r]   r   zMatrix([[1, 2], [3, 4]]))r   r.   re   re   re   rf   test_issue_5964m	  s   $r  c                  C   s<   t d\} }tt| d| g|d | d ggdksJ d S )Nx yr^   r]   z'Matrix([
[   x,   2*y],
[y**2, x + 3]]))r   r    r.   )rX   rY   re   re   rf   test_issue_7604q	  s   "r  c                	   C   s   t djsJ t d jsJ tdjrJ tdjrJ tg dgjr(J tddddddjs5J tddtdjr@J tdddddjrLJ tddddddddjr[J d S )	Nr]   r  r~   )r   r   r  r^   r   )r   r   )r   r   r  r   )r   r^   )r2   is_IdentityrY  r;   r5   r.   r/   r   re   re   re   rf   test_is_Identityw	  s   "r  c                  C   s  t ddt dddksJ t ddg ddksJ tg dtg ddks.J tdddt gttddt gdt ksGJ tdddt gjttddt gdd	dt ksbJ tdddt gjttddt gd
d	dt ks}J tdddt gjttddt gd
dddt ksJ tdddt gjtddt dgd
ddddt  ksJ tdddt gjtddt dgd
ddddt  ksJ ttdt gjttdt gddddksJ ttdt gjttdt gdddksJ ttdd  t ) tddgddgg} tddgddgg}| |g dks0J W d    d S 1 s<w   Y  d S )Nr~   r]   r  r   rl  r^   r  Fr  Trk  physicsr  conjugate_conventionr   r   r   rightr   left)r  c                   S   s    t ddgjt ddgdddS )Nr~   r^   r]   r   Tr  r  r  re   re   re   rf   r   	  s     ztest_dot.<locals>.<lambda>)rj  r   ry  r   )r5   r  r.   r	   rI   r   rM   )r   r  re   re   rf   test_dot	  s"   "2668<<00$r  c                  C   s   t ddd\} }}}}}td|||f| d|| f| | d| f| ||  dff}td|  | | f| d|| f|| d|f||| dff}| |sQJ td tds^J |  | sjJ d S )NzB_x B_y B_z E_x E_y E_zTr  r   r]   )r   r.   dualequalsr2   r;   )B_xB_yB_zE_xE_yE_zFFdre   re   rf   	test_dual	  s$   
r*  c                  C   s   t ddg du sJ t dddtd dt  d ttd d  dtt t t t dg	} |  du s6J | jdddu s@J | jdd	 ddu sLJ | d
  | d
< |  du s[J | d
  | d
< |  } | jdddu spJ d| d< |  du s|J d S )Nr~   r^   Fr]   r   Tr@  c                 S   s   | S r_   re   r   re   re   rf   r   	  r  z%test_anti_symmetric.<locals>.<lambda>r   r   )r.   is_anti_symmetricrX   rY   r   r   re   re   rf   test_anti_symmetric	  s   Dr,  c                  C   s   t d} | jdd\}}||j |j|   kr t|jks#J  J | jddd\}}||j |j|   kr@t|jksCJ  J || |  | ksOJ d S )N)r   r   T)	normalize)r-  sort)r.   r,  rW  r2   rm   r   )r   r   rP   re   re   rf   #test_normalize_sort_diogonalization	  s   ..r/  c                   C   r  )Nc                   S   s   t g dt ddg gS )Nr   r   r~   r   re   re   re   rf   r   	  r,  z!test_issue_5321.<locals>.<lambda>)rI   r   re   re   re   rf   test_issue_5321	  r  r0  c                  C   s   t tddtd t g dg dgksJ t tddtd t ddgddgddgddggks6J t} | | td| dtd t g dg dgksTJ d S )Nr^   )r~   r   r^   r   )r   r~   r   r^   r~   r   )r.   hstackr2   vstackr/   r  re   re   rf   test_issue_5320	  s    r3  c                  C   sV   t dgg} t| }t || t ddggksJ t || t dgdggks)J d S r  )r.   r   r1  r2  )r   AImre   re   rf   test_issue_11944	  s   $r5  c                     s   g d} g d}t g d}|j} fdd}tD ].  | } |}|||| |||j| ||j|j| ||j|| qttdd  d S )Nr   r   )r   r   r   c                    s    || ksJ t |  ksJ d S r_   )r`   )r   r  r  re   rf   r  	  s   ztest_cross.<locals>.testc                   S   s"   t ddddgt ddddgS r}   r  re   re   re   rf   r   	  s   "ztest_cross.<locals>.<lambda>)r.   rW  ri   r  rI   r%   )rT   rU   r  r  r  r   r  re   r  rf   
test_cross	  s   r6  c                  C   sr   t dd  D ]} | d| dh}t|dkr!| | dks#J qt d d D ]} t| dtr6J q*d S )Nr   r~   r^   )ri   r2   r}  popr   r   )rt   r  re   re   rf   	test_hash	  s   $r8  c                      s   t d  tt fdd d S )Nr   c                      s   t  dS r  )hashr2   re   r  re   rf   r   
  r   z!test_issue_3979.<locals>.<lambda>)ri   rI   r  re   re   r  rf   test_issue_3979 
  s   r:  c                  C   sH   dt gddgg} tddgt  dgg}tD ]}|||  ks!J qd S Nr   r~   )r	   r.   ri   adjoint)r]  r  rt   re   re   rf   test_adjoint
  s
   r=  c                   C   s8   t tttd ttd  ggtdggksJ d S )Nr^   r~   )r#   r,   r   rX   r   re   re   re   rf   test_simplify_immutable
  s   "
r>  c                     sT   t dtd\ tddfdd} tdd fdd}| }|| ks(J d S )NF, Gr  r^   c                        | | S r_   re   r   )Gre   rf   r   
  r   ztest_replace.<locals>.<lambda>c                    r@  r_   re   r   r(  re   rf   r   
  r   )r   r   r.   replace)Kr   Nre   )r(  rA  rf   test_replace
  s
   rF  c                     s   t dtd\ } t : tdd| d d| dif| d d| dif| d d| dif| d d| difg}W d    n1 sHw   Y  tdd fdd}ttdd	 | | d
}W d    n1 sow   Y  ||kszJ d S )Nr?  r  r^   r   r~   c                    r@  r_   re   r   rB  re   rf   r   
  r   z"test_replace_map.<locals>.<lambda>F)test_stacklevelT)r   r   rM   r.   rN   rH   rC  )rA  rD  r   rE  re   rB  rf   test_replace_map
  s   2,rH  c                  C   sT   t ddgtddt  gg} |  tjtdtjthksJ | tthks(J d S r}   )r.   rX   atomsr   rb  NegativeOner   r   re   re   rf   
test_atoms#
  s    rK  c            	         s  t ttgttgg} t| jddt|  ksJ t ddgddgddggt g d	g d
gt ttgg}|D ]2}|jdd}|| }|| }t|| |ksRJ t|| |ks\J |j|kscJ |j|ksjJ q8|D ]4}t|jdd}|| }|| }t|| |ksJ t|| |ksJ |j|ksJ |j|ksJ qmddl	m
  | jdd}|  }tdtdtdtdi}t fddt||||D sJ d S )NRDr1  rk  h   i  r]   r   r   )r~   r   r   )rj  r     EDr   compi_ib,  i  ij  c                 3   s&    | ]\}} |  |  V  qd S r_   r   )rc   rd   r   rP  re   rf   rg   P
  s
    
ztest_pinv.<locals>.<genexpr>)r.   rT   rU   rV   rW   r#   pinvr   r  sympy.core.numbersrQ  rk   zipr   )	A1Asr   A_pinvAApApAr[  wrepsre   rP  rf   	test_pinv)
  s:    
r\  c                  C   st   t g dg dg dg dg dg dgg} | D ]}|jdd}|| }|| }|j|ks0J |j|ks7J qd S )	N)=   r   7   rL  r  r   )>   `   U   ra  ry  r   )E   8   r  r   6   r   )r   rd  [   )   r  r   )r   r  r   r   Z   r   )r   r   r   r   r   r   rO  r1  )r.   rR  r  )rV  r   rW  rX  rY  re   re   rf   3test_pinv_rank_deficient_when_diagonalization_failsV
  s    	rh  c                   C   sL   t ddt dd tddg ksJ t ddt dd tddg ks$J d S r;  )r5   r.   re   re   re   rf   test_issue_7201l
  s   $(ri  c                  C   s2   t tttfD ]} | tgdggjthksJ qd S r  )r,   r-   r.   r/   rX   free_symbolsr   re   re   rf   test_free_symbolsp
  s   rk  c                      s^  zddl m  W n ty   td Y nw t g dtg dks&J t g dgtg dgks8J t g dg dgtg dg dgksPJ t tttgttttgksbJ tt	 fdd t dd	g d
dggtdd	gd
dggksJ t dd	gd
dggtdd	gd
dggksJ t g  g gtg ksJ dS )zSee issue 7465.r   array?NumPy must be available to test creating matrices from ndarraysr   r  c                      s(   t  ddgddggddgddgggS )	Nr~   r^   r]   r   r   r   r   r   r   re   rl  re   rf   r   
  r  z#test_from_ndarray.<locals>.<lambda>r~   r^   r]   r   N)
numpyrm  ImportErrorrL   r.   rX   rY   rZ   rI   NotImplementedErrorre   re   rl  rf   test_from_ndarrayt
  s"    $$
40$rr  c                  C   s   ddl m}  z
ddlm}m} W n ty   td Y nw | |ddgddgg}|d dks2J t|g d	ks<J tt	 | |ddgddgg}W d    n1 sWw   Y  |d dksdJ t|g d	ksnJ d S )
Nr   
_matrixify)rm  matrixzPNumPy must be available to test indexing matrixified NumPy ndarrays and matricesr~   r^   r]   r   rs  )
sympy.matrices.commonrt  ro  rm  ru  rp  rL   ro   rG   PendingDeprecationWarning)rt  rm  ru  ru   re   re   rf   test_17522_numpy
  s   
rx  c                  C   x   ddl m}  zddlm} W n ty   td Y nw | |ddgddgg}|d dks0J t|g d	ks:J d S )
Nr   rs  )ru  zEmpmath must be available to test indexing matrixified mpmath matricesr~   r^   r]   r   rs  )rv  rt  mpmathru  rp  rL   ro   )rt  ru  ru   re   re   rf   test_17522_mpmath
     r{  c                  C   ry  )
Nr   rs  )
csr_matrixzJSciPy must be available to test indexing matrixified SciPy sparse matricesr~   r^   r]   r   rs  )rv  rt  scipy.sparser}  rp  rL   ro   )rt  r}  ru   re   re   rf   test_17522_scipy
  r|  r  c                  C   sr   t dtgt dgg} | jsJ dt | d< | jdu sJ t| d< | jd u s(J | d t | d< | jdu s7J d S )Nr~   r^   r   Fr   r   )r.   r	   is_hermitianrX   r  re   re   rf   test_hermitian
  s   
r  c                  C   sJ   t tttddgg} | d dt ksJ |  t dt ggks#J d S )NFrO  r   r^   )r.   r   rX   r   r  re   re   rf   	test_doit
  s    r  c                     s   t g dg dg dg} | d | t g dg dgks J t g dg dg dg}|d |t g dg dgks@J t g dg dg dg}|d |t g dg dgks`J t g dg dg dg tt fd	d
 t g dg dg dgttfdd
 t g dg dg dg} | d | t ddgddgddggksJ t g dg dg dg}|d |t ddgddgddggksJ t g dg dg dg tt fdd
 t g dg dg dgttfdd
 d S )Nr   r  r   r~   r   )r   r   r   )r   r   rj  r   c                      r  r   row_delre   r   re   rf   r   
  r   z+test_issue_9457_9467_9876.<locals>.<lambda>c                      r  Nr   r  re   rO   re   rf   r   
  r   r]   r^   r   r   c                      r  r   col_delre   r  re   rf   r   
  r   c                      r  r  r  re   rO   re   rf   r   
  r   )r.   r  rI   rU  r  )r   rE  Ore   )r   rP   rf   test_issue_9457_9467_9876
  s.   



"
"r  c                  C   s   t ddd\} }t d\}}td}tdd| ||tg}||  | | | | ks*J || | || | ks8J | | ||  ksBJ || || ksLJ ||  | t||  dgd||  ggksbJ d S )Nr  F)commutativeza br^   r   )r   r2   r.   rZ   )rX   rY   rT   rU   r   M1re   re   rf   test_issue_9422
  s   0r  c            	      C   s   t g } ddgt g df}ddg|d jf}ddgt ddgdd	ggf}|||fD ])\}}|D ]"}t| |}d
|v r?||n|d|}||krPt|t|ksRJ q0q*d S )Nr  r  )r   r   r]   r  r  r~   r^   r]   r   joinr  )r.   rW  r  id)	r   rT   rU   rV   opsru   opr  newre   re   rf   test_issue_10770
  s   
r  c                  C   s>  t g dg dg dg} | g dg dt ddgdd	gd
dggks&J | g dg dt dgdgd
ggks<J | g dg dt g dgksOJ | g dg dt g dg dgkseJ | g dg dt ddg kswJ | g dg dt ddg ksJ | g dg dt dgdggksJ d S )Nr   r  r  r   )TTFr~   r^   r   r   r   r   )TFF)TFT)FFFr]   r   )FTF)r.   r   r   re   re   rf   test_issue_10658
  s   ,&$$r  c                  C   s~  t ddtd  dgdtd d d dtd d gg} |  dks&J t ddtd t  dgdddtd t  gg} t|  d	 t ddddtd t   gd	d	gg tddkscJ td
\}}}}}}}}}	}
}}t |||| || d	g|||| || d	g|||| || dg|||| || dg|	|
d|	 | |	|  d|
 | |
|  d	gg} |  dksJ d S )Nr  r   r^   r~   r]   rQ  r   r   r   z/a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1)r.   r   rC  r	   r#   r  r;   r   )ru   axaybxbycxcydxdyexeyt0t1re   re   rf   !test_opportunistic_simplification
  s   <4F r  c                  C   s   t g dg dg} |  d t g dg dg  dk s J t g dg dg d	g}t g d
g dg dg}t g dg dg d	g}| |  dk sSJ | |  dk s_J d S )N)g~jth?gRM@g(\M@)gDl)@gQgp=
cG@r   )r   r   r   )r   r   r   V瞯<)q7K<r   r   )      r   r   r   )r  r   g      @)r                 @)r  r  r   )r   r  r  )r   r  g      )r.   r  r  r   )mmm_mixedm_floatm_invre   re   rf   test_partial_pivoting  s(   r  c                  C   st   t g dg dg dg} | jdd dd }t g dg d	g d
g}|| }| dk s0J |d dks8J dS )z When doing numerical computations, all elements that pass
    the iszerofunc test should be set to numerically zero if they
    aren't already. )?皙gɿr   )皙r  gٿr   )r  r  g333333?r   c                 S   s   t | dk S )Ng [n<)r   r   re   re   rf   r   +  r   z*test_iszero_substitution.<locals>.<lambda>r  r   )r   r   g4iҤIӿr   )r   r   glٲer   rq  r  r  N)r.   r  r  )ru   m_rref	m_correctm_diffre   re   rf   test_iszero_substitution$  s   r  c            
      C   sL  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sJ |jd|	ddksJ |jd|	ddksJ d S )Nr   )Pointr   rk  -   r]   rR  r^   r   r   r~   c                 S   s   t |  dk S )Ng#B;)r   rs   r   re   re   rf   r   @  r   z"test_issue_11238.<locals>.<lambda>T)r#   r  )	sympy.geometry.pointr  r   r   r   r   r.   r#   rC  )
r  xxyyp1p2p0rn  ro  m3Zre   re   rf   test_issue_112382  s   0R

r  c                  C   sh   t ddg d} | tj }| | }tD ]}|| \}}t|t| ks'J t|t| ks1J qd S )Nr^   rs  )r.   r   ImaginaryUnitri   as_real_imagro   )rn  ro  r  klsrT   rU   re   re   rf   test_as_real_imagE  s   
r  c                  C   s   t ddg d} |  \}}|d t dddgksJ |d t ddg dks)J t $ t ddgddggt ddgddggg d	ksHJ W d    d S 1 sSw   Y  d S )
Nr]   rO  r~   r^   r   )r^   r~   r   r^   r   r   )r   rN  rl  r  )r.   jordan_cellsrM   r  )ru   r   Jcellsre   re   rf   test_deprecatedO  s   8"r  c                  C   s\   ddl m}  tg d}tg d}| |dtg dksJ | |dtg dks,J d S )	Nr   )Mod)r   r~   r^   )r   rL  rP  r]   )r^   r~   r^   r   )r^   r   r~   )sympy.core.modr  r.   )r  r   r  re   re   rf   test_issue_14489]  s
   r  c                  C   s\   zddl m}  W n ty   td Y nw tddgddgg}| |tdjjd	ks,J d S )
Nr   rl  rn  r~   r^   r]   r   )dtypefloat64)ro  rm  rp  rL   r.   floatr  name)rm  r   re   re   rf   test_issue_14943e  s   r  c                  C   s4   t ddd} td}| d dk}t|dksJ d S )Nru   r~   rT   r   r   zm[0, 0] > 0)r>   r   r   )ru   rT   re   re   rf   test_case_6913o  s   r  c                  C   s.   t ddd} td}| ||| iksJ d S )Nr   r]   rT   )r>   rB   match)r   rT   re   re   rf   test_issue_11948u  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s%J 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sVJ t dtgdt gg}| \}}||j t dkssJ d S )Nr~   r   r^   )r.   r	   orthogonalizer   QRdecompositionr  r2   )vecsrz   rP   r   re   re   rf   test_gramschmidt_conjugate_dotz  s    4r  c                  C   sf   t tddd} t tddd}| |}t|| d }t|| d }||d ks+J |dks1J d S )NrT   r]   r~   rU   r   r   )r.   r>   r  r   )rT   rU   rV   rW   r  re   re   rf   test_issue_8207  s   
r  c                     s<  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s4J 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shJ t
tdd	  t
t fd
d	 tg dg dg dg dg  ttt  ksJ t
t fdd	 tddgddgg t t	ttd  ksJ tg dg dg dg t | tdtd  ksJ tg dg dg dg dg  ttt  ksJ tg dg dg dg dg  ttt ttt t  ksJ d S )Nr   nthrootr~   r^   r]   r   r   c                   S   s   t dtttS r  )r;   analytic_funcr   rX   re   re   re   rf   r     r   ztest_func.<locals>.<lambda>c                      s    t  tt t S r_   )rX   r  r   re   r   re   rf   r     r   )r   r   r   r]   )r   r~   r   r   )r   r   r   r~   c                      s     tttS r_   )r  r   rX   re   r   re   rf   r     r   rf  r   "   )r]   rI  r   )r   r   r   )r   r   r   r   )r~   r^   r   r   )r   r~   r]   r   )r   r   r~   r]   )r   r^   r~   r   )r   r   r~   r^   )r   r   r   r]   rq  )sympy.simplify.simplifyr  r.   r  r   rX   r[   r   r   r   rI   r   r   r#   r   r  re   r   rf   	test_func  s$   HT  "  2r  c               	   C   s   t rtd dd } td1 tj }|| }| s J W d    n1 s*w   Y  W d    d S W d    d S 1 sBw   Y  d S )Nzcan't run on pyodidec                  S   s&   t jd ksJ tdgg} | |  } dS r   )r@   stater.   r   re   re   rf   r    s   ztest_issue_19809.<locals>.fT)r\   rL   r?   
concurrentfuturesThreadPoolExecutorsubmitresult)r  executorfuturere   re   rf   test_issue_19809  s   

"r  c                  C   s   t  + ddlm}  tddgddgg}tddgddgg}| ||tks'J W d    n1 s1w   Y  t   ddlm} |dddksIJ W d    d S 1 sTw   Y  d S )	Nr   )classofr~   r^   r]   r   )a2idxr   )rM   sympy.matrices.matricesr  r.   r,   r=   r  )r  r   IMr  re   re   rf   test_deprecated_classof_a2idx  s   "r  c                  C   s<   t ttg} t| tddftddft dgdggksJ d S )Nr   r~   r   r  r   re   re   rf   test_issue_23276  s
   r  (2  r  concurrent.futuresr  collections.abcr   sympy.core.addr   sympy.core.functionr   r   r   rS  r   r   r	   r
   r   r   r   r   sympy.core.powerr   sympy.core.singletonr   sympy.core.symbolr   r   sympy.core.sympifyr   $sympy.functions.elementary.complexesr   &sympy.functions.elementary.exponentialr   r   (sympy.functions.elementary.miscellaneousr   r   r   (sympy.functions.elementary.trigonometricr   r   r   sympy.integrals.integralsr   sympy.polys.polytoolsr   r   sympy.printing.strr    sympy.sets.setsr!   r  r"   r#   sympy.simplify.trigsimpr$   r  r%   r&   r'   r(   r)   r*   sympy.matricesr+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   sympy.matrices.utilitiesr@   
sympy.corerA   rB   (sympy.functions.special.tensor_functionsrC   sympy.utilities.iterablesrD   rE   rF   sympy.utilities.exceptionsrG   rH   sympy.testing.pytestrI   rJ   rK   rL   rM   rN   sympy.assumptionsrP   sympy.tensor.arrayrQ   sympy.matrices.expressionsrR   sympy.externalrS   r   rT   rU   rV   rW   rX   rY   rZ   r[   r\   ri   rv   r|   r   r   r   r   r   r   r   r   r   r   r   r   r  r	  r  r  r  r  r  r  r  r   r"  r%  r'  r)  r-  r5  r8  r:  r>  r@  rD  rE  rG  rH  rK  r_  ra  re  rg  rp  rz  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r!  r%  r.  r0  r4  r5  r7  r>  rD  rK  rN  rY  r^  r`  ra  rg  rl  rn  rp  rr  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/  r0  r3  r5  r6  r8  r:  r=  r>  rF  rH  rK  r\  rh  ri  rk  rr  rx  r{  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  re   re   re   rf   <module>   s   ( \ (,Ma,	O			:		
	
 HK
?7(]
		
-


	