o
    3Ih                    @   s^  d dl Zd dlZd dlmZ d dlmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZL d dlMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZU d dlVmWZWmXZX d dlYmZZZ d dl[m\Z\m]Z]m^Z^ d dl_m`Z` d d	lambZbmcZcmdZd d d
lemfZf d dlgmhZhmiZimjZjmkZkmlZlmmZm d dlnmoZompZp d dlqmrZr ee%eefZsee%fZteefZudd Zvdd Zwdd Zxdd Zydd Zzdd Z{dd Z|dd Z}dd Z~d d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ Zd|d} Zd~d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddÄ Zddń ZddǄ ZddɄ Zdd˄ Zdd̈́ Zddτ Zddф Zddӄ ZddՄ Zddׄ Zddل Zddۄ Zdd݄ Zdd߄ Zdd Zeldd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d Zdd Zdd Zdd Zdd	 Zd
d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Z d$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Z	d6d7 Z
d8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Z ddde Z!dfdg Z"dhdi Z#djdk Z$dldm Z%dndo Z&dpdq Z'drds Z(dtdu Z)dvdw Z*dxdy Z+dzd{ Z,d|d} Z-d~d Z.dd Z/dd Z0dd Z1dd Z2dd Z3dd Z4dd Z5dd Z6dd Z7eldd Z8dd Z9dd Z:dd Z;dd Z<dd Z=dd Z>dd Z?dd Z@dd ZAdd ZBdd ZCdd ZDdd ZEdd ZFdd ZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOddÄ ZPekdădŐdƄ ZQdǐdȄ ZRdɐdʄ ZSdS (      N)Hashable)GAbsAddArrayDeferredVectorEExpr	FiniteSetFloatFunctionGramSchmidtIImmutableDenseMatrixImmutableMatrixImmutableSparseMatrixIntegerKroneckerDeltaMatPowMatrixMatrixSymbolMaxMinMutableDenseMatrixMutableSparseMatrixPolyPowPurePolyQ
QuaternionRationalRootOfSSparseMatrixSymbolTupleWildbanded
casoratiancosdiagdiffexpexpandeyefloorhessian	integratelogmatrix_multiply_elementwisenanonesoopi
randMatrix	rot_axis1	rot_axis2	rot_axis3rot_ccw_axis1rot_ccw_axis2rot_ccw_axis3signsimpsimplifysinsqrtsstrsymbolssympifytantrigsimp	wronskianzeroscancel)abcdtxyz)
NumberKindUndefinedKind)_find_reasonable_pivot_naive)MatrixErrorNonSquareMatrixError
ShapeError)
MatrixKind)_dotprodsimp_state	_simplifydotprodsimp)ArrayDerivative)ignore_warningsraisesskipskip_under_pyodideslowwarns_deprecated_sympy)captureiterable)versionc                  C   sr  t ddg d} | jdksJ | jdksJ | d dksJ | d dks&J t| g dks0J t| dd d f g dks@J t| d d df ddgksPJ t| d d d d f t| ksbJ | d d d d f | kspJ t | | ksxJ t g dg dg| ksJ t g dg df| ksJ t ddg| ksJ t d	| ksJ t ddgdd
gddgg| krJ d S )N      )   rf   rg            rh   rh   rj   rh   ri   rj   rk   rh   rf   rg   )rn   rm   ri   rk   )r   rowscolslistrO    rs   d/home/air/sanwanet/gpt-api/venv/lib/python3.10/site-packages/sympy/matrices/tests/test_matrixbase.pytest__MinimalMatrix#   s      $&ru   c                   C   s   t ddgddggjttksJ t ddgddggjttks"J t ddg jttks/J t tggjttks<J t dt dggggjttksNJ tdggjttks[J tdt dggggjttksmJ d S Nrh   rf   rg   ri   r   )r   kindrX   rR   rO   rS   r"   rs   rs   rs   rt   	test_kind6   s   ""$(rx   c                  C   s   t d\} }}}t| |g||gg}t| |g||gg}t| |g||gg}t| |g||gg}| |   krR|   krR|   krR| |||dksUJ  J d S )Nza:d)r   r   r   rh   rh   r   rl   )rC   r   r   r   r   todok)rJ   rK   rL   rM   m1m2m3m4rs   rs   rt   
test_todok@   s   0r   c                  C   s   t jt jtt t jgttttd gtt j tt dgg} t jt jtt t jttttd tt j tt dg}tdd|}| | ksCJ d S )Nrf   rg   ri   )	r!   OneHalfrO   rP   ZerorQ   r   tolist)lstflat_lstmrs   rs   rt   test_tolistJ   s   82r   c                  C   sN   t tjdgdtjgtdgg} dtjidtjidtid}|  |ks%J d S )Nr   rh   r   rh   rf   )r   r!   r   r   rO   todod)r   dictrs   rs   rt   
test_tododQ   s   r   c                      sH  t ddg d tt fdd tt fdd tt fdd tt fdd  d d	  krEtg d
g dgksHJ  J  d d	  krdtddgddgddggksgJ  J  d d  krtg d
g dgksJ  J  d d  krtddgddgddggksJ  J d S )Nrg   	rh   rf   rg   ri   rj   rk         	   c                      
     dS Nrj   row_delrs   ers   rt   <lambda>Y      
 z"test_row_col_del.<locals>.<lambda>c                      r   Nr   rs   r   rs   rt   r   Z   r   c                      r   r   col_delrs   r   rs   rt   r   [   r   c                      r   r   r   rs   r   rs   rt   r   \   r   rf   rn   rm   rh   ri   rj   r   r   r   r   r   rk   r   )r   r^   
IndexErrorr   r   r   rs   rs   r   rt   test_row_col_delW   s   8>8Br   c                  C   s   t ddgddgg} t dtgtdgg}t dtdgtdtgtttgg}|  | gks-J | |gks6J | |gks?J d S Nrh   rf   rg   )r   rO   rP   rQ   get_diag_blocks)rJ   rK   rL   rs   rs   rt   test_get_diag_blocks1e   s    r   c                  C   s  t ddgddgg} t dtgtdgg}t dtdgtdtgtttgg}t| ||t| ||t| ||t|||f\}}}}t |j|j|}t |j|j|}t |j|j|}t |j|j|}| | ||gksiJ | | ||gkstJ | | ||gksJ | |||gksJ d S r   )r   rO   rP   rQ   r)   ro   rp   r   )rJ   rK   rL   ABCDrs   rs   rt   test_get_diag_blocks2n   s    4r   c                  C   sP   t ddg d} | dt ddg dksJ | dt ddg dks&J d S )Nrg   r   r   rh   rn   rh   ri   r   )r   rowcolr   rs   rs   rt   test_row_col~   s   "r   c                   C   s8   t dtg dtg dg dg dgksJ d S )Nrg   r   r   r   )rh   r   r   r   )r   rh   r   r   )r   r   rh   r   )r-   row_joinr   rs   rs   rs   rt   test_row_join   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 )Nrg   r   rh   r   r   r   rh   r   r   r   rh   )r-   col_joinr   rs   rs   rs   rt   test_col_join   s   r   c                  C   sX   t g dg} tddD ]}g d}||d td|| d |ks)J qd S )Nri   ri   ri   rj   r   ri   rg   r   )r   rangeinsertr-   
row_insertr   flat)r4ilrs   rs   rt   test_row_insert   s   $r   c                  C   s   t g d} tddD ]}g d}||d td|| d |ks(J qtddt d	d	gd	d	gd	d	gd	d	gd	d	gd	d	ggt g d
g dg dg dg dg dgks]J d S )Nr   r   rj   r   r   r   ri   rg   r   rk   rf   )rh   r   r   rf   rf   r   r   r   )r   rh   r   rf   rf   r   r   r   )r   r   rh   rf   rf   r   r   r   )r   r   r   rf   rf   rh   r   r   )r   r   r   rf   rf   r   rh   r   )r   r   r   rf   rf   r   r   rh   )r   r   r   rH   
col_insertr   r   r-   )c4r   r   rs   rs   rt   test_col_insert   s   $6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 )Nri   rg   c                 S      | d | S Nrg   rs   r   jrs   rs   rt   r          ztest_extract.<locals>.<lambda>)r   rh   rg   r   rh   rf   )r   rh   rg   ri   r   
   r   r   rf   )r   r   rf   r   r      c                           dgdgS )Nri   r   extractrs   r   rs   rt   r          c                      r   )Nr   rg   r   rs   r   rs   rt   r      r   )r   r   r   r^   r   rs   rs   r   rt   test_extract   s   ((r   c                     s   t dddd  t dddd    ksJ     t      kr<t g dg dg dg d	gks?J  J tt fd
d t  t  ksRJ t dd} t dd}t dd}t dd}t | |||  jdkr| jdks~J d S )Nri   rg   c                 S   r   r   rs   r   rs   rs   rt   r      r   ztest_hstack.<locals>.<lambda>c                 S   r   r   rs   r   rs   rs   rt   r      r   )	r   rh   rf   r   rh   rf   r   rh   rf   )	rg   ri   rj   rg   ri   rj   rg   ri   rj   )	rk   r   r   rk   r   r   rk   r   r   )	r   r   r   r   r   r   r   r   r   c                            S N)hstackrs   r   r~   rs   rt   r      r   r   rh   rf   rk   )r   r   r^   rW   rH   ro   rp   )M1M2M3M4rs   r   rt   test_hstack   s"   "r   c                      s   t dddd  t dddd    ksJ     t      krTt 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ksWJ  J tt fd
d t  t  ksjJ d S )Nri   rg   c                 S   r   r   rs   r   rs   rs   rt   r      r   ztest_vstack.<locals>.<lambda>c                 S   r   r   rs   r   rs   rs   rt   r      r   r   rg   ri   rj   rk   r   r   r   r   r   c                      r   r   )vstackrs   r   rs   rt   r      r   )r   r   r^   rW   rs   rs   r   rt   test_vstack   s&   "r   c                  C   s\   t ttfdf} | tsJ | trJ | tsJ t dtfdf} | tr,J d S )Nrf   rg   rf   )r   rO   rP   hasrQ   r#   r   rs   rs   rt   test_has   s   r   c                  C   s  t d} tddddg du sJ tddd| d d|   d t| d d  d| t t |  t dg	}| du s<J |jddd u sFJ |jd	d
 dd u sRJ tdddd |D }|jdddu sgJ tdddd tjgt|dd   D }| du sJ d S )NrO   rf   rh   Frg   r   Tr?   c                 S      | S r   rs   rr   rs   rs   rt   r          z(test_is_anti_symmetric.<locals>.<lambda>c                 S      g | ]}|  qS rs   r,   .0rO   rs   rs   rt   
<listcomp>       z*test_is_anti_symmetric.<locals>.<listcomp>c                 S   r   rs   r   r   rs   rs   rt   r      r   )rC   r   is_anti_symmetricrP   r!   r   rq   )rO   r   rs   rs   rt   test_is_anti_symmetric   s   D*r   c                  C   s   t dtgt dgg} | jsJ t dt tgt dgg} | jdu s$J t ttgt dgg} | jd u s6J t tdgt dgg} | jdu sHJ d S )Nrh   rf   Fr   r   is_hermitianrO   rJ   rs   rs   rt   test_is_hermitian   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 )NTrh   rf   rg   ri   rj   rk   r   r   Frj   rk   r   rh   rg   rn   rf   )r   rO   is_symbolicr   rs   rs   rt   test_is_symbolic  s   r   c                  C   s<   t dgdgg} t ddgddgg}| jrJ |jsJ d S Nrh   rf   )r   	is_squarer   rs   rs   rt   test_is_square  s   
r   c                  C   s<   t ddg d} |  sJ t ddg d} |  rJ d S )Nrf   r   rh   rh   r   r   rh   r   rh   )r   is_symmetricr   rs   rs   rt   test_is_symmetric  s   r   c                  C   s   t g dg dg dg} | jsJ t ddg d} | jsJ t ddg d} | jdu s.J | jdu s5J t g dg dg dg} | jrGJ d S )	Nrg   ri   rh   rf   ri   rj   r   rg   )	rg   rf   r   ri   ri   rh   rh   rj   rf   )	rg   rf   r   ri   ri   rh   rh   rj   rf   Frg   rh   rf   )r   is_upper_hessenbergis_lower_hessenbergr   rs   rs   rt   test_is_hessenberg   s   

r  c                  C   s\   t tddg d h dksJ tddd} t tdd| dddg | dhks,J d S )	Nrf   r   rh   rf   rg   >   rh   rf   rg   rO   Trealr   rh   )setr   valuesr#   rr   rs   rs   rt   test_values-  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   rj   rh   rf   r   rh   rf   )r   r   Tr   	conjugateHMrs   rs   rt   test_conjugate5  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 )NFevaluater   rf   )r   r   rO   doitr   rs   rs   rt   	test_doitG  s    r  c                      sr   t dd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 s7J d S )	Nrf   rh   rj   rk   c                 3   s(    | ]}   |  |   kV  qd S r   evalfr   r   r   rs   rt   	<genexpr>O  s   & ztest_evalf.<locals>.<genexpr>c                 3   ,    | ]}  d |  |  d kV  qdS rf   Nr  r  r   rs   rt   r  P     * c                 3   r  r  nr  r   rs   rt   r  Q  r  )r   rA   allr   rs   rs   r   rt   
test_evalfM  s   "r   c                     sT   t dtd\ tddfdd} tdd fdd}| }|| ks(J d S )NF, Gclsrf   c                        | | S r   rs   r   Grs   rt   r   V  r   ztest_replace.<locals>.<lambda>c                    r$  r   rs   r   Frs   rt   r   W  r   rC   r   r   replace)Kr  Nrs   r(  r&  rt   test_replaceT  s
   r.  c                     s   t dtd\ tdd fdd} |  d\}}|tddfddks)J | dd d	d	 ddiksAJ d S )
Nr!  r"  rf   c                    r$  r   rs   r   r'  rs   rt   r   ^  r   z"test_replace_map.<locals>.<lambda>Tc                    r$  r   rs   r   r%  rs   rt   r   `  r   r   rh   r)  )r  r,  rM   rs   r-  rt   test_replace_map\  s
   4r/  c                     s   z
ddl mm}  W n ty   td Y nw tddgddgg ddgddgg}|  |s5J |  dd	|s@J ttd
dd dkrYt	t
 fdd d S d S )Nr   )arrayarray_equal?NumPy must be available to test creating matrices from ndarraysrh   rf   rg   ri   Tcopynumpy.c                      s    ddS )NFr3  rs   rs   r   r0  rs   rt   r   m  r   z'test_numpy_conversion.<locals>.<lambda>)r5  r0  r1  ImportErrorr_   r   intre   splitr^   	TypeError)r1  np_arrayrs   r7  rt   test_numpy_conversionc  s   r=  c                  C   s   t ddgddgg} | | d  kr| dksJ  J | d| d  kr9| d  kr9t dks<J  J | d| d	  krW| d
  krWt dksZJ  J |  | d  krt| d  krtt dkswJ  J d S )Nrh   rf   rg   ri   r   r   rk   ))ri   rg   rf   rh   r   r   ))rf   ri   rh   rg   )rg   rh   )ri   rf   )r   rot90r   rs   rs   rt   
test_rot90o  s
   (<<>rD  c                   C   s@  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gjttd ttd idd	t td td  ggksJ d S )
Nrh   ri   rj   rf   r   r   rA  T)simultaneous)r   rO   subsrP   rs   rs   rs   rt   	test_subsw  s   4(($(rG  c                     s  t ddg d tt fdd tt fdd  ddgdd	gg}  ddgdd	gg|   krDt g d
g dg dgksGJ  J  ddgdd	gg}  jddgdd	ggdd|   krst g dg dg dgksvJ  J  jddgdd	ggdd}  jddgdd	ggddd|   krt g dg dg dgksJ  J  g dt g d
g dg dgksJ ddlm}  |g dt g d
g dg dgksJ d S )Nrg   ri   )rh   rf   rg   ri   rj   rk   r   r   r   r   r      c                      s     ddggS )Nr   rj   )permuters   r   rs   rt   r     r   ztest_permute.<locals>.<lambda>c                           tdS )NrO   )rI  r#   rs   r   rs   rt   r         r   rf   rh   r   r   r   r   rH  r   rp   )orientation)rf   rg   rh   ri   )rk   r   rj   r   )r   r   r   rH  backward)	direction)rM  rO  )rg   rh   rf   ri   )r   rj   rk   r   )r   r   r   rH  )rh   rf   r   rg   )Permutation)	r   r^   r   
ValueErrorpermute_rowsrI  permute_colssympy.combinatoricsrP  )rK   rP  rs   r   rt   test_permute  sH    "$rU  c                  C   s   t g dg dg dg dg} | d}|t g dg dg dg dgks)J | d}|t g dg dg dg dgksBJ |  }|t g dg dg dg dgksZJ d S )Nrh   rh   rh   rh   rf   r   r   rh   rh   r   r   r   rh   r   r   r   r   r   )r   rh   rh   rh   )r   upper_triangular)r   Rrs   rs   rt   test_upper_triangular  s6   

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 | d}|t g dg dg dg dgksAJ | d}|t g dg dg dg dgksZJ d S )NrV  rh   r   r   r   rh   rh   r   r   rh   rh   rh   r   rf   r   rY  )r   lower_triangularr   Lrs   rs   rt   test_lower_triangular  s6   

rc  c                         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 )
Nrn   rf   rf   ri   rk   ri   rh   c                           S r   rs   rs   r   r  rs   rt   r         ztest_add.<locals>.<lambda>r   rO   rP   rQ   r^   rW   rs   rs   ri  rt   test_add     &Brl  c                  C   s   t ddgddgg} | dtksJ | dtksJ ztd W n ty+   Y n	 ty3   Y nw ztd W d S  tyE   Y d S  tyN   Y d S w )Nrh   rf   rg   ri   z2 @ aza @ 2)r   
__matmul__NotImplemented__rmatmul__evalSyntaxErrorr;  r   rs   rs   rt   test_matmul  s"   rs  c                  C   s   G dd dt } tddgddgg}|  }|| t|d| gd| d| ggks+J || t|d| gd| d| ggksAJ dS )zd
    Test that if explicitly specified as non-matrix, mul reverts
    to scalar multiplication.
    c                   @   s   e Zd ZdZdZdZdS )ztest_non_matmul.<locals>.fooFrl   N)__name__
__module____qualname__	is_Matrixis_MatrixLikeshapers   rs   rs   rt   foo  s    rz  rh   rf   rg   ri   N)r   r   )rz  r   rK   rs   rs   rt   test_non_matmul	  s
   ,0r{  c                  C   s.   t ddddg} |  t ddddgksJ d S )Nrh   rf   r   r   r   r  rs   rs   rt   test_neg  s   r}  c                  C   s0   t ddddg} | |  t ddddgksJ d S )Nrh   rf   r   r|  r  rs   rs   rt   test_sub  s    r~  c                  C   s:   t ddddg} | d t ddtjtdd gksJ d S r   )r   r!   r   r  rs   rs   rt   test_div#  s   *r  c                   C   sj   t tddg dksJ t tdg dksJ ttdtks&J ttjdtdtks3J d S )Nrf   rh   r   r   rh   r"  )rq   r   r-   typers   rs   rs   rt   test_eye(  s   r  c                   C      t tddg dksJ t tdg dksJ tddtg dg dgks-J ttdtks8J ttjdtdtksEJ d S )Nrf   rV  rg   rh   rh   rh   r"  )rq   r   r4   r  rs   rs   rs   rt   	test_ones/  
   $r  c                   C   r  )Nrf   rY  rg   r   r"  )rq   r   rH   r  rs   rs   rs   rt   
test_zeros7  r  r  c                      s  t j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 dg ddddtddgddtdddgdddddtgddddtdggksUJ  t g dg ddddtdddgddtddddgdddddtdgddddtdtgddddtttggksJ  t g dg ddddtdddgddtdtddgddtttddgddddddtgdddddtdggksJ t tttg t ddgdd	ggt d
dgg dt tdddddgtdddddgtdddddgg dg dg dg dgksJ tt fdd dt dggks)J dddt ddgddggks<J dddt ddgddggksOJ ddddt ddgddgddggksfJ ddg t ddgddggksyJ t ddgt dgdggksJ dddgd	gdddgddgd	ggdd  krt ddgddgd	dggksJ  J tdt ksJ tdt dt ksJ t g dt dddksJ t jg dddjdksJ t g dgjdksJ t jg dgddjdksJ t g dggjdks J t t	ddddt g dg dgks7J t t	ddddt ddgddgddgddggksTJ d S )Nrh   rf   rg   )rh   rf   r   r   r   r   )rf   rg   r   r   r   r   r   )rh   rf   r   r   r   r   r   )rf   rg   r   r   r   r   r   ri   rj   rk   r   )r   r   r   r   r   r   )r   r   rh   rf   r   r   )r   r   rg   ri   r   r   )r   r   r   r   rj   rk   c                      s    dddS )Nr   rj   ro   rs   rs   rJ   rK   rL   r)   rs   rt   r   l      z test_diag_make.<locals>.<lambda>r  )rp   )ro   rp   F)unpackr"  rn   rB  r?  r   r   rh   r   )r   r   r   rf   )
r   r)   rO   rP   rQ   r^   rQ  r  ry  r4   rs   rs   r  rt   test_diag_make?  s    		&&.
" r  c                     s@  t ddtd } | dksJ t| dksJ tddks(J tddks3J td	d
ks>J t tksJJ tddddi}t| t|ks^J tt|kshJ ttfdd ttfdd ttfdd td	d t	 fddtd j
  jD  ksJ d S )Nrg   r   r   )r   ri   r   rh   rh   rj   r   )rg   r   rf   rf   rl   c                      r   r   diagonalrs   r   rs   rt   r     r   ztest_diagonal.<locals>.<lambda>c                      r   )NrA  r  rs   r   rs   rt   r     r   c                      s
     tS r   )r  r6   rs   r   rs   rt   r     r   c                    s   i | ]
}|t  |qS rs   )rq   r  r  r  rs   rt   
<dictcomp>  s    z!test_diagonal.<locals>.<dictcomp>)r   r   r  tupler  r"   r^   rQ  r4   r&   ro   rp   )rM   srs   )r  r   rt   test_diagonal  s(   
r  c                   C   s  t ddt jddd  kr?t jddd  kr?t jdddd  kr?t jdddd  kr?t g dg d	g d
gksBJ  J t jddddt g dg dg dgksYJ ttdd  ttdd  ttdd  ttdd  t jdddt jdddksJ d S )Nrg   rf   
eigenvalue)sizer  upper)band)r  eigenvalr  rf   rh   r   )r   rf   rh   r   lowerrf   r   r   r  r   c                   S   
   t dS Nrf   r   jordan_blockrs   rs   rs   rt   r     r   z#test_jordan_block.<locals>.<lambda>c                   S   s   t ddS )Ng      @rf   r  rs   rs   rs   rt   r     r   c                   S   s   t jddS )Nrf   r  r  rs   rs   rs   rt   r     r   c                   S   s   t jdddS )Nrf   ri   )r  r  r  rs   rs   rs   rt   r     s    )r  r  )r   r  r^   rQ  rs   rs   rs   rt   test_jordan_block  s:   
r  c                     s  t ddgddgg} | t dgdggt dgdgggks J | jt dgdggddt dtd d gtdd gggksBJ | t dgdggt dgdggt dgdggt td	dgtd
dgggkslJ | t dgdggt dgdggt dgdgggksJ | t dgdggg ksJ t g dg dg dg}t dgdggt dgdggt dgdggg |j  t dgdggt tddgtddgggksJ t g dt g dt g dg tt fdd t g dt g dt g dg tt fdd d S )Nrh   rf   rg   ri   T	normalizerj   r   rk   r   )r   rh   r   )rg   rk   r   )r   rj   rf   r   r         r   rn   )rh   ri   rj   c                         t j ddiS N	rankcheckTr   orthogonalizers   vecsrs   rt   r     r   z$test_orthogonalize.<locals>.<lambda>rm   r   c                      r  r  r  rs   r  rs   rt   r     r   )r   r  rA   r   r^   rQ  ri  rs   r  rt   test_orthogonalize  s*   ,$"*".*""r  c               
   C   s   t d\} }| t g dg dg dgksJ |t g dg dg dgks)J t d\} }| t g dg dg d	g d
g dg dg dgksMJ |t g dg dg dg d
g dg dg dgksjJ d S )Nrh   )r   rh   r   rh   r   rh   )r   rh   rh   rh   rh   r   rg   )rA  rh   r   r   r   r   r   )rh   r   rh   r   r   r   r   )r   rh   r   rh   r   r   r   )r   r   rh   r   rh   r   r   )r   r   r   rh   rh   rh   r   )r   r   r   r   rh   rf   rh   )r   r   r   r   r   rh   rg   )rg   rh   r   r   r   r   r   )rh   rf   rh   r   r   r   r   )r   rh   rh   rh   r   r   r   )r   	wilkinson)wminuswplusrs   rs   rt   test_wilkinson  s<   
r  c                  C   s   t d\} }tddd|  |g}|| dtddtdd|gks#J tddt| |  f|ddfdd| d d ff}|| dtd|ddfd	fksMJ d S )
Nx yrf   rh   rj   ri   r   r   )rh   ri   rh   )r   rj   rh   )rC   r   limitr   r@   )rO   rP   r   r   rs   rs   rt   
test_limit  s
   &0(r  c                      sN   t g dg dg dg g dtt fdd tt fdd d S )Nrn   rm   r   r  c                      s     S r   rs   rs   r  vrs   rt   r     rj  z"test_issue_13774.<locals>.<lambda>c                           S r   rs   rs   r  rs   rt   r     rj  )r   r^   r;  rs   rs   r  rt   test_issue_13774   s   r  c                     s   t d t dttdd  tt fdd tt fdd tt fdd td\} }}ttd	| g t|  gksDJ ttd	|| g td
|  gd	| ggks]J ttd	||| g td
d
|  gd	d
| gd
d	| ggks~J d S )NrO   rP   c                   S   r  Nrh   )r   	companionrs   rs   rs   rt   r   
  r   z test_companion.<locals>.<lambda>c                      s   t tdg S r  r   r  r   rs   rr   rs   rt   r     r  c                      s   t tddg S )Nrf   rh   r  rs   rr   rs   rt   r     r   c                      s   t t   gS r   r  rs   rO   rP   rs   rt   r         zc0:3rh   r   )r#   r^   rQ  rC   r   r  r   )c0c1c2rs   r  rt   test_companion  s   $$r  c                  C   s   t d\} }}t| ||g}|t| ||gg d}|tdgdgdggks)J t| | | | | g| | | | | g| | | | | gg}|t| gdg}|tg dg dg dgksZJ d S )Nzx, y zrn   rh   rf   rg   )rh   rh   rh   rh   rh   )rC   r   rF  zip)rO   rP   rQ   r   r   rs   rs   rt   test_issue_10589  s   ,&r  c                  C   sf   G dd dt } tddg d}| ddg d}|| }t|| s#J |tddgddggks1J d S )	Nc                   @   s   e Zd Zejd ZdS )ztest_rmul_pr19860.<locals>.Foog{Gz?N)rt  ru  rv  r   _op_priorityrs   rs   rs   rt   Foo#  s    r  rf   r   r   r         )r   r   
isinstance)r  rJ   rK   rL   rs   rs   rt   test_rmul_pr19860"  s    r  c                      sT   t ddgddgg tddgddggtt fdd tt fdd d S )Nrh   rf   rg   ri   c                      s     S r   rs   rs   r   r   rs   rt   r   4  rj  z"test_issue_18956.<locals>.<lambda>c                      rh  r   rs   rs   r  rs   rt   r   5  rj  )r   r   r^   r;  rs   rs   r  rt   test_issue_189561  s   r  c                  C   sP   G dd dt } tddddg}||  ksJ G dd d| }|| ks&J d S )Nc                   @   s   e Zd Zdd Zdd ZdS )ztest__eq__.<locals>.Myc                 s   s    dV  dV  d S r   rs   selfrs   rs   rt   __iter__:  s   ztest__eq__.<locals>.My.__iter__c                 S   s   t | | S r   )rq   )r  r   rs   rs   rt   __getitem__>  s   z"test__eq__.<locals>.My.__getitem__N)rt  ru  rv  r  r  rs   rs   rs   rt   My9  s    r  rf   rh   c                   @      e Zd Zdd ZdS )ztest__eq__.<locals>.My_sympyc                 S   s   t | S r   r|  r  rs   rs   rt   _sympy_C  s   z$test__eq__.<locals>.My_sympy._sympy_N)rt  ru  rv  r  rs   rs   rs   rt   My_sympyB      r  )objectr   )r  rJ   r  rs   rs   rt   
test__eq__8  s
   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 )Nrg   rf   )rg   rf   c                 s   s    | ]	}t |tu V  qd S r   )r  r9  r  rs   rs   rt   r  L      ztest_args.<locals>.<genexpr>)	enumerateall_classesrH   ry  r  ro   r  r9  rp   r   rq   r  r$   r|   r   )r  r#  r   rs   rs   rt   	test_argsH  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 Nrg   rf   )
r   r   rH   rb   _matr   r"   r   _smatr|   )r#  r   matsmatrs   rs   rt   test_deprecated_mat_smatU  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 r   )r   rO   rP   rQ   )r  rs   rs   rt   test_divisionb  s   (r  c                      rd  )
Nrn   rf   re  rf  ri   rg  rh   c                      rh  r   rs   rs   ri  rs   rt   r   k  rj  ztest_sum.<locals>.<lambda>rk  rs   rs   ri  rt   test_sumg  rm  r  c                  C   st   t ddgttgg} t| t ddgttttggksJ t dddtg} t dddttg}t| |ks8J d S )Nrh   r   rf   rA  rg   )r   rO   rP   absr   ri  rs   rs   rt   test_absn  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)rh   rf   rB  r  )rg   r   rf   ri   rk   rh   )r   addrJ   rK   rs   rs   rt   test_additionv  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 )Nrg   r   rh   r   r   r   r   rf   ri   rk   r   ry   )r   rf   rh   rf   rh   r   )rg   rj   ri   rj   ri   )rk   r   r   r   r   r  rz   rf   r   )rf   rf   rf   r   )rh   r   rh   rf   )rf   r   rh   r   rf   r   r   r   )r   r   rg   r   )r   ri   r   ri   )r   r"   r   rH   r   )r  rJ   rs   rs   rt   test_fancy_index_matrix  sZ   $ ,&&2,2&&
r  c                     s  t d t dtt fdd tt fdd   } | d dks'J | d d	ks/J | d
 dks7J | d dks?J | d dksGJ | d dksOJ   } | d dks[J | d d	kscJ | d
 dkskJ | d dkssJ | d dks{J | d dksJ 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sJ d } t| t sJ | d dksJ | d dks%J | d
 dks.J | d dks7J t t	dgdt	gg}|d	 |ksJJ t t	t	gddgg}|d	 t t
t
gt
t
ggkseJ t tdd}tdd	 }t |||g}||t |g|g|ggksJ d S )N)r  rB  r   rk   r  c                      r  r   rs   rs   r  rs   rt   r     rj  z%test_multiplication.<locals>.<lambda>c                      s    i  S r   rs   rs   r   rs   rt   r     rj  ry   r   rz   rf   r{   rk   rl   r     r>  r   ri   c                      s
   t  S r   )r2   rs   r  rs   rt   r     r   rO   rg   rj   r   r  rh   )r   r^   rW   r;  r2   multiply_elementwiser#   r  rO   r5   r3   r4   r   )rL   hr  r  r   _hr   rs   r  rt   test_multiplication  sj   
"
r  c                	      s  t tdd  tddgddgg  d tddgd	d
ggks!J tg dg dg dg  d tg dg dg dgksAJ  d tdksKJ  d  ksSJ tdggd d dd kscJ tddgddggtd tddgddggks}J tddgddgg  jddd jdddksJ  td tddgdd ggksJ tdd! td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s7J ttt
gdtgg tt t
td    gdt ggks\J 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sJ  J tg d)g d*g d+g d,g d-gt tfd.d t td/d  tg d0g d1g d2g  d3 tg d2g d2g d2gksKJ t t fd4d t t fd5d td6dgddgg  d3 td7d8gd9d:ggksxJ tg d1g d1g d1g  d3 tg d1g d1g d1gksJ tg d0g d1g d1g  d3 tg d1g d1g d1gksJ td;d<d=t  tsJ td;d<d<d>t t fd?d td;d<d<d@  ttdtdtd td d gdtddtd gg d1gksJ  d  tg d1g d1g d1gks'J t t fdAd tg d1g dBg dCg  dD tg dEg dFg dGgksQJ  dD  d ks\J tg d0g dHg d2g td;  d  d ksJ t tfdId   d  ksJ tg d2g d2g d2g td;d<d<dJ   ksJ td;d<d<d@  td d d ksJ   dtdksJ   dtdksJ tg dKg dLg dMg  dN tdOdOdOksJ  t tdt dt dt ksJ tg d0g d1g d1g t t fdPd t t fdQd ttjtjgtjtjgg  tj  ksPJ 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stJ d S )RNc                   S   s   t dd S Nr  rf   r|  rs   rs   rs   rt   r     r   ztest_power.<locals>.<lambda>rf   rg   ri   rj   i  i  i,*  i7  )rf   rh   rg   )ri   rf   ri   )rk   rH  rh   )i"  i     )i  i  ip  )i  i  i  r   rh   d   ry   r   r   r  r     cayleymethodmultiplyr   rH     !   i 0   9   )rj   rf   ri   r   r   g      ?r  i   )rg   r   r   r   rA  )r   rA  rA  r   rg   )r   rg   r   rg   r   )r   r   rg   r   rg   )rg   r   r   rg   r   c                      rJ  Nr   )_matrix_pow_by_jordan_blocksr!   rs   r   rs   rt   r   %  rK  c                   S   s   t ddgddggtdS )Nrh   rg   )r   r  r!   rs   rs   rs   rt   r   (  s    r   r   r         $@c                          d S N @rs   rs   r   rs   rt   r   +  rj  c                          t dd S r  r   rs   r   rs   rt   r   ,  rK  r   ihiO<iv0ir  T)integer)r  negativec                      s     S r   rs   rs   )r   r  rs   rt   r   6  rj  )r  nonnegativec                      r  r  r  rs   r   rs   rt   r   =  rK  )rg   r   rh   )ri   rg   rh   g      @)   H   Y   )i#        )i<  i  iI  r   r   r   c                      s     d S )Nr   )rF  r  rs   )Anr  rs   rt   r   E  r   )r  positiver  )r   rf   r   r   r
  gd%%@c                      r  r	  rs   rs   r   rs   rt   r   T  rj  c                      s    t  S r   r   rs   r   rs   rt   r   U  rj  )r^   rV   r   r-   r   powr!   r   	sympy.abcr  rJ   rK   r  _eval_pow_by_recursionrU   rQ  r#   r  r   r   rF  r  r)   rH   r   rs   rs   )r   r  r   r  rt   
test_power  s    & 4 $426J<$0&("((*,(&&8r  c                  C   s   t dt dt gdt dt gg} tdE |   t tdt td d tdt  td d gtdt  td d tdt td d ggksSJ W d    d S 1 s^w   Y  d S )Nrh   Trf   )r   rO   r[   r+   r,   r  rs   rs   rt   $test_issue_17247_expression_blowup_1\  s   $
00"r  c                  C   sr   t dt dt gdt dt gg} td |  \}}|| |  s'J W d    d S 1 s2w   Y  d S Nrh   T)r   rO   r[   jordan_forminvr  PJrs   rs   rt   $test_issue_17247_expression_blowup_2d  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 )Nrh   Tr  l                )r   rO   r[   r  rs   rs   rt   $test_issue_17247_expression_blowup_3k  s   $
"r%  c                  C   sR   t td} td | d t tdksJ W d    d S 1 s"w   Y  d S )Na1  [
        [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64],
        [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512],
        [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64],
        [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128],
        [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16],
        [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128]]Tr   a  [
            [     7369525394972778926719607798014571861/604462909807314587353088 - 229284202061790301477392339912557559*I/151115727451828646838272,   -19704281515163975949388435612632058035/1208925819614629174706176 + 14319858347987648723768698170712102887*I/302231454903657293676544,      -3623281909451783042932142262164941211/604462909807314587353088 - 6039240602494288615094338643452320495*I/604462909807314587353088,    109260497799140408739847239685705357695/2417851639229258349412352 - 7427566006564572463236368211555511431*I/2417851639229258349412352, -16095803767674394244695716092817006641/2417851639229258349412352 + 10336681897356760057393429626719177583*I/1208925819614629174706176,    -42207883340488041844332828574359769743/2417851639229258349412352 - 182332262671671273188016400290188468499*I/4835703278458516698824704],
            [50566491050825573392726324995779608259/1208925819614629174706176 - 90047007594468146222002432884052362145*I/2417851639229258349412352,  74273703462900000967697427843983822011/1208925819614629174706176 + 265947522682943571171988741842776095421*I/1208925819614629174706176, -116900341394390200556829767923360888429/2417851639229258349412352 - 53153263356679268823910621474478756845*I/2417851639229258349412352, 195407378023867871243426523048612490249/1208925819614629174706176 - 1242417915995360200584837585002906728929*I/9671406556917033397649408,   -863597594389821970177319682495878193/302231454903657293676544 + 476936100741548328800725360758734300481*I/9671406556917033397649408, -3154451590535653853562472176601754835575/19342813113834066795298816 - 232909875490506237386836489998407329215*I/2417851639229258349412352],
            [   -1715444997702484578716037230949868543/302231454903657293676544 + 5009695651321306866158517287924120777*I/302231454903657293676544,     -30551582497996879620371947949342101301/604462909807314587353088 - 7632518367986526187139161303331519629*I/151115727451828646838272,           312680739924495153190604170938220575/18889465931478580854784 - 108664334509328818765959789219208459*I/75557863725914323419136,    -14693696966703036206178521686918865509/604462909807314587353088 + 72345386220900843930147151999899692401*I/1208925819614629174706176,  -8218872496728882299722894680635296519/1208925819614629174706176 - 16776782833358893712645864791807664983*I/1208925819614629174706176,      143237839169380078671242929143670635137/2417851639229258349412352 + 2883817094806115974748882735218469447*I/2417851639229258349412352],
            [   3087979417831061365023111800749855987/151115727451828646838272 + 34441942370802869368851419102423997089*I/604462909807314587353088, -148309181940158040917731426845476175667/604462909807314587353088 - 263987151804109387844966835369350904919*I/9671406556917033397649408,   50259518594816377378747711930008883165/1208925819614629174706176 - 95713974916869240305450001443767979653*I/2417851639229258349412352,  153466447023875527996457943521467271119/2417851639229258349412352 + 517285524891117105834922278517084871349*I/2417851639229258349412352,  -29184653615412989036678939366291205575/604462909807314587353088 - 27551322282526322041080173287022121083*I/1208925819614629174706176,   196404220110085511863671393922447671649/1208925819614629174706176 - 1204712019400186021982272049902206202145*I/9671406556917033397649408],
            [     -2632581805949645784625606590600098779/151115727451828646838272 - 589957435912868015140272627522612771*I/37778931862957161709568,     26727850893953715274702844733506310247/302231454903657293676544 - 10825791956782128799168209600694020481*I/302231454903657293676544,      -1036348763702366164044671908440791295/151115727451828646838272 + 3188624571414467767868303105288107375*I/151115727451828646838272,     -36814959939970644875593411585393242449/604462909807314587353088 - 18457555789119782404850043842902832647*I/302231454903657293676544,      12454491297984637815063964572803058647/604462909807314587353088 - 340489532842249733975074349495329171*I/302231454903657293676544,      -19547211751145597258386735573258916681/604462909807314587353088 + 87299583775782199663414539883938008933*I/1208925819614629174706176],
            [  -40281994229560039213253423262678393183/604462909807314587353088 - 2939986850065527327299273003299736641*I/604462909807314587353088, 331940684638052085845743020267462794181/2417851639229258349412352 - 284574901963624403933361315517248458969*I/1208925819614629174706176,      6453843623051745485064693628073010961/302231454903657293676544 + 36062454107479732681350914931391590957*I/604462909807314587353088,  -147665869053634695632880753646441962067/604462909807314587353088 - 305987938660447291246597544085345123927*I/9671406556917033397649408,  107821369195275772166593879711259469423/2417851639229258349412352 - 11645185518211204108659001435013326687*I/302231454903657293676544,     64121228424717666402009446088588091619/1208925819614629174706176 + 265557133337095047883844369272389762133*I/1208925819614629174706176]])r   r!   r[   r  rs   rs   rt   $test_issue_17247_expression_blowup_4s  s   
"r&  c                  C   s   t dddd } td+ | dttd ddt  td   dt td	   td
dks/J W d    d S 1 s:w   Y  d S )Nrk   c                 S      dd| |  t   S Nrh   r   r  r   rs   rs   rt   r     r   z6test_issue_17247_expression_blowup_5.<locals>.<lambda>TrO   rj   $   ri   EXdomain)r   r[   charpolyr   rO   r   r  rs   rs   rt   $test_issue_17247_expression_blowup_5  s   
F"r/  c                  C   Z   t dddd tdD } td | ddksJ W d    d S 1 s&w   Y  d S )Nr   c                 S      g | ]}t | qS rs   rr   r  rs   rs   rt   r     r   z8test_issue_17247_expression_blowup_6.<locals>.<listcomp>@   Tbareissr   r   r   r[   detr  rs   rs   rt   $test_issue_17247_expression_blowup_6     
"r6  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 )Nrk   c                 S   r'  r(  r  r   rs   rs   rt   r     r   z6test_issue_17247_expression_blowup_7.<locals>.<lambda>T	berkowitzr   )r   r[   r5  r  rs   rs   rt   $test_issue_17247_expression_blowup_7  s   
"r9  c                  C   r0  )Nr   c                 S   r1  rs   rr   r  rs   rs   rt   r     r   z8test_issue_17247_expression_blowup_8.<locals>.<listcomp>r2  Tlur   r4  r  rs   rs   rt   $test_issue_17247_expression_blowup_8  r7  r;  c                  C   s   t dddd tdD } td- |  t g dg dg dg dg dg dg dg dgd	fks6J W d    d S 1 sAw   Y  d S )
Nr   c                 S   r1  rs   rr   r  rs   rs   rt   r     r   z8test_issue_17247_expression_blowup_9.<locals>.<listcomp>r2  T)rh   r   r   r   rA  r   r   r)  r   rh   rf   rg   ri   rj   rk   r   r   r   r   r   r   r   r   r   rz   )r   r   r[   rrefr  rs   rs   rt   $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 )Nrk   c                 S   r'  r(  r  r   rs   rs   rt   r     r   z7test_issue_17247_expression_blowup_10.<locals>.<lambda>Tr   )r   r[   cofactorr  rs   rs   rt   %test_issue_17247_expression_blowup_10  s   
"rA  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 )Nrk   c                 S   r'  r(  r  r   rs   rs   rt   r     r   z7test_issue_17247_expression_blowup_11.<locals>.<lambda>Tr   r*  )r   r[   cofactor_matrixr  rs   rs   rt   %test_issue_17247_expression_blowup_11  s   
 "rC  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 )Nrk   c                 S   r'  r(  r  r   rs   rs   rt   r     r   z7test_issue_17247_expression_blowup_12.<locals>.<lambda>Trh   r   ri   )r   r[   	eigenvalsr   r  rs   rs   rt   %test_issue_17247_expression_blowup_12  s   
""rE  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   rh   rf   )r   r   r   rh   FT)deepnumerr   )r   rO   
eigenvectsrA   r,   )r  evrs   rs   rt   %test_issue_17247_expression_blowup_13  s0    ("P"("P"rJ  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   rh   ri   Tr   r=  )r   rO   r[   echelon_formr  rs   rs   rt   %test_issue_17247_expression_blowup_14  s   4
2""rL  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   rh   ri   Tr   )r   rO   r[   rowspacer  rs   rs   rt   %test_issue_17247_expression_blowup_15  s   4
r"rN  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   rh   ri   T)r   rO   r[   columnspacer  rs   rs   rt   %test_issue_17247_expression_blowup_16  s   4
"rP  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   r1  rs   rr   r  rs   rs   rt   r     r   z9test_issue_17247_expression_blowup_17.<locals>.<listcomp>r2  Trh   r   r   rf   rA  rg   r   ri   r   rj   r)  rk   r@  )r   r   r[   	nullspacer  rs   rs   rt   %test_issue_17247_expression_blowup_17  s   
&&&&&&"rR  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 )Nrk   rh   rg   T)r   rO   r[   is_nilpotentr  rs   rs   rt   %test_issue_17247_expression_blowup_18  s   4
"rT  c                  C   sF   t td} td |  rJ W d    d S 1 sw   Y  d S )Nay  [
        [             -3/4,                     0,         1/4 + I/2,                     0],
        [                0, -177/128 - 1369*I/128,                 0, -2063/256 + 541*I/128],
        [          1/2 - I,                     0,                 0,                     0],
        [                0,                     0,                 0, -177/128 - 1369*I/128]]T)r   r!   r[   is_diagonalizabler  rs   rs   rt   %test_issue_17247_expression_blowup_19   s   
"rV  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 )	Nrh   r   T)rh   r   r   r   r_  rX  r  rf   )r   rO   r[   diagonalizer  rs   rs   rt   %test_issue_17247_expression_blowup_20*  s*   
"rX  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GEr  v  [
            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
            [0, 0, 0, -11328/952745 + 87616*I/952745]]r   r!   r[   r   r  rs   rs   rt   %test_issue_17247_expression_blowup_21=     
"r^  c                  C   rY  )NrZ  TLUr  r\  r]  r  rs   rs   rt   %test_issue_17247_expression_blowup_22K  r_  ra  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 )NrZ  TADJr  r\  )r   r!   r[   r   r,   r  rs   rs   rt   %test_issue_17247_expression_blowup_23Y  s   
""rc  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 )NrZ  TCHr  r\  r"   r!   r[   r   r   r  rs   rs   rt   %test_issue_17247_expression_blowup_24g  r_  rg  c                  C   rd  )NrZ  TLDLr  r\  rf  r  rs   rs   rt   %test_issue_17247_expression_blowup_25u  r_  ri  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]]Tri   r   r!   r[   rankr  rs   rs   rt   %test_issue_17247_expression_blowup_26  s   
	"rm  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   rh   Ta  [
            [    0,  4*x/(x**2 - 2*x + 1), -(-17*x**4 + 12*sqrt(2)*x**4 - 4*sqrt(2)*x**3 + 6*x**3 - 6*x - 4*sqrt(2)*x + 12*sqrt(2) + 17)/(-7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 + 8*x**3 - 2*x**2 + 8*x + 6*sqrt(2)*x - 5*sqrt(2) - 7), -(12*sqrt(2)*x**4 + 17*x**4 - 6*x**3 - 4*sqrt(2)*x**3 - 4*sqrt(2)*x + 6*x - 17 + 12*sqrt(2))/(7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 - 8*x**3 + 2*x**2 - 8*x + 6*sqrt(2)*x - 5*sqrt(2) + 7)],
            [x - 1, x/(x - 1) + 1/(x - 1),                       (-7*x**3 + 5*sqrt(2)*x**3 - x**2 + sqrt(2)*x**2 - sqrt(2)*x - x - 5*sqrt(2) - 7)/(-3*x**3 + 2*sqrt(2)*x**3 - 2*sqrt(2)*x**2 + 3*x**2 + 2*sqrt(2)*x + 3*x - 3 - 2*sqrt(2)),                       (7*x**3 + 5*sqrt(2)*x**3 + x**2 + sqrt(2)*x**2 - sqrt(2)*x + x - 5*sqrt(2) + 7)/(2*sqrt(2)*x**3 + 3*x**3 - 3*x**2 - 2*sqrt(2)*x**2 - 3*x + 2*sqrt(2)*x - 2*sqrt(2) + 3)],
            [    0,                     1,                                                                                            -(-3*x**2 + 2*sqrt(2)*x**2 + 2*x - 3 - 2*sqrt(2))/(-x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x + 1 + sqrt(2)),                                                                                            -(2*sqrt(2)*x**2 + 3*x**2 - 2*x - 2*sqrt(2) + 3)/(x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x - 1 + sqrt(2))],
            [1 - x,                     0,                                                                                                                                                                                               1,                                                                                                                                                                                             1]]a  [
            [0, 1,                       0,                       0],
            [0, 0,                       0,                       0],
            [0, 0, x - sqrt(2)*(x - 1) + 1,                       0],
            [0, 0,                       0, x + sqrt(2)*(x - 1) + 1]])r   rO   r[   r  r,   r!   r!  rs   rs   rt   %test_issue_17247_expression_blowup_27  s   
"rn  c                  C   sN   t td} td |  tdksJ W d    d S 1 s w   Y  d S )NrZ  Ta  [
            sqrt(14609315/131072 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2)])r   r!   r[   singular_valuesr  rs   rs   rt   %test_issue_17247_expression_blowup_28  s   
"rp  c                  C   rj  )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   rk  r  rs   rs   rt   test_issue_16823  s   
"rq  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)	rh   rh   rh   rh   rh   r   rh   r   r   rh   rf   r   r   r@  r   r   rA  rg   r   ri   r  rH  T)	r   r   r   r   rh   r   r   r   r   )	r   r   r   r   r   r   rh   r   r   r<  )r   rA   r[   r>  r!   r  rs   rs   rt   test_issue_18531  s0   6DDDDD6

$rr  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 )Nrj   r  )r   r   rs   rs   rs   rt   r     r   ztest_creation.<locals>.<lambda>c                   S   s   t ddg S )Nrj   r   r|  rs   rs   rs   rt   r     r   c                   S      t dd S r  r|  rs   rs   rs   rt   r     r   rj   r  rg   r   rh   rf   r  ry   r   r   r   ri   )rh   rh   rf   rf   rf   )rg   rg   rg   ri   ri   Fr  r   rz   r{   rl   c                 S   s   g | ]}|gqS rs   rs   r  rs   rs   rt   r   #  r  z!test_creation.<locals>.<listcomp>c                   S      t tdtddgS )Nrf   r   rg   r   r4   rs   rs   rs   rt   r   '      c                   S   rt  )Nrf   rg   r   ru  rs   rs   rs   rt   r   (  rv  )rj   rk   rk   )r^   rQ  r   r   rb   r   r  r!   EmptySetrO   rp   ro   r   r-   r   as_immutable
as_mutabler4   r   )
r  rJ   r   rK   c23c13rL   datr   r   rs   rs   rt   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 )Nrg   rf   rh   ri   rj   rk   r   )rh   rf   rf   rf   rg   rg   )ri   rf   rf   rf   rj   rj   )rk   rk   r   r   rj   rj   )r   	irregularr4   rs   rs   rs   rt   test_irregular_block0  s   &0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 )Nri   rg   rf   r   c                 S      | | S r   rs   r   rs   rs   rt   r   >  rj  ztest_slicing.<locals>.<lambda>rh   r   r   r  )ri   rj   rk   r   )r   r   r   r   )rH        r  r   )rg   r   r   r  r   )r-   rH   r   )m0r}   r~   rs   rs   rt   test_slicing9  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 )
Nri   rf   )rY  rY  r  rX  rh   r   r   )r]  )rf   rh   r   r   )rg   r   rh   r   )ri   r   r   rh   r   r   rL  r  r  r     ))r   rf   rg   ri   )r   rk   r   r   rL  r  )rH   r-   r   r   rs   rs   rt   test_submatrix_assignmentG  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 )Nrg   rh   r   )	rh   r   r   r   rh   r   r   r   rh   ri   c                 S   r  r   rs   r   rs   rs   rt   r   f  rj  ztest_reshape.<locals>.<lambda>)r   r  )rg   ri   rf   r   rf   rk   ))r   rh   rf   rg   rh   rf   )rg   ri   rf   rg   ri   rj   )r-   reshaper   r  r}   rs   rs   rt   test_reshapec  s   r  c                  C   sD   t d} | dd t dd ksJ | dd tdks J d S )Nrg   c                 S   s   d|  S r  rs   rr   rs   rs   rt   r   n  rj  z test_applyfunc.<locals>.<lambda>rf   c                 S      dS Nr   rs   rr   rs   rs   rt   r   o  r   )r-   	applyfuncrH   )r  rs   rs   rt   test_applyfuncl  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 )Nrf   rg   rJ   Tr  )complexr   )r   r   r   r   rh   )r   rh   r   r   )
r   rO   rP   r,   r#   r+   r   r(   r@   r   )r  r}   rJ   rs   rs   rt   test_expandr  s   8F
r  c                  C   s@  t ttd ttd gttd ttd  ttd ttd  gg} | tttt@ }|t td ttgtd tt td tt ggksQJ | tttt@ }|t td tgttd  td t ggksvJ | t	tt	t@ }|t td t gt td  td  t ggksJ d S r  )
r   r   rO   rA   rP   refiner   r  r  r  r  rs   rs   rt   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 )Nrg   )seedri   r      T)r  	symmetric)r  prng)r   r   )r  F      )r  percentr  r   rh   r  )minr  r  )r7   r4  r?   randomRandomr  r   ry  )r  r!   rngr  r  
zero_countr   r   rs   rs   rt   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 ).Nri   r`  r  rb  re  rh  QR)rf   rg   rj   )rg   rk   rf   )r   rg   rk   rg   )r   r   r   r   rh   r   r   rh   r   rh   rh   rh   r   r   r   rh   rh   r   r   r   r   rh   rh   r   r   )rh   r   rh   r   r   rh   r   r   rh   r   rh   r   rh   rh   rh   r   rh   rh   r   r   r   r   r   rh   r   )rh   rh   rh   rh   r   rh   r   r   rh   rh   r   r   r   rh   rh   rh   rh   r   r   rh   rh   r   r   rh   rh   )rh   r   r   r   r   r   rh   rh   r   r   rh   rh   rh   r   r   r   r   r   r   rh   r   r   rh   r   r   )rh   r   r   rh   rh   rh   r   rh   r   r   rh   r   r   rh   rh   rh   r   rh   r   r   r   rh   r   r   r   )rh   r   r   r   r   r   r   r   rh   rh   rh   r   rh   r   rh   rh   rh   rh   r   r   r   rh   rh   r   rh   )r   rh   rh   rh   r   r   r   r   rh   rh   rh   r   rh   r   rh   r   rh   r   rh   r   rh   r   r   rh   r   )rh   rh   r   r   r   rh   rh   r   r   rh   rh   r   rh   rh   r   rh   rh   r   rh   r   rh   rh   r   rh   rh   )r   r   rh   rh   rh   r   r   rh   rh   r   rh   rh   r   rh   r   r   r   r   r   r   rh   r   rh   r   rh   )rh   r   rh   rh   rh   r   rh   r   r   rh   rh   r   rh   rh   r   rh   rh   rh   rh   r   rh   rh   rh   r   r   )r   rh   rh   r   r   r   r   rh   rh   r   rh   r   rh   r   rh   rh   r   r   rh   r   r   r   rh   rh   r   )rh   r   r   rh   r   rh   r   rh   rh   r   r   rh   r   rh   r   rh   r   rh   r   rh   r   rh   rh   r   r   )r   rh   rh   r   r   rh   rh   r   r   rh   rh   r   rh   r   r   r   rh   r   r   rh   r   rh   rh   r   rh   )rh   rh   rh   r   rh   r   r   rh   r   r   rh   r   rh   rh   r   r   rh   rh   rh   r   rh   r   rh   rh   r   )r   rh   r   r   r   r   rh   rh   r   rh   rh   r   r   r   r   rh   r   rh   rh   rh   r   r   rh   r   r   )rh   rh   rh   rh   r   rh   rh   rh   rh   rh   rh   r   r   r   rh   r   rh   r   rh   r   r   rh   r   r   r   )r   r   r   rh   r   rh   rh   r   rh   r   r   r   r   r   rh   r   rh   rh   r   rh   r   rh   rh   r   rh   )r   rh   r   rh   r   r   r   r   rh   rh   rh   r   r   rh   rh   rh   r   r   rh   r   rh   rh   r   rh   rh   )rh   r   rh   rh   r   rh   r   rh   rh   r   rh   rh   rh   r   rh   r   r   r   r   rh   r   r   rh   r   rh   )r   r   r   rh   r   r   rh   rh   r   rh   rh   r   rh   r   rh   rh   r   r   r   r   r   r   r   r   r   )rh   r   r   r   r   rh   r   rh   r   r   rh   rh   r   rh   r   rh   rh   rh   rh   r   rh   rh   rh   rh   rh   )r   r   rh   rh   r   rh   r   r   r   rh   r   r   rh   r   r   rh   r   r   r   rh   r   rh   r   rh   rh   )r   r   r   r   r   rh   rh   rh   r   rh   rh   rh   r   r   r   rh   r   rh   rh   r   rh   rh   r   r   r   )r   r   rh   r   rh   rh   r   rh   rh   rh   r   r   rh   r   rh   r   r   rh   r   rh   r   r   r   r   r   )r   r   r   rh   rh   r   rh   rh   rh   r   r   rh   r   rh   r   rh   rh   r   rh   rh   rh   r   r   rh   r   BLOCKr   )r  1      )r   G   ^   );      A   c                 3   "    | ]}t | u V  qd S r   r  r   r   r  r#  r   rs   rt   r         ztest_inverse.<locals>.<genexpr>zGE ADJ LU CH LDL QRc                 3   r  r   r  r  r  rs   rt   r    r  )r-   r   r   ry  r   r  r:  r   )r   AinvAArs   r  rt   test_inverse  sr   ""&r  c                  C   s  t d\} }}}}t d}tdddddd|  | d| |  d|  d|   d|  | d|  d|   gdddddd|  | d| |  d|  | d|d    dgdd|  | d| |  d|  d|   d|  | d|  d|   ddddgdd|  | d| |  d|  | d|d    dddddgdddd|  | d| |  d|  d|   d|  | d|  d|   ddgdddd|  | d| |  d|  | d|d    dddgdd|  | | d| |  d| |   dd|  | | d| |  d| |   dd|  | | d| |  d| |   dgg}| }|| td ttdks1J td	d
 |t	D dk sBJ d S )Nz)Tau Tau_syn_in Tau_syn_ex C_m Tau_syn_gap__hr         ?       @      rf   r   c                 s       | ]}t |V  qd S r   r  r   frs   rs   rt   r        z:test_inverse_symbolic_float_issue_26821.<locals>.<genexpr>     @@)
rC   r   r   r-   r  rI   rH   maxatomsr
   )Tau
Tau_syn_in
Tau_syn_exC_mTau_syn_gapr  r  Mirs   rs   rt   'test_inverse_symbolic_float_issue_26821  s   L<L<L<|
$&r  c                  C   s   t d\} }}}}t d}tg dd|d  d| dddddgg dddd|d  d| dddgg d	ddddd|d  d| dgd
| dd
| dd
| dd|  gg}||  }||||  ttdkslJ tdd |t	D dk s|J d S )Nz-Tau, Tau_syn_in, Tau_syn_ex, C_m, Tau_syn_gapr  )r   r  r   r   r   r   r   r   rf   r   r   )r   r   r   r  r   r   r   )r   r   r   r   r   rh   r   rh   r   c                 s   r  r   r  r  rs   rs   rt   r    r  z6test_matrix_exponential_issue_26821.<locals>.<genexpr>r  )
rC   r   r+   r*   r  rI   rH   r  r  r
   )rJ   rK   rL   rM   r   rN   r  Mers   rs   rt   #test_matrix_exponential_issue_26821  s    
$$r  c                  C   s:  t ddtd t dtd  tt  g} ttg}| |t dt t td gtdt t ggks3J t ddttd td  g} | |t ddgdt td  td d td  ggks`J td t }ttg}t||t dt dt gdt dggksJ td td  }t||t dtd  dt td  gdt td  dtd  t ggksJ tttd   }td dtd   }t ddt gdt dt gg}|t|t ttgksJ |t|t ttgjksJ t|ttf|gt ddtd  dt gdtd  dt dt gdt dt dggksJ d S )Nrh   rf   ri   rg   r   rk   )r   rO   rP   jacobianr/   rQ   r  )rb  symsr  gansrs   rs   rt   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 )Nrf   rg   rh   r)  rk   r8  r  )rG   r(   rO   r@   r+   r,   )w1w2rs   rs   rt   test_wronskian4  s&   2**J("R("
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 )	Nrh   ri   rj   rf   r   r   rA  r   )r   rO   xreplacerP   r  r-   r"  rs   rs   rt   test_xreplaceE  s   $.r  c               
   C   s  t d} td}tdt dt  ttt  t g|tt|t  |t dd|  t| t |    t gg}|  |ttt tt  dt gdt dddtt|    t|    ggksbJ dt d }t|gg}|  |t|ggks|J |jtd |t|jtdggksJ t d} td}t	dt dt  ttt  t g|tt|t  |t dd|  t| t |    t gg}| ttt tt  dt gdt dddtt|    t|    ggksJ dt d }t	|gg}| t|ggks	J |jtdt|jtdggksJ tt	t
td ttd  ggt	dggks7J tddgddgg}d|   tdd	ksQJ d S )
Nr  r  rh   rf   )ratior  rg   ri   "   )r#   r   r   rO   rP   r(   r6   r?   r5   r   r@   tracer   )r  r  r  eqr   rs   rs   rt   test_simplifyN  sD    :&:&&"

$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)
rh   rf   rg   ri   rj   rk   r   r   r   r   rh   rf   rg   ri   rj   rk   r   r   r   r   )r   r  	transposer  rs   rs   rt   test_transposev  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   )r-   r   rs   rs   rs   rt   r     r   z!test_conj_dirac.<locals>.<lambda>rh   r   rX  r]  r   )r^   AttributeErrorr   r   r   r  rs   rs   rt   test_conj_dirac  s   

r  c                  C   s.   t g dg dg dg} |  dksJ d S )Nr   )r   rj   r   )r   r   r   r  r   r  r  rs   rs   rt   
test_trace  s
   r  c                  C   sH   t ddddg} | jdksJ t tddgdtdgg}|jdks"J d S )Nrh   rf   r   r  r   )r   ry  rO   rP   )r   r  rs   rs   rt   
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   rh   c                 S   s   | | d S r  rs   )rr   rs   rs   rt   r     r   z!test_col_row_op.<locals>.<lambda>rf   rg   c                 S   s   | t |  S r   )rP   )rL   r   rs   rs   rt   r     r   *   ry   r   )r   rO   rP   row_opcol_opr   r   )r  r1r  rs   rs   rt   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 )
Nrn   rm   rh   rg   r{   rH  ry   r  r  )r   row_multr  rs   rs   rt   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$J | d dks,J d S )Nrn   rm   r  rf   r   rj   ry   rk   r{   ri   r   rf   r   )r   row_addr  rs   rs   rt   test_row_add  s   r  c                  C   s   t D ]H} | d}|dddd  || g dg dg dgks#J | dd	 }d
|d< |dddd  | || g dg dg dgksJJ qd S )Nrg   rh   r   c                 S      | d|  S r  rs   r  urs   rs   rt   r     r   z!test_zip_row_op.<locals>.<lambda>r   r  r   rf   r   rz   c                 S   r  r  rs   r  rs   rs   rt   r     r   )rf   r   r   )ri   r   r   r   )mutable_classesr-   
zip_row_op)r#  r  rs   rs   rt   test_zip_row_op  s   


r  c                  C   sd   t g d} t g d}t g d}| dvsJ | dvsJ | dks$J | |ks*J | |ks0J d S )Nrn   )rf   rf   rg   rs   )rh   rh   r|  )r   rJ   rK   rs   rs   rt   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                   @   r  )ztest_issue_3981.<locals>.Index1c                 S   r  r  rs   r  rs   rs   rt   	__index__     z)test_issue_3981.<locals>.Index1.__index__Nrt  ru  rv  r  rs   rs   rs   rt   Index1  r  r  c                   @   r  )ztest_issue_3981.<locals>.Index2c                 S   r  r  rs   r  rs   rs   rt   r    r  z)test_issue_3981.<locals>.Index2.__index__Nr  rs   rs   rs   rt   Index2  r  r  rn   rg   rj   rf   rm   rk   rh   ri   r  r   r|  )r  r  index1index2r   rs   rs   rt   test_issue_3981  s$   r  c                  C   sZ   t g dg} | jdu sJ t dgdgdgg} | jdu sJ tdd} | jdu s+J d S )Nrn   Trh   rf   rg   Fri   )r   is_upperrH   r   rs   rs   rt   test_is_upper  s   
r  c                  C   sB   t g dg} | jdu sJ t dgdgdgg} | jdu sJ d S )Nrn   Frh   rf   rg   T)r   is_lowerr   rs   rs   rt   test_is_lower  s   r  c                  C   sT   t ddg d} |  sJ t ddgddgg} |  rJ t g } |  s(J d S )Nri   )r   rf   rh   rk   r   r   rh   rf   r   r   r   rg   r   r   r   r   rh   r   r   rS  r   rs   rs   rt   test_is_nilpotent  s   r  c                  C   s"  d\} }t | |}|d dt| | }||ksJ |j|j  kr(dks+J  J |j|j  kr8dks;J  J |j|j  krHdksKJ  J t dt ddksVJ tdtddksaJ t ddtdddgd ksqJ tddtdddgd ksJ |d |t | |ksJ d S )N)rg   rj   rj   rg   rf   r   rk   rh   )rH   fillr4   ro   rp   ry  r   )r  r   rJ   rK   rs   rs   rt   test_zeros_ones_fill'  s   

     
r  c                  C   sf   t d} | t ksJ t dd} | jdksJ | jdksJ t dd} | jdks*J | jdks1J d S )Nr   rf   )rH   r   ro   rp   r   rs   rs   rt   test_empty_zeros<  s   

r  c                  C   s  t td tt gttt ttt gg} | tt dt tgttttggks-J t tt td gttdt tt  tdt  ggttt tt tgtdtggks\J t ttd t dt tt  tt gdt t	tt	ttd ggtdt g dtdtdggksJ | 
tt tddtd  ttd  d gtd tt d td tt d ggksJ d S )Nrf   rh   r   r  rg   )r   rO   rP   r@   r(   r*   r+   r  r5   r  r0   r   r   rs   rs   rt   test_issue_3749G  s(   ,."$
 &r   c                  C   sD   t d} | dd dD ]}| j|dd d| jdd	ksJ qd S )
Nri   r   rh   )r[  r`  c                 S   s   | dkS r  rs   rr   rs   rs   rt   r   [  rj  z%test_inv_iszerofunc.<locals>.<lambda>)r  
iszerofuncrb  r  )r-   col_swapr   )r   r  rs   rs   rt   test_inv_iszerofuncW  s   

r  c                  C   s   t d\} }t| t| | t| g}t| |g}||}|||jks)J ||j|ks3J ||j|jks>J |jt|jd  | }|t	}|tddgd| d ggks_J d S )Nrho,phir   rh   rf   )
rC   r   r(   r@   r  r  r-   ry  r  rF   )rhophiXYr#  r  rs   rs   rt   test_jacobian_metrics_  s   

$r	  c                  C   s   t d\} }t| t| | t| | d g}t| |g}tt||  t| gt|| t| gd|  dgg}|||ksBJ d S )Nr  rf   r   )rC   r   r(   r@   r  )r  r  r  r  r#  rs   rs   rt   test_jacobian2l  s   "
r
  c                  C   s   t ttt t ttt t ttt t g} t tttg}tddD ]D}tddD ]<}| d |d d f }|d |d d f }||}|j|ksNJ |j|ksUJ t|D ]}|d d |f |ksgJ qYq,q%d S Nrh   rg   )	r   r+   rO   rP   rQ   r   r  ro   rp   )r  r  r   r   X_sliceY_slicer#  krs   rs   rt   test_issue_4564x  s   2
r  c                      s   t ttt t ttt t gttt t ttt t gg tt fdd  dd d f  t ttgttggtt fdd tt fdd d S )Nc                      s     ttttgS r   r  r   rO   rP   rQ   rs   r  rs   rt   r     r   z(test_nonvectorJacobian.<locals>.<lambda>r   c                      s
     S r   )r  rs   r  r  rs   rt   r     r   c                      s     tttgttggS r   r  rs   r  rs   rt   r         )r   r+   rO   rP   rQ   r^   r;  rs   rs   r  rt   test_nonvectorJacobian  s    r  c                  C   sP   t ddgddgg} |  }|jdksJ tdD ]}|| |d ks%J qd S Nrh   rg   rf   ri   )r   vecrp   r   )r   m_vecr   rs   rs   rt   test_vec  s   r  c                  C   s6  t ddgddgg} |  }|jdksJ tdD ]}|| |d ks%J q| jdd}|d dks4J t dttt  gtt td  dgg} | jdd}|d tt td  ks\J t dttt  gtt dgg} | jddd}|d tt ks}J ttdd	  ttd
d	  ttdd	  ttdd	  d S )Nrh   rf   rg   Fr  r   )r  check_symmetryc                   S      t ddgg S r  r   vechrs   rs   rs   rt   r     r  ztest_vech.<locals>.<lambda>c                   S      t ddgddgg S r  r  rs   rs   rs   rt   r     r  c                   S   r  r  r  rs   rs   rs   rt   r     r  c                   S   r  r  r  rs   rs   rs   rt   r     r  )	r   r  rp   r   rO   rP   r^   rW   rQ  )r   m_vechr   rs   rs   rt   	test_vech  s"   ( r  c                      sZ   t g dtg dksJ dddgg tt fdd t  ddtg dks+J d S )	Nrn   rh   rf   rg   c                      s   t  S r   )r)   rs   r   rs   rt   r     rj  ztest_diag.<locals>.<lambda>F)strict)r)   r   r^   rQ  rs   rs   r   rt   	test_diag  s    r!  c               
   C   s  t ddgddgg} t dtgtdgg}t dtdgtdtgtttgg}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 )	Nrh   rf   rg   T)try_block_diagrb  )r"  r  r  )r   rO   rP   rQ   r)   r   )rJ   rK   rL   r   rs   rs   rt   test_inv_block  s"    ((($
r#  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 )Nrg   r   rH   rs   rs   rs   rt   r     r   z$test_creation_args.<locals>.<lambda>c                   S   s   t ddddS Nrh   rf   rg   ri   r%  rs   rs   rs   rt   r     rK  rg   c                   S      t dS N      @r%  rs   rs   rs   rt   r     rj  c                   S   r'  r(  r-   rs   rs   rs   rt   r     rj  ri   c                   S   r'  r   r|  rs   rs   rs   rt   r     rj  c                   S   r$  r   r|  rs   rs   rs   rt   r     r   c                   S   s   t ddggS r   r|  rs   rs   rs   rt   r     rK  N)r^   rQ  r;  rH   r9  r   r-   r4   rs   rs   rs   rt   test_creation_args  s    r+  c                  C   sX  t ddg d} |  rJ |  sJ | jddsJ t ddg d} |  s*J tddd} |  s6J |  s<J t ddg d} | tdddksNJ t ddtdd} |  r]J |  scJ t d	} |  smJ t d
} |  swJ t dddtd dt  d ttd d ddtddg	} |  sJ | jddrJ |  jddsJ d S )Nrf   r   Fr   r  rh   rg   )	rh   r   r   r   rf   r   r   r   rg   ))rj   r   r  ry   )rj   r   r   )r   rk   r   r   )r   is_diagonalr   r)   rH   rO   rP   r,   r   rs   rs   rt   test_diagonal_symmetrical  s,   6r.  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 )Nrh   rf   rg   rA  rh   rA  r  rg   r   c                            S r   rW  rs   r   rs   rt   r   	  rj  z&test_diagonalization.<locals>.<lambda>r   )rh   r   r   rg   r^  )	rh   rf   r   r   rg   r   rf   r   rf   r]  r   )r   rh   r   r   Tc                      r   )NTr1  rs   r   rs   rt   r   /	  r   r   rh   r   r   c                      r0  r   r1  rs   r   rs   rt   r   7	  rj  )	rA  rh   rA  r  rg   r   rf   r   ri   c                      r0  r   r1  rs   r   rs   rt   r   ;	  rj  za b c d)r   r   rU  r   r^   rV   r)   rW  r-   r   as_numer_denomr-  rU   rC   )r"  r   r   rJ   rK   rL   rM   rs   r   rt   test_diagonalization  sl   r4  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   rh   Tr{   Fc                      r0  r   r1  rs   r   rs   rt   r   N	  rj  z"test_issue_15887.<locals>.<lambda>)r   rU  rW  r^   rU   rs   rs   r   rt   test_issue_15887D	  s   r5  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 )Nrg   rf   r/  c                      r0  r   )r  rs   r   rs   rt   r   T	  rj  z"test_jordan_form.<locals>.<lambda>)	r   r  rk   r   ir   rH  ir  )	r   r   r   r   rh   r   r   r   rh   rh   	r   rh   r   r   ri   r   r   rh   rf   )	rf   rh   r   r   rf   r   r   r   rf   )	rf   rk   rh   rh   r   rh   rf   r)  )	r   rh   r   r   r   r   r   r   r   )	ri   r   rf   rj   r@  rg   rk   ri   )	r   rh   r   r   r   r   r   r   rh   ri   )rk   rj   r   rA  rA  r   rg   rg   rf   rh   r   rA  r   rh   rj   rj   )rf   rh   r   r   r   rf   r   r   r   r   rf   rh   r   r   r   rf   )rk   rf   r)  rA  rf   r   rk   rf   r   r9  r)  r   r   rg   ri   )r   r   r   r   r   rf   rh   r   r   r   rf   r   r   r   r   rf   )rj   ri   rf   rh   r   rh   r   r   r   r   rg   r   rh   rh   r   rf   )rh   r   r   r   r   rf   r   r   r   r   ri   rh   r   r   r   ri   z1.0n   )	precisionz2.0z3.14159265358979323846264338327z4.0)
r   r^   rV   r  rW  rU  r
   r	  r  _prec)Jmustr"  r#  termrs   r   rt   test_jordan_formQ	  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)rf   ri   rh   r   )r   rf   r   rh   )r   r   rf   ri   )r   r   r   rf   rf   ri   rh   r   )r   r   r  r?   r   )r   pqJmust1Jmust2r"  r#  rs   rs   rt   #test_jordan_form_complex_issue_9274	  s(   





 rD  c                  C   s   t g dg dg dg dg} |  \}}|t g dg dg dg dgks*J |t g d	g dg dg dgks>J d S )
Nr  r   rW  rX  r   r]  r2  r  r^  )r   r  r!  rs   rs   rt   test_issue_10220	  s"   
rE  c               
   C   s   t g dg dg dg dg} |  \}}| t t t d ttd gdt ddt dgdtd d td  dtd d td  gg d	gksNJ |t t dddgdt ddgddtdgdddtggkslJ d S )
Nr_  )r   r   r   r   )r   r   r   r   )r   r   rf   rh   rf   r   r   rh   r   )r   r  r,   r   r!   )r   r"  r#  rs   rs   rt   test_jordan_form_issue_15858	  s&   .

rF  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_wrf   zZZ(K_i,K_w,UA)r,  rh   rg   r   rk   )
rC   r   r.  rO   r   r  r   genas_exprrF  )UAK_iK_wr   r.  r@  rs   rs   rt   test_Matrix_berkowitz_charpoly	  s&   *$
06
*rL  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lamdarh   rg   rf   r   )r#   r   r  _eval_matrix_exp_jblockr+   )r   r   rs   rs   rt   test_exp_jordan_block	  s   rO  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 )	Nrg   ri   r   r   r   rj   rh   r   )r   r+   r   r(   r@   )r   m_exprs   rs   rt   test_exp	  s   8  FrQ  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 )NrM  rh   ri   r   rf   rg   r   r   r   r  c                      r0  r   )r1   rs   r   rs   rt   r   
  rj  ztest_log.<locals>.<lambda>)r#   r   r  _eval_matrix_log_jblockr1   r^   rU   )r   rs   r   rt   test_log
  s(   *
rS  c                  C   sR   t d} tdd| t| d t| d  tjg}t|\}}}}|tjks'J d S )NrO   rg   rh   rf   )r#   r   r(   r@   r!   r   rT   rO   columnpivot_offset	pivot_valpivot_assumed_nonzero
simplifiedrs   rs   rt   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero1!
  s
   (
rZ  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 )NrO   rg   rh   rf   simpfunc)r#   r   r(   r@   rT   rZ   rT  rs   rs   rt   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero2.
  s   

r]  c                  C   s   t d} tdd| t| d t| d  |  t| d t| d  g}t|td\}}}}t|dks5J |d d dks?J |d d d|  ksKJ |d d dksUJ |d d dks_J d S )NrO   rg   rh   rf   r[  r   )r#   r   r(   r@   rT   rZ   lenrT  rs   rs   rt   +test_find_reasonable_pivot_naive_simplifies>
  s   

r_  c                      s  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t td	d  t td
d  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t tdd  t td d  t td!d  t td"d  t td#d  t td$d  t td%d  t td&d  t td'd  t td(d  t td)d  td* t t fd+d tg d,gtg d-g d.g d/g t t fd0d tg d-g d.g d/g t t fd1d d S )2Nc                   S   s   t ddgdggS r   r|  rs   rs   rs   rt   r   R
  r  ztest_errors.<locals>.<lambda>c                   S      t ddggd S )Nrh   rf   )g333333?rj   r|  rs   rs   rs   rt   r   S
  r  c                   S   r`  )Nrh   rf   )rh   g@r|  rs   rs   rs   rt   r   T
  r  c                   S   s   t ddddS )Nrg   ri   T)rL   r  )r7   rs   rs   rs   rt   r   U
  rK  c                   S   s   t ddgddS )Nrh   rf   ri   rk   )r   r  rs   rs   rs   rt   r   V
  r   c                   S   s(   t ddgddggddgt ddgS rv   )r   copyin_matrixrs   rs   rs   rt   r   X
     ( c                   S   s"   t ddgddggddgt S rv   )r   copyin_listr  rs   rs   rs   rt   r   Y
  s
    c                   S   s   t g dg dg S )Nrn   )rf   rg   r   r   r   rs   rs   rs   rt   r   [
  r  c                   S   s&   t ddddgt ddgddggS r&  )r   r   rs   rs   rs   rt   r   ]
     & c                   S   s"   t ddgt ddgddggS r&  )r   r   rs   rs   rs   rt   r   _
  s   " c                   S   "   t dgdt ddgddggS r&  )r   r   rs   rs   rs   rt   r   `
  
    c                   S   rf  r&  )r   r   rs   rs   rs   rt   r   b
  rg  c                   S      t ddg S r   r  rs   rs   rs   rt   r   d
  r   c                   S   s   t dgdS r  )r   r  rs   rs   rs   rt   r   e
  r   c                   S      t ddgddggddS Nrh   rf   rg   ri   rj   )r   minorrs   rs   rs   rt   r   f
      c                   S   ri  rj  )r   minor_submatrixrs   rs   rs   rt   r   g
  rl  c                   S      t g ddS Nrn   rh   r   crossrs   rs   rs   rt   r   h
  r  c                   S   rn  ro  r   dotrs   rs   rs   rt   r   i
  r  c                   S   s   t g dt ddgS )Nrn   rh   rf   rr  rs   rs   rs   rt   r   j
  r  c                   S   s   t ddgg S r   rr  rs   rs   rs   rt   r   k
  r  c                   S   s   t ddgdS )Nrh   rf   rJ   rr  rs   rs   rs   rt   r   l
  r  c                   S   s   t ddgg dS )Nrh   rf   rn   rr  rs   rs   rs   rt   r   m
  rv  c                   S   s   t g d S )Nrn   )r   r+   rs   rs   rs   rt   r   n
  r   c                   S   r  r&  )r   
normalizedrs   rs   rs   rt   r   o
  r  c                   S   s   t ddgjddS )Nrh   rf   znot a methodr  rd  rs   rs   rs   rt   r   p
  r   c                   S   rh  r   r   
inverse_GErs   rs   rs   rt   r   q
  r   c                   S      t ddgddgg S r   ru  rs   rs   rs   rt   r   r
  r  c                   S   rh  r   r   inverse_ADJrs   rs   rs   rt   r   s
  r   c                   S   rw  r   rx  rs   rs   rs   rt   r   t
  r  c                   S   rh  r   )r   
inverse_LUrs   rs   rs   rt   r   u
  r   c                   S   rh  r   r  rs   rs   rs   rt   r   v
  r   c                   S   rh  r   r   r5  rs   rs   rs   rt   r   w
  r   c                   S   s   t ddgddggjddS )Nrh   rf   rg   ri   zNot a real methodr  r{  rs   rs   rs   rt   r   y
  rl  c                   S   (   t g dg dg dg dgjddS )Nr   r   rL  r  zNot functionr  r{  rs   rs   rs   rt   r   {
  
    c                   S   r|  )Nr   r   rL  r  Fr}  r{  rs   rs   rs   rt   r   ~
  r~  c                   S   s*   t tddgddggtddgddggS r&  r/   r   rs   rs   rs   rt   r   
  s   * c                   S   s   t tddgddggg S r&  r  rs   rs   rs   rt   r   
  r  c                   S   s   t tdd dS )NrO   rf   rJ   )r/   r#   rs   rs   rs   rt   r   
  r  c                   S   rs  )Nrg   )rj   rf   r*  rs   rs   rs   rt   r   
  r   c                   S   rs  )Nrg   )rf   rj   r*  rs   rs   rs   rt   r   
  r   r  c                      r   )Nzmethod=LU_decomposition())r5  rs   r  rs   rt   r   
  r   )r   r   r   rn   rf   rg   ri   r   c                           dS )Ng@)r   rs   r  Vrs   rt   r   
  r   c                      r  )Ng)r   rs   r  rs   rt   r   
  r   )r^   rQ  r   rW   r;  rV   r   rs   rs   r  rt   test_errorsQ
  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   rh   rf   c                 S   r  r  rs   r   rs   rs   rt   r   
  r   ztest_len.<locals>.<lambda>c                 S   r  r  rs   r   rs   rs   rt   r   
  r   r   r   rk   )r^  r   rs   rs   rs   rt   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 t ddttg}|tt ddtd d tt gksJ d S )Nrh   ri   rf   r   rj   rg   )r   rO   rP   r0   )r   r   rs   rs   rt   test_integrate
  s   $FF.r  c                  C   s  t ddtftddfddtd d ff} t| tt| s J | tt dddddt ffks3J | tt d	ks>J t| tt dddddt ffksQJ t| tt d	ks\J |  }t|tt|slJ |ttdddddt ffksJ |ttd	ksJ t|ttdddddt ffksJ t|ttd	ksJ | jtd
dt| td
dksJ t| td
dt| td
dksJ d S )Nrh   ri   rf   r   rj   r   r   r   )r   r   r   Fr  )	r   rO   rP   r  r*   r  rx  r   r\   )r   A_immrs   rs   rt   	test_diff
  s   (&&&& $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 )Nrh   r   rf   )rf   rf   rh   r  rg   r   r  c                    s&   g | ]  fd dt ttfD qS )c                    s   g | ]
}  | qS rs   )r*   r  )fxyzr   rs   rt   r   
  rl  z2test_diff_by_matrix.<locals>.<listcomp>.<listcomp>)rO   rP   rQ   )r   r  )r   rt   r   
  re  z'test_diff_by_matrix.<locals>.<listcomp>)r   rO   rP   rQ   rN   r*   r   rx  rJ   r   rK   rH   ry  r   r@   r+   r(   r   r  )r   r  r   dBr  exprresrs   r  rt   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 )Nrh   ri   rf   r   rj   c                      s    j S r   )nonexistantattributers   r   rs   rt   r   
  s    ztest_getattr.<locals>.<lambda>r*   r   r   r   )r   rO   rP   r^   r  getattrrs   rs   r   rt   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 )
Nr   r   r   rh   )r   r   Fr  rj   rf   )r   r  r  r  rH   r   rs   rs   rt   test_hessenberg
  s   



r  c                  C   s&  t tdd  t tdd  t tdd  t tdd  t tdd  tdt dfd	fjd
dttdt dgddggksAJ td} | jd
d}|tddgddtd t ggks_J ||j | kshJ td} |  }||j | ksyJ |js~J |tg dg dg dgksJ tddt ddt  fdt ddt fddt  dt dff} |  	 tdtddfdt ddffksJ t tdd  t tdd  t tdd  t tdd  t tdd  t
dt dfd	fjd
dttdt dgddggksJ t
d} | jd
d}|tddgddtd t ggks'J ||j | ks1J t
d} |  }||j | ksCJ |jsIJ |tg dg dg dgks[J t
ddt ddt  fdt ddt fddt  dt dff} |  tdtddfdt ddffksJ d S )Nc                   S      t d S Nr  r   choleskyrs   rs   rs   rt   r     r   ztest_cholesky.<locals>.<lambda>c                   S   r  Nr  )rg   ri   r  rs   rs   rs   rt   r     r   c                   S      t dt dfdf S Nrj   r   rz   )r   r   r  rs   rs   rs   rt   r     r  c                   S   r  Nr  )rj   rh   r  rs   rs   rs   rt   r   	  r   c                   S      t djddS Nr  F	hermitianr  rs   rs   rs   rt   r   
  r   rj   r   rz   Fr  rh   r  rf   rk   ))r  r  r   )r  r  r   )r   r   r   r,  )rg   rg   r   )r   rh   rg   ri   r   r   r   r  rg   c                   S   r  r  r"   r  rs   rs   rs   rt   r     r   c                   S   r  r  r  rs   rs   rs   rt   r     r   c                   S   r  r  )r"   r   r  rs   rs   rs   rt   r     r  c                   S   r  r  r  rs   rs   rs   rt   r     r   c                   S   r  r  r  rs   rs   rs   rt   r     r   )r^   rV   rQ  r   r   r  rA   r  r  r,   r"   ra  rs   rs   rt   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 )NrO   Tr  rf   rh   r   rj   rg   r  r   ri   r   r   	frobeniusfro%   )rh   rf   rA  r  i  r   iI3 r   alpha)r  rf   r   rA  )r   r   r   g      Y@r   )	rh   rg   r   r   r   r   rg   r   rk   )r#   r   r(   r@   rF   normr   r   r!   r   r5   r  r  r-   rP   r6   rA   r  r   r   rH   r?   r   InfinityNegativeInfinitytrue)rO   r  r   r   r   r   rb  r  orderr  r  difr  rJ   rK   rL   rM   r   rs   rs   rt   test_matrix_norm-  s   2"0,(

r  c                     s   t dddtd} d| d< tdd| d< |  d	ksJ | d
< |  tdtttddt ks8J ttt	gt	 tgg}|  t
 fddtddtjtddtd tttdd fD sqJ tg  dks{J d S )NrO   Tr  rg   r   ry   rh   rf   rf   r  rl   c                 3   s*    | ]}t d  | V  qdS )r  N)r
   
epsilon_eqrF  r  )r   valMcrO   rs   rt   r    s   ( z(test_condition_number.<locals>.<genexpr>rj   rf   r   ri   r   )r#   r-   r   condition_numberr   r   r   r   r(   r@   r  r!   r   r6   )r   r  rs   r  rt   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$J | |kr*J | |ks0J | dks6J | dkr<J td}t d}||ksJJ ||krPJ d S )N)rn   rm   r   ))r   r   r   )rk   rj   ri   )rg   rf   rh   r   )r   r   r   )r   r"   )r   r   r   r   rs   rs   rt   test_equality  s   r  c                  C   s|   t ddg t tddtddgksJ t g d t g dks&J t g d} | jdd dt g dks<J d S )	Nrg   ri   rj   r   )r   r   g0.++c                 S   s   | j dddjS )Nr   T)r  chop)r  is_zerorr   rs   rs   rt   r     r   z!test_normalized.<locals>.<lambda>r}  )r   rt  r   r   rs   rs   rt   test_normalized  s    
r  c                   C   s,   t dd dks
J t dd dksJ d S )Nc                   S   r  r   r-   print_nonzerors   rs   rs   rt   r     r   z$test_print_nonzero.<locals>.<lambda>z[X  ]
[ X ]
[  X]
c                   S   s   t ddS )Nrg   r6  r  rs   rs   rs   rt   r     rK  z[.  ]
[ . ]
[  .]
)rc   rs   rs   rs   rt   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 )Nrg   ri   rh   rH  r   rf   r"  )r   r-   rH   r4   r  r  )r   rQ   r#  r   rs   rs   rt   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   rg   ri   rh   FrJ   T)nonzero)	r   is_zero_matrixrH   r-   rO   r"   r   r   r#   r   rs   rs   rt   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 )Nrg   rh   rf   r   r   r   r   )r6   r:   r9   r8   r-   r  r(   r   from_axis_angleto_rotation_matrixr;   r<   r=   )
thetar3_plusr3_minusr2_plusr2_minusr1_plusr1_minusq1q2q3rs   rs   rt   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vectorri   z	vector[4]rM   c                   S   rs  )NrM   r   )r   rs   rs   rs   rt   r     r   z%test_DeferredVector.<locals>.<lambda>testzDeferredVector('test'))strr   rD   r^   r   reprrs   rs   rs   rt   test_DeferredVector  s
   r  c                   C   s   t tdrJ d S )Nr  )rd   r   rs   rs   rs   rt    test_DeferredVector_not_iterable  s   r  c                   C      t tdd  d S )Nc                   S   s   t tdS )Nr  )r   r   rs   rs   rs   rt   r     r   z,test_DeferredVector_Matrix.<locals>.<lambda>r^   r;  rs   rs   rs   rt   test_DeferredVector_Matrix     r  c                  C   s8  t } tddddg}tddddg}t||gtddddgtdd| dd | dd ggks2J t|j|jgtddddgtdd| dd | dd ggksTJ ttddgtddggdtdtd d tdd gttd d dtd d ggksJ ttdg}t|tdgggksJ d S )Nrh   rf   rg   rj   r   Tr   )r   r   r   r  rA   r	   )r[  r}   r~   rb  rs   rs   rt   test_GramSchmidt  s   
.. 
r  c                   C   s4   t g dddksJ t g dddddksJ d S )Nr   rh   r   F)zero)r'   rs   rs   rs   rt   test_casoratian)  s   r  c                   C   s^   t  tdd jdksJ tddtdd tddksJ tddtdd t  ks-J d S )Nr   rg   )r   rg   )r   rH   ry  rs   rs   rs   rt   test_zero_dimension_multiply.  s   ""r  c                      s   t ddtd  dd d f t ddggksJ  dd d f t ddggks*J  d d df t ddggjks<J  d d df t ddggjksNJ tt fdd tt fdd d S )	Nrf   ri   rh   rg   r   c                      s    dd d f S r  rs   rs   r   rs   rt   r   :  r   z'test_slice_issue_2884.<locals>.<lambda>c                      s    d S )Nr  rs   rs   r   rs   rt   r   ;  rj  )r   r   r  r^   r   rs   rs   r   rt   test_slice_issue_28844  s   ""$$r  c                   C   sJ   t ddd d df jdksJ t dddd d f tddg ks#J d S )Nr   rg   r   rz   rh   )rH   ry  r   rs   rs   rs   rt   test_slice_issue_3401>  s    *r  c                  C   s  t dd} d| d< | d d df tg dksJ | d dks!J | dd dgks,J d| d< | d dks8J | ddd f tddggksIJ tdd	gg| ddd f< | dd d f tg d
gksgJ ddgg| ddd f< | dd d f tg dgksJ d| d< | d d d df tg dksJ g d| d< | d d df tg dksJ tg d| d< | d d df tg dksJ tg d| d< | d d df tg dksJ d S )Nrg   rh   r   r   ri   r  rl   rj   rk   )rh   rj   rk   +   )rh   r  r     ry   )r  rh   r   r  )rH   r   r"   )r  rs   rs   rt   test_copyinC  s(   
 """$  $r  c                      s   t ddgddgg t ddgddggdfksJ ttdd  t g dtddgdtdgg t  d  jks=J   d td	ksIJ  jtd
d td	ksWJ tt fdd tt fdd tt fdd d S )Nrh   rf   r   )r   c                   S   rw  r   rd  rs   rs   rs   rt   r   ^  r  z'test_invertible_check.<locals>.<lambda>)r   r   r   r   rg   r   c                          j ddS )Nrb  r  r   rs   r   rs   rt   r   i  r   c                      r  )Nr[  r  r  rs   r   rs   rt   r   j  r   c                      r  )Nr`  r  r  rs   r   rs   rt   r   k  r   )	r   r>  r^   rQ  rO   r^  ro   r-   r>   rs   rs   r   rt   test_invertible_checkZ  s   4r  c                  C   s@   t d\} }| | }|| tg dtg d| ksJ d S )Nzx, y)rg   rj   rg   )rC   rF  r   )rO   rP   r   rs   rs   rt   test_issue_3959n  s   ,r  c                   C   s$   t tddgddggdksJ d S )Nrh   rf   rg   ri   zMatrix([[1, 2], [3, 4]]))r  r   rs   rs   rs   rt   test_issue_5964t  s   $r  c                  C   s<   t d\} }tt| d| g|d | d ggdksJ d S )Nr  rf   rg   z'Matrix([
[   x,   2*y],
[y**2, x + 3]]))rC   rB   r   r  rs   rs   rt   test_issue_7604x  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 )	Nrg   r   rh   )ry   rl   r  rf   rk   )ry   rl   )ry   rl   r  rz   r  )r-   is_Identityrx  rH   r4   r   r"   r   rs   rs   rs   rt   test_is_Identity~  s   "r  c                   C   s  t ddt dddksJ t ddg ddksJ tg dtg ddks.J tdddt gttddt gdt ksGJ tdddt gjttddt gdd	dt ksbJ tdddt gjttddt gd
d	dt ks}J tdddt gjttddt gd
dddt ksJ tdddt gjtddt dgd
ddddt  ksJ tdddt gjtddt dgd
ddddt  ksJ ttdt gjttdt gddddksJ ttdt gjttdt gdddksJ ttdd  d S )Nrh   rg   r  rn   r  rf   r   Fr  Tr  physicsr  conjugate_conventionri   rj   rk   rightr   left)r  c                   S   s    t ddgjt ddgdddS )Nrh   rf   rg   ri   Tr  r  rr  rs   rs   rs   rt   r     s     ztest_dot.<locals>.<lambda>)r4   rs  r   r   r^   rQ  rs   rs   rs   rt   test_dot  s   "2668<<00r  c                  C   s   t ddd\} }}}}}td|||f| d|| f| | d| f| ||  dff}td|  | | f| d|| f|| d|f||| dff}| |sQJ td tds^J |  | sjJ d S )NzB_x B_y B_z E_x E_y E_zTr  r   rg   )rC   r   dualequalsr-   rH   )B_xB_yB_zE_xE_yE_zr(  Fdrs   rs   rt   	test_dual  s$   
r  c                  C   s   t ddg du sJ t dddtd dt  d ttd d  dtt t t t dg	} |  du s6J | jddd u s@J | jdd	 dd u sLJ | d
  | d
< |  d u s[J | d
  | d
< |  } | jdddu spJ d| d< |  du s|J d S )Nrh   rf   Frg   r   Tr   c                 S   r   r   rs   rr   rs   rs   rt   r     r   z%test_anti_symmetric.<locals>.<lambda>r>  ry   )r   r   rO   rP   r,   r   rs   rs   rt   test_anti_symmetric  s   Dr  c                  C   s   t d} | jdd\}}||j |j|   kr t|jks#J  J | jddd\}}||j |j|   kr@t|jksCJ  J || |  | ksOJ d S )N)r  r>  Tr  )r  sort)r   rW  r  r-   rp   r   )r   r"  r   rs   rs   rt   #test_normalize_sort_diogonalization  s   ..r  c                   C   r  )Nc                   S   s   t g dt ddg gS )Nrn   r   rh   r|  rs   rs   rs   rt   r     r  z!test_issue_5321.<locals>.<lambda>)r^   rQ  rs   rs   rs   rt   test_issue_5321  r  r  c                  C   s   t tddtd t g dg dgksJ t tddtd t ddgddgddgddggks6J t} | | td| dtd t g dg dgksTJ d S )Nrf   )rh   r   rf   r   )r   rh   r   rf   rh   r   )r   r   r-   r   r"   r"  rs   rs   rt   test_issue_5320  s    r  c                  C   sV   t dgg} t| }t || t ddggksJ t || t dgdggks)J d S r  )r   rD   r   r   )r   AImrs   rs   rt   test_issue_11944  s   $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 )Nrn   r   )r   ri   r   c                    s    || ksJ t |  ksJ d S r   )r  )r  r  r"  rs   rt   r    s   ztest_cross.<locals>.testc                   S   s"   t ddddgt ddddgS r   rp  rs   rs   rs   rt   r     s   "ztest_cross.<locals>.<lambda>)r   r  r  rq  r^   rW   )rJ   rK   r   r   r  r   r   rs   r"  rt   
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 r   )r   rO   rP   rQ   rJ   rK   rL   hatrq  r   vee)v1v2rs   rs   rt   test_hat_vee  s
   r  c                  C   sb   t D ]} | d| dh}t|dkr| | dksJ qtD ]} t| dtr.J q"d S r  )immutable_classesr-   r^  popr  r  r   )r#  r  rs   rs   rt   	test_hash  s   $r  c                  C   sH   dt gddgg} tddgt  dgg}tD ]}|||  ks!J qd S Nr   rh   )r   r   r  adjoint)r|  r  r#  rs   rs   rt   test_adjoint  s
   r
  c                  C   sT   t ddgtddt  gg} |  tjtdtjthksJ | tthks(J d S r   )r   rO   r  r!   r   NegativeOner#   r   rs   rs   rt   
test_atoms  s    r  c            	         s  t ttgttgg} t| jddt|  ksJ t ddgddgddggt g d	g d
gt ttgg}|D ]2}|jdd}|| }|| }t|| |ksRJ t|| |ks\J |j|kscJ |j|ksjJ q8|D ]4}t|jdd}|| }|| }t|| |ksJ t|| |ksJ |j|ksJ |j|ksJ qmddl	m
  | jdd}|  }tdtdtdtdi}t fddt||||D sJ d S )NRDr  r  h   i  rg   rA  rj   )rh   r   r   )r   r     EDr   compi_ib,  i  ij  c                 3   s&    | ]\}} |  |  V  qd S r   r  )r   r   r   r  rs   rt   r  A  s
    
ztest_pinv.<locals>.<genexpr>)r   rJ   rK   rL   rM   r?   pinvr   r  sympy.core.numbersr  r  r  rF  )	A1Asr   A_pinvAApApArA  wrepsrs   r  rt   	test_pinv  s:    
r  c                  C   s~   t g dg dg dg dg dg dgg} | D ]#}|jdd}|| }|| }|j|ks0J d	d
 }||j|s<J qd S )N)=   r  7   r  r  r   )>   `   U   r!  r  r   )E   8   r  ri   6   r   )r   r$  [   )   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 rs   r  )r   r  rs   rs   rt   r  f  rv  zYtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose.<locals>.<dictcomp>c                 s   s    | ]	}t |d k V  qdS )g|=Nr  )r   r   rs   rs   rt   r  h  r  zXtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose.<locals>.<genexpr>)r  r    r  r  r  )r   r   rootofsrootofs_approxdiff_approxrs   rs   rt   allclosed  s   
zEtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose)r   r  r  )r  r   r  r  r  r+  rs   rs   rt   3test_pinv_rank_deficient_when_diagonalization_failsG  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$J d S r  )r4   r   rs   rs   rs   rt   test_issue_7201m  s   $(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  )r   r   r   r"   rO   free_symbolsr  rs   rs   rt   test_free_symbolsr  s   r/  c                      sv  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g ksJ  J dS )zSee issue 7465.r   r0  r2  rn   rm   c                      s(   t  ddgddggddgddgggS )	Nrh   rf   rg   ri   rj   rk   r   r   r|  rs   r0  rs   rt   r     rb  z#test_from_ndarray.<locals>.<lambda>rh   rf   rg   ri   N)
r5  r0  r8  r_   r   rO   rP   rQ   r^   NotImplementedErrorrs   rs   r0  rt   test_from_ndarrayw  s"    $$
40<r2  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)r0  matrixzPNumPy must be available to test indexing matrixified NumPy ndarrays and matricesrh   rf   rg   ri   r   )
sympy.matrices.commonr4  r5  r0  r5  r8  r_   rq   r]   PendingDeprecationWarning)r4  r0  r5  r   rs   rs   rt   test_17522_numpy  s   
r8  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   r3  )r5  zEmpmath must be available to test indexing matrixified mpmath matricesrh   rf   rg   ri         @)r  r  r)  r9  )r6  r4  mpmathr5  r8  r_   rq   )r4  r5  r   rs   rs   rt   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   r3  )
csr_matrixzJSciPy must be available to test indexing matrixified SciPy sparse matricesrh   rf   rg   ri   r   )r6  r4  scipy.sparser=  r8  r_   rq   )r4  r=  r   rs   rs   rt   test_17522_scipy  r<  r?  c                  C   sr   t dtgt dgg} | jsJ dt | d< | jdu sJ t| d< | jd u s(J | d t | d< | jdu s7J d S )Nrh   rf   ry   Fr{   rz   r   r   rs   rs   rt   test_hermitian  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 )Nrn   r  r   rh   r   )rj   rk   r   r   r   c                      r   r  r   rs   r"  rs   rt   r     r   z+test_issue_9457_9467_9876.<locals>.<lambda>c                      r   Nr  r   rs   r   rs   rt   r     r   rg   rf   ri   rj   c                      r   r  r   rs   rA  rs   rt   r     r   c                      r   rB  r   rs   rC  rs   rt   r     r   )r   r   r^   r   r   )r  r,  Ors   )r"  r   rt   test_issue_9457_9467_9876  s.   



"
"rE  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 brf   r   )rC   r-   r   rQ   )rO   rP   rJ   rK   r  r   rs   rs   rt   test_issue_9422  s   0rG  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   rk   rg   r   r   rh   rf   rg   ri   joinr  )r   r  r  id)	r  rJ   rK   rL   opsr   opr  newrs   rs   rt   test_issue_10770  s   
rM  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 )Nrn   rm   r   r   )TTFrh   rf   ri   rj   r   r   )TFF)TFT)FFFrg   r   )FTF)r   r   r   rs   rs   rt   test_issue_10658  s   ,&$$rN  c                  C   s~  t ddtd  dgdtd d d dtd d gg} |  dks&J t ddtd t  dgdddtd t  gg} t|  d	 t ddddtd t   gd	d	gg tddkscJ td
\}}}}}}}}}	}
}}t |||| || d	g|||| || d	g|||| || dg|||| || dg|	|
d|	 | |	|  d|
 | |
|  d	gg} |  dksJ d S )Nr   rj   rf   rh   rg   r8  ri   rA  r   z/a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1)r   rA   rl  r   r?   r>  rH   rC   )r   axaybxbycxcydxdyexeyt0t1rs   rs   rt   !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  ri   )r  r   r   r   )r]  r  r9  )r                 @)r^  r^  r  )r   r  r_  )r  r]  g      )r   r>  r  r   )mmm_mixedm_floatm_invrs   rs   rt   test_partial_pivoting  s(   rd  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re  gٿr   )rf  rg  g333333?r   c                 S   s   t | dk S )Ng [n<r  rr   rs   rs   rt   r   2  r   z*test_iszero_substitution.<locals>.<lambda>r}  r   )r  r   g4iҤIӿr   )r   r  glٲer   rY  r\  r  N)r   r>  r  )r   m_rref	m_correctm_diffrs   rs   rt   test_iszero_substitution+  s   rk  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  -   rg   r9  rf   r   rA  rh   c                 S   s   t |  dk S )Ng#B;)r  r  rr   rs   rs   rt   r   H  r   z"test_issue_11238.<locals>.<lambda>T)r?   r  )	sympy.geometry.pointrl  rE   r6   r   rA   r   r?   rl  )
rl  xxyyp1p2p0r}   r~   r   Zrs   rs   rt   test_issue_11238:  s   0R

ru  c                  C   sh   t ddg d} | tj }| | }tD ]}|| \}}t|t| ks'J t|t| ks1J qd S )Nrf   r   )r   r!   ImaginaryUnitr  as_real_imagrq   )r}   r~   r   klsrJ   rK   rs   rs   rt   test_as_real_imagN  s   
ry  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 )Nrg   r6  rh   rf   r   )rf   rh   r   rf   )r   jordan_cells)r   r"  Jcellsrs   rs   rt   test_deprecatedY  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   rh   rf   )r   r  r7  rg   )rf   rh   rf   ri   )rf   r   rh   )sympy.core.modr}  r   )r}  r   r   rs   rs   rt   test_issue_14489d  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   r0  r2  rh   rf   rg   ri   )dtypefloat64)r5  r0  r8  r_   r   floatr  name)r0  r  rs   rs   rt   test_issue_14943m  s   r  c                  C   s4   t ddd} td}| d dk}t|dksJ d S )Nr   rh   rJ   ry   r   zm[0, 0] > 0)r   r#   r  )r   rJ   rs   rs   rt   test_case_6913x  s   r  c                  C   s.   t ddd} td}| ||| iksJ d S )Nr   rg   rJ   )r   r%   match)r   rJ   rs   rs   rt   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 )Nrh   r   rf   )r   r   r  r!   QRdecompositionr  r-   )r  r  r   r[  rs   rs   rt   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 )NrJ   rg   rh   rK   ry   r   )r   r   rs  r*   )rJ   rK   rL   rM   r   rs   rs   rt   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   nthrootrh   rf   rg   rk   ri   c                   S   s   t dtttS r   )rH   analytic_funcr1   rO   rs   rs   rs   rt   r     r   ztest_func.<locals>.<lambda>c                      s    t  tt t S r   )rO   r  r1   rs   r   rs   rt   r     r   )r   r   r   rg   )r   rh   r   r   )r   r   r   rh   c                      s     tttS r   )r  rA   rO   rs   r   rs   rt   r     r   r&  rH  r  )rg   r  ri   )r   r   r   )r   rj   r   r  )rh   rf   r   r   )r   rh   rg   r   )r   r   rh   rg   )r   rf   rh   rk   )r   r   rh   rf   )r   r   r   rg   rY  )sympy.simplify.simplifyr  r   r  r@   rO   rN   r6   r(   rA   r^   rQ  r+   r?   r,   r  rs   r   rt   	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$w   Y  W d    d S W d    d S 1 s<w   Y  d S )Nc                  S   s&   t jd ksJ tdgg} | |  } dS r  )rY   stater   r   rs   rs   rt   r    s   ztest_issue_19809.<locals>.fT)r[   
concurrentfuturesThreadPoolExecutorsubmitresult)r  executorfuturers   rs   rt   test_issue_19809  s   

"r  c                  C   s@   t ttg} t| tddftddft tjgtjggksJ d S r  )r   rO   rP   r0   r!   r   r  rs   rs   rt   test_issue_23276  s
   r  c                   C   r  )Nc                   S   s   t tg dS )Nr  )r.   r   rs   rs   rs   rt   r     r   z"test_issue_27225.<locals>.<lambda>r  rs   rs   rs   rt   test_issue_27225  s   r  (T  concurrent.futuresr  r  collections.abcr   sympyr   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   r  rJ   rK   rL   rM   rN   rO   rP   rQ   sympy.core.kindrR   rS   sympy.matrices.determinantrT   sympy.matrices.exceptionsrU   rV   rW   sympy.matrices.kindrX   sympy.matrices.utilitiesrY   rZ   r[   $sympy.tensor.array.array_derivativesr\   sympy.testing.pytestr]   r^   r_   r`   ra   rb   sympy.utilities.iterablesrc   rd   importlib.metadatare   r  r  r  ru   rx   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r
  r  r  r   r.  r/  r=  rD  rG  rU  r\  rc  rl  rs  r{  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r$  r%  r&  r/  r6  r9  r;  r?  rA  rC  rE  rJ  rL  rN  rP  rR  rT  rV  rX  r^  ra  rc  rg  ri  rm  rn  rp  rq  rr  r}  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r	  r
  r  r  r  r  r!  r#  r+  r.  r4  r5  r?  rD  rE  rF  rL  rO  rQ  rS  rZ  r]  r_  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
  r  r  r,  r-  r/  r2  r8  r;  r?  r@  rE  rG  rM  rN  r[  rd  rk  ru  ry  r|  r  r  r  r  r  r  r  r  r  r  rs   rs   rs   rt   <module>   s   & ( 

		
$" O!,Jb-
R		:
	(	
		
 HK>
7(]%
		-%	
