o
    3Ih|}                    @   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- d dl.m/Z/m0Z0m1Z1 d dl2m3Z3m4Z4 d dl5m6Z6 d dl7m8Z8 d dl9m:Z: d dl;m<Z<m=Z= d dl>m?Z? d dl@mAZAmBZBmCZC d dlDmEZE d dlFmGZG d dlHmIZI d dlJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZb d dlHmcZc d dldmeZemfZf d dlgmhZh d dlimjZjmkZkmlZl d d lmmnZn d d!lompZpmqZqmrZrmsZsmtZtmuZu d d"lvmwZw d d#lxmyZy d d$lzm{Z{ d d%l|m}Z} d d&l~mZ d d'lmZ d d(lmZmZmZmZmZmZmZmZ eNeOeLeMfZd d)lmZmZ d d*lmZmZ eu  G d+d, d,eeeZW d   n	1 sw   Y  eu  G d-d. d.eeeZW d   n	1 sw   Y  d/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Zd=d> Zd?d@ ZdAdB ZdCdD ZdEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZdSdT ZdUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zdudv Zdwdx Zdydz Zd{d| Zd}d~ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddĄ ZddƄ ZddȄ Zddʄ Zdd̄ Zdd΄ ZddЄ Zdd҄ ZddԄ Zddք Zdd؄ Zddڄ Zdd܄ Zddބ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zdd Zdd Zdd Zdd Z d	d
 Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Z	dd Z
dd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Zd=d> Zd?d@ ZdAdB ZdCdD ZdEdF ZdGdH Z dIdJ Z!dKdL Z"dMdN Z#dOdP Z$dQdR Z%dSdT Z&dUdV Z'dWdX Z(dYdZ Z)eqd[d\ Z*d]d^ Z+d_d` Z,dadb Z-dcdd Z.dedf Z/dgdh Z0erdidj Z1dkdl Z2dmdn Z3dodp Z4dqdr Z5dsdt Z6dudv Z7dwdx Z8dydz Z9d{d| Z:d}d~ Z;dd Z<dd Z=dd Z>dd Z?dd Z@dd ZAdd ZBdd ZCdd ZDdd ZEdd ZFdd ZGdd ZHdd ZIdd ZJetddd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd ZTdd ZUdd ZVdd ZWdd ZXdd ZYdd ZZd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)	transpose)HermitianOperatorOperatorDagger)PolyPurePoly)RootOf)sstr)	FiniteSet)signsimpsimplify)trigsimp)
ShapeErrorMatrixErrorNonSquareMatrixErrorDeferredVector)_find_reasonable_pivot_naive)	_simplify)GramSchmidtImmutableMatrixImmutableSparseMatrixMatrixSparseMatrix
casoratiandiageyehessianmatrix_multiply_elementwiseones
randMatrix	rot_axis1	rot_axis2	rot_axis3	wronskianzerosMutableDenseMatrixImmutableDenseMatrixMatrixSymboldotprodsimprot_ccw_axis1rot_ccw_axis2rot_ccw_axis3)_dotprodsimp_state)TupleWild)KroneckerDelta)flattencaptureiterable)ignore_warnings)raisesXFAILslowskipskip_under_pyodidewarns_deprecated_sympyQ)Array)ArrayDerivative)MatPow)
Quaternion)O)abcdxyzt)_MinimalMatrix_CastableMatrix)MatrixSubspacesMatrixReductionsc                   @      e Zd ZdS )SubspaceOnlyMatrixN__name__
__module____qualname__ rp   rp   b/home/air/sanwanet/gpt-api/venv/lib/python3.10/site-packages/sympy/matrices/tests/test_matrices.pyrk   G       rk   c                   @   rj   )ReductionsOnlyMatrixNrl   rp   rp   rp   rq   rs   L   rr   rs   c                 C      t | | dd S )Nc                 S   s   t | |kS N)intijrp   rp   rq   <lambda>Q       z eye_Reductions.<locals>.<lambda>rs   nrp   rp   rq   eye_ReductionsP      r   c                 C   rt   )Nc                 S      dS Nr   rp   rw   rp   rp   rq   rz   U       z"zeros_Reductions.<locals>.<lambda>r|   r}   rp   rp   rq   zeros_ReductionsT   r   r   c                  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 ru   )typerv   .0rx   rp   rp   rq   	<genexpr>\       ztest_args.<locals>.<genexpr>)	enumerateclassesrA   shapeallrowsr   rv   colsflatlisttuplerJ   todokdict)r~   clsmrp   rp   rq   	test_argsX   s   "r   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   )
r4   r2   rA   rV   _matr   r5   r3   _smatr   )r   r   matsmatrp   rp   rq   test_deprecated_mat_smate   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   )r4   rb   rc   rd   )vrp   rp   rq   test_divisionr   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 ru   rp   rp   r   r~   rp   rq   rz   {       ztest_sum.<locals>.<lambda>)r4   rb   rc   rd   rQ   r*   rp   rp   r   rq   test_sumw   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   )r4   rb   r   absr   rp   rp   rq   test_abs}   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   )r4   addr^   r_   rp   rp   rq   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   )r4   r5   rangerA   extract)Mr^   rp   rp   rq   test_fancy_index_matrix   sZ   $ ,&&2,2&&
r   c                     s  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 d S w t| t sIJ | d dksRJ | d dks[J | d dksdJ | d	 dksmJ 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 ru   )r:   rp   r   rp   rq   rz         
 z%test_multiplication.<locals>.<lambda>rb   r   r   
      z	c = 5 @ b)
r4   evalSyntaxErrorr:   multiply_elementwiserQ   r*   r   
isinstancerb   )r`   hc2rp   r   rq   test_multiplication   sj   
r   c                     s  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s,J t dddtd d gg dg dtd d dddgg t ttd  dtt td  d tt td  d  ttd  ttd  d ttd  td	  d
  tt t td	  d  ttd  td	  d
  ttd  gdttd  d ttd	 ttd gtt td  d tt td  d  ttd  ttd	 ttd  td	  d
 tt t td	  d  ttd  td	  d
  ttd  tt td	  d tt td	  d  ttd  gttd  d ttd  td	  d
  tt t td	  d  ttd  td	  d
  ttd  ttd tt td	  d tt td	  d  ttd  ttd	  d dt td  td  d  tt t td  d
  dt td  td  d  ttd  ggt t td  d ttd  td	  d  tt t td	  d  ttd  td	  d  ttd  ttd t t td	  d tt td	  d  ttd  t td	  d	 dt td  td  d  tt t td  d  dt td  td  d  ttd  gdttd  d ttd	 ttd gtt td  d tt td  d  ttd  ttd	 ttd  td	  d
 tt t td	  d  ttd  td	  d
  ttd  tt td	  d tt td	  d  ttd  gt td  d dt t td  d tt td  d  ttd  t td  d ttd  td	  d  tt t td	  d  ttd  td	  d  ttd  gg}t dd fdd}  |  kr|ksJ  J d S )Nr   r   r   r   r   r   r   r   r   r   r   r   r   r   r       0   r      r   @   r   `            c                    s    t  fddtdD  S )Nc                 3   s(    | ]} |f |f  V  qd S ru   rp   )r   k)ABrx   ry   rp   rq   r        & zAtest_multiplication_inf_zero.<locals>.<lambda>.<locals>.<genexpr>r   )r   r   rw   r   r   rw   rq   rz          z.test_multiplication_inf_zero.<locals>.<lambda>)	r4   r   r   r   r   rb   r_   r^   r]   )r   CC2rp   r   rq   test_multiplication_inf_zero  s4    &  &(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d/d t t fd0d td	dgddgg  d. td1d2gd3d4g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d5d6d7t  tsJ td5d6d6d8t t fd9d td5d6d6d:  ttdtdtd td d gdtddtd gg d,gks J  d  tg d,g d,g d,gksJ t t fd;d tg d,g d<g d=g  d> tg d?g d@g dAgks@J  d>  d ksKJ tg d+g dBg d-g td5  d  d ksoJ t tfdCd   d  ksJ tg d-g d-g d-g td5d6d6dD   ksJ td5d6d6d:  td d d ksJ   dtdksJ   dtdksJ tg dEg dFg dGg  dH tdIdIdIksJ  t tdt dt dt ksJ tg d+g d,g d,g t t fdJd t t fdKd ttjtjgtjtjgg  tj  k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 )LNc                   S   s   t dd S Nr   r   r4   rp   rp   rp   rq   rz   #  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   r   )	i"  i     i  i  ip  i  i  i  r   r   d   r   i r   r   r      !   r   r   9   )r   r   r   r   g      ?r}   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   rp   r   rp   rq   rz   L      c                   S   s   t ddgddggtdS )Nr   r   )r4   r   r   rp   rp   rp   rq   rz   O  s    r   r   r   r   r   r   r         $@c                          d S N @rp   rp   r   rp   rq   rz   R  r   c                          t dd S r   r   rp   r   rp   rq   rz   S  r   ihiO<iv0ir~   T)integer)r   negativec                      s     S ru   rp   rp   )r   r~   rp   rq   rz   ]  r   )r   nonnegativec                      r   r   r   rp   r   rp   rq   rz   d  r   )r   r   r   )r   r   r   g      @)   H   Y   )i#        )i<  i  iI  r   r   r   c                      s     d S )N)subsdoitrp   )Anr~   rp   rq   rz   l      )r   positiver   r   r   )r   r   r   r   r   r   r   gd%%@c                      r   r   rp   rp   r   rp   rq   rz   {  r   c                      s    t  S ru   r	   rp   r   rp   rq   rz   |  r   )rQ   r,   r   r4   r8   r
   r   Half	sympy.abcr~   r^   r_   r   _eval_pow_by_recursionr+   
ValueErrorr   r   r[   rL   r  r  r7   rA   r	   )Rrp   )r   r  r   r~   rq   
test_power"  s   @ 4426J<$0&("((*,(&&8r  c                  C   s   t dt dt gdt dt gg} tdE |   t tdt td d tdt  td d gtdt  td d tdt td d ggksSJ W d    d S 1 s^w   Y  d S )Nr   Tr   )r4   rb   rE   r   r   r   rp   rp   rq   $test_issue_17247_expression_blowup_1  s   $
00"r  c                  C   sr   t dt dt gdt dt gg} td |  \}}|| |  s'J W d    d S 1 s2w   Y  d S Nr   T)r4   rb   rE   jordan_forminvr   PJrp   rp   rq   $test_issue_17247_expression_blowup_2  s
   $
"r  c                  C   s   t dt dt gdt dt gg} td1 | d t dtd  d ddtd   gddtd   dtd  d ggks?J W d    d S 1 sJw   Y  d S )Nr   Tr   l                )r4   rb   rE   r  rp   rp   rq   $test_issue_17247_expression_blowup_3  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]])r4   r   rE   r  rp   rp   rq   $test_issue_17247_expression_blowup_4  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  rw   rp   rp   rq   rz         z6test_issue_17247_expression_blowup_5.<locals>.<lambda>Trb   r   $   r   EXdomain)r4   rE   charpolyr#   rb   r	   r  rp   rp   rq   $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 rp   rb   r   rp   rp   rq   
<listcomp>  r!  z8test_issue_17247_expression_blowup_6.<locals>.<listcomp>r   Tbareissr   r4   r   rE   detr  rp   rp   rq   $test_issue_17247_expression_blowup_6     
"r0  c                  C   sP   t dddd } td | ddksJ W d    d S 1 s!w   Y  d S )Nr   c                 S   r  r   r  rw   rp   rp   rq   rz     r!  z6test_issue_17247_expression_blowup_7.<locals>.<lambda>T	berkowitzr   )r4   rE   r/  r  rp   rp   rq   $test_issue_17247_expression_blowup_7  s   
"r3  c                  C   r)  )Nr   c                 S   r*  rp   r+  r   rp   rp   rq   r,    r!  z8test_issue_17247_expression_blowup_8.<locals>.<listcomp>r   Tlur   r.  r  rp   rp   rq   $test_issue_17247_expression_blowup_8  r1  r5  c                  C   s   t dddd tdD } td- |  t g dg dg dg dg dg dg dg dgd	fks6J W d    d S 1 sAw   Y  d S )
Nr   c                 S   r*  rp   r+  r   rp   rp   rq   r,    r!  z8test_issue_17247_expression_blowup_9.<locals>.<listcomp>r   T)r   r   r   r  r   r"  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r4   r   rE   rrefr  rp   rp   rq   $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  rw   rp   rp   rq   rz     r!  z7test_issue_17247_expression_blowup_10.<locals>.<lambda>Tr   )r4   rE   cofactorr  rp   rp   rq   %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  rw   rp   rp   rq   rz     r!  z7test_issue_17247_expression_blowup_11.<locals>.<lambda>Tr   r#  )r4   rE   cofactor_matrixr  rp   rp   rq   %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  rw   rp   rp   rq   rz     r!  z7test_issue_17247_expression_blowup_12.<locals>.<lambda>Tr   r   r   )r4   rE   	eigenvalsr	   r  rp   rp   rq   %test_issue_17247_expression_blowup_12  s   
""rA  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numerr6  )r4   rb   
eigenvectsr   r   )r   evrp   rp   rq   %test_issue_17247_expression_blowup_13  s0    ("P"("P"rF  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   r9  )r4   rb   rE   echelon_formr  rp   rp   rq   %test_issue_17247_expression_blowup_14  s   4
2""rH  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   )r4   rb   rE   rowspacer  rp   rp   rq   %test_issue_17247_expression_blowup_15  s   4
r"rJ  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)r4   rb   rE   columnspacer  rp   rp   rq   %test_issue_17247_expression_blowup_16!  s   4
"rL  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*  rp   r+  r   rp   rp   rq   r,  '  r!  z9test_issue_17247_expression_blowup_17.<locals>.<listcomp>r   Tr   r  r   r   r   r   r6  r   r7  r   r"  r   )r4   r   rE   	nullspacer  rp   rp   rq   %test_issue_17247_expression_blowup_17&  s   
&&&&&&"rO  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)r4   rb   rE   is_nilpotentr  rp   rp   rq   %test_issue_17247_expression_blowup_181  s   4
"rQ  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)r4   r   rE   is_diagonalizabler  rp   rp   rq   %test_issue_17247_expression_blowup_196  s   
"rS  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   )r4   rb   rE   diagonalizer  rp   rp   rq   %test_issue_17247_expression_blowup_20?  s*   
"rW  c                  C   V   t td} td | jddt tdksJ W d    d S 1 s$w   Y  d S )N  [
        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
        [                0,                     0,                   0, -177/128 - 1369*I/128]]TGEmethodv  [
            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
            [0, 0, 0, -11328/952745 + 87616*I/952745]]r4   r   rE   r  r  rp   rp   rq   %test_issue_17247_expression_blowup_21Q     
"r_  c                  C   rX  )NrY  TLUr[  r]  r^  r  rp   rp   rq   %test_issue_17247_expression_blowup_22^  r`  rb  c                  C   sZ   t td} td | jdd t tdksJ W d    d S 1 s&w   Y  d S )NrY  TADJr[  r]  )r4   r   rE   r  r   r  rp   rp   rq   %test_issue_17247_expression_blowup_23k  s   
""rd  c                  C   V   t td} td | jddttdksJ W d    d S 1 s$w   Y  d S )NrY  TCHr[  r]  r5   r   rE   r  r4   r  rp   rp   rq   %test_issue_17247_expression_blowup_24x  r`  rh  c                  C   re  )NrY  TLDLr[  r]  rg  r  rp   rp   rq   %test_issue_17247_expression_blowup_25  r`  rj  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   r4   r   rE   rankr  rp   rp   rq   %test_issue_17247_expression_blowup_26  s   
	"rn  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]])r4   rb   rE   r  r   r   r  rp   rp   rq   %test_issue_17247_expression_blowup_27  s   
"ro  c                  C   sN   t td} td |  tdksJ W d    d S 1 s w   Y  d S )NrY  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)])r4   r   rE   singular_valuesr  rp   rp   rq   %test_issue_17247_expression_blowup_28  s   
"rq  c                  C   rk  )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   rl  r  rp   rp   rq   test_issue_16823  s   
"rr  c                  C   s  t g ddtd dtd dtd td d dddddg	ddtd  ddtd  ddtd  ddtd  dddddg	d	td d dd
td  dd
td  dd
td  ddddd
g	ddtd  dtd d dtd d ddtd  dddddg	dd
td  dd
td  d	td d dd
td  ddddd
g	d	dtd  d	dtd  d	dtd  d	dtd  dddddg	dtd td d dtd dtd dddddg	g} tdt |  t ddddddddtdd g	ddddddddtd d g	ddddddddtdd g	ddddddddtd d g	g dddddddddtd d g	g dddddddddtd d g	gdfksWJ W d    d S 1 scw   Y  d S )N)	r   r   r   r   r   r   r   r   r   r   r   r   r7  rM  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   r8  )r4   r   rE   r:  r   r  rp   rp   rq   test_issue_18531  s0   6DDDDD6

$rt  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rAtddg ksDJ  J tg gtd	dg ksQJ tg g gtd
dg ks_J t  td	gdgg d	gdggksuJ W d    n1 sw   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sJ |j
d
ksJ |d d  t	dddgksJ ||ks%J t||ks.J td
dtd	d}td	dtdd}t||g}|j
dksNJ |jdksVJ |d d  g dkscJ ttd
td
kspJ tttd
ttd
ksJ t|| ksJ 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s1J W d    n	1 s<w   Y  ttd
tdgttd
gksUJ t tdd  t tdd  td	d
gddgg} t| dg}	|	td	d
gddgddggksJ d S )Nc                   S   s   t ddtdS )Nr      )r4   r   rp   rp   rp   rq   rz     r	  ztest_creation.<locals>.<lambda>c                   S   s   t ddg S )Nr   r   r   rp   rp   rp   rq   rz     r{   c                   S      t dd S r   r   rp   rp   rp   rq   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   Fevaluater   r   r   r   c                 S   s   g | ]}|gqS rp   rp   r   rp   rp   rq   r,  0      z!test_creation.<locals>.<listcomp>c                   S      t tdtddgS )Nr   r   r   r4   r;   rp   rp   rp   rq   rz   4      c                   S   r{  )Nr   r   r   r|  rp   rp   rp   rq   rz   5  r}  )r   r   r   )rQ   r  
IndexErrorr4   rV   tolistTr   EmptySetrb   r   r   r   r8   r2   as_immutable
as_mutabler;   rD   )
r   r^   r   r_   c23c13r`   datr   M2rp   rp   rq   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   )r4   	irregularr;   rp   rp   rp   rq   test_irregular_block=  s   &0r  c                  C   sT   t jt jtt t jgttttd gtt j tt dgg} t| }| | ks(J d S )Nr   r   )	r   Oner  rb   rc   Zerord   r4   r  )lstr   rp   rp   rq   test_tolistF  s   8r  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   )rA   r  r  r2   rp   rp   rp   rq   test_as_mutableL  s    $r  c                  C   s  t d} | d dd df t dksJ | ddddf tdks$J tdddd }|dd d f tdddks<J |dddf tddd	ksLJ tg d
g dg dg dg}|d d df tddg dksnJ |dd d d f tg dg dgksJ d S )Nr   r   r   r   c                 S      | | S ru   rp   rw   rp   rp   rq   rz   W  r   ztest_slicing.<locals>.<lambda>r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r      r         r   r   )r   r   r  r   r  )r8   rA   r4   )m0m1m2rp   rp   rq   test_slicingR  s        $0r  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   r  r   rU  r   r   r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   r  r   r   r   r   r   r   r  r   r  r  r   r   ))r   r   r   r   )r   r   r   r   r  r  )rA   r8   r4   r   rp   rp   rq   test_submatrix_assignment`  s   r  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   rp   rw   rp   rp   rq   rz   }  r{   ztest_extract.<locals>.<lambda>)r   r   r   r   r   r   )r   r   r   r   r   r   r  )r   r   r   r   r   r  c                           dgdgS )Nr   r   r   rp   r   rp   rq   rz     r	  c                      r  r  r  rp   r   rp   rq   rz     r	  )r4   r   r   rQ   r~  rp   rp   r   rq   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   r  ru   rp   rw   rp   rp   rq   rz     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   )r8   reshaper4   r  r  rp   rp   rq   test_reshape  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   rp   r+  rp   rp   rq   rz     r   z test_applyfunc.<locals>.<lambda>r   c                 S   r   r   rp   r+  rp   rp   rq   rz     r   )r8   	applyfuncrA   )r  rp   rp   rq   test_applyfunc  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   r^   Treal)complexr   )r   r   r   r   r   )r   r   r   r   )
r4   rb   rc   r   r   r   r	   r   r   r   )r  r  r^   rp   rp   rq   test_expand  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  )
r4   r   rb   r   rc   refinerX   r  r
  r   r  rp   rp   rq   test_refine  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   r  )r   F      )r  percentr  r   r   r  )minr  r  )r<   copyr(   randomRandomr  r   r   )r   r   rngsizer  
zero_countrx   ry   rp   rp   rq   test_random  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   ra  r[  rc  rf  ri  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 ru   r   r  r   sr   r   rp   rq   r          ztest_inverse.<locals>.<genexpr>zGE ADJ LU CH LDL QRc                 3   r  ru   r  r  r  rp   rq   r     r  )r8   r  r4   r   r2   r   splitr3   )r   AinvAArp   r  rq   test_inverse  sr   ""&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   )r4   rb   rc   jacobianr9   rd   r  )Lsymsfgansrp   rp   rq   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   r2  r[  )r@   r   rb   r   r   r   )w1w2rp   rp   rq   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   )r4   rb   r  rc   r   r8   r   rp   rp   rq   	test_subs7  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   )r4   rb   xreplacerc   r   r8   r  rp   rp   rq   test_xreplaceE  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 )Nr~   r  r   r   )ratio)	r   r   r4   rb   rc   r   r   r(   r   )r~   r  r   eqrp   rp   rq   test_simplifyM  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   )r4   r  r   r  rp   rp   rq   test_transpose^  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   )r4   r	   r  r   	conjugateHr  rp   rp   rq   test_conjugateo  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  )r8   Drp   rp   rp   rq   rz     r   z!test_conj_dirac.<locals>.<lambda>r   r   rU  r  r   )rQ   AttributeErrorr4   r	   r  r  rp   rp   rq   test_conj_dirac  s   

r  c                  C   s.   t g dg dg dg} |  dksJ d S )Nr   r   r   r   r   r   )r   r   r   r  r4   tracer  rp   rp   rq   
test_trace  s
   r  c                  C   s*   t tddgdtdgg} | jdksJ d S )Nr   r  )r4   rb   rc   r   r  rp   rp   rq   
test_shape  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   rp   )rry   rp   rp   rq   rz     r{   z!test_col_row_op.<locals>.<lambda>r   r   c                 S   s   | t |  S ru   )rc   )r`   ry   rp   rp   rq   rz     r{   *   r   r   )r4   rb   rc   row_opcol_oprowcol)r   r1c1rp   rp   rq   test_col_row_op  s2   
"

r   c                  C   sT   t g dg dg} | dd | d dksJ | d dks J | d d	ks(J d S )
Nr   r   r   r   r   r   r   r   r   r   r   )r4   row_multr  rp   rp   rq   test_row_mult  s   r  c                  C   s\   t g dg dg dg} | ddd | d dksJ | d	 d
ks$J | d dks,J d S )Nr   r  r   r   r   r   r   r   r   r   r   r   r   r   r   )r4   row_addr  rp   rp   rq   test_row_add  s   r  c                  C   s   t d d D ]H} | d}|dddd  || g dg dg d	gks'J | dd }d
|d< |dddd  | || g dg dg dgksNJ qd S )Nr   r   r   r   c                 S      | d|  S r  rp   r   urp   rp   rq   rz     r{   z!test_zip_row_op.<locals>.<lambda>r  r   r   r   r   r   r   c                 S   r  r  rp   r	  rp   rp   rq   rz     r{   )r   r   r   )r   r   r   r  )r   r8   
zip_row_op)r   r   rp   rp   rq   test_zip_row_op  s   


r  c                  C   sd   t g d} t g d}t g d}| dvsJ | dvsJ | dks$J | |ks*J | |ks0J d S )Nr   )r   r   r   rp   )r   r   r   )r   r^   r_   rp   rp   rq   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  rp   selfrp   rp   rq   	__index__     z)test_issue_3981.<locals>.Index1.__index__Nrm   rn   ro   r  rp   rp   rp   rq   Index1      r  c                   @   r  )ztest_issue_3981.<locals>.Index2c                 S   r   r  rp   r  rp   rp   rq   r    r  z)test_issue_3981.<locals>.Index2.__index__Nr  rp   rp   rp   rq   Index2  r  r  r   r   r   r   r  r   r   r   r   r   r   )r  r  index1index2r   rp   rp   rq   test_issue_3981  s$   r  c                      sn   t tddg t fddtdD sJ t fddtdD s&J t fddtdD s5J d S )Nr   r   c                 3   s(    | ]}   |  |   kV  qd S ru   evalfr   r^   rp   rq   r     r   ztest_evalf.<locals>.<genexpr>r   c                 3   ,    | ]}  d |  |  d kV  qdS r   Nr  r   r  rp   rq   r        * c                 3   r  r  r}   r   r  rp   rq   r   	  r   )r4   r   r   r   rp   rp   r  rq   
test_evalf  s   "r!  c                  C   s   t ttgttgg} |  du sJ t g dg dg} |  du s$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 )NTr  r  Fr   r   r   r   r   r   r   )r4   rb   is_symbolicr  rp   rp   rq   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   )r4   is_upperrA   r  rp   rp   rq   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)r4   is_lowerr  rp   rp   rq   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   r4   rP  r  rp   rp   rq   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   )rA   fillr;   r   r   r   r4   )r~   r   r^   r_   rp   rp   rq   test_zeros_ones_fill6  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   )rA   r4   r   r   r  rp   rp   rq   test_empty_zerosK  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   )r4   rb   rc   r   r   r   r   limitr   r   r   r   r  rp   rp   rq   test_issue_3749V  s(   ,."$
 &r.  c                  C   sD   t d} | dd dD ]}| j|dd d| jdd	ksJ qd S )
Nr   r   r   )rZ  ra  c                 S   s   | dkS r   rp   r+  rp   rp   rq   rz   j  r   z%test_inv_iszerofunc.<locals>.<lambda>)r\  
iszerofuncrc  r[  )r8   col_swapr  )r   r\  rp   rp   rq   test_inv_iszerofuncf  s   

r1  c                  C   s   t d\} }t| t| | t| g}t| |g}||}|||jks)J ||j|ks3J ||j|jks>J |jt|jd  | }|t	}|tddgd| d ggks_J d S )Nrho,phir   r   r   )
r   r4   r   r   r  r  r8   r   r  r)   )rhophiXYr  r  rp   rp   rq   test_jacobian_metricsn  s   

$r7  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 )Nr2  r   r   )r   r4   r   r   r  )r3  r4  r5  r6  r  rp   rp   rq   test_jacobian2{  s   "
r8  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   )	r4   r   rb   rc   rd   r   r  r   r   )r5  r6  rx   ry   X_sliceY_slicer  r   rp   rp   rq   test_issue_4564  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 ru   r  r4   rb   rc   rd   rp   r5  rp   rq   rz     r!  z(test_nonvectorJacobian.<locals>.<lambda>r   c                      s
     S ru   )r  rp   r5  r6  rp   rq   rz     r   c                      s     tttgttggS ru   r=  rp   r>  rp   rq   rz         )r4   r   rb   rc   rd   rQ   	TypeErrorrp   rp   r?  rq   test_nonvectorJacobian  s    rB  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   )r4   vecr   r   )r   m_vecrx   rp   rp   rq   test_vec  s   rF  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   )rG  check_symmetryc                   S      t ddgg S r9  r4   vechrp   rp   rp   rq   rz     rz  ztest_vech.<locals>.<lambda>c                   S      t ddgddgg S rC  rJ  rp   rp   rp   rq   rz         c                   S   rI  r9  rJ  rp   rp   rp   rq   rz     rz  c                   S   rL  rC  rJ  rp   rp   rp   rq   rz     rM  )	r4   rK  r   r   rb   rc   rQ   r*   r  )r   m_vechrx   rp   rp   rq   	test_vech  s"   ( rO  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 ru   )r7   rp   r   rp   rq   rz     r   ztest_diag.<locals>.<lambda>F)strict)r7   r4   rQ   r  rp   rp   r   rq   	test_diag  s    rQ  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   )r4   rb   rc   rd   get_diag_blocksr^   r_   r`   rp   rp   rq   test_get_diag_blocks1  s    rU  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 rR  )r4   rb   rc   rd   r7   rS  rT  rp   rp   rq   test_get_diag_blocks2  s    "rV  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_diagrc  )rW  r\  r[  )r4   rb   rc   rd   r7   r  )r^   r_   r`   r   rp   rp   rq   test_inv_block  s"    ((($
rX  c                   C   s   t tdd  t tdd  ttdtdksJ ttdtdks&J t tdd  ttdtdks9J ttdtdksEJ t tdd  ttdtdtddks\J t tdd  t td	d  t td
d  dS )zg
    Check that matrix dimensions can be specified using any reasonable type
    (see issue 4614).
    c                   S   
   t ddS )Nr   r   rA   rp   rp   rp   rq   rz     r   z$test_creation_args.<locals>.<lambda>c                   S   s   t ddddS Nr   r   r   r   rZ  rp   rp   rp   rq   rz     r   r   c                   S      t dS N      @rZ  rp   rp   rp   rq   rz     r   c                   S   r\  r]  r8   rp   rp   rp   rq   rz     r   r   c                   S   r\  Nr   r   rp   rp   rp   rq   rz     r   c                   S   rY  r   r   rp   rp   rp   rq   rz     r   c                   S   s   t ddggS r   r   rp   rp   rp   rq   rz     r   N)rQ   r  rA  rA   rv   r
   r8   r;   rp   rp   rp   rq   test_creation_args  s    ra  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   r   r   )r4   is_diagonalis_symmetricr7   rA   rb   rc   r   r   rp   rp   rq   test_diagonal_symmetrical  s,   6rh  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   ru  r   r   c                            S ru   rV  rp   r   rp   rq   rz   %  r   z&test_diagonalization.<locals>.<lambda>rb  )r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r6  r   r  r   )r   r   r   r   Tc                      
     dS )NTrk  rp   r   rp   rq   rz   Q  r   r   c                      rj  ru   rk  rp   r   rp   rq   rz   Y  r   )	r   r   r   ru  r   r   r   r  r   c                      rj  ru   rk  rp   r   rp   rq   rz   ]  r   a b c d)r4   r	   rR  rg  rQ   r,   r7   rV  r8   r  as_numer_denomrf  r+   r   )r  r  rx   r^   r_   r`   ra   rp   r   rq   test_diagonalization  sl   rp  c                      sv   t ddgddgg   du sJ d d<   du sJ t ddgddgg    d d< tt fdd d S )Nr   r   Tr   Fc                      rj  ru   rk  rp   r  rp   rq   rz   p  r   z"test_issue_15887.<locals>.<lambda>)rB   rR  rV  rQ   r+   rp   rp   r  rq   test_issue_15887f  s   rq  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   ri  c                      rj  ru   )r  rp   r   rp   rq   rz   v  r   z"test_jordan_form.<locals>.<lambda>)	r   rs  r   r   ir   r   ir  )	r   r   r   r   r   r   r   r   r   r   	r   r   r   r6  r   r   r  r   r   )	r   r   r   r   r   r   r   r   r   )	r   r   r   r   r7  r   r   r"  )	r   r   r   r   r   r   r   r   r   )	r   r7  r   r   rM  r   r   r   )	r   r   r   r   r   r   r   r   r   r   )r   r   r  r   r   r   r   r   r   r   r  r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r"  r   r   r   r   r   r  ru  r"  r   r   r   r   )r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   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)
r4   rQ   r,   r  rV  rR  r   valuesr   _prec)Jmustr  r  termrp   r   rq   test_jordan_forms  sR   
r|  c                  C   s   t g dg dg dg dg} ddt  }ddt  }t |dddgd|ddgdd|dgddd|gg}t |dddgd|ddgdd|dgddd|gg}|  \}}||ks\||ks\J t|| |  | ksjJ d S )	N)r   r   r   r   )r6  r   r   r   )r   r   r   r   )r   r   r6  r   r   r   r   r   )r4   r	   r  r(   r  )r   pqJmust1Jmust2r  r  rp   rp   rq   #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 )
Nrd  rb  )r   r   r   r   rU  r   r   r   r   r  r   r   rl  )r4   r  r  rp   rp   rq   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 )
NrT  r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  )r4   r  r   r	   r   )r   r  r  rp   rp   rq   test_jordan_form_issue_15858  s&   .

r  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   r4   r'  rb   r"   r   r#   genas_exprr  )UAK_iK_wr   r'  r}  rp   rp   rq   test_Matrix_berkowitz_charpoly  s&   *$
06
*r  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   r4   jordan_block_eval_matrix_exp_jblockr   )lr   rp   rp   rq   test_exp_jordan_block  s   r  c                  C   s  t ddgddgg} t tddtd d dtd d  gdtdgg}|  |ks.J t| |k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  r6  r   r   r   )r4   r   r   r   r   )r   m_exprp   rp   rq   test_exp  s   8  Fr  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 )Nr  r   r   r   r   r   r   r   r   r  c                      rj  ru   )r   rp   r   rp   rq   rz   =  r   ztest_log.<locals>.<lambda>)r   r4   r  _eval_matrix_log_jblockr   rQ   r+   )r  rp   r   rq   test_log'  s(   *
r  c                  C   sX   t ttfdf} | tsJ | trJ | tsJ | td} | tr*J d S )Nr  r   )r4   rb   rc   hasrd   r   r  r   rp   rp   rq   test_has@  s   r  c                  C   sR   t d} tdd| t| d t| d  tjg}t|\}}}}|tjks'J d S )Nrb   r   r   r   )r   r4   r   r   r   r  r/   rb   columnpivot_offset	pivot_valpivot_assumed_nonzero
simplifiedrp   rp   rq   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero1J  s
   (
r  c                  C   sn   t d} tdd| t| d t| d  | d  t| d t| d  g}t|td\}}}}|dks5J d S )Nrb   r   r   r   simpfunc)r   r4   r   r   r/   r0   r  rp   rp   rq   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero2V  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 )Nrb   r   r   r   r  r   )r   r4   r   r   r/   r0   lenr  rp   rp   rq   +test_find_reasonable_pivot_naive_simplifiese  s   

r  c                      s  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t td	d  t td
d  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t td d  t td!d  t td"d  t td#d  t td$d  t td%d  t td&d  t td'd  t td(d  t td)d  td* t t fd+d tg d,gtg d-g d.g d/g t t fd0d tg d-g d.g d/g t t fd1d d S )2Nc                   S   s   t ddgdggS r   r   rp   rp   rp   rq   rz   x  rz  ztest_errors.<locals>.<lambda>c                   S      t ddggd S )Nr   r   )g333333?r   r   rp   rp   rp   rq   rz   y  rz  c                   S   r  )Nr   r   )r   g@r   rp   rp   rp   rq   rz   z  rz  c                   S   s   t ddddS )Nr   r   T)r`   r  )r<   rp   rp   rp   rq   rz   {  r   c                   S   s   t ddgddS )Nr   r   r   r   )r4   r  rp   rp   rp   rq   rz   |  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   )r4   copyin_matrixrp   rp   rp   rq   rz   ~     ( c                   S   s"   t ddgddggddgt S r  )r4   copyin_listsetrp   rp   rp   rq   rz     s
    c                   S   s   t g dg dg S )Nr   )r   r   r   r4   r  rp   rp   rp   rq   rz     rM  c                   S   s&   t ddddgt ddgddggS r[  )r4   row_joinrp   rp   rp   rq   rz        & c                   S   s"   t ddgt ddgddggS r[  )r4   col_joinrp   rp   rp   rq   rz     s   " c                   S   "   t dgdt ddgddggS r[  )r4   
row_insertrp   rp   rp   rq   rz     
    c                   S   r  r[  )r4   
col_insertrp   rp   rp   rq   rz     r  c                   S      t ddg S r   r  rp   rp   rp   rq   rz     r	  c                   S   s   t dgdS r  )r4   r  rp   rp   rp   rq   rz     r	  c                   S      t ddgddggddS Nr   r   r   r   r   )r4   minorrp   rp   rp   rq   rz         c                   S   r  r  )r4   minor_submatrixrp   rp   rp   rq   rz     r  c                   S      t g ddS Nr   r   r4   crossrp   rp   rp   rq   rz     rz  c                   S   r  r  r4   dotrp   rp   rp   rq   rz     rz  c                   S   s   t g dt ddgS )Nr   r   r   r  rp   rp   rp   rq   rz     r@  c                   S   s   t ddgg S r   r  rp   rp   rp   rq   rz     rz  c                   S   s   t ddgdS )Nr   r   r^   r  rp   rp   rp   rq   rz     rz  c                   S   s   t ddgg dS )Nr   r   r   r  rp   rp   rp   rq   rz     r}  c                   S   s   t g d S )Nr   )r4   r   rp   rp   rp   rq   rz     r	  c                   S   rL  r[  )r4   
normalizedrp   rp   rp   rq   rz     rM  c                   S   s   t ddgjddS )Nr   r   znot a methodr[  r  rp   rp   rp   rq   rz     r!  c                   S   r  r   r4   
inverse_GErp   rp   rp   rq   rz     r	  c                   S      t ddgddgg S r   r  rp   rp   rp   rq   rz     rM  c                   S   r  r   r4   inverse_ADJrp   rp   rp   rq   rz     r	  c                   S   r  r   r  rp   rp   rp   rq   rz     rM  c                   S   r  r   )r4   
inverse_LUrp   rp   rp   rq   rz     r	  c                   S   r  r   r(  rp   rp   rp   rq   rz     r	  c                   S   r  r   r4   r/  rp   rp   rp   rq   rz     r	  c                   S   s   t ddgddggjddS )Nr   r   r   r   zNot a real methodr[  r  rp   rp   rp   rq   rz     r  c                   S   (   t g dg dg dg dgjddS )Nr  r  r  r  zNot functionr/  r  rp   rp   rp   rq   rz     
    c                   S   r  )Nr  r  r  r  Fr  r  rp   rp   rp   rq   rz     r  c                   S   s*   t tddgddggtddgddggS r[  r9   r4   rp   rp   rp   rq   rz     s   * c                   S   s   t tddgddggg S r[  r  rp   rp   rp   rq   rz     r@  c                   S   s   t tdd dS )Nrb   r   r^   )r9   r   rp   rp   rp   rq   rz     rz  c                   S   rv  )Nr   )r   r   r_  rp   rp   rp   rq   rz     r{   c                   S   rv  )Nr   )r   r   r_  rp   rp   rp   rq   rz     r{   r  c                      rm  )Nzmethod=LU_decomposition())r/  rp   r  rp   rq   rz     r   )r   r   r   r   r   r   r   r   c                           dS )Ng@)r  rp   r   Vrp   rq   rz     r{   c                      r  )Ng)r  rp   r  rp   rq   rz     r{   )rQ   r  r~  r*   rA  r,   r4   rp   rp   r  rq   test_errorsw  sz   r  c                   C   s   t t dks	J t tddggt tdgdgg  k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   rp   rw   rp   rp   rq   rz     r   ztest_len.<locals>.<lambda>c                 S   r   r   rp   rw   rp   rp   rq   rz     r   r   r   r   )r  r4   rp   rp   rp   rq   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   )r4   rb   rc   r   r   rp   rp   rq   test_integrate  s   $FFr  c                  C   sX   t ddttt ftddfddtd d ff} | tdt dtddfdfks*J d S )	Nr   r   r   r   r   r   )r   r   r   )r   r   r   )r4   r   rb   rc   r-  r   rp   rp   rq   
test_limit  s   0(r  c                  C   s  t ddtftddfddtd d ff} t| tt| s J | tt dddddt ffks3J | tt d	ks>J t| tt dddddt ffksQJ t| tt d	ks\J |  }t|tt|slJ |ttdddddt ffksJ |ttd	ksJ t|ttdddddt ffksJ t|ttd	ksJ | jtd
dt| td
dksJ t| td
dt| td
dksJ d S )Nr   r   r   r   r   r   r   r   )r   r  r   Frx  )	rB   rb   rc   r   r   r   r  rC   rZ   )r   A_immrp   rp   rq   	test_diff  s   (&&&& $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 rp   )r   r   )fxyzry   rp   rq   r,    r  z2test_diff_by_matrix.<locals>.<listcomp>.<listcomp>)rb   rc   rd   )r   r  )ry   rq   r,    r  z'test_diff_by_matrix.<locals>.<listcomp>)rB   rb   rc   rd   re   r   rY   r  r^   rC   r_   rA   r   r   r   r   r   r4   r   )r   r  r   dBr  exprresrp   r  rq   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 ru   )nonexistantattributerp   r   rp   rq   rz     s    ztest_getattr.<locals>.<lambda>r   r   r   r   )r4   rb   rc   rQ   r  getattrrp   rp   r   rq   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   )r4   is_upper_hessenbergr  is_lower_hessenbergrA   r   rp   rp   rq   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   r4   choleskyrp   rp   rp   rq   rz   .  r{   ztest_cholesky.<locals>.<lambda>c                   S   r  Nr   )r   r   r  rp   rp   rp   rq   rz   /  r{   c                   S      t dt dfdf S Nr   r   r   )r4   r	   r  rp   rp   rp   rq   rz   0  rM  c                   S   r  N)r   r   )r   r   r  rp   rp   rp   rq   rz   1  r{   c                   S      t djddS Nr  F	hermitianr  rp   rp   rp   rq   rz   2  r	  r   r   r   Fr  r   r  r   r   ))   r   r7  )r   r   r   )r7  r   r  re  )r   r   r   )r   r   r   r   r  r   r  r  r   c                   S   r  r  r5   r  rp   rp   rp   rq   rz   A  r{   c                   S   r  r  r  rp   rp   rp   rq   rz   B  r{   c                   S   r  r  )r5   r	   r  rp   rp   rp   rq   rz   C  rM  c                   S   r  r  r  rp   rp   rp   rq   rz   D  r{   c                   S   r  r  r  rp   rp   rp   rq   rz   E  r	  )rQ   r,   r  r4   r	   r  r   r  r&  r   r5   )r   r  rp   rp   rq   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 )Nrb   Tr  r   r   r   r   r   r  r   r   r  r   	frobeniusfro%   )r   r   r   r  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   r4   r   r   r)   normr   r   r   r  r   maxr  r8   rc   r   r   r   r  r	   rA   r(   r
   InfinityNegativeInfinitytrue)rb   r   r   r   r   r  r  r  orderr5  r6  difr   r^   r_   r`   ra   erp   rp   rq   test_matrix_normU  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 )Nrb   Tr  r   r   r   r   r   r   r   r   c                 3   s*    | ]}t d  | V  qdS )      ?N)r   
epsilon_eqr  r  )r   valMcrb   rp   rq   r     s   ( z(test_condition_number.<locals>.<genexpr>r   r   r   r   r   )r   r8   r   condition_numberr   r   r   r4   r   r   r   r   r  r   )r   r   rp   r  rq   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$J | |kr*J | |ks0J | dks6J | dkr<J td}t d}||ksJJ ||krPJ d S )N)r   r  r   r   r   ))r   r   r   )r   r   r   )r   r   r   r   )r  r   r   )r4   r5   )r   r   r   r  rp   rp   rq   test_equality  s   r  c                   C   s@   t dtg dgtg dg dg dg dgksJ d S )Nr   )r   r   r   r  r   r   )r8   r  r4   rp   rp   rp   rq   test_col_join  s   r	  c                  C   s\   t g dg} tddD ]}g d}||d ttd|| d |ks+J qd S )Nr   r   r   r6  r   r  r   r   r   )r4   r   insertrM   r8   r  r  r  )r4rx   r  rp   rp   rq   test_row_insert  s   (r  c                  C   sZ   t g d} tddD ]}g d}||d ttd|| d |ks*J qd S )Nr
  r6  r   r   r   r   r   )r4   r   r  rM   rA   r  r  r  )c4rx   r  rp   rp   rq   test_col_insert  s   (r  c                  C   s|   t ddg t tddtddgksJ t g d t g dks&J t g d} | jdd dt g dks<J d S )	Nr   r   r   r   )r   r   g0.++c                 S   s   | j dddjS )Nr   T)r~   chop)r  is_zeror+  rp   rp   rq   rz     r	  z!test_normalized.<locals>.<lambda>r  )r4   r  r   r   rp   rp   rq   test_normalized  s    
r  c                   C   s,   t dd dks
J t dd dksJ d S )Nc                   S   r  r  r8   print_nonzerorp   rp   rp   rq   rz     r{   z$test_print_nonzero.<locals>.<lambda>z[X  ]
[ X ]
[  X]
c                   S   s   t ddS )Nr   .r  rp   rp   rp   rq   rz     r   z[.  ]
[ . ]
[  .]
)rN   rp   rp   rp   rq   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  )r4   r8   rA   r;   r   r   )rx   rd   r   r   rp   rp   rq   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   Fr^   T)nonzero)	r4   is_zero_matrixrA   r8   rb   r5   r2   r3   r   r  rp   rp   rq   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 tg dt d }tg dt d }tg dt d }	tt  d |	 ksJ tt  d |	 ksJ tt  d |		 ksJ t
t 
 d |	 ksJ tt 
 d |	 ksJ tt 
 d |		 ksJ d S )Nr   r   r   r   r  r   r   )r   r?   r>   r=   r8   r  r   r\   from_axis_angleto_rotation_matrixrF   rG   rH   )
thetar3_plusr3_minusr2_plusr2_minusr1_plusr1_minusq1q2q3rp   rp   rq   test_rotation_matrices#	  s2   


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]ra   c                   S   rv  )Nra   r   r-   rp   rp   rp   rq   rz   K	  r{   z%test_DeferredVector.<locals>.<lambda>testzDeferredVector('test'))strr.   r   rQ   r~  reprrp   rp   rp   rq   test_DeferredVectorH	  s
   r,  c                   C   s   t tdrJ d S )Nr5  )rO   r.   rp   rp   rp   rq    test_DeferredVector_not_iterableO	  s   r-  c                   C      t tdd  d S )Nc                   S   s   t tdS )Nr  )r4   r.   rp   rp   rp   rq   rz   S	  r{   z,test_DeferredVector_Matrix.<locals>.<lambda>)rQ   rA  rp   rp   rp   rq   test_DeferredVector_MatrixR	     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   r4   r1   r  r   r&   )r  r  r  r  rp   rp   rq   test_GramSchmidtU	  s   
.. 
r1  c                   C   s4   t g dddksJ t g dddddksJ d S )Nr  r   r   F)zero)r6   rp   rp   rp   rq   test_casoratianf	  s   r3  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   )r4   rA   r   rp   rp   rp   rq   test_zero_dimension_multiplyk	  s   ""r4  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  rp   rp   r   rp   rq   rz   w	  r	  z'test_slice_issue_2884.<locals>.<lambda>c                      s    d S )Nr  rp   rp   r   rp   rq   rz   x	  r   )r4   r   r  rQ   r~  rp   rp   r   rq   test_slice_issue_2884q	  s   ""$$r5  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   )rA   r   r4   rp   rp   rp   rq   test_slice_issue_3401{	  s    *r6  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  r7     r   )r8  r   r   r  )rA   r4   r5   )r  rp   rp   rq   test_copyin	  s(   
 """$  $r9  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  rp   rp   rp   rq   rz   	  rM  z'test_invertible_check.<locals>.<lambda>)r   r   r   r   r   rc  c                          j ddS )Nrc  r[  r  rp   r   rp   rq   rz   	  r{   c                      r:  )NrZ  r[  r;  rp   r   rp   rq   rz   	  r{   c                      r:  )Nra  r[  r;  rp   r   rp   rq   rz   	  r{   )	r4   r:  rQ   r  rb   r  r   r8   r'   rp   rp   r   rq   test_invertible_check	  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  r4   )rb   rc   r  rp   rp   rq   test_issue_3959	  s   ,r=  c                   C   s$   t tddgddggdksJ d S )Nr   r   r   r   zMatrix([[1, 2], [3, 4]]))r*  r4   rp   rp   rp   rq   test_issue_5964	  s   $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%   r4   )rb   rc   rp   rp   rq   test_issue_7604	  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  )r8   is_Identityr  rA   r;   r4   r5   r   rp   rp   rp   rq   test_is_Identity	  s   "rB  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  d S )Nr   r   r  r   r  r   r7  Fr  Tr  physicsr  conjugate_conventionr   r   r   rightr   left)rE  c                   S   s    t ddgjt ddgdddS )Nr   r   r   r   Tr)  rD  r  rp   rp   rp   rq   rz   	  r   ztest_dot.<locals>.<lambda>)r;   r  r4   r	   rQ   r  rp   rp   rp   rq   test_dot	  s   "2668<<00rH  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   r4   dualequalsr8   rA   )B_xB_yB_zE_xE_yE_zFFdrp   rp   rq   	test_dual	  s$   
rS  c                  C   s   t ddg du sJ t dddtd dt  d ttd d  dtt t t t dg	} |  du s6J | jddd u s@J | jdd	 dd u sLJ | d
  | d
< |  d u s[J | d
  | d
< |  } | jdddu spJ d| d< |  du s|J d S )Nr   r   Fr   r   Trc  c                 S   s   | S ru   rp   r+  rp   rp   rq   rz   	  r   z%test_anti_symmetric.<locals>.<lambda>r   r   )r4   is_anti_symmetricrb   rc   r   r   rp   rp   rq   test_anti_symmetric	  s   DrU  c                  C   s   t d} | jdd\}}||j |j|   kr t|jks#J  J | jddd\}}||j |j|   kr@t|jksCJ  J || |  | ksOJ d S )N)r   r   T)	normalize)rV  sort)r4   rV  r  r8   r   r  )r   r  rX   rp   rp   rq   #test_normalize_sort_diogonalization	  s   ..rX  c                   C   r.  )Nc                   S   s   t g dt ddg gS )Nr   r   r   r   rp   rp   rp   rq   rz   	
  rM  z!test_issue_5321.<locals>.<lambda>)rQ   r  rp   rp   rp   rq   test_issue_5321
  r0  rY  c                  C   s   t tddtd t g dg dgksJ t tddtd t ddgddgddgddggks6J t} | | td| dtd t g dg dgksTJ d S )Nr   )r   r   r   r   )r   r   r   r   r   r   )r4   hstackr8   vstackr5   r  rp   rp   rq   test_issue_5320
  s    r\  c                  C   sV   t dgg} t| }t || t ddggksJ t || t dgdggks)J d S r  )r4   r   rZ  r[  )r   AImrp   rp   rq   test_issue_11944
  s   $r^  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 ru   )r   )r   r  r  rp   rq   r)  )
  s   ztest_cross.<locals>.testc                   S   s"   t ddddgt ddddgS r   r  rp   rp   rp   rq   rz   3
  s   "ztest_cross.<locals>.<lambda>)r4   r  r   r  rQ   r*   )r^   r_   r  r  r)  r   r   rp   r  rq   
test_cross#
  s   r_  c                  C   s^   t tttg} t tttg}|  | | |ksJ |  	 s#J |  
 | ks-J d S ru   )r4   rb   rc   rd   r^   r_   r`   hatr  rT  vee)v1v2rp   rp   rq   test_hat_vee6
  s
   rd  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   )r   r8   r  popr   r   )r   r  rp   rp   rq   	test_hash=
  s   $rf  c                      s   t d  tt fdd d S )Nr   c                      s   t  dS r  )hashr8   rp   r  rp   rq   rz   K
  r   z!test_issue_3979.<locals>.<lambda>)r   rQ   r  rp   rp   r  rq   test_issue_3979F
  s   rh  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	   r4   r   adjoint)r  r  r   rp   rp   rq   test_adjointN
  s
   rk  c                  C   sv   dd l } | jjjd}| jj|}dt| gd|gg}tddgt | |gg}tD ]}|||	 ks8J q,d S )Nr   r^   )
sympy.physics.quantumrC  quantumoperatorr    r!   r	   r4   r   rj  )sympyr^   a_dagr  r  r   rp   rp   rq   test_adjoint_with_operatorU
  s   rq  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(   r2   r   rb   r   rp   rp   rp   rq   test_simplify_immutable`
  s   "
rr  c                     sT   t dtd\ tddfdd} tdd fdd}| }|| ks(J d S )NzF, Gr  r   c                        | | S ru   rp   rw   )Grp   rq   rz   f
  r{   ztest_replace.<locals>.<lambda>c                    rs  ru   rp   rw   )rQ  rp   rq   rz   g
  r{   )r   r   r4   replace)Kr   Nrp   )rQ  rt  rq   test_replaced
  s
   rx  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   )r4   rb   atomsr   r  NegativeOner   r   rp   rp   rq   
test_atomsl
  s    r{  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RDr[  r  h   i  r   r   r   )r   r   r   )r  r8     EDr   compi_ib,  i  ij  c                 3   s&    | ]\}} |  |  V  qd S ru   r}   )r   rx   ry   r  rp   rq   r   
  s
    
ztest_pinv.<locals>.<genexpr>)r4   r^   r_   r`   ra   r(   pinvr  r  sympy.core.numbersr  r   zipr  )	A1Asr   A_pinvAApApAr~  wrepsrp   r  rq   	test_pinvr
  s:    
r  c                  C   s~   t g dg dg dg dg dg dgg} | D ]#}|jdd}|| }|| }|j|ks0J d	d
 }||j|s<J qd S )N)=   r  7   ru  r  r   )>   r   U   r  r   r   )E   8   r8  r   6   r   )r   r  [   )   r  r   )r   r  r   r   Z   r   )r   r   r   r   r   r   r  r[  c                 S   s<   |  t}dd |D }| | | }tdd |D S )Nc                 S   s   i | ]}||  qS rp   r  )r   r  rp   rp   rq   
<dictcomp>
  r}  zYtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose.<locals>.<dictcomp>c                 s   s    | ]	}t |d k V  qdS )g|=Nr   r   r  rp   rp   rq   r   
  r   zXtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose.<locals>.<genexpr>)ry  r$   r  r  r   )M1r  rootofsrootofs_approxdiff_approxrp   rp   rq   allclose
  s   
zEtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose)r4   r  r  )r  r   r  r  r  r  rp   rp   rq   3test_pinv_rank_deficient_when_diagonalization_fails
  s"   	r  c                   C   sL   t ddt dd tddg ksJ t ddt dd tddg ks$J d S ri  )r;   r4   rp   rp   rp   rq   test_issue_7201
  s   $(r  c                  C   s2   t tttfD ]} | tgdggjthksJ qd S r   )r2   r3   r4   r5   rb   free_symbolsr  rp   rp   rq   test_free_symbols
  s   r  c                      sz  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d	dg   krtddg ksJ  J dS )zSee issue 7465.r   array?NumPy must be available to test creating matrices from ndarraysr   r  c                      s(   t  ddgddggddgddgggS )	Nr   r   r   r   r   r   r   r   r   rp   r  rp   rq   rz   
  r  z#test_from_ndarray.<locals>.<lambda>r   r   r   r   N)
numpyr  ImportErrorrT   r4   rb   rc   rd   rQ   NotImplementedErrorrp   rp   r  rq   test_from_ndarray
  s"    $$
40@r  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)r  matrixzPNumPy must be available to test indexing matrixified NumPy ndarrays and matricesr   r   r   r   r  )
sympy.matrices.commonr  r  r  r  r  rT   r   rP   PendingDeprecationWarning)r  r  r  r   rp   rp   rq   test_17522_numpy
  s   
r  c                  C   sx   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   r  )r  zEmpmath must be available to test indexing matrixified mpmath matricesr   r   r   r         @)r   g       @r^  r  )r  r  mpmathr  r  rT   r   )r  r  r   rp   rp   rq   test_17522_mpmath
     r  c                  C   sx   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   r  )
csr_matrixzJSciPy must be available to test indexing matrixified SciPy sparse matricesr   r   r   r   r  )r  r  scipy.sparser  r  rT   r   )r  r  r   rp   rp   rq   test_17522_scipy
  r  r  c                  C   s   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 td}td}t |ggjd	u sJJ t ||gt||ggjd	u s[J t ||g||ggjdu sjJ t ||gt||ggjdu s{J d S )
Nr   r   r   Fr   r   r_   r`   T)r4   r	   is_hermitianrb   r   r    r!   r   rT  rp   rp   rq   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 )NFrx  r   r   )r4   r   rb   r  r  rp   rp   rq   	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   r  r   c                      rm  r   row_delrp   r  rp   rq   rz   &  r   z+test_issue_9457_9467_9876.<locals>.<lambda>c                      rm  Nr   r  rp   rW   rp   rq   rz   (  r   r   r   r   r   c                      rm  r   col_delrp   r  rp   rq   rz   2  r   c                      rm  r  r  rp   rW   rp   rq   rz   4  r   )r4   r  rQ   r~  r  )r   rw  r]   rp   )r  rX   rq   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   r8   r4   rd   )rb   rc   r^   r_   r   r  rp   rp   rq   test_issue_94226  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  )r4   r  r  id)	r   r^   r_   r`   opsr   opr  newrp   rp   rq   test_issue_10770B  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)r4   r   r   rp   rp   rq   test_issue_10658N  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 )Nr7  r   r   r   r   rt  r   r   r   /a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1)r4   r   rm  r	   r(   r:  rA   r   )r   axaybxbycxcydxdyexeyt0t1rp   rp   rq   !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   r  )r                 @)r  r  r   )r   r  r  )r   r  g      )r4   r:  r  r  )mmm_mixedm_floatm_invrp   rp   rq   test_partial_pivotingk  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+  rp   rp   rq   rz     r{   z*test_iszero_substitution.<locals>.<lambda>r  r   )r   r   g4iҤIӿr   )r   r   glٲer   r  r  r  N)r4   r:  r  )r   m_rref	m_correctm_diffrp   rp   rq   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   r  -   r   ru  r   r   r   r   c                 S   s   t |  dk S )Ng#B;)r   r~   r+  rp   rp   rq   rz     r	  z"test_issue_11238.<locals>.<lambda>T)r(   r/  )	sympy.geometry.pointr  r   r   r   r   r4   r(   rm  )
r  xxyyp1p2p0r  r  m3Zrp   rp   rq   test_issue_11238  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   r  )r4   r   ImaginaryUnitr   as_real_imagr   )r  r  r  klsr^   r_   rp   rp   rq   test_as_real_imag  s   
r  c                  C   sV   t ddg d} |  \}}|d t dddgksJ |d t ddg dks)J d S )Nr   rr  r   r   r   )r   r   r   r   )r4   jordan_cells)r   r  Jcellsrp   rp   rq   test_deprecated  s    r  c                  C   s\   ddl m}  tg d}tg d}| |dtg dksJ | |dtg dks,J d S )	Nr   )Mod)r   r   r   )r   ru  rs  r   )r   r   r   r   )r   r   r   )sympy.core.modr  r4   )r  r   r   rp   rp   rq   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   r  r  r   r   r   r   )dtypefloat64)r  r  r  rT   r4   floatr  name)r  r   rp   rp   rq   test_issue_14943  s   r  c                  C   s4   t ddd} td}| d dk}t|dksJ d S )Nr   r   r^   r   r   zm[0, 0] > 0)rD   r   r*  )r   r^   rp   rp   rq   test_case_6913  s   r  c                  C   s.   t ddd} td}| ||| iksJ d S )Nr   r   r^   )rD   rK   match)r   r^   rp   rp   rq   test_issue_11948  s   r  c                  C   s   t dtgt dt gg} t j|  t dgtggt dgt gggk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   )r4   r	   orthogonalizer   QRdecompositionr  r8   )vecsr   rX   r  rp   rp   rq   test_gramschmidt_conjugate_dot  s    4r	  c                  C   sf   t tddd} t tddd}| |}t|| d }t|| d }||d ks+J |dks1J d S )Nr^   r   r   r_   r   r   )r4   rD   r  r   )r^   r_   r`   ra   r  rp   rp   rq   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`  )rA   analytic_funcr   rb   rp   rp   rp   rq   rz     r!  ztest_func.<locals>.<lambda>c                      s    t  tt t S ru   )rb   r  r   rp   r   rp   rq   rz     r!  )r   r   r  r   )r   r   r   r   )r   r   r   r   c                      s     tttS ru   )r  r   rb   rp   r   rp   rq   rz     r	  r  r   "   )r   rs  r   )r   r   r  )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   r  )sympy.simplify.simplifyr  r4   r  r   rb   re   r   r   r   rQ   r  r   r(   r   r  rp   r   rq   	test_func  s$   HT  "  2r  z$Cannot create threads under pyodide.c               	   C   s   dd } t d1 tj }|| }| sJ W d    n1 s$w   Y  W d    d S W d    d S 1 s<w   Y  d S )Nc                  S   s&   t jd ksJ tdgg} | |  } dS r  )rI   stater4   r   rp   rp   rq   r    s   ztest_issue_19809.<locals>.fT)rE   
concurrentfuturesThreadPoolExecutorsubmitresult)r  executorfuturerp   rp   rq   test_issue_19809
  s   

"r  c                  C   s@   t ttg} t| tddftddft tjgtjggksJ d S ri  )r4   rb   rc   r   r   r  r  rp   rp   rq   test_issue_23276  s
   r  c                  C   s   t g dg dg dg dg} |  }|d tg dks J |d tg dks,J |d	 tg d
ks8J t|dks@J tj| g|R   |ksOJ d S )Nr   r   r   r   r   r  r7  r   r   ru  r   r   r   r   r   r   r   r   rM  r   r   )r   r  r   r   r   )r   r7  r   r   r   )r   r   r   rM  r   )rk   rK  r4   r  rZ  r   basisrp   rp   rq   test_columnspace_one!  s   "r!  c                  C   s   t g dg dg dg dg} |  }|d tg dgks!J |d tg dgks.J |d tg d	gks;J t|d
ksCJ d S )Nr  r  r  r  r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )rk   rI  r4   r  r  rp   rp   rq   test_rowspace0  s   r"  c                  C   s   t g dg dg dg dg} |  }|d tg dks J |d tg dks,J td	d
 | |d  D s;J tdd
 | |d  D sJJ d S )Nr  r  r  r  r   )r  r   r   r   r   r   )r   r   r   r   r   c                 s       | ]}|j V  qd S ru   r  r  rp   rp   rq   r   H      z%test_nullspace_one.<locals>.<genexpr>c                 s   r#  ru   r$  r  rp   rp   rq   r   I  r%  )rk   rN  r4   r   r  rp   rp   rq   test_nullspace_one>  s   "r&  c                     sP  t d tt fdd tt fdd tt fdd tt fdd tt fdd tt fdd tt fd	d tt fd
d tt fdd tt fdd tt fdd tt fdd tt fdd  dddtg dg dg dgksJ  dddtg dg dg dgksJ  jddddtg dg dg dgksJ  jddddtg dg dg dgksJ  dddtg dg dg dgksJ  jddddtg dg dg dgksJ  jddddtg dg dg dgksJ  ddddtg dg dg dgks1J  jddddd tg dg dg dgksJJ  jddddd!tg dg dg dgkscJ td"ddgd# } | dddtd"ddgd# ksJ | dddtd"ddgd# ksJ | ddddtd"ddgd# ksJ d S )$Nr   c                      rm  Nabcelementary_row_oprp   r  rp   rq   rz   P  r   ztest_row_op.<locals>.<lambda>c                      rj  ru   r)  rp   r+  rp   rq   rz   Q  r   c                          j ddddS )Nn->knr   r  r   r)  rp   r+  rp   rq   rz   R  r	  c                          j ddddS )Nr-  r7  r   r.  r)  rp   r+  rp   rq   rz   S  r	  c                      r/  )Nn<->mr   r   row1row2r)  rp   r+  rp   rq   rz   T  r	  c                      r/  )Nr0  r   r   r1  r)  rp   r+  rp   rq   rz   U  r	  c                      r/  )Nr0  r7  r   r1  r)  rp   r+  rp   rq   rz   V  r	  c                      r/  )Nr0  r   r7  r1  r)  rp   r+  rp   rq   rz   W  r	  c                          j dddddS Nn->n+kmr   r   r2  r3  r   r)  rp   r+  rp   rq   rz   X  rz  c                          j dddddS )Nr6  r   r   r7  r)  rp   r+  rp   rq   rz   Y  rz  c                          j dddddS )Nr6  r7  r   r   r7  r)  rp   r+  rp   rq   rz   Z  rz  c                      r9  )Nr6  r   r7  r   r7  r)  rp   r+  rp   rq   rz   [  rz  c                          j dddddS r5  r)  rp   r+  rp   rq   rz   \  rz  r-  r   r   re  r   r   r   r  r  r.  )r2  r   r0  r1  )r  r3  r6  )r   r   r   )r  r   r3  )r2  r   r3  r   r   )r   rQ   r  r*  r4   rs   r  rp   r+  rq   test_row_opM  8   ,,..,00022&&,r;  c                     sP  t d tt fdd tt fdd tt fdd tt fdd tt fdd tt fdd tt fd	d tt fd
d tt fdd tt fdd tt fdd tt fdd tt fdd  dddtg dg dg dgksJ  dddtg dg dg dgksJ  jddddtg dg dg dgksJ  jddddtg dg dg dgksJ  dddtg dg dg dgksJ  jddddtg dg dg dgksJ  jddddtg dg dg dgksJ  ddddtg dg dg dgks1J  jddddd tg dg dg dgksJJ  jddddd!tg dg dg dgkscJ td"ddgd# } | dddtd"ddgd# ksJ | dddtd"ddgd# ksJ | ddddtd"ddgd# ksJ d S )$Nr   c                      rm  r'  elementary_col_oprp   r+  rp   rq   rz   t  r   ztest_col_op.<locals>.<lambda>c                      rj  ru   r=  rp   r+  rp   rq   rz   u  r   c                      r,  )Nr-  r   r  r   r=  rp   r+  rp   rq   rz   v  r	  c                      r/  )Nr-  r7  r   r?  r=  rp   r+  rp   rq   rz   w  r	  c                      r/  )Nr0  r   r   col1col2r=  rp   r+  rp   rq   rz   x  r	  c                      r/  )Nr0  r   r   r@  r=  rp   r+  rp   rq   rz   y  r	  c                      r/  )Nr0  r7  r   r@  r=  rp   r+  rp   rq   rz   z  r	  c                      r/  )Nr0  r   r7  r@  r=  rp   r+  rp   rq   rz   {  r	  c                      r4  Nr6  r   r   rA  rB  r   r=  rp   r+  rp   rq   rz   |  rz  c                      r8  )Nr6  r   r   rD  r=  rp   r+  rp   rq   rz   }  rz  c                      r9  )Nr6  r7  r   r   rD  r=  rp   r+  rp   rq   rz   ~  rz  c                      r9  )Nr6  r   r7  r   rD  r=  rp   r+  rp   rq   rz     rz  c                      r:  rC  r=  rp   r+  rp   rq   rz     rz  r-  r   r   re  r   r   r   r  r  r?  )rA  r   r0  r@  )r  rB  r6  )r   r   r   )r  r   rB  )rA  r   rB  r   r   )r   rQ   r  r>  r4   rs   r  rp   r+  rq   test_col_opq  r<  rE  c                  C   s   t d} td}| jsJ |jsJ tddg }|jsJ tddg d}|js*J tddg d}|jr7J td}tdd|ddg}|jsIJ tdd||dg}|jrWJ tddg d}|jrdJ d S )	Nr   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   rb   r   	r   r   r   r   r   r   r   r   r   )r   r   
is_echelonrs   r   )zroidentr^   rb   rp   rp   rq   test_is_echelon  s"   






rJ  c                     s  t d td}    ksJ |  | ksJ tddg     ks&J tdddg    ks5J fdd}tddg d tdgdgdggg} fd	d
t jD }  jscJ | || tddg d g } fdd
t jD }  jsJ | || tddg d ttddgdgdggttddgdgdggg} fdd
t jD }  jsJ | || tddg d tdgdgdggg} fdd
t jD }  jsJ | || tddg d tdgdgdggtdgdgdggg} fdd
t jD }  js+J | || tddg d tdgdgdggg} fdd
t jD }  jsZJ | || d S )Nr   r   r   r   c                    sb   |D ]}t dd  | D sJ q|D ]}t dd |D s.t dd  |  D r.J qd S )Nc                 s   r#  ru   r$  r   re   rp   rp   rq   r     r%  zCtest_echelon_form.<locals>.verify_row_null_space.<locals>.<genexpr>c                 s   r#  ru   r$  rK  rp   rp   rq   r     r%  c                 s   r#  ru   r$  rK  rp   rp   rq   r     r%  )r   r   )r   r   nullsr   )	a_echelonrp   rq   verify_row_null_space  s   z0test_echelon_form.<locals>.verify_row_null_spacerw  r  c                       g | ]
} |d d f qS ru   rp   r   r  rp   rq   r,    r  z%test_echelon_form.<locals>.<listcomp>)	r   r   r   r   r   r   r   r   r   c                    rO  ru   rp   r   r  rp   rq   r,    r  )	r   r   r   r   r   r   r   r   r   r   r   r   c                    rO  ru   rp   r   r  rp   rq   r,    r  )	r   r   r   r   r   r   r   r   r   c                    rO  ru   rp   r   r  rp   rq   r,    r  )	r   r   r   r   r   r   r   r   r   c                    rO  ru   rp   r   r  rp   rq   r,    r  )r   r   r   r   r   r   c                    rO  ru   rp   r   r  rp   rq   r,  	  r  )	r   r   rG  rs   r4   r   r   rG  r   )r  rN  rL  r   rp   )r^   rM  rq   test_echelon_form  s   





rP  c               
   C   sH  t ddg } | jdd| ksJ t dddg} t dddg}| jdd|jdd  kr1| ks4J  J t ddg d}|jddtdgdgdggksNJ t ddg d}|jddtg dgkseJ t ddg d}|jddtg d	g d
g dgksJ t ddg d}t ddg d}t ddg d}t ddg d}|jdd|jdd  kr|jdd  kr|jdd  kr|ksJ  J td} td}| jdd| ksJ |jdd|ksJ t g dg dg dg dg}| \}}|tg dg dg dg dgksJ |dksJ t tddtddddgg dg dg dg}|jddtdddtddgdddtd dgdddtd!dgg d"gksXJ td#}t dd|ddt||dg}t|jddddt|| d  |tdd  |  dddt|| d  gD ]\}	}
t	|	|
 j
sJ qd S )$Nr   F)pivotsr   r   r   r   rw  )r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   rF  )	r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r7  r   )r   r   r   r   r   rM  r   )r   r   r  r   r   r   r7  )r   r   r   r   r  r   r   )r   r7  r   r   r   r   r   )r   r   r   r   r   r   r   )r   r   r   r   r   r  r   )r   r   r   r   r   r   r   )r   r   r   r~  r   r  r  r  i   r7     r  rb   )rs   r:  r4   r   r   r   r   r   r  r(   r  )r  r^   r_   r`   ra   rd   r   pivot_offsetsrb   rx   ry   rp   rp   rq   	test_rref  s   ,$



(rU  c                  C   s   t d\} }}}tddgddgddgddgg}t| |||g}||tddgddgddgddggtd| | gd| d |d  g| g|ggfksOJ d S )Nrn  r   r   r   r   r   r  )r   r4   rref_rhs)r^   r_   r`   ra   r   r   rp   rp   rq   test_rref_rhsP  s     
rW  c                     s   t g dg dg dg dg dg dg  jddd	d
}  jdd	ddd} jdd	dd}| d	d d f t g dgks@J |d	d d f t g dgksQJ |d	d d f t g dgksbJ tt fdd tt fdd tt fdd d S )N)r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r  )r   r   r   r7  )r   r   r   r   r0  r   r   r1  r6  r   r6  r7  r-  r.  )r   r   r   r  )r   r  r   r   c                      r/  )Nr0  r   r   r1  r)  rp   r   rp   rq   rz   p  r	  z"test_issue_17827.<locals>.<lambda>c                      r/  )Nr-  r   r   r.  r)  rp   rX  rp   rq   rz   q  r	  c                      r9  )Nr6  r   r   r   r7  r)  rp   rX  rp   rq   rz   r  rz  )r4   r*  rQ   r  )r  r   rQ  rp   rX  rq   test_issue_17827_  s"   	"""rY  c                  C   sj   t ddgtddt  gg} |  dksJ t ddtdd}| dks'J td}| dks3J d S )Nr   r   r   r   r   )r4   rb   rm  r   rA   )r   r~   r}  rp   rp   rq   	test_rankt  s   rZ  c                  C   s   t d\} }}}}}}}}}	}
}t| || |
 ||
 dg||||
 ||
 dg||||
 ||
 dg||||
 ||
 dg||	d| | ||
  d|	 | |	|
  dgg}| dksZJ d S )Nr  r   r   r   r   )r   r4   rm  )r  r  r  r  r  r  r  r  r  r  r  r  r   rp   rp   rq   test_issue_11434|  s   ,r[  c               	   C   s   t d\} }td|  dddgd|  d|  d ddgdd|  d|  | d dgdd| | dgg}tdddd| d | |    gdddd| | |    gdddd| |   gg d	g}d
}| \}}t|| t|j kspJ ||ksvJ d S )Nz
nu, lambdar   r   r   r   r  r   r   r  r   )r   r4   r:  r(   rA   r   )nulambr   expected_reducedexpected_pivotsreducedrQ  rp   rp   rq   test_rank_regression_from_so  s   ra  c                  C   sn   t g dg dg dg dg} | t dt  }| dks!J |d  dks+J |d  dks5J d S )NrT  r  r  r  r   r   r   )r4   r8   r	   rm  r   rp   rp   rq   test_issue_15872  s
    rb  ([  r  concurrent.futuresr  collections.abcr   sympy.core.addr   sympy.core.functionr   r   r   r  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   $sympy.matrices.expressions.transposer   sympy.physics.quantum.operatorr   r    r!   sympy.polys.polytoolsr"   r#   sympy.polys.rootoftoolsr$   sympy.printing.strr%   sympy.sets.setsr&   r  r'   r(   sympy.simplify.trigsimpr)   sympy.matrices.exceptionsr*   r+   r,   sympy.matrices.matrixbaser.   sympy.matrices.determinantr/   sympy.matrices.utilitiesr0   sympy.matricesr1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   
sympy.corerJ   rK   (sympy.functions.special.tensor_functionsrL   sympy.utilities.iterablesrM   rN   rO   sympy.utilities.exceptionsrP   sympy.testing.pytestrQ   rR   rS   rT   rU   rV   sympy.assumptionsrX   sympy.tensor.arrayrY   $sympy.tensor.array.array_derivativesrZ   sympy.matrices.expressionsr[   sympy.algebrasr\   ro  r]   r  r^   r_   r`   ra   rb   rc   rd   re   r   r  rf   rg   sympy.matrices.matricesrh   ri   rk   rs   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r(  r0  r3  r5  r;  r=  r?  rA  rF  rH  rJ  rL  rO  rQ  rS  rW  r_  rb  rd  rh  rj  rn  ro  rq  rr  rt  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r!  r#  r%  r'  r)  r+  r,  r.  r1  r7  r8  r<  rB  rF  rO  rQ  rU  rV  rX  ra  rh  rp  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  r  r  r  r  r'  r,  r-  r/  r1  r3  r4  r5  r6  r9  r<  r=  r>  r@  rB  rH  rS  rU  rX  rY  r\  r^  r_  rd  rf  rh  rk  rq  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  r  r	  r
  r  r  r  r!  r"  r&  r;  rE  rJ  rP  rU  rW  rY  rZ  r[  ra  rb  rp   rp   rp   rq   <module>   s  (h (,Ga,	R			:	
		
	
 HK

=7(]%
		-%

	$$_A
