
    sgr                       d dl Z d dlZd dlmZ d dlmZ d dlmZm	Z	m
Z
 d dlmZmZmZmZmZmZmZmZ d dlmZ d dlmZ d dlmZmZ d d	lmZ d d
lmZ d dlm Z m!Z! d dl"m#Z#m$Z$m%Z% d dl&m'Z'm(Z(m)Z) d dl*m+Z+ d dl,m-Z-m.Z. d dl/m0Z0 d dl1m2Z2 d dl3m4Z4 d dl5m6Z6m7Z7 d dl8m9Z9 d dl:m;Z;m<Z<m=Z= d dl>m?Z? d dl@mAZA d dlBmCZC d dlDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\ d dlBm]Z] d dl^m_Z_m`Z` d dlambZb d dlcmdZdmeZemfZf d dlgmhZh d dlimjZjmkZkmlZlmmZmmnZnmoZo d d lpmqZq d d!lrmsZs d d"ltmuZu d d#lvmwZw d d$lxmyZy d d%lzm{Z{m|Z|m}Z}m~Z~mZmZmZmZ eHeIeFeGfZd d&lmZmZ d d'lmZmZ  eo       5   G d( d)eee      Zddd        eo       5   G d* d+eee      Zddd       d, Zd- Zd. Zd/ Zd0 Zd1 Zd2 Zd3 Zd4 Zd5 Zd6 Zd7 Zd8 Zd9 Zd: Zd; Zd< Zd= Zd> Zd? Zd@ ZdA ZdB ZdC ZdD ZdE ZdF ZdG ZdH ZdI ZdJ ZdK ZdL ZdM ZdN ZdO ZdP ZdQ ZdR ZdS ZdT ZdU ZdV ZdW ZdX ZdY ZdZ Zd[ Zd\ Zd] Zd^ Zd_ Zd` Zda Zdb Zdc Zdd Zde Zdf Zdg Zdh Zdi Zdj Zdk Zdl Zdm Zdn Zdo Zdp Zdq Zdr Zds Zdt Zdu Zdv Zdw Zdx Zdy Zdz Zd{ Zd| Zd} Zd~ Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Z d Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Z ekd        Z!d Z"dÄ Z#dĄ Z$dń Z%dƄ Z&eldǄ        Z'dȄ Z(dɄ Z)dʄ Z*d˄ Z+d̄ Z,d̈́ Z-d΄ Z.dτ Z/dЄ Z0dф Z1d҄ Z2dӄ Z3dԄ Z4dՄ Z5dք Z6dׄ Z7d؄ Z8dل Z9dڄ Z:dۄ Z;d܄ Z<d݄ Z=dބ Z>d߄ Z?d Z@ end      d        ZAd ZBd ZCd ZDd ZEd ZFd ZGd ZHd ZId ZJd ZKd ZLd ZMd ZNd ZOd ZPy# 1 sw Y   xY w# 1 sw Y   xY w)    N)Hashable)Add)Functiondiffexpand)EFloatIIntegerRationalnanoopi)Pow)S)Symbolsymbols)sympify)Abs)explog)MaxMinsqrt)cossintan)	integrate)PolyPurePoly)RootOf)sstr)	FiniteSet)signsimpsimplify)trigsimp)
ShapeErrorMatrixErrorNonSquareMatrixErrorDeferredVector)_find_reasonable_pivot_naive)	_simplify)GramSchmidtImmutableMatrixImmutableSparseMatrixMatrixSparseMatrix
casoratiandiageyehessianmatrix_multiply_elementwiseones
randMatrix	rot_axis1	rot_axis2	rot_axis3	wronskianzerosMutableDenseMatrixImmutableDenseMatrixMatrixSymboldotprodsimprot_ccw_axis1rot_ccw_axis2rot_ccw_axis3)_dotprodsimp_state)TupleWild)KroneckerDelta)flattencaptureiterable)ignore_warnings)raisesXFAILslowskipskip_under_pyodidewarns_deprecated_sympyQ)Array)ArrayDerivative)MatPow)
Quaternion)abcdxyzt)_MinimalMatrix_CastableMatrix)MatrixSubspacesMatrixReductionsc                       e Zd Zy)SubspaceOnlyMatrixN__name__
__module____qualname__     U/var/www/html/venv/lib/python3.12/site-packages/sympy/matrices/tests/test_matrices.pyrg   rg   C       rm   rg   c                       e Zd Zy)ReductionsOnlyMatrixNrh   rl   rm   rn   rq   rq   H   ro   rm   rq   c                     t        | | d       S )Nc                     t        | |k(        S N)intijs     rn   <lambda>z eye_Reductions.<locals>.<lambda>M   s    3qAv; rm   rq   ns    rn   eye_Reductionsr}   L   s    1&>??rm   c                     t        | | d       S )Nc                      yNr   rl   rv   s     rn   ry   z"zeros_Reductions.<locals>.<lambda>Q       rm   rz   r{   s    rn   zeros_Reductionsr   P   s    1n55rm   c                     t        t              D ]  \  } }|j                  dd      }|j                  dk(  rt	        d |j                  D              sJ |j
                  dk(  rt        |j
                        t        u sJ |j                  dk(  rt        |j                        t        u sJ | dz  s-t        |j                               t        t        t        fv rJ t        |j                               t        u rJ  y )N      )r   r   c              3   >   K   | ]  }t        |      t        u   y wrt   )typeru   ).0rw   s     rn   	<genexpr>ztest_args.<locals>.<genexpr>X   s     (IAaC(Is   )	enumerateclassesr>   shapeallrowsr   ru   colsflatlisttuplerG   todokdict)r|   clsms      rn   	test_argsr   T   s    G$ 	+3IIaOww& S(I(I%IIIvv{tAFF|s222vv{tAFF|s2221u>dE5%9999	?d***	+rm   c                     t         t        fD ]H  } | j                  dd      }t               5  |j                  }d d d        |j                         k(  rHJ  t        t        fD ]H  } | j                  dd      }t               5  |j                  }d d d        |j                         k(  rHJ  y # 1 sw Y   xxY w# 1 sw Y   -xY wNr   r   )
r1   r/   r>   rS   _matr   r2   r0   _smatr   )r   r   matsmats       rn   test_deprecated_mat_smatr   a   s    & IIaO#% 	&&C	affh	
 22 !IIaO#% 	77D	qwwy   	!	 	
	 	s   B0B<0B9	<C	c                      t        ddt        t        g      } | t        z  t        ddt        t        z  t        t        z  g      k(  sJ y N   r   )r1   r^   r_   r`   )vs    rn   test_divisionr   n   s;    q!aVAQ3&A!QqSz****rm   c            	      F    t        g dt        t        t        gdt        z  dt        t        z  gg         z   t        g ddt        z  dt        z  dt        z  gdt        z  ddt        z  t        z  gg      k(  sJ t        ddddg      t	        t
         fd       y )	Nr   r   r   r   i)r         r   ir   c                       z   S rt   rl   r   r|   s   rn   ry   ztest_sum.<locals>.<lambda>w   s    q1u rm   )r1   r^   r_   r`   rN   r'   r   s   @@rn   test_sumr   s   s    	Aq!9qsC1o67Aq5FI!QqS!A#1dAaCE8JKLLLLq!aVA
:}%rm   c                      t        dddt        g      } t        dddt        t              g      }t        |       |k(  sJ y )Nr   r   r   )r1   r^   r   absr   s     rn   test_absr   y   s:    q!b!WAq!aQ[!Aq6Q;;rm   c                      t        d      } t        d      }| |z    | j                  |      cxk(  rt        ddgddgg      k(  sJ  J y )N)r   r   r   r   r   )r   r   r   r   r   r   )r1   addrZ   r[   s     rn   test_additionr   ~   s]      	A
 	  	A
 q5EAEE!H8AA'7 888888rm   c            
         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(  sJ |ddgdf   |ddgdgf   k(  sJ |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(  sJ |d   dk(  sJ |ddd d f   t        g dg dg      k(  sJ |d d ddf   t        ddgdd	gd
dgg      k(  sJ |d d ddf   |ddgdf   k(  sJ |dd d df   |dddgf   k(  sJ  | 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(  rJ  t        j                  d      }d|d<   d|d<   d	|d<    |j                  ddgdg      t        dgdgg      k(  sJ  |j                  ddgg d      t        g dg dg      k(  sJ  |j                  g dg d      t        g dg dg dg dg      k(  sJ y )Nr   	   r   r   r      )r   r      r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   )r   r      )r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   r   )r   r   r   r   r   r   r   r   )r   r   r   r   )r   r   r   r   )r1   r2   ranger>   extract)MrZ   s     rn   test_fancy_index_matrixr      s!   l# aE!HAadG||Aw&Ay1111Aw&++++!Q|vy)&<====!Q|q!Q!~---QF|q!q!f~---QF|v1v1v1v&>????w!||1ayFIy#9::::AaCyFQFQFQF#;<<<<1ayAq!faiL(((CaCyAa!QiL(((aE!H!#$0 )  	  K F, %  	 +4 	1AAdGAdGAdG199aVaS!VCC-	 &
 
 
 
 199aVY'63 ,    199\<0F	< 5   rm   c                     t        d      t        d      z  } | d   dk(  sJ | d   dk(  sJ | d   dk(  sJ | d	   dk(  sJ | d
   dk(  sJ | d   dk(  sJ 	 t        d       | d   dk(  sJ | d   dk(  sJ | d   dk(  sJ | d	   dk(  sJ | d
   dk(  sJ | d   dk(  sJ t        |       }| j                  |       k(  sJ |d   dk(  sJ |d   dk(  sJ |d   dk(  sJ |d	   dk(  sJ |d
   dk(  sJ |d   dk(  sJ t        t        fd       t        d      z  } t        | t               sJ | d   t        k(  sJ | d   dt        z  k(  sJ | d   dt        z  k(  sJ | d	   dk(  sJ t        z  }| |k(  sJ dz  } t        | t               sJ | d   dk(  sJ | d   dk(  sJ | d   dk(  sJ | d	   dk(  sJ 	 t        d       t        | t               sJ | d   dk(  sJ | d   dk(  sJ | d   dk(  sJ | d	   dk(  sJ t        t        dgdt        gg      }|dz  |k(  sJ t        t        t        gddgg      }|dz  t        t        t        gt        t        gg      k(  sJ y # t        $ r Y w xY w# t        $ r Y w xY w)N)r   r   r   r   r   r   r   r   r   r   r   r   r   r   r      r   r   r   z	c = a @ br   c                      t               S rt   )r7   r   s   rn   ry   z%test_multiplication.<locals>.<lambda>   s    :1a@ rm   r^   r   r   
      z	c = 5 @ b)r1   evalSyntaxErrorr7   multiply_elementwiserN   r'   r   
isinstancer^   r   r   )r\   hc2r   rZ   r[   s       @@rn   test_multiplicationr      sL     	A 	  	A
 	
!AT7a<<T7a<<T7a<<T7a<<T7b==T7a<<
[ w!||w!||w!||w!||w"}}w!||#Aq)A&&&q))))T7a<<T7a<<T7b==T7a<<T7a<<T7a<<
:@A	F3KAa   T7a<<T7ac>>T7ac>>T7a<<	
QB7N7	AAa   T7a<<T7c>>T7c>>T7a<<	[ !V$$$w!||w#~~w#~~w!||Q!R!"A6Q;;R1a&!"A6Vc3Z#s45555i  N  s$   I* ?I: *	I76I7:	JJc                      t        t        d        t        } t        ddgddgg      dz  d d   | d      dz   | d	      dz   | d
      dz   | d      dz  gk(  sJ dz  d d  g dk(  sJ t        g dg dg dg      dz  d d  g dk(  sJ dz  t	        d      k(  sJ dz  k(  sJ t        dgg      dz  d   ddz  k(  sJ t	        d      dz  t	        d      k(  sJ t        ddgddgg      t        d      z  t        ddgddgg      k(  sJ t        ddgddgg      t        j                  z  d d  g dk(  sJ t        ddgddgg      t        j                  z  dz  k(  sJ t        ddgddgg      t        j                  z  t        ddgt        j                  dgg      k(  sJ t        ddgddgg      d z  t        ddgd dgg      k(  sJ dd!lm	 t        dt        gddgg      z  t        dt        z  gddgg      k(  sJ t        t        t        gdt        gg      z  t        t        z  t        t        dz
  z  z  z  gdt        z  gg      k(  sJ t        t        z  t        dz
  z  z  t        z  dz  z  t        z  z  z
  dt        dz  z  z  gdt        z  t        dz
  z  z  gddt        z  gg      sJ t        t        ddgdt        dgddt        gg      z  t        t        z  t        dz
  z  z  dgdt        z  dgddt        z  gg      k(  sJ t        ddgddgg      j                  t        d            j                  d      k(  sJ t        dgg      dz  t        d"gg      cxk(  r3j                  t        d            cxk(  rj                  d      k(  sJ  J t        g d#g d$g d%g d&g d'g      t        t        fd(       t        t        d)        t        g d*g d+g d,g      d-z  t        g d,g d,g d,g      k(  sJ t        t        fd.       t        t        fd/       t        ddgddgg      d-z  t        d0d1gd2d3gg      k(  sJ t        g d+g d+g d+g      d-z  t        g d+g d+g d+g      k(  sJ t        g d*g d+g d+g      d-z  t        g d+g d+g d+g      k(  sJ t!        d4d56      t#        z  t$              sJ t!        d4d5d57      t        t        fd8       t!        d4d5d59      z  t        t'        d      t'        d      t'        d       t'        d      z
  dz   gdt'        d      dt'        d      z
  gg d+g      k(  sJ dz   z  t        g d+g d+g d+g      k(  sJ t        t        fd:       t        g d+g d;g d<g      d=z  t        g d>g d?g d@g      k(  sJ d=z  dz  k(  sJ t        g d*g dAg d,g      t!        d4      z  j)                  d      j+                         dz  k(  sJ t        t        fdB       z  dz  z  k(  sJ t        g d,g d,g d,g      t!        d4d5d5C      z  k(  sJ t!        d4d5d59      z  t-        dz  dz  dz        k(  sJ z  j)                  d      t	        d      k(  sJ z  j)                  d      t/        d      k(  sJ t        g dDg dEg dFg      dGz  t-        dHdHdH      k(  sJ t0        z  t-        dt0        z  dt0        z  dt0        z        k(  sJ t        g d*g d+g d+g      t        t        fdI       t        t        fdJ       t        t        j                  t        j                  gt        j                  t        j                  gg      t        j                  z  k(  sJ t        ddgddgg      t        j                  z  t        t        j                  t        j                  gdt        j                  z  dt        j                  z  gg      k(  sJ y )KNc                      t        d      dz  S Nr   r   r1   rl   rm   rn   ry   ztest_power.<locals>.<lambda>  s    ): rm   r   r   r   r   r   ir      3   i)i  i  i,*  i7  )r   r   r   )r   r   r   )r      r   )	i"  i     i  i  ip  i  i  i  r   r   d   r   i r   r   r      !      0   9   )r   r   r   r   g      ?r{   i   )r   r   r   r   r   )r   r   r   r   r   )r   r   r   r   r   )r   r   r   r   r   )r   r   r   r   r   c                  8     j                  t        d            S Nr   )_matrix_pow_by_jordan_blocksr   r   s   rn   ry   ztest_power.<locals>.<lambda>/  s     > >qu E rm   c                  T    t        ddgddgg      j                  t        d            S )Nr   r   )r1   r   r   rl   rm   rn   ry   ztest_power.<locals>.<lambda>2  s*    AA'7 8 U UVWX[V\ ] rm   r   r   r   r   r   r   r         $@c                       dz  S N @rl   As   rn   ry   ztest_power.<locals>.<lambda>5      q#v rm   c                  "     t        dd      z  S r   r   r   s   rn   ry   ztest_power.<locals>.<lambda>6      q(1a.0 rm   ihiO<iv0ir|   T)integer)r   negativec                       z  S rt   rl   )r   r|   s   rn   ry   ztest_power.<locals>.<lambda>@  s    q!t rm   )r   nonnegativec                  "     t        dd      z  S r   r   r   s   rn   ry   ztest_power.<locals>.<lambda>G  r   rm   )r   r   r   )r   r   r   g      @)   H   Y   )i#        )i<  i  iI  r   r   r   c                  D     j                  d      j                         S )N)subsdoit)Anr|   s   rn   ry   ztest_power.<locals>.<lambda>O  s    rwwq"~224 rm   )r   positiver   r   r   )r   r   r   r   r   r   r   gd%%@c                       dz  S r   rl   r   s   rn   ry   ztest_power.<locals>.<lambda>^  r   rm   c                       t         z  S rt   r
   r   s   rn   ry   ztest_power.<locals>.<lambda>_  s    q!t rm   )rN   r)   r   r1   r5   r   r   Half	sympy.abcr|   rZ   r[   r   _eval_pow_by_recursionr(   
ValueErrorr   r   rX   rI   r  r  r4   r>   r
   )Rr   r  r   r|   s    @@@@rn   
test_powerr    s   
!:;AAA ArE1:!D'!)QsVAXquQw#qAAAAqD!92222	9j12AqD!9EEEEa43q6>>a4199QC5MS $'1c6111q68s1v%%%Aq6Aq6"#WQZ/6Ar7RH:M3NNNNR2r(#$AqvvIq>\)))AQ !AqvvI>QAq6Aq6"#QVV+v1v{6K/LLLLAq6Aq6"#S(FQFS!H3E,FFFFAq6Aq6"#Q&&1ac(QF1C*DDDDAq6Aq6"#Q&&1a41qs8A2FAqD	1R*SSSS	
Aq1q5z!|ad1a4i!Q$q&01QT6:;q!ta!a%jl;!ad;= > > > Aq!9q!Qi!Q34a76	
Aq1Q3xz1	
AqD!	
Aq!tC <   
 	AA A))!A$/13K3KA3NNNNuAb5FUG9% %)G)G")N %	  $% % % % % 	 "3_oWfghA
;EF ;]^	9i01Ad7fiI>????
:~&
:01AA Ad7fz95	97MNOOOO	9i01Ad7fiI>????	9i01Ad7fiI>????sD!AadF###sD40A
:|$sDd3Aa46	1	~a3nQ6J5J^\]_`Ma5ade5ef~a3QQ_`acdQeMeffh i i i i q1u:Iy ABBBB
:01	9i01Ac6V_oOPPPPc6QT>>	*Y/0AsA	
AB771a=1a4'''
:457a!A#h 	()AsD40Aa4199sDd3Aa441adAqD))))qD;;q!A&&&qD;;q!a((()*Ac6T6662222a44Aq!tQT****	9i01A
:~&
:|$ 166166"234Aaff9>>A1vAaff9!&&!&&!1AaffHah3G HIIIIrm   c            
          t        dt        z   dt        z
  gdt        z
  dt        z   gg      } t        d      5  | j                         j	                         t        t        dt        z        t        d      z   dz  t        dt        z         t        d      z   dz  gt        dt        z         t        d      z   dz  t        dt        z        t        d      z   dz  gg      k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   Tr   )r1   r^   rB   r   r   r   s    rn   $test_issue_17247_expression_blowup_1r  f  s    1ac
QqS!A#J'(A	T	 ?uuw~~61Q3x#a& !#s1Q3xi#a&&8!%;<1Q3xi#a& !#s1Q3x#a&'8!&;<+> $? ? 	? ?? ? ?s   B1C44C=c                      t        dt        z   dt        z
  gdt        z
  dt        z   gg      } t        d      5  | j                         \  }}||z  |j	                         z  sJ 	 d d d        y # 1 sw Y   y xY wNr   T)r1   r^   rB   jordan_forminvr   PJs      rn   $test_issue_17247_expression_blowup_2r  m  sl    1ac
QqS!A#J'(A	T	 }}1s1557{{  s   ,A//A8c            	      :   t        dt        z   dt        z
  gdt        z
  dt        z   gg      } t        d      5  | dz  t        dt        dz  z  dz   ddt        dz  z  z
  gddt        dz  z  z
  dt        dz  z  dz   gg      k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   Tr   l                )r1   r^   rB   r  s    rn   $test_issue_17247_expression_blowup_3r  s  s    1ac
QqS!A#J'(A	T	 _#v+AsF25SSUs  wU  VW  Y\  V\  w\  V\  ]+.LQPSV.SSUstuwztzUz  ~\  V\  ]!^ _ _ 	_ __ _ _s   ABBc                      t        t        d            } t        d      5  | dz  t        t        d            k(  sJ 	 d d d        y # 1 sw Y   y xY w)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]])r1   r   rB   r  s    rn   $test_issue_17247_expression_blowup_4r!  z  so    8 	q K L 	MA 
T	 J"uq "H  I J J 	J JJ J Js   AAc                     t        ddd       } t        d      5  | j                  d      t        t        dz  ddt
        z  z
  t        dz  z  z   dt
        z  t        dz  z  z   t        d	
      k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   c                 &    dd| |z   z  t         z  z   S Nr   r   r  rv   s     rn   ry   z6test_issue_17247_expression_blowup_5.<locals>.<lambda>      !rQqSk!m"3 rm   Tr^   r   $   r   EXdomain)r1   rB   charpolyr    r^   r
   r  s    rn   $test_issue_17247_expression_blowup_5r,    s|    q!34A	T	 _zz#(1a42!8QT/+ABqDAI+MqY]"^^^^_ _ _s   AA==Bc            	          t        ddt        d      D  cg c]  } t        | z    c}       }t        d      5  |j	                  d      dk(  sJ 	 d d d        y c c} w # 1 sw Y   y xY w)Nr   @   Tbareissr   r1   r   r^   rB   detrw   r   s     rn   $test_issue_17247_expression_blowup_6r3    sa    q!5":.aac./A	T	 %uuY1$$$% % /% %   AAA&c                      t        ddd       } t        d      5  | j                  d      dk(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   c                 &    dd| |z   z  t         z  z   S r$  r  rv   s     rn   ry   z6test_issue_17247_expression_blowup_7.<locals>.<lambda>  r%  rm   T	berkowitzr   )r1   rB   r1  r  s    rn   $test_issue_17247_expression_blowup_7r8    sE    q!34A	T	 'uu[!Q&&&' ' 's	   ;Ac            	          t        ddt        d      D  cg c]  } t        | z    c}       }t        d      5  |j	                  d      dk(  sJ 	 d d d        y c c} w # 1 sw Y   y xY w)Nr   r.  Tlur   r0  r2  s     rn   $test_issue_17247_expression_blowup_8r;    s`    q!5":.aac./A	T	  uuT{a    /   r4  c                     t        ddt        d      D  cg c]  } t        | z    c}       }t        d      5  |j	                         t        g dg dg dg dg dg dg dg dg      dfk(  sJ 	 d d d        y c c} w # 1 sw Y   y xY w)Nr   r.  T)r   r   r   r  r   r&  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r1   r   r^   rB   rrefr2  s     rn   $test_issue_17247_expression_blowup_9rB    s    q!5":.aac./A	T	 	6vvxF********$, - /56 6 	6 6	6 	6 /	6 	6s   A:9A??Bc                      t        ddd       } t        d      5  | j                  dd      dk(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   c                 &    dd| |z   z  t         z  z   S r$  r  rv   s     rn   ry   z7test_issue_17247_expression_blowup_10.<locals>.<lambda>  r%  rm   Tr   )r1   rB   cofactorr  s    rn   %test_issue_17247_expression_blowup_10rF    sG    q!34A	T	 %zz!Q1$$$% % %s	   <Ac                      t        ddd       } t        d      5  | j                         t        dddgdz        k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   c                 &    dd| |z   z  t         z  z   S r$  r  rv   s     rn   ry   z7test_issue_17247_expression_blowup_11.<locals>.<lambda>  r%  rm   Tr   r'  )r1   rB   cofactor_matrixr  s    rn   %test_issue_17247_expression_blowup_11rJ    sT    q!34A	T	 ;  "fQA3r6&::::; ; ;s   %A		Ac                      t        ddd       } t        d      5  | j                         dddt        z  dddik(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   c                 &    dd| |z   z  t         z  z   S r$  r  rv   s     rn   ry   z7test_issue_17247_expression_blowup_12.<locals>.<lambda>  r%  rm   Tr   r   r   )r1   rB   	eigenvalsr
   r  s    rn   %test_issue_17247_expression_blowup_12rN    sS    q!34A	T	 5{{}AqsAq! 44445 5 5s   #AAc            
         t        ddt        z
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  dgg      } | j                         }|d   ddt        g d      gfk(  sJ |d   d   t        t        d      t        dz
  z  z
  dz   k(  sJ |d   d   dk(  sJ |d   d   d   j	                  dd      t        t         t        d      t        dz
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  z  gdgg      k(  sJ |d   d   t        t        d      t        dz
  z  z   dz   k(  sJ |d   d   dk(  sJ |d   d   d   j	                  dd      t        t         t        d      t        dz
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  dz
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  z  gdt        z  t        dz  dt        z  z
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  dz
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  z  gdgg      k(  sJ y )	Nr   r   r   )r   r   r   r   FT)deepnumerr=  )r1   r^   
eigenvectsr   r   )r   evs     rn   %test_issue_17247_expression_blowup_13rT    s   Aq1ua!e$	
QA1a!e$Aq1ua!e$A1q5!$	& 	'A 
Ba5QF=123333a58q47AE?*Q....a58q==a58A;55"tAwA

"QU	+,	Aq!taczA~	!a%!d1gq1uo*=*A!BAqD1Q3JQRN!S	ST"tAwA

"QU	+,	
	A :    a58q47AE?*Q....a58q==a58A;55"tAwA

"QU	+,	Aq!taczA~	!a%!d1gq1uo*=*A!BAqD1Q3JQRN!S	ST"tAwA

"QU	+,	
	A :   rm   c                     t        dddt        z   dt        z
  gdz  dt        z
  dt        z   gdz  z   dz        } t        d      5  | j                         t        t        dz   dt        z
  t        dz   dt        z
  t        dz   dt        z
  t        dz   dt        z
  gddt        z  ddt        z  ddt        z  ddt        z  gg dg dg dg dg dg dg      k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   r   r   Tr   r@  )r1   r^   rB   echelon_formr  s    rn   %test_issue_17247_expression_blowup_14rW    s    q!qsAaCjlac1Q3Z\1145A	T	 	G~~6UAE1q5!a%QAq1ua!eDacqAaCQ!A#1!DDDDDDD+F $G G 	G G	G 	G 	Gs   BC&&C/c                     t        dddt        z   dt        z
  gdz  dt        z
  dt        z   gdz  z   dz        } t        d      5  | j                         t        t        dz   dt        z
  t        dz   dt        z
  t        dz   dt        z
  t        dz   dt        z
  gg      t        ddt        z  ddt        z  ddt        z  ddt        z  gg      gk(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   r   r   Tr   )r1   r^   rB   rowspacer  s    rn   %test_issue_17247_expression_blowup_15rZ    s"   q!qsAaCjlac1Q3Z\1145A	T	 Pzz|QAq1ua!eQUAPQESTWXSXZ[^_Z_(`'a bdjmnpqrspsuvxyz{x{}~  AB  CD  AD  FG  IJ  KL  IL  mM  lN  eO   P  P  	P  PP P Ps   BCC(c                  *   t        dddt        z   dt        z
  gdz  dt        z
  dt        z   gdz  z   dz        } t        d      5  | j                         t        t        dz   gdt        z
  gt        dz   gdt        z
  gt        dz   gdt        z
  gt        dz   gdt        z
  gg      t        dt        z
  gt        dz   gdt        z
  gt        dz   gdt        z
  gt        dz   gdt        z
  gt        dz   gg      gk(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   r   r   T)r1   r^   rB   columnspacer  s    rn   %test_issue_17247_expression_blowup_16r]    s   q!qsAaCjlac1Q3Z\1145A	T	 y}}6AE7AE7AE7AE7APQE7TUXYTYSZ\]`a\a[bdehidicj*k#lntwx{|w|v}  @A  DE  @E  F  HI  LM  HM  GN  PQ  TU  PU  OV  XY  \]  X]  W^  `a  de  `e  _f  hi  lm  hm  gn  pq  tu  pu  ov  vw  ox  #y  y  	y  yy y ys   B:D		Dc                     t        ddt        d      D  cg c]  } t        | z    c}       }t        d      5  |j	                         t        dgdgdgdgdgdgdgdgg      t        dgdgdgdgdgdgdgdgg      t        d	gd
gdgdgdgdgdgdgg      t        dgdgdgdgdgdgdgdgg      t        dgdgdgdgdgdgdgdgg      t        dgdgdgdgdgdgdgdgg      gk(  sJ 	 d d d        y c c} w # 1 sw Y   y xY w)Nr   r.  Tr   r  r   r   r   r   r=  r   r>  r   r&  r   )r1   r   r^   rB   	nullspacer2  s     rn   %test_issue_17247_expression_blowup_17ra  	  s]   q!5":.aac./A	T	 8{{}QCaS!aS!aS!56QCaS!aS!aS!56QCaS!aS!aS!56QCaS!aS!aS!56QCaS!aS!aS!56QCaS!aS!aS!56!8 8 	8 88 8 /8 8s   C3B2C88Dc                      t        dddt        z   dt        z
  gdz  dt        z
  dt        z   gdz  z   dz        } t        d      5  | j                         rJ 	 d d d        y # 1 sw Y   y xY w)Nr   r   r   T)r1   r^   rB   is_nilpotentr  s    rn   %test_issue_17247_expression_blowup_18rd    sj    q!qsAaCjlac1Q3Z\1145A	T	 $>>####$ $ $s   A""A+c                      t        t        d            } t        d      5  | j                         rJ 	 d d d        y # 1 sw Y   y xY w)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)r1   r   rB   is_diagonalizabler  s    rn   %test_issue_17247_expression_blowup_19rg    sO    q a b 	cA
 
T	 )&&(((() ) )s	   =Ac                     t        t        dz   dt        z
  ddgdt        z
  t        dz   dt        dz   gddt        z
  t        dz   dgdddt        dz   gg      } t        d      5  | j                         t        dddt        dz   t        dz
  z  gg dg dg dg      t        g dddt        z  ddgddt        dz   dgdddt        dz   gg      fk(  sJ 	 d d d        y # 1 sw Y   y xY w)	Nr   r   T)r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r1   r^   rB   diagonalizer  s    rn   %test_issue_17247_expression_blowup_20rl  "  s   UQU#UQUQU#	
QUQU#	
QU#	% 	&A
 
T	 
&}}6AAA''''	+) $*
 "!"!QU"!AE"	$ %	#& 	& 		& 	&
& 
& 
&s   #A0CC&c                      t        t        d            } t        d      5  | j                  d      t        t        d            k(  sJ 	 d d d        y # 1 sw Y   y xY w)N  [
        [             -3/4,       45/32 - 37*I/16,                   0,                     0],
        [-149/64 + 49*I/32, -177/128 - 1369*I/128,                   0, -2063/256 + 541*I/128],
        [                0,         9/4 + 55*I/16, 2473/256 + 137*I/64,                     0],
        [                0,                     0,                   0, -177/128 - 1369*I/128]]TGEmethodv  [
            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
            [0, 0, 0, -11328/952745 + 87616*I/952745]]r1   r   rB   r  r  s    rn   %test_issue_17247_expression_blowup_21rt  4  j    q c d 	eA
 
T	 <uuDu!VA /: -; &< < 	< << < <   *AAc                      t        t        d            } t        d      5  | j                  d      t        t        d            k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nrn  TLUrp  rr  rs  r  s    rn   %test_issue_17247_expression_blowup_22ry  A  ru  rv  c                      t        t        d            } t        d      5  | j                  d      j	                         t        t        d            k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nrn  TADJrp  rr  )r1   r   rB   r  r   r  s    rn   %test_issue_17247_expression_blowup_23r|  N  ss    q c d 	eA
 
T	 <uuEu"))+va 9: 7; 0< < 	< << < <s   8A""A+c                      t        t        d            } t        d      5  | j                  d      t	        t        d            k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nrn  TCHrp  rr  r2   r   rB   r  r1   r  s    rn   %test_issue_17247_expression_blowup_24r  [  sj    Q c d 	eA
 
T	 <uuDu!VA /: -; &< < 	< << < <rv  c                      t        t        d            } t        d      5  | j                  d      t	        t        d            k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nrn  TLDLrp  rr  r  r  s    rn   %test_issue_17247_expression_blowup_25r  h  sj    Q c d 	eA
 
T	 <uuEu"fQ 0: .; '< < 	< << < <rv  c                      t        t        d            } t        d      5  | j                         dk(  sJ 	 d d d        y # 1 sw Y   y xY w)Na  [
        [             -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,      1/4 - 5*I/16,      65/128 + 87*I/64,         -9/32 - I/16,      183/256 - 97*I/128],
        [-149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,  85/256 - 33*I/16,  805/128 + 2415*I/512, -219/128 + 115*I/256, 6301/4096 - 6609*I/1024],
        [          1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,         1/4 + I/2,      -129/64 - 9*I/64,         1/4 - 5*I/16,        65/128 + 87*I/64],
        [   -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,  125/64 + 87*I/64, -2063/256 + 541*I/128,     85/256 - 33*I/16,    805/128 + 2415*I/512],
        [            1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,              -3/4,       45/32 - 37*I/16,            1/4 + I/2,        -129/64 - 9*I/64],
        [         21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128,     125/64 + 87*I/64,   -2063/256 + 541*I/128],
        [               -2,         17/4 - 13*I/2,             1 + I,         -19/4 + 5*I/4,           1/2 - I,         9/4 + 55*I/16,                 -3/4,         45/32 - 37*I/16],
        [     1/4 + 13*I/4,    -825/64 - 147*I/32,          21/8 + I,    -537/64 + 143*I/16,    -5/8 - 39*I/16,   2473/256 + 137*I/64,    -149/64 + 49*I/32,   -177/128 - 1369*I/128]]Tr   r1   r   rB   rankr  s    rn   %test_issue_17247_expression_blowup_26r  u  sL    q z { 	|A 
T	 vvx1}}     A  A	c            	         t        ddt        z
  t        dz   dt        z
  gdt        z
  t        dz   dt        dz   gddt        z
  t        dz   dt        z
  gdddt        z
  dgg      } t        d      5  | j                         \  }}|j	                         t        t        d            j	                         k(  sJ |t        t        d            k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nr   r   Ta  [
            [    0,  4*x/(x**2 - 2*x + 1), -(-17*x**4 + 12*sqrt(2)*x**4 - 4*sqrt(2)*x**3 + 6*x**3 - 6*x - 4*sqrt(2)*x + 12*sqrt(2) + 17)/(-7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 + 8*x**3 - 2*x**2 + 8*x + 6*sqrt(2)*x - 5*sqrt(2) - 7), -(12*sqrt(2)*x**4 + 17*x**4 - 6*x**3 - 4*sqrt(2)*x**3 - 4*sqrt(2)*x + 6*x - 17 + 12*sqrt(2))/(7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 - 8*x**3 + 2*x**2 - 8*x + 6*sqrt(2)*x - 5*sqrt(2) + 7)],
            [x - 1, x/(x - 1) + 1/(x - 1),                       (-7*x**3 + 5*sqrt(2)*x**3 - x**2 + sqrt(2)*x**2 - sqrt(2)*x - x - 5*sqrt(2) - 7)/(-3*x**3 + 2*sqrt(2)*x**3 - 2*sqrt(2)*x**2 + 3*x**2 + 2*sqrt(2)*x + 3*x - 3 - 2*sqrt(2)),                       (7*x**3 + 5*sqrt(2)*x**3 + x**2 + sqrt(2)*x**2 - sqrt(2)*x + x - 5*sqrt(2) + 7)/(2*sqrt(2)*x**3 + 3*x**3 - 3*x**2 - 2*sqrt(2)*x**2 - 3*x + 2*sqrt(2)*x - 2*sqrt(2) + 3)],
            [    0,                     1,                                                                                            -(-3*x**2 + 2*sqrt(2)*x**2 + 2*x - 3 - 2*sqrt(2))/(-x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x + 1 + sqrt(2)),                                                                                            -(2*sqrt(2)*x**2 + 3*x**2 - 2*x - 2*sqrt(2) + 3)/(x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x - 1 + sqrt(2))],
            [1 - x,                     0,                                                                                                                                                                                               1,                                                                                                                                                                                             1]]a  [
            [0, 1,                       0,                       0],
            [0, 0,                       0,                       0],
            [0, 0, x - sqrt(2)*(x - 1) + 1,                       0],
            [0, 0,                       0, x + sqrt(2)*(x - 1) + 1]])r1   r^   rB   r  r   r   r  s      rn   %test_issue_17247_expression_blowup_27r    s   Aq1ua!e$	
QA1a!e$Aq1ua!e$A1q5!$	& 	'A
 
T	 K}}1xxzVA 'o %p q rx  rx  rz	z 	z z
 F1 I J K K 	K KK K Ks   1A"CC&c                      t        t        d            } t        d      5  | j                         t        d      k(  sJ 	 d d d        y # 1 sw Y   y xY w)Nrn  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)])r1   r   rB   singular_valuesr  s    rn   %test_issue_17247_expression_blowup_28r    sj    q c d 	eA
 
T	 d  "a )c 'd d 	d dd d ds   A		Ac                      t        t        d            } t        d      5  | j                         dk(  sJ 	 d d d        y # 1 sw Y   y xY w)Na	  [
        [1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I,3/64+13/64*I,-23/32-59/256*I,15/128-3/32*I,19/256+551/1024*I],
        [21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I,119/128+143/128*I,-10879/2048+4343/4096*I,129/256-549/512*I,42533/16384+29103/8192*I],
        [-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I,3/64+13/64*I,-23/32-59/256*I],
        [1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I,119/128+143/128*I,-10879/2048+4343/4096*I],
        [-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I,-9/32-1/16*I,183/256-97/128*I],
        [1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I,-219/128+115/256*I,6301/4096-6609/1024*I],
        [-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I,1/4-5/16*I,65/128+87/64*I],
        [-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I,85/256-33/16*I,805/128+2415/512*I],
        [0,-6,-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I,1/4+1/2*I,-129/64-9/64*I],
        [1,-9/4+3*I,-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I,125/64+87/64*I,-2063/256+541/128*I],
        [0,-4*I,0,-6,-4,9-5*I,-4*I,27/2+6*I,-2,17/4-13/2*I,1+I,-19/4+5/4*I,1/2-I,9/4+55/16*I,-3/4,45/32-37/16*I],
        [0,1/4+1/2*I,1,-9/4+3*I,-2*I,119/8+29/4*I,1/4+5/2*I,-23/8-57/16*I,1/4+13/4*I,-825/64-147/32*I,21/8+I,-537/64+143/16*I,-5/8-39/16*I,2473/256+137/64*I,-149/64+49/32*I,-177/128-1369/128*I]]Tr   r  r  s    rn   test_issue_16823r    sL    q F G 	HA 
T	 vvx1}}  r  c                  f   t        g ddt        d      z   dt        d      z   dt        d      z
  t        d       dz
  dddddg	ddt        d      z  z   ddt        d      z  z
  ddt        d      z  z
  ddt        d      z  z   dddddg	d	t        d      z  dz
  dd
t        d      z  z
  dd
t        d      z  z   dd
t        d      z  z   ddddd
g	ddt        d      z  z
  dt        d      z  dz   dt        d      z  dz   ddt        d      z  z
  dddddg	dd
t        d      z  z   dd
t        d      z  z   d	t        d      z  dz
  dd
t        d      z  z
  ddddd
g	d	dt        d      z  z   d	dt        d      z  z
  d	dt        d      z  z
  d	dt        d      z  z   dddddg	dt        d      z
  t        d       dz
  dt        d      z   dt        d      z   dddddg	g      } t        d      5  | j                         t        ddddddddt	        d      dz  g	ddddddddt	        d       dz  g	ddddddddt	        d      dz  g	ddddddddt	        d       dz  g	g dddddddddt	        d       dz  g	g dddddddddt	        d       dz  g	g      dfk(  sJ 	 d d d        y # 1 sw Y   y xY w)N)	r   r   r   r   r   r   r   r   r   r   r   r   r>  r_  r  r   r   r   r   r   r   T)	r   r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   r?  )r1   r   rB   rA  r   r  s    rn   test_issue_18531r    s   #	
T!Wb47lAQK$q'Aq!RAN	aQiaQiaQiaQiQPRTVXYZ	DGaQtAwYQtAwYAd1gIr2qRTVWX	
QtAwY$q'	Aqay1}a!DG)mQQPRTUV	aQiQtAwY47
QAd1gIq"bRTVWX	aQiaQiaQiaQiQPRTVXYZ	
T!WtAwhlAQKd1gr1aAN	
 		A 
T	 	KvvxF1aAq!ad1f-1aAq!adU1W-1aAq!ad1f-1aAq!adU1W-*1aAq!adU1W-*1aAq!adU1W-$/ 0 2JK K 	K K	K 	K 	Ks   .B/J''J0c            	      D
   t        t        d        t        t        d        t        t        d        t        t              5  dt        d      d<   d d d        t               t        g       cxk(  r!t        g g      cxk(  rt        ddg       k(  sJ  J t	               5  t        dgd	gg      j                         dgd	ggk(  sJ 	 d d d        t	               5  t        dgd	gg      j                  j                         dggd	ggk(  sJ 	 d d d        t        dgg      } t	               5  t        j                  | d
<   d d d        t        t        dgddgg      }|}|j                  |j                  k(  sJ |j                  dk(  sJ |d d  t        dddgk(  sJ 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(  sJ |j                  dk(  sJ |d d  g dk(  sJ t        t        d            t        d      k(  sJ t        t        t        d                  t        t        d            k(  sJ t        |       |j                         k(  sJ t        t        |            t        |      j!                         k(  sJ |t        |      usJ t#        dd      t#        dd      dz  gt#        dd      dz  t#        dd      dz  gg}t        |      } | t        g dg dg dg dg dg      k(  sJ | j                         |k7  sJ t        |d      j                         |k(  sJ 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	               5  t        |d      j                         |D 	cg c]  }	|	g c}	k(  sJ 	 d d d        t        t#        d      t#        d      g      t        t#        d      g      k(  sJ t        t        d        t        t        d        t        ddgddgg      } t        | dg      }
|
t        ddgddgddgg      k(  sJ y # 1 sw Y   xY w# 1 sw Y   $xY w# 1 sw Y   xY w# 1 sw Y   xY wc c}	w # 1 sw Y   xY w)Nc                  .    t        ddt        d            S )Nr      )r1   r   rl   rm   rn   ry   ztest_creation.<locals>.<lambda>  s    vaE"I6 rm   c                      t        ddg       S )Nr   r   r   rl   rm   rn   ry   ztest_creation.<locals>.<lambda>  s    vaR0 rm   c                      t        d      d   S r   r   rl   rm   rn   ry   ztest_creation.<locals>.<lambda>  s    vf~a0 rm   r   r   r   r   r   )r   r   r   r   r   	r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   )r   r   r   r   r   Fevaluater   r   r   r   c                  B    t        t        d      t        dd      g      S )Nr   r   r   r1   r8   rl   rm   rn   ry   ztest_creation.<locals>.<lambda>      vtAwQ
&;< rm   c                  B    t        t        d      t        dd      g      S )Nr   r   r   r  rl   rm   rn   ry   ztest_creation.<locals>.<lambda>  r  rm   )r   r   r   )rN   r  
IndexErrorr1   rS   tolistTr   EmptySetr^   r   r   r   r5   r/   as_immutable
as_mutabler8   rA   )r   rZ   r   r[   c23c13r\   datr   rw   M2s              rn   test_creationr    s   
:67
:01
:01	
	 vq 8vbzEVRD\EVAq"5EEEEEE		! ?T{m$++-A3+>>>?		! CT{m$&&--/aSED6?BBBCuA		! **$ 	AA A	A66QVV66Q;;Q4Aq!Q<q!aAq\"A	A66QVV66Q;;Q4Aq!Q<6M6!9>>
AuQ{
#C
AuQ|
$CSzA66Q;;66Q;;Q4....#a&>SV###?3q623s1v7NNNN1!1111/!$%);)F)F)HHHHF1I1ItAay{#d1Qik4!9Q;%?
@CsA     88:#&--/3666S!QA7A,C#;&AAtWagtWag	"    
 
 	! JcE*113S7I7IIIIJ 47DG$%a	)::::
:<=
:<= 	AA A	F	B!Q!Q!Q01111Q 
? ?C C h 8JJ JsN   S 'S*2S7,TT2
T<TS'*S47TTTTc                      t        j                  dt        dd      t        dd      dz  t        dd      dz  t        dd      dz  t        dd      dz  t        dd      dz  t        dd      dz        t        g dg dg d	g d
g      k(  sJ y )Nr   r   r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )r1   	irregularr8   rl   rm   rn   test_irregular_blockr    s    AtAay$q)A+tAay{Qq	!T!AYq[$q)A+tAay{<?E	G @  rm   c                  2   t         j                  t         j                  t        t        z  t         j
                  gt        t        t        t        dz  gt        t         j                   t        t        z  dgg} t        |       }|j                         | k(  sJ y )Nr   r   )	r   Oner  r^   r_   Zeror`   r1   r  )lstr   s     rn   test_tolistr  &  sc    EE1661Q3'!Q1a41quufac1:M
NCsA88:rm   c                     t        dd      j                         t        dd      k(  sJ t        dd      j                         t        t        dd            k(  sJ t        dd      j                         t        t        dd            k(  sJ y Nr   r   )r>   r  r  r/   rl   rm   rn   test_as_mutabler  ,  su    A;!!#uQ{222A;##%q!)EEEEA;##%q!)EEEErm   c                     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 f   t        ddd      k(  sJ |dddf   t        ddd      k(  sJ t        g d	g d
g dg dg      }|d d df   t        ddg d      k(  sJ |dd d d f   t        g dg dg      k(  sJ y )Nr   r   r   r   c                     | |z   S rt   rl   rv   s     rn   ry   ztest_slicing.<locals>.<lambda>7  
    1q5 rm   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r      r         r   r   )r   r   r  r   r  )r5   r>   r1   )m0m1m2s      rn   test_slicingr  2  s    	QBbqb"1"f:Qac1Q3h<58###	1(	)Bad8vaI....ac1f:1f----	|^=MN	OBae9q!^4444bc1f:1A BCCCCrm   c                     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(  sJ g d| d d d d f<   | t        d      k(  sJ ddg| d ddf<   | t        d	      k(  sJ y )
Nr   r   )r   r   r   r   r  r   r   r   r   rj  r   r   r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   r  r   r   r   r   r   r   r  r   r  r  r      ))r   r   r   r   )r   r   r   r   r  r  )r>   r5   r1   r   s    rn   test_submatrix_assignmentr  @  s$   aAa&Aac1Q3hK & ' ' ' ' AAbqb"1"fIA;;Q<(AadG & ' ' ' ' AhAadGa==MAadG * + + + + 1vAbqb!eH * + + + +rm   c                  `    t        ddd         j                  g dddg      t        ddg d      k(  sJ  j                  ddgg d	      t        ddg d
      k(  sJ  j                  t        d      t        d             k(  sJ t        t         fd       t        t         fd       y )Nr   r   c                     | dz  |z   S Nr   rl   rv   s     rn   ry   ztest_extract.<locals>.<lambda>]  s    !A#' rm   )r   r   r   r   r   r   )r   r   r   r   r   r   r	  )r   r   r   r   r   r  c                  ,     j                  dgdg      S )Nr   r   r   r   s   rn   ry   ztest_extract.<locals>.<lambda>a      qyy!qc2 rm   c                  ,     j                  dgdg      S r  r  r   s   rn   ry   ztest_extract.<locals>.<lambda>b  r  rm   )r1   r   r   rN   r  r   s   @rn   test_extractr  \  s    q!)*A99YA'6!Q8K+LLLL99aVY'6!Q8K+LLLL99U1XuQx(A---
:23
:23rm   c                      t        d      } | j                  dd      t        ddd      k(  sJ t        ddd       }|j                  dd      t        d      k(  sJ |j                  dd	      t        d
      k(  sJ y )Nr   r   r   )	r   r   r   r   r   r   r   r   r   r   c                     | |z   S rt   rl   rv   s     rn   ry   ztest_reshape.<locals>.<lambda>h  r  rm   )r   r   r   r   )r   r   r   r   r   r   ))r   r   r   r   r   r   )r   r   r   r   r   r   )r5   reshaper1   r  r  s     rn   test_reshaper  e  s    	QB::ava,GHHHH	1(	)B::	1DEF F F::av&NOOOOrm   c                      t        d      } | j                  d       t        d      dz  k(  sJ | j                  d       t        d      k(  sJ y )Nr   c                     d| z  S Nr   rl   r^   s    rn   ry   z test_applyfunc.<locals>.<lambda>p  s
    !A# rm   r   c                      yr   rl   r  s    rn   ry   z test_applyfunc.<locals>.<lambda>q  r   rm   )r5   	applyfuncr>   )r  s    rn   test_applyfuncr  n  sE    	QB<<&#a&(222<<$a000rm   c            	         t        t        t        t        z   z  dgt        t        z   t        z  t        z  t        t        t        t        t        z   z  z   z  gg      } | j                         }|t        t        t        z  t        dz  z   dgt        t        dz  z  t        t        dz  z  z   t        t        z  t        t        dz  z  z   t        dz  z   gg      k(  sJ t	        dd      }t        t        t        |z        g      j                  d      t        t        |      t        t        |      z  z   g      k(  sJ t        g dg dg d	g      j                         t        d
d
t        dd      gg dg dg      k(  sJ y )Nr   r   rZ   Treal)complexr   )r   r   r   r   r   )r   r   r   r   )
r1   r^   r_   r   r   r   r
   r   r   r   )r  r  rZ   s      rn   test_expandr  t  sW   	!QU)QAE19a-A1q5	M1B!CD	EB	B
A#1*a1QT6AadF?AaC!AqD&L1a4,?@AC C C C 	sA3qs8*$$T$2A3q6!"#$ $ $ 9j)4599;v	
Ax1~G @   rm   c            	      (   t        t        t              dz  t        t        dz        gt        t        dz        t        t              dz  z  t        t        dz        t        t              dz  z  gg      } | j                  t        j                  t              t        j                  t              z        }|t        t        dz  t        t              gt        dz  t        t              z  t        dz  t        t              z  gg      k(  sJ | j                  t        j                  t              t        j                  t              z        }|t        t        dz  t        gt        t        dz  z  t        dz  t        z  gg      k(  sJ | j                  t        j                  t              t        j                  t              z        }|t        t        dz  t         gt         t        dz  z  t        dz   t        z  gg      k(  sJ y r  )
r1   r   r^   r   r_   refinerU   r  r  r   r  s     rn   test_refiner    st   	#a&!)T!Q$Z(adCFAI%tAqDz#a&!)';<> 
?B	166!9qvvay(	)B!Q$A!Q$s1v+q!tCF{)CDEEEE	1::a=1::a=0	1B!Q$Qq!tVQT!V$456666	1::a=1::a=0	1B!Q$qbAg1uQw%789999rm   c                  z   t        dd      } t        ddd      } | t        ddd      k(  sJ t        dddd      } t        ddd      } | t        ddd      k(  sJ | j                         } |j                          || k(  sJ t        j                  d      }| t        dd|      k(  sJ d	D ])  }d
D ]"  }t        |d||      } | | j
                  k(  r"J  + t        ddd      } d}t        | j                  d         D ]/  }t        | j                  d         D ]  }| ||f   dk(  s|dz  } 1 |dk(  sJ y )Nr   )seedr   r      T)r  	symmetric)r  prng)r   r  )r   F      )r  percentr  r   r   r  )minr  r  )r9   copyr%   randomRandomr  r   r   )r   r   rngsizer  
zero_countrw   rx   s           rn   test_randomr    sb   1aA1aa A
1aa((((1aC A11-A
115555	AAJJL6M6
--
C
137777  $ 	G44sKA8O8	
 	21b)AJ1771:  qwwqz" 	 AAw!|a
	   rm   c                     t        d      } | j                         t        d      k(  sJ | j                  d      t        d      k(  sJ | j                  d      t        d      k(  sJ | j                  d      t        d      k(  sJ | j                  d      t        d      k(  sJ | j                  d      t        d      k(  sJ t        g dg d	g d
g      } | j                         }| |z  t        d      k(  sJ | j                  d      |k(  sJ | j                  d      |k(  sJ | j                  d      |k(  sJ | j                  d      |k(  sJ | j                  d      |k(  sJ t        g dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg dg d g d!g d"g d#g d$g      }|j                  d%      |z  t        |j                  d&         k(  sJ t         g d'g d(g d)g      t        fd*d+j                         D              sJ t         g d'g d(g d)g      t        fd,d+j                         D              sJ y )-Nr   rx  rp  r{  r~  r  QR)r   r   r   )r   r   r   )r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   BLOCKr   )r   1      )r   G   ^   );      A   c              3   V   K   | ]   }t        j                  |            u  " y wrt   r   r  r   sr   r   s     rn   r   ztest_inverse.<locals>.<genexpr>  "     LtAEE!H~$L   &)zGE ADJ LU CH LDL QRc              3   V   K   | ]   }t        j                  |            u  " y wrt   r  r  s     rn   r   ztest_inverse.<locals>.<genexpr>  r	  r
  )r5   r  r1   r   r/   r   splitr0   )r   AinvAAr   r   s      @@rn   test_inverser    sm   AA557c!f555Q'''555#a&(((555Q'''555#a&(((555Q'''	 	A 557DT6SV555%%%555$&&&555%%%555$&&&555%%%	\WWWWWWWWWWWWWWWWWWWWWWWW1Y 
ZB2 666!B&#bhhqk*::::
C\ 	A L.C.I.I.KLLLL
C\ 	A L.C.I.I.KLLLLrm   c                     t        ddt        dz  t        z  dt        dz  z  t        t        z  z   g      } t        t        g}| j                  |      t        dt        z  t        z  t        dz  gt        dt        z  t        z   gg      k(  sJ t        ddt        t        dz  t        dz  z  g      } | j                  |      t        ddgdt        z  t        dz  z  t        dz  dz  t        dz  z  gg      k(  sJ t        dz  t        z  }t        t        g}t	        ||      t        dt        z  dt        z  gdt        z  dgg      k(  sJ t        dz  t        dz  z  }t	        ||      t        dt        dz  z  dt        z  t        dz  z  gdt        z  t        dz  z  dt        dz  z  t        z  gg      k(  sJ t
        t        t        dz  z  z   }t        dz  dt        dz  z  z   }t        ddt        z  gdt        z  dt        z  gg      }|t	        |t        t        t        g            k(  sJ |t	        |t        t        t        g      j                        k(  sJ t	        |t        t        f|g      t        ddt        dz  z  dt        z  gdt        dz  z  dt        z  dt        z  gdt        z  dt        z  dgg      k(  sJ y )Nr   r   r   r   r   r   )r1   r^   r_   jacobianr6   r`   r  )Lsymsfganss        rn   test_jacobian_hessianr    s   q!ad1fa1fqsl+,Aq6D::dv!Aq!t}q!A#'l&CDDDDq!aAad^$A::dv1v!AqD!Q$q&A+/F&GHHHH	1QAq6D1dv!QqSzAaC8&<====	1QT	A1d1a41QT"QqSAXqAvax$89:; ; ; 	
AadF
A	1qAvA
1!*Q3!* C'!VQF^,,,,'!VQF^--....1q!fqc"f1a41	
1a4AaC1aCAaC1. '       rm   c                     t        t        t              t        t              gt              t        t              dz  t        t              dz  z   k(  sJ t        t	        t              t	        dt        z        gt              t	        dt        z        k(  sJ t        t	        t              t        gt              t	        t              t        t	        t              z  z
  k(  sJ t        dt        t        dz  gt              dk(  sJ dt	        t              z  t        t              z  t        z  dt        t              z  t	        t              z  t        dz  z  z   dt	        t              z  t        t              z  t        z  z
  t	        t              t        t              z  t        dz  z  z
  t	        t              t        t              z  t        dz  z  z   } t        t	        t              t        t              t        dz  gt              j                         | k(  sJ t        t	        t              t        t              t        dz  gt        d      j                         | k(  sJ t        dz   t        t              dz  z  t        dz  t        t              dz  z  z
  dt        z  t        t              dz  z  z
  dt        z  t        t              dz  z  z
  }t        t        t              t        t              t        dz  gt              j                         |k(  sJ t        t        t              t        t              t        dz  gt        d      j                         |k(  sJ t        g t              dk(  sJ y )Nr   r   r   r&  r   r7  rp  )r=   r   r^   r   r   r   )w1w2s     rn   test_wronskianr    s   c!fc!f%q)SVQYQ-BBBBc!fc!A#h'+s1Q3x777c!fa[!$A3q6(9999aAqD\1%***	CF3q6	!	aAhs1voad2	2Qs1vXc!f_Q5F	FAs1vad
 VCF]1a4/
0Bc!fc!fad+Q/668B>>>c!fc!fad+Q{CJJL  
Q$s1vqy1a4A	>	)AaCA	M	9AaCA	M	IBc!fc!fad+Q/668B>>>c!fc!fad+Q{CJJL  Rq   rm   c                     t        dt        gt        dgg      j                  t        d      t        ddgddgg      k(  sJ t        t        dgt        t        z   dgg      j                  t        dgt        dgg      t        ddgddgg      k(  sJ t        t        dgt        t        z   dgg      j                  t        dft        dfg      t        ddgddgg      k(  sJ t        t        dgt        t        z   dgg      j                  t        dt        di      t        ddgddgg      k(  sJ t        t        t        z  g      j                  t        t        dz
  t        t        dz
  id	      t        t        dz
  t        dz
  z  g      k(  sJ t        D ]7  } t        dd
gd
dgg      | j                  d      j                  dd      k(  r7J  y )Nr   r   r   r   r   r  r   T)simultaneousr   )r1   r^   r  r_   r   r5   r   s    rn   	test_subsr    s   Aq6Aq6"#((A.&1a&1a&9I2JJJJAq6AE1:&',,q"g2w-?@Q"a!"# # #Aq6AE1:&',,q"g2w-?@Q"a!"# # #Aq6AE1:&',,aQ^<Q"a!"# # #1Q3%=q!a%AE2FQQ !" " "  A1v1v&'3771:??1a+@@@@Arm   c                     t        dt        gt        dgg      j                  t        di      t        ddgddgg      k(  sJ t        t        dgt        t        z   dgg      j                  t        dt        di      t        ddgddgg      k(  sJ t        D ]8  } t        ddgddgg      | j                  d      j                  ddi      k(  r8J  y )	Nr   r   r   r   r   r  r   r   )r1   r^   xreplacer_   r   r5   r  s    rn   test_xreplacer"  %  s    Aq6Aq6"#,,aV4AA ! ! !Aq6AE1:&'00!RB@Q"a!"# # # G1v1v&'3771:+>+>1v+FFFFGrm   c                     t        d      } t        d      }t        dt        z  dt        z  z   t        t        t        z  z   t        z  g |t              t         |t              z  z    |t              z  dd| z  t        | t        z        | z  z
  z  t        z  gg      }|j                          |t        t        t        z   t        t        z  z  dt        z   gdt        z   dddt        t        | z        z  z
  t        | z  z  z  gg      k(  sJ dt        z   dz  }t        |gg      }|j                          |t        |gg      k(  sJ |j                  t               |t        |j                  t              gg      k(  sJ y )Nr|   r  r   r   )ratio)	r   r   r1   r^   r_   r   r   r%   r   )r|   r  r   eqs       rn   test_simplifyr&  -  s\   sAAQqS1Q3YQqSAHQ4!AaD&=!A$&QqS3q2v;q=-@(AB(FHJ 	KAJJL1q51q5/!a%I$%E1q1SAY;A.F+GIK L L L L
a%!BvAJJLvJJRJ2./01111rm   c                  
   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(  sJ | j                  j                  | k(  sJ | j                  | j                         k(  sJ y )N)
r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r1   r  	transposer  s    rn   test_transposer)  >  s    ..0 	1A33&QFFFFFFFFFF	% 	& 	& 	& 	& 3355A::33!++-rm   c                     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                  | j	                         k(  sJ | j
                  | j                  j                  k(  sJ | j
                  t        ddgt         dgddgg      k(  sJ y )Nr   r   )r   r   r   r   r   )r1   r
   r  C	conjugateHr  s    rn   test_conjugater.  O  s    Aq	 	A 33&1a&a&a&" # # # # 33&1qb!*$& ' ' ' '33!++-33!##%%<<33&Aq'2q'q'# $ $ $ $rm   c            
      "   t        t        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 y )Nc                  ,    t        d      j                  S r  )r5   Drl   rm   rn   ry   z!test_conj_dirac.<locals>.<lambda>b  s    3q688 rm   r   r   rj  r  r   )rN   AttributeErrorr1   r
   r1  r  s    rn   test_conj_diracr3  a  s    
>+,Aq!Aq!Aq! 	A
 33&*2A*2r2*2rAr*, - - - -rm   c                  V    t        g dg dg dg      } | j                         dk(  sJ y )Nr   r   r   r   r   r   )r   r   r   r  r1   tracer  s    rn   
test_tracer9  o  s-    	 	A 779??rm   c                  \    t        t        ddgdt        dgg      } | j                  dk(  sJ y )Nr   r  )r1   r^   r_   r   r  s    rn   
test_shaper;  v  s4    Aq	Aq	 	A77frm   c                     t        t        ddgdt        dgg      } | j                  dd        | t        t        ddgdt        dz   dgg      k(  sJ | j	                  dd        | t        t        dz   ddgdt        z   t        dz   dgg      k(  sJ | j                  d      t        t        dz   ddgg      k(  sJ | j                  d      }d|d<   | d   t        dz   k(  sJ | dd d	f   }d|d<   | d   t        dz   k(  sJ | j                  d      }|t        t        dz   dt        z   g      k(  sJ d|d<   | d   t        dz   k(  sJ | d d df   }d|d<   | d   t        dz   k(  sJ y )
Nr   r   c                     | |z   dz   S Nr   rl   )rrx   s     rn   ry   z!test_col_row_op.<locals>.<lambda>  s    QUQY rm   r   r   c                     | t         |z  z   S rt   )r_   )r\   rx   s     rn   ry   z!test_col_row_op.<locals>.<lambda>  s    QAX rm   *   r   r   )r1   r^   r_   row_opcol_oprowcol)r   r1c1s      rn   test_col_row_oprH  |  s   Aq	Aq	 	AHHQ&'1AE1' ( ( ( ( HHQ%&QAq)QAq)+ , , , ,
 558vAq!}o....	
qBBqET7a!e	
1crc6BBqET7a!e	
qBQA''''BqET7a!e	
1a4BBqET7a!erm   c                      t        g dg dg      } | j                  dd       | d   dk(  sJ | d   dk(  sJ | d   d	k(  sJ y )
Nr   r   r   r   r   r   r   r   r   r   r   )r1   row_multr  s    rn   test_row_multrL    sS     	AJJqOS6R<<S6Q;;S6R<<rm   c                      t        g dg dg dg      } | j                  ddd       | d   dk(  sJ | d	   d
k(  sJ | d   dk(  sJ y )Nr   rJ  r   r   r   r   r   r   r   r   r   r   r   r   r   )r1   row_addr  s    rn   test_row_addrQ    s[     	A IIa!S6Q;;S6Q;;S6Q;;rm   c                      t         d d D ]  } | j                  d      }|j                  ddd        | | g dg dg dg      k(  sJ | j                  d      dz  }d	|d
<   |j                  ddd        | | | g dg dg dg      k(  rJ  y )Nr   r   r   r   c                     | d|z  z   S r  rl   r   us     rn   ry   z!test_zip_row_op.<locals>.<lambda>      AaC rm   r5  r   r   r   r   r   r   c                     | d|z  z   S r  rl   rT  s     rn   ry   z!test_zip_row_op.<locals>.<lambda>  rV  rm   )r   r   r   )r   r   r   r	  )r   r5   
zip_row_op)r   r   s     rn   test_zip_row_oprZ    s    r{ &GGAJ	Q/0C""$ % % 	% % GGAJqL$	Q/0!C##% & & 	& &&rm   c                      t        g d      } t        g d      }t        g d      }| dvsJ | dvsJ | dk7  sJ | |k(  sJ | |k7  sJ y )Nr   )r   r   r   rl   )r   r   r   )r   rZ   r[   s      rn   test_issue_3950r\    sY    yAyAyARS6M66M66M6rm   c                  d    G d d      }  G d d      } |        } |       }t        g d      }||   dk(  sJ d||<   |d   dk(  sJ t        g dg d	g      }|||f   d
k(  sJ |d|f   d
k(  sJ ||df   d
k(  sJ d|||f<   |d   dk(  sJ d
|d|f<   |d   d
k(  sJ d||df<   |d   dk(  sJ y )Nc                       e Zd Zd Zy)test_issue_3981.<locals>.Index1c                      yr>  rl   selfs    rn   	__index__z)test_issue_3981.<locals>.Index1.__index__      rm   Nri   rj   rk   rc  rl   rm   rn   Index1r_        	rm   rf  c                       e Zd Zd Zy)test_issue_3981.<locals>.Index2c                      yr  rl   ra  s    rn   rc  z)test_issue_3981.<locals>.Index2.__index__  rd  rm   Nre  rl   rm   rn   Index2ri    rg  rm   rk  r   r   r   r   rJ  r   r   r   r   r   r   )rf  rk  index1index2r   s        rn   test_issue_3981rn    s      XFXFyAV9>>AfIQ4199	9%&AVV^!!!QY<1VQY<1AffnT7a<<AaiLT7a<<AfaiLT7a<<rm   c                       t        t        d      dg       t         fdt        d      D              sJ t         fdt        d      D              sJ t         fdt        d      D              sJ y )Nr   r   c              3   n   K   | ],  } j                          |   |   j                         k(   . y wrt   evalfr   rw   rZ   s     rn   r   ztest_evalf.<locals>.<genexpr>  s,     >wqwwy|qtzz|+>   25r   c              3   r   K   | ].  } j                   d       |   |   j                  d       k(   0 ywr   Nrq  rs  s     rn   r   ztest_evalf.<locals>.<genexpr>  s0     @!wqwwqz!}!

1-@   47c              3   r   K   | ].  } j                   d       |   |   j                  d       k(   0 ywrv  r{   rs  s     rn   r   ztest_evalf.<locals>.<genexpr>  s0     8!sqss1vayAaDFF1I%8rw  )r1   r   r   r   rZ   s   @rn   
test_evalfrz    s]    Q|A>U1X>>>>@uQx@@@@8uQx8888rm   c                  J   t        t        t        gt        t        gg      }  | j                         du sJ t        g dg dg      }  | j                         du sJ t        g dddt        dgg      }  | j                         du sJ t        dt        d	gg      }  | j                         du sJ t        g d
g      }  | j                         du sJ t        dgt        gd	gg      }  | j                         du sJ t        dgdgd	gg      }  | j                         du sJ y )NTr  r  Fr   r   r   r   r   r   r   )r1   r^   is_symbolicry  s    rn   test_is_symbolicr}    s#   AA A1==?d"""l+,A1==?e###q!Ql+,A1==?d"""Aq	{A1==?d"""	{A1==?e###aS1#A1==?d"""aS1#A1==?e###rm   c                      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 y )Nr   Tr   r   r   Fr   )r1   is_upperr>   ry  s    rn   test_is_upperr    se    	{A::aS1#A::aA::rm   c                      t        g dg      } | j                  du sJ t        dgdgdgg      } | j                  du sJ y )Nr   Fr   r   r   T)r1   is_lowerry  s    rn   test_is_lowerr    sH    	{A::aS1#A::rm   c                      t        ddg d      }  | j                         sJ t        ddgddgg      }  | j                         rJ t        g       }  | j                         sJ y )Nr   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r1   rc  ry  s    rn   test_is_nilpotentr    sg    q!EFA1>>AA Aq~~r
A1>>rm   c                  |   d\  } }t        | |      } |j                  d       dt        | |      z  }||k(  sJ |j                  |j                  cxk(  rdk(  sJ  J |j                  |j                  cxk(  rdk(  sJ  J |j
                  |j
                  cxk(  rdk(  sJ  J t        d      t        dd      k(  sJ t        d      t        dd      k(  sJ t        dd      t        dddgdz        k(  sJ t        dd      t        dddgdz        k(  sJ  |j                  d       |t        | |      k(  sJ y )N)r   r   r   r   r   r   r   r   )r>   fillr8   r   r   r   r1   )r|   r   rZ   r[   s       rn   test_zeros_ones_fillr    s7   DAqaA
AFFAK	DAJA6M666QVV q     66QVV q     77agg''''''8uQ{"""7d1aj   A;&As1u----1:1qc!e,,,,
AFF1Iarm   c                      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(  sJ y )Nr   r   )r>   r1   r   r   ry  s    rn   test_empty_zerosr  +  so    aA==aA66Q;;66Q;;aA66Q;;66Q;;rm   c                     t        t        dz  t        t        z  gt        t        t              z  t        t	        t              z  gg      }  | j
                  t              t        dt        z  t        gt        t              t	        t              gg      k(  sJ t        t        t         t        dz  gt        t              dt        z  t        t               z
  t        dt        z  z   gg      j                  t        t              t        t        t         t        gt        dt        gg      k(  sJ t        t        t              dz
  t        z  dt        z  t        t        z  z   t        t        z  gdt        z  t        t              t        t        t        dz               gg      j                  t        d      t        g dt        dt        d      gg      k(  sJ  | j                  t              t        t        dd      t        dz  z  t        t        dz  z  dz  gt        dz  t        t              z  dz  t        dz  t	        t              z  dz  gg      k(  sJ y )Nr   r   r   )r   r   r   r   )r1   r^   r_   r   r   r   r   limitr   r   r   r   ry  s    rn   test_issue_3749r  6  s   AqsaAh#a&123A166!91a3q63q6*:;<<<<	
QB1	Q1sA2wAaC(* ++05B<bS"Ar{+,- - - 
a&1*a1qsAqD*	
1c!fc#a!e*o&( )).q!	B3q6?+,- - - 1;;q>V	!Q1	a1fQh'	
Ac!fQ1SVA&%( ) ) ) )rm   c                      t        d      } | j                  dd       dD ]+  }| j                  |d       | j                  d      k(  r+J  y )	Nr   r   r   )ro  rx  c                     | dk(  S r   rl   r  s    rn   ry   z%test_inv_iszerofunc.<locals>.<lambda>J  s
    a rm   )rq  
iszerofuncr{  rp  )r5   col_swapr  )r   rq  s     rn   test_inv_iszerofuncr  F  sV    AAJJq!  uuF/?u@EEE  	    rm   c                  &   t        d      \  } }t        | t        |      z  | t        |      z  g      }t        | |g      }|j	                  |      }||j	                  |j
                        k(  sJ ||j
                  j	                  |      k(  sJ ||j
                  j	                  |j
                        k(  sJ |j
                  t        |j                  d         z  |z  }|j                  t              }|t        ddgd| dz  gg      k(  sJ y )Nrho,phir   r   r   )
r   r1   r   r   r  r  r5   r   r  r&   )rhophiXYr  r  s         rn   test_jacobian_metricsr  N  s    y!HCCHc#c(l+,ASzA	

1A

133q!!!!qss####	C
OAA	HAACF,----rm   c                  <   t        d      \  } }t        | t        |      z  | t        |      z  | dz  g      }t        | |g      }t        t        |      |  t        |      z  gt        |      | t        |      z  gd| z  dgg      }|j	                  |      |k(  sJ y )Nr  r   r   )r   r1   r   r   r  )r  r  r  r  r  s        rn   test_jacobian2r  [  s    y!HCCHc#c(lCF34ASzA	SC4C=!	SCCL!cEq! 	A
 ::a=Arm   c                     t        t        t        t        z   t        z         t        t        t        z   t        z         t        t        t        z   t        z         g      } t        t        t        t        g      }t        dd      D ]z  }t        dd      D ]i  }| d |d d f   }|d |d d f   }|j                  |      }|j                  |k(  sJ |j                  |k(  sJ t        |      D ]  }|d d |f   |k(  rJ  k | y Nr   r   )	r1   r   r^   r_   r`   r   r  r   r   )r  r  rw   rx   X_sliceY_slicer  ks           rn   test_issue_4564r  g  s    AEAIAEAIAEAI?@A1ayA1a[ *q! 	*AAhGAhG  )A66Q;;66Q;;1X *Aw')))*	**rm   c                      t        t        t        t        z   t        z         t        t        t        z   t        z         gt        t        t        z   t        z         t        t        t        z   t        z         gg       t        t         fd        dd d f    t        t        t        gt        t        gg      t        t         fd       t        t         fd       y )Nc                  V     j                  t        t        t        t        g            S rt   r  r1   r^   r_   r`   r  s   rn   ry   z(test_nonvectorJacobian.<locals>.<lambda>x  s    ajjAq	):; rm   r   c                  &     j                        S rt   )r  r  r  s   rn   ry   z(test_nonvectorJacobian.<locals>.<lambda>{  s    ajjm rm   c                  d     j                  t        t        t        gt        t        gg            S rt   r  r  s   rn   ry   z(test_nonvectorJacobian.<locals>.<lambda>|  s"    ajj1a&1a&0B)CD rm   )r1   r   r^   r_   r`   rN   	TypeErrorr  s   @@rn   test_nonvectorJacobianr  u  s    QUQYQUQY0QUQYQUQY02 	3A
9;<	!Q$AAA A
9+,
9DErm   c                      t        ddgddgg      } | j                         }|j                  dk(  sJ t        d      D ]  }||   |dz   k(  rJ  y Nr   r   r   r   )r1   vecr   r   )r   m_vecrw   s      rn   test_vecr    s]    AA AEEGE::??1X !Qx1q5   !rm   c                     t        ddgddgg      } | j                         }|j                  dk(  sJ t        d      D ]  }||   |dz   k(  rJ  | j                  d      }|d   dk(  sJ t        dt        t        t
        z   z  gt
        t        z  t        dz  z   dgg      } | j                  d      }|d   t
        t        z  t        dz  z   k(  sJ t        dt        t        t
        z   z  gt
        t        z  dgg      } | j                  dd      }|d   t
        t        z  k(  sJ t        t        d        t        t        d	        t        t        d
        t        t        d        y )Nr   r   r   F)diagonalr   )r  check_symmetryc                  :    t        ddgg      j                         S r  r1   vechrl   rm   rn   ry   ztest_vech.<locals>.<lambda>      v1vh/446 rm   c                  @    t        ddgddgg      j                         S r  r  rl   rm   rn   ry   ztest_vech.<locals>.<lambda>  !    v1v1v&67<<> rm   c                  :    t        ddgg      j                         S r  r  rl   rm   rn   ry   ztest_vech.<locals>.<lambda>  r  rm   c                  @    t        ddgddgg      j                         S r  r  rl   rm   rn   ry   ztest_vech.<locals>.<lambda>  r  rm   )	r1   r  r   r   r^   r_   rN   r'   r  )r   m_vechrw   s      rn   	test_vechr    sO   AA AVVXF;;!1X "ayAE!!!"VVUV#F!9>>Aq1uI1q!tQ01AVVUV#F!9!ad
"""Aq1uI1a)*AVVU5V9F!9!
:67
:>?
:67
:>?rm   c                       t        g d      t        g d      k(  sJ dddgg t        t         fd       t         d      t        g d      k(  sJ y )Nr   r   r   r   c                      t               S rt   )r4   r   s   rn   ry   ztest_diag.<locals>.<lambda>  s    tAw rm   F)strict)r4   r1   rN   r  r   s   @rn   	test_diagr    sK    	?fY////	
AsA
:'% F9$5555rm   c                  @   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      } | j                         | gk(  sJ  |j                         |gk(  sJ  |j                         |gk(  sJ y Nr   r   r   )r1   r^   r_   r`   get_diag_blocksrZ   r[   r\   s      rn   test_get_diag_blocks1r    s    AA AAA AAq	Aq!9q!Qi01A11#%%%11#%%%11#%%%rm   c                     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                         | ||gk(  sJ t	        | ||      j                         | ||gk(  sJ t	        | ||      j                         | ||gk(  sJ t	        |||      j                         |||gk(  sJ y r  )r1   r^   r_   r`   r4   r  r  s      rn   test_get_diag_blocks2r    s    AA AAA AAq	Aq!9q!Qi01A1a=((*q!Qi7771a=((*q!Qi7771a=((*q!Qi7771a=((*q!Qi777rm   c                     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      t	         | j
                          |j
                          |j
                               k(  sJ t	        | ||      }|j                  d      t	         | j
                          |j
                          |j
                               k(  sJ t	        | ||      }|j                  d      t	         | j
                          |j
                          |j
                               k(  sJ t	        | | || ||       }|j                  d      t	         | j
                          | j
                          |j
                          | j
                          |j
                          | j
                               k(  sJ |j                  dd      t	         | j
                  d       | j
                  d       |j
                  d       | j
                  d       |j
                  d       | j
                  d            k(  sJ y )	Nr   r   r   T)try_block_diagr{  )r  rq  rp  )r1   r^   r_   r`   r4   r  )rZ   r[   r\   r   s       rn   test_inv_blockr    s   AA AAA AAq	Aq!9q!Qi01AQ1A555%eaeeguquuw)HHHHQ1A555%eaeeguquuw)HHHHQ1A555%eaeeguquuw)HHHHQ1aAA555%%!%%'51557EAEEGUQUUW*> > > >55U53tUUQUU%0%!%%u2EUUQUU%0%!%%u2E8G G G Grm   c                  \   t        t        d        t        t        d        t        t	        d            t        d      k(  sJ t        t        d            t        d      k(  sJ t        t        d        t        t	        d            t        d      k(  sJ t        t        d            t        d      k(  sJ t        t        d        t        t	        d      t        d            t        dd      k(  sJ t        t        d        t        t        d        t        t        d	        y
)zg
    Check that matrix dimensions can be specified using any reasonable type
    (see issue 4614).
    c                      t        dd      S )Nr   r   r>   rl   rm   rn   ry   z$test_creation_args.<locals>.<lambda>  s    uQ| rm   c                      t        dddd      S Nr   r   r   r   r  rl   rm   rn   ry   z$test_creation_args.<locals>.<lambda>  s    eAq!Q/ rm   r   c                      t        d      S N      @r  rl   rm   rn   ry   z$test_creation_args.<locals>.<lambda>  s
    uRy rm   c                      t        d      S r  r5   rl   rm   rn   ry   z$test_creation_args.<locals>.<lambda>  s
    s2w rm   r   c                      t        d      S Nr   r   rl   rm   rn   ry   z$test_creation_args.<locals>.<lambda>  s
    fQi rm   c                      t        dd      S r   r   rl   rm   rn   ry   z$test_creation_args.<locals>.<lambda>  s    fQl rm   c                      t        ddgg      S r   r   rl   rm   rn   ry   z$test_creation_args.<locals>.<lambda>  s    vq1#h/ rm   N)rN   r  r  r>   ru   r   r5   r8   rl   rm   rn   test_creation_argsr    s    
 :+,
9/0Q=E!H$$$a(((
:()s1v;#a&   wqz?c!f$$$
:'A
#tAqz111
9'(
9*+
:/0rm   c                  j   t        ddg d      } | j                         rJ | j                         sJ | j                  d      sJ t        ddg d      } | j                         sJ t        ddd      } | j                         sJ | j                         sJ t        ddg d      } | t        ddd      k(  sJ t        ddt	        dd            } | j                         rJ | j                         sJ t        d	      } | j                         sJ t        d
      } | j                         sJ t        dddt
        dz  dt
        z  z   dz   t        t
        dz   dz  ddt        ddg	      } | j                         sJ | j                  d      rJ | j                         j                  d      sJ y )Nr   r   r   r   r   Fr%   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   ))r   r   r   r   )r   r   r   )r   r   r   r   )r1   is_diagonalis_symmetricr4   r>   r^   r_   r   r   s    rn   test_diagonal_symmetricalr    s   q!\"A}}>>>>5>)))q!\"A==??Q1A==??>>q!01AQ1q!U1a[!A~~==??'(A==??%&A==??q!aA!aQUQJ1aAFGA>>~~u~---88:""E"222rm   c                     t        ddt        z   gdt        z
  dgg      j                         sJ t        ddg d      j                         rJ j                         rJ t	        t
        fd       t        ddd      j                         \  } }| t        d      k(  sJ |k(  sJ t        ddg d      j                         sJ j                         sJ j                         \  } }| j                         z  | z  |k(  sJ t        ddg d      j                         sJ j                         sJ j                         \  } }| j                         z  | z  |k(  sJ | t        d      k(  sJ |k(  sJ t        ddg d      j                         sJ j                         \  } }| j                         z  | z  |k(  sJ t        ddg d	      j                         sJ j                         \  } }| j                         z  | z  |k(  sJ | D ]  }|j                         d   dk(  rJ  t        ddg d
      j                         sJ j                         sJ j                         \  } }| j                         z  | z  |k(  sJ | t        ddgddgg      k(  sJ t        ddg d      j                  d      rJ t	        t        fd       j                         sJ j                         \  } }| j                         z  | z  |k(  sJ t        ddg d      j                         rJ t	        t        fd       t        ddg d      j                         rJ t	        t        fd       t        d      \  }}}}t        dd||||g      j                         sJ j                         sJ y )Nr   r   r   r   r   r   r  r   r   c                  $     j                         S rt   rk  r   s   rn   ry   z&test_diagonalization.<locals>.<lambda>       rm   r  )r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r=  r   r  r   )r   r   r   r   Tc                  &     j                  d      S )NTr  r   s   rn   ry   z&test_diagonalization.<locals>.<lambda>1  s    d 3 rm   r   r   r   r   c                  $     j                         S rt   r  r   s   rn   ry   z&test_diagonalization.<locals>.<lambda>9       rm   )	r   r   r   r  r   r   r   r  r   c                  $     j                         S rt   r  r   s   rn   ry   z&test_diagonalization.<locals>.<lambda>=  r  rm   a b c d)r1   r
   rf  r  rN   r)   r4   rk  r5   r  as_numer_denomr  r(   r   )r  r1  rw   rZ   r[   r\   r]   r   s          @rn   test_diagonalizationr    s   AaC1Q3(#$A   q!+,A""$$$~~
!89 	Q1A]]_FQA;;6M6q!\"A>>   ]]_FQ557Q;?aq!\"A>>   ]]_FQ557Q;?aA;;6M6q!\"A   ]]_FQ557Q;?aq!12A   ]]_FQ557Q;?a *!!$)))* 	q!\"A==??   ]]_FQ557Q;?aAA'(((( 	q!]#A""4(((
;34   ]]_FQ557Q;?a 	q!\"A""$$$
;/0q!56A""$$$
;/0 #JAq!Qq!aAq\"A>>   rm   c                       t        ddgddgg         j                         du sJ d d<     j                         du sJ t        ddgddgg         j                          d d<   t        t         fd       y )Nr   r   Tr   Fc                  &      j                          S rt   r  ry  s   rn   ry   z"test_issue_15887.<locals>.<lambda>P  s     rm   )r?   rf  rk  rN   r(   ry  s   @rn   test_issue_15887r  F  s    QFQF+,A1 D(((AdG1 E)))QFQF+,AAMMOAdG
;/0rm   c                     t        ddg d      t        t        fd       t        ddg d      t        ddg d      } j                         \  }}| |k(  sJ | j	                         d   k(  sJ t        ddg d      t        ddg d	      } j                         \  }}| |k(  sJ t        ddg d
      t        ddg d      } j                         \  }}| |k(  sJ t        ddg d      t        ddg d      } j                         \  }}| |k(  sJ t        ddg d      t        ddg d      } j                         \  }}| |k(  sJ t        ddg d      t        ddg d      } j                         \  }}| |k(  sJ t        ddg d      j                         rJ t        ddg d      } j                         \  }}| |k(  sJ t        t        dd      t        dd      gt        dd      t        dd      gg      j                         \  }}|j                         D ]$  }t        |t              s|j                  dk(  r$J  y )Nr   r   r  c                  $     j                         S rt   )r  r   s   rn   ry   z"test_jordan_form.<locals>.<lambda>V  r  rm   )	r   r  r   r   ir   r   ir  )	r   r   r   r   r   r   r   r   r   r   	r   r   r   r=  r   r   r  r   r   )	r   r   r   r   r   r   r   r   r   )	r   r   r   r   r>  r   r   r&  )	r   r   r   r   r   r   r   r   r   )	r   r>  r   r   r_  r   r   r   )	r   r   r   r   r   r   r   r   r   r   )r   r   r  r   r   r   r   r   r   r   r  r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r&  r   r   r   r   r   r  r  r&  r   r   r   r   )r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   z1.0n   )	precisionz2.0z3.14159265358979323846264338327z4.0)
r1   rN   r)   r  rk  rf  r	   valuesr   _prec)Jmustr  r  termr   s       @rn   test_jordan_formr   S  ss   q!+,A
!89 	q!:;A1a56E==?DAqA::AMMOA&&&& 	q!23A 1a45E==?DAqA:: 	q!45A 1a78E==?DAqA:: 	q!34A1a45E==?DAqA::q!LMA1a  E
 ==?DAqA::q!LMA 1a ' (E ==?DAqA::q!JKA""$$$1aIJE==?DAqA:: 	u,eES.IJ8CH%PUadJefh 	iA==?DAq
 %dE"::$$$%rm   c            	      d   t        g dg dg dg dg      } ddt        z  z
  }ddt        z  z   }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      }| j                         \  }}||k(  s||k(  sJ t        ||z  |j	                         z        | k(  sJ y )	N)r   r   r   r   )r=  r   r   r   )r   r   r   r   )r   r   r=  r   r   r   r   r   )r1   r
   r  r%   r  )r   pqJmust1Jmust2r  r  s          rn   #test_jordan_form_complex_issue_9274r    s        " 	#A 	
AaCA	AaCAaAq\Aq\Aq\Aq\# $F aAq\Aq\Aq\Aq\# $F ==?DAq;!v+%%AaCK A%%%rm   c                      t        g dg dg dg dg      } | j                         \  }}|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 y )
Nr  r  )r   r   r   r   rj  r   r   r   r   r  r  r  r  )r1   r  r  s      rn   test_issue_10220r	    s     	A ==?DAq$$$& ' ' ' ' $$$$	& ' ' ' 'rm   c                     t        g dg dg dg dg      } | j                         \  }}|j                         t        t         t         dz  t        t        dz  gdt        z   ddt        z
  dgdt	        d       dz  t        dz  z
  dt	        d       dz  t        dz  z   gg d	g      k(  sJ |t        t         dddgdt         ddgddt        dgdddt        gg      k(  sJ y )
Nri  r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  )r1   r  r   r
   r   )r   r  r  s      rn   test_jordan_form_issue_15858r    s   	 	A
 ]]_FQ88:R1"Q$Q!A#6	aQQA6!A$q1Q3Q1a!A#66	!8 9 9 9 9
 
Q1	
QB1	
Aq!	
Aq!	    rm   c                  N   t        d      \  } }}t        | | z
  |dz  ||z   z  z   ||z  ||z   z  g||z  ||z   z  | |dz  ||z   z  z   gg      }|j                  t              }|t	        t        dz  || z  || z  z   d|z  |z  z   ||z   z  t        z  z   ||z  | z  ||z   z  z   t        d      k(  sJ t        |      t        u sJ t        ddgddgg      }|j                         |j                  t              cxk(  r t        t        dz  t        z
  dz
        k(  sJ  J t        ddgt        dgg      }|j                  t              }|j                  t        k7  sJ |j                         j                  |j                  t              t        dz  dt        z  z
  k(  sJ y )	Nz
UA K_i K_wr   zZZ(K_i,K_w,UA)r)  r   r   r   r   )
r   r1   r+  r^   r   r   r    genas_exprr  )UAK_iK_wr   r+  r  s         rn   test_Matrix_berkowitz_charpolyr    s   <(LBS#S!VS3Y//s3wc	7JKGS3Y/#Qc	8J1JKM 	NA zz!}HQTSVc"f_quSy039=a??C
C#I !*:	<< < < >X%%%AA A::<1::a=BHQTAX\,BBBBBBAA A	

1A55A::99;AEE1%A!333rm   c            
         t        d      } t        j                  d|       }|j                         t        t	        |       gg      k(  sJ t        j                  d|       }|j                         t        t	        |       t	        |       t	        |       dz  gdt	        |       t	        |       gddt	        |       gg      k(  sJ y )Nlamdar   r   r   r   )r   r1   jordan_block_eval_matrix_exp_jblockr   lr   s     rn   test_exp_jordan_blockr    s    wAAq!A$$&&3q6(*<<<<Aq!A$$&VSVSVAX&AA3q6N 	  rm   c            	         t        ddgddgg      } t        t        d      dt        d      z  dz  dt        d      z  dz  z   gdt        d      gg      }| j                         |k(  sJ t        |       |k(  sJ t        ddgddgg      } | j                         t        t        dgdt        gg      k(  sJ t        |       t        t        dgdt        gg      k(  sJ t        ddgddgg      } | j                         t        t        t        d      z  t         t	        d      z  gt        t	        d      z  t        t        d      z  gg      k(  sJ y )	Nr   r   r   r  r=  r   r   r   )r1   r   r   r   r   )r   m_exps     rn   test_expr    s<   AB !ASVRBZ\Ac!fHQJ67!SWFGE557eq6U??AA A557fq!fq!f-....q6VaVaV,----B!Q !A557fqQx!CF3aAh#a&5IJKKKKrm   c                     t        d      } t        j                  d|       j                         t        t	        |       gg      k(  sJ t        j                  d|       j                         t        t	        |       d| z  dd| dz  z  z  dd| dz  z  z  gdt	        |       d| z  dd| dz  z  z  gddt	        |       d| z  gdddt	        |       gg      k(  sJ t        g dg d	g d
g      t        t        fd       y )Nr  r   r   r   r   r   r   r   r   r  c                  $     j                         S rt   )r   r   s   rn   ry   ztest_log.<locals>.<lambda>  s     rm   )r   r1   r  _eval_matrix_log_jblockr   rN   r(   r  s    @rn   test_logr#    s   wAAq!A$$&&3q6(*<<<<Aq!A$$&Q1b!AqD&k1a1f:6CFAaCQq!tV-As1vqs#Aq#a&!		

 
 
 				A
 ;(rm   c                     t        t        t        fdf      } | j                  t              sJ | j                  t              rJ | j                  t
              sJ | j                  t        d      } | j                  t              rJ y )Nr  r   )r1   r^   r_   hasr`   r   r  r   s    rn   test_hasr&     se    A A558O8uuQx<55==	q!AuuQx<xrm   c            	          t        d      } t        dd| t        |       dz  t        |       dz  z   t        j
                  g      }t        |      \  }}}}|t        j
                  k(  sJ y )Nr^   r   r   r   )r   r1   r   r   r   r  r,   r^   columnpivot_offset	pivot_valpivot_assumed_nonzero
simplifieds         rn   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero1r.  *  sc     	sAAq1c!fai#a&!)3QVV<=F$V, ?L)2Jrm   c            
          t        d      } t        dd| t        |       dz  t        |       dz  z   | dz  z   t        |       dz  t        |       dz  z   g      }t	        |t
              \  }}}}|dk(  sJ y )Nr^   r   r   r   simpfunc)r   r1   r   r   r,   r-   r(  s         rn   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero2r2  6  s     	sAAqVQYs1vqy(A-VQYs1vqy(*+F
 	%Vi@ ?L)2J>>rm   c            
      f   t        d      } t        dd| t        |       dz  t        |       dz  z   | z   t        |       dz  t        |       dz  z   g      }t	        |t
              \  }}}}t        |      dk(  sJ |d   d   dk(  sJ |d   d   d| z   k(  sJ |d   d   dk(  sJ |d   d   dk(  sJ y )Nr^   r   r   r   r0  r   )r   r1   r   r   r,   r-   lenr(  s         rn   +test_find_reasonable_pivot_naive_simplifiesr5  E  s     	sAAqVQYs1vqy(*VQYs1vqy(*+F
 	%Vi@ ?L)2J z?aa=q   a=qs"""a=q   a=q   rm   c                  P    t        t        d        t        t        d        t        t        d        t        t        d        t        t        d        t        t        d        t        t        d        t        t
        d        t        t        d	        t        t        d
        t        t        d        t        t        d        t        t
        d        t        t        d        t        t        d        t        t        d        t        t        d        t        t        d        t        t        d        t        t        d        t        t        d        t        t        d        t        t
        d        t        t        d        t        t        d        t        t
        d        t        t        d        t        t
        d        t        t        d        t        t
        d        t        t
        d        t        t
        d         t        t        d!        t        t        d"        t        t        d#        t        t        d$        t        t        d%        t        t        d&        t        t        d'        t        t        d(        t        d)       t        t         fd*       t        g d+g      t        g d,g d-g d.g       t        t         fd/       t        g d,g d-g d.g       t        t         fd0       y )1Nc                  "    t        ddgdgg      S r   r   rl   rm   rn   ry   ztest_errors.<locals>.<lambda>X  s    v1vsm4 rm   c                  $    t        ddgg      d   S )Nr   r   )g333333?r   r   rl   rm   rn   ry   ztest_errors.<locals>.<lambda>Y      v1vh/7 rm   c                  $    t        ddgg      d   S )Nr   r   )r   g@r   rl   rm   rn   ry   ztest_errors.<locals>.<lambda>Z  r9  rm   c                      t        ddd      S )Nr   r   T)r\   r  )r9   rl   rm   rn   ry   ztest_errors.<locals>.<lambda>[  s    z!qDA rm   c                  <    t        ddg      j                  dd      S )Nr   r   r   r   )r1   r  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>\  s    vq!f~55a; rm   c                  ^    t        ddgddgg      j                  ddgt        ddg            S Nr   r   r   r   r   )r1   copyin_matrixrl   rm   rn   ry   ztest_errors.<locals>.<lambda>^  s1    AA'(661vvq!f~N rm   c                  X    t        ddgddgg      j                  ddgt                     S r>  )r1   copyin_listsetrl   rm   rn   ry   ztest_errors.<locals>.<lambda>_  s3    fq!fq!f%56BBADu rm   c                  @    t        g dg dg      j                         S )Nr   )r   r   r   r1   r  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>a  s    I0F)G)K)K)M rm   c                  \    t        ddddg      j                  t        ddgddgg            S r  )r1   row_joinrl   rm   rn   ry   ztest_errors.<locals>.<lambda>c  s0    q!aV$--fq!fq!f5E.FG rm   c                  X    t        ddg      j                  t        ddgddgg            S r  )r1   col_joinrl   rm   rn   ry   ztest_errors.<locals>.<lambda>e  s+    FAq6N33FQFQF;K4LM rm   c                  X    t        dg      j                  dt        ddgddgg            S r  )r1   
row_insertrl   rm   rn   ry   ztest_errors.<locals>.<lambda>f  8    vqc{55a!B1vA :   rm   c                  X    t        dg      j                  dt        ddgddgg            S r  )r1   
col_insertrl   rm   rn   ry   ztest_errors.<locals>.<lambda>h  rK  rm   c                  8    t        ddg      j                         S r   r7  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>j  s    A)=)=)? rm   c                  8    t        dg      j                  d      S r>  )r1   r  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>k  s    faSk33A6 rm   c                  D    t        ddgddgg      j                  dd      S Nr   r   r   r   r   )r1   minorrl   rm   rn   ry   ztest_errors.<locals>.<lambda>l  s%    v1v1v&67==aC rm   c                  D    t        ddgddgg      j                  dd      S rQ  )r1   minor_submatrixrl   rm   rn   ry   ztest_errors.<locals>.<lambda>m  s%    v1v1v&67GG1M rm   c                  :    t        g d      j                  d      S Nr   r   r1   crossrl   rm   rn   ry   ztest_errors.<locals>.<lambda>n  s    fY/55a8 rm   c                  :    t        g d      j                  d      S rV  r1   dotrl   rm   rn   ry   ztest_errors.<locals>.<lambda>o  s    fY/33A6 rm   c                  P    t        g d      j                  t        ddg            S )Nr   r   r   rZ  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>p  s    vi044VQF^D rm   c                  :    t        ddg      j                  g       S r   rZ  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>q  s    vq!f~11"5 rm   c                  :    t        ddg      j                  d      S )Nr   r   rZ   rZ  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>r  s    faVn005 rm   c                  >    t        ddg      j                  g d      S )Nr   r   r   rZ  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>s  s    vq!f~11)< rm   c                  8    t        g d      j                         S )Nr   )r1   r   rl   rm   rn   ry   ztest_errors.<locals>.<lambda>t  s    	):)>)>)@ rm   c                  @    t        ddgddgg      j                         S r  )r1   
normalizedrl   rm   rn   ry   ztest_errors.<locals>.<lambda>u  !    v1v1v&67BBD rm   c                  <    t        ddg      j                  d      S )Nr   r   znot a methodrp  rD  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>v  s    vq!f~111H rm   c                  8    t        ddg      j                         S r   r1   
inverse_GErl   rm   rn   ry   ztest_errors.<locals>.<lambda>w      A)B)B)D rm   c                  @    t        ddgddgg      j                         S r   rf  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>x  rc  rm   c                  8    t        ddg      j                         S r   r1   inverse_ADJrl   rm   rn   ry   ztest_errors.<locals>.<lambda>y  s    A)C)C)E rm   c                  @    t        ddgddgg      j                         S r   rk  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>z  s!    v1v1v&67CCE rm   c                  8    t        ddg      j                         S r   )r1   
inverse_LUrl   rm   rn   ry   ztest_errors.<locals>.<lambda>{  rh  rm   c                  8    t        ddg      j                         S r   r  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>|  s    A)D)D)F rm   c                  8    t        ddg      j                         S r   r1   r1  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>}  s    A););)= rm   c                  D    t        ddgddgg      j                  d      S )Nr   r   r   r   zNot a real methodrp  rr  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>  s'    AA'(,,4G,H rm   c                  P    t        g dg dg dg dg      j                  d      S )Nr  r  r  r  zNot functionr  rr  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>  s)    l)+ ,,/C>C,J rm   c                  P    t        g dg dg dg dg      j                  d      S )Nr  r  r  r  Fru  rr  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>  s)    l)+ ,,/C5C,A rm   c                  V    t        t        ddgddgg      t        ddgddgg            S r  r6   r1   rl   rm   rn   ry   ztest_errors.<locals>.<lambda>  s1    AA/0&1a&1a&9I2JK rm   c                  8    t        t        ddgddgg      g       S r  rx  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>  s    wv1v1v.>'?D rm   c                  2    t        t        d      dz  d      S )Nr^   r   rZ   )r6   r   rl   rm   rn   ry   ztest_errors.<locals>.<lambda>  s    wvc{A~s; rm   c                      t        d      d   S )Nr   )r   r   r  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>      s1vd| rm   c                      t        d      d   S )Nr   )r   r   r  rl   rm   rn   ry   ztest_errors.<locals>.<lambda>  r|  rm   r  c                  &     j                  d      S )Nzmethod=LU_decomposition())r1  r  s   rn   ry   ztest_errors.<locals>.<lambda>  s    quu%@A rm   )r   r   r   r   r   r   r   r   c                  (     j                  d      S )Ng@)rJ  r   Vs   rn   ry   ztest_errors.<locals>.<lambda>  s    q||C3 rm   c                  (     j                  d      S )Ng)rM  r  s   rn   ry   ztest_errors.<locals>.<lambda>  s    q||D!4 rm   )rN   r  r  r'   r  r)   r1   r  s   @@rn   test_errorsr  W  sI   
:45
:78
:78
:AB
:;<
:NP
9  
!MN
:GI
MO
:  
:  
!?@
967
:CD
:MN
989
967
:DE
:56
956
:<=
!@A
:DE
:HI
!DE
:DE
!EF
:EF
!DE
!FG
!=>
:HJ
:	KL :	BC :KM
:DE
:;<
:+,
:+,NOA
:AB~A	9i01A
:34	9i01A
:45rm   c                     t        t                     dk(  sJ t        t        ddgg            t        t        dgdgg            cxk(  rdk(  sJ  J t        t        ddd             t        t        ddd             cxk(  rdk(  sJ  J t        t        g dg dg            dk(  sJ t        dg      t        dgg      k(  sJ t               rJ t               t        g       k(  sJ y )	Nr   r   r   c                      yr   rl   rv   s     rn   ry   ztest_len.<locals>.<lambda>  r   rm   c                      yr   rl   rv   s     rn   ry   ztest_len.<locals>.<lambda>  r   rm   r   r   r   )r4  r1   rl   rm   rn   test_lenr    s    vx=Av1vh CaSz(:$;@q@@@@@vaN+,F1a()/-./ / / / /vy),-.!3331#;&1#-'''x<8vbz!!!rm   c            
      ,   t        ddt        ft        ddfddt        dz  ff      } | j                  t              t        t        dt        z  t        dz  dz  ft        t        z  dt        z  dt        z  fdt        z  dt        z  t        dz  dz  ff      k(  sJ | j                  t              t        t        dt        z  t        t        z  ft        dz  dz  dt        z  dt        z  fdt        z  dt        z  t        t        dz  z  ff      k(  sJ y )Nr   r   r   r   r   r   )r1   r^   r_   r   r   s    rn   test_integrater    s    Aq	Aq!9r1adm45A;;q>AaCAa 1Q3!QqS/BqD!A#q!tAv3FGHI I I;;q>AaC11Q!QqS1BqD!A#qAv3FGHI I Irm   c                      t        ddt        t              t        z  ft        ddfddt        dz  dz   ff      } | j	                  t        d      t        dt        ddfdf      k(  sJ y )	Nr   r   r   r   r   r   )r   r   r   )r   r   r   )r1   r   r^   r_   r  r   s    rn   
test_limitr    sa    As1vax 1a)b!QTAX->?@A771a=FI1ay*#EFFFFrm   c            	      4   t        ddt        ft        ddfddt        dz  dz   ff      } t        | j	                  t              t        |             sJ | j	                  t              t        dddddt        z  ff      k(  sJ | j	                  t              t        d	      k(  sJ t	        | t              t        dddddt        z  ff      k(  sJ t	        | t              t        d	      k(  sJ | j                         }t        |j	                  t              t        |            sJ |j	                  t              t        dddddt        z  ff      k(  sJ |j	                  t              t        d	      k(  sJ t	        |t              t        dddddt        z  ff      k(  sJ t	        |t              t        d	      k(  sJ | j	                  t        d
      t        | t        d
      k(  sJ t	        | t        d
      t        | t        d
      k(  sJ y )Nr   r   r   r   r   r   r   r   )r   r5  r   Fr  )	r?   r^   r_   r   r   r   r  r@   rW   )r   A_imms     rn   	test_diffr    s   Q1I1ay2q!Q$(2CDEAaffQia)))66!9*Iy1a1++NOOOO66!9*+LMMMM1:+Y	Aq!A#;,OPPPP1:+,MNNNNNNEejjmT%[111::a=0)YAqQRs1TUUUU::a=01RSSSSq>19i!QPQRSPS2UVVVVq>12STTTT66!e6$1u(MMMM1u%A)NNNNrm   c                     t        t        t        gt        t        gg      } | 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(  sJ t        | |       t        ddgddggddgddgggddgddggddgddgggg      k(  sJ | j                         }|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(  sJ t        ||      t        ddgddggddgddgggddgddggddgddgggg      k(  sJ | j                  t              t        ddgddgg      k(  sJ t        t        t        g      }| j                  |      t        j                  dddd      k(  sJ | 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(  sJ |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              }|j                  t        t        t        gg      t        |j                  t              |j                  t              |j                  t              g      k(  sJ |j                  t        t        t        gdf      t        |j                  t        d      |j                  t        t              |j                  t        t              g|j                  t        t              |j                  t        d      |j                  t        t              g|j                  t        t              |j                  t        t              |j                  t        d      gg      k(  sJ t        t              t        t              z  }|j                  t        t        gg      t        t!        t              t        t              z  t        t              t        t              z  g      k(  sJ |j                  t        t        t        ff      t        t!        t              t        t              z  t        t              t        t              z  g      k(  sJ |j                  t        t        t        ff      t        t        t               t        t              z  t!        t              t        t              z  g      k(  sJ |j                  t        t        fft        t        gg      t        t!        t              t        t              z  t        t               t        t              z  gt        t              t        t              z  t!        t              t        t              z  gg      k(  sJ |j                  t              j                  t              j                  t              |j                  t        t        t        ffd      d   k(  sJ |j                  t              j                  t              j                  t              |j                  t        t        t        ffd      d   k(  sJ |j                  t        t        t        ggt        t        t        ff      t        t        t        t        fD cg c]?  }t        t        t        fD cg c]"  }|j                  |      j                  |      $ c}A c}}      k(  sJ t        j
                  t#        t        t        gg            }	t%        |	t              sJ |	t#        ddgg      k(  sJ t        dz  j                  t#        t        t        gg            }	t%        |	t              sJ |	t#        dt        dz  z  dgg      k(  sJ y c c}w c c}}w )	Nr   r   r   )r   r   r   r  r   r   rW  )r?   r^   r_   r`   ra   r   rV   r  rZ   r@   r[   r>   r   r   r   r   r   r1   r   )
r   r  BdBr  fxyzexprrx   rw   ress
             rn   test_diff_by_matrixr    s    	QFQF+,A66!9!Q!Q 0Aq6Aq62BC1vPQSTvFVZ[]^Y_bcefagXhEijkkkk1:1a&1a&!1QFQF3C DAQRTUPVGW[\^_Z`cdfgbhYiFjkllllNNE::e!Q!Q(8Aq6Aq6:J'KPQSTvXY[\W]N^bcefagjkmnio`pMq&r ssssu1a&1a&)9QFQF;K(LQRTUPVYZ\]X^O_cdfgbhklnojpaqNr's!tttt 66!9*QFQF+;<<<<aV$A66!9Aq!Q////66!9!Q!Q 0Aq6Aq62BC1vPQSTvFVZ[]^Y_bcefagXhEijkkkk 
!Q	B88y   !qc
aS1#J/0000AQ1:D99q!Qi[!UDIIaL$))A,		RS+U%VVVV99q!Qi^$	1a$))Aq/499Q?;	1a$))Aq/499Q?;	1a$))Aq/499Q?;/ )    q6#a&=D99q!fX%QAAs1v(F"GGGG99Q!Q	"eSVCF]CF3q6M,J&KKKK99Q!Q	"ec!fWSV^SVCF],K&LLLL99q!fY!Q)USVCF]SVGCPQFN4SVYZ[V\]`ab]cVcehijeklopqlrerUs3t-uuuu 99Q<Q$$Q'499q!Qi\1+Eg+NNNN99Q<Q$$Q'499q!Qi\1+Eg+NNNN99q!Qi[Aq!9,/5noqrtumv9whiZ[]^`aYb:cTU499Q<;L;LQ;O:c9w3xxxx &&!Q!
"Cc/000&1a&""""a4++fq!fX&
'Cc/000&1QT61+'''' ;d9ws   ;^:'^5:^:5^:c            	           t        ddt        ft        ddfddt        dz  dz   ff       t        t         fd        t         d      t              t        dd	d
d
dt        z  ff      k(  sJ y )Nr   r   r   r   r   c                       j                   S rt   )nonexistantattributer   s   rn   ry   ztest_getattr.<locals>.<lambda>  s    1#9#9 rm   r   r   r   r   )r1   r^   r_   rN   r2  getattrr   s   @rn   test_getattrr    sl    Aq	Aq!9r1adQh&789A
>9:71fa FIy1a1++N$OOOOrm   c                     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                  rJ t	        dd	      } | j                  sJ y )
N)r   r   r   )r   r   r   r   r   )r   r   Fr  r   r   )r1   is_upper_hessenbergr  is_lower_hessenbergr>   r   s    rn   test_hessenbergr    s    	9i01A    	A    AeH  E)))	9i01A$$$$aA    rm   c            	      @   t        t        d        t        t        d        t        t        d        t        t        d        t        t        d        t        dt        z   dfdf      j                  d	
      t        t        dt        z         dgddgg      k(  sJ t        d      } | j                  d	
      }|t        ddgddt        d      z  t        z  gg      k(  sJ ||j                  z  | k(  sJ t        d      } | j                         }||j                  z  | k(  sJ |j                  sJ |t        g dg dg dg      k(  sJ t        ddt        z  ddt        z  z   fdt        z  ddt        z   fddt        z  z
  dt        z
  dff      } | j                         j                         t        dt        ddfdt        z
  ddff      k(  sJ t        t        d        t        t        d        t        t        d        t        t        d        t        t        d        t        dt        z   dfdf      j                  d	
      t        t        dt        z         dgddgg      k(  sJ t        d      } | j                  d	
      }|t        ddgddt        d      z  t        z  gg      k(  sJ ||j                  z  | k(  sJ t        d      } | j                         }||j                  z  | k(  sJ |j                  sJ |t        g dg dg dg      k(  sJ t        ddt        z  ddt        z  z   fdt        z  ddt        z   fddt        z  z
  dt        z
  dff      } | j                         t        dt        ddfdt        z
  ddff      k(  sJ y )Nc                  4    t        d      j                         S Nr   r1   choleskyrl   rm   rn   ry   ztest_cholesky.<locals>.<lambda>  s    )@)@)B rm   c                  4    t        d      j                         S Nr   )r   r   r  rl   rm   rn   ry   ztest_cholesky.<locals>.<lambda>      v&67@@B rm   c                  J    t        dt        z   dfdf      j                         S Nr   r   r   )r1   r
   r  rl   rm   rn   ry   ztest_cholesky.<locals>.<lambda>  s!    vAqz6&:;DDF rm   c                  4    t        d      j                         S N)r   r   )r   r   r  rl   rm   rn   ry   ztest_cholesky.<locals>.<lambda>  r  rm   c                  8    t        d      j                  d      S Nr  F	hermitianr  rl   rm   rn   ry   ztest_cholesky.<locals>.<lambda>  s    v&67@@5@Q rm   r   r   r   Fr  r   r  r   r   ))   r   r>  )r   r   r   )r>  r   r  r  )r   r   r   )r   r   r   r   r  r   r  r  r   c                  4    t        d      j                         S r  r2   r  rl   rm   rn   ry   ztest_cholesky.<locals>.<lambda>!  s    f)=)F)F)H rm   c                  4    t        d      j                         S r  r  rl   rm   rn   ry   ztest_cholesky.<locals>.<lambda>"      |,<=FFH rm   c                  J    t        dt        z   dfdf      j                         S r  )r2   r
   r  rl   rm   rn   ry   ztest_cholesky.<locals>.<lambda>#  s!    |a!eQZ,@AJJL rm   c                  4    t        d      j                         S r  r  rl   rm   rn   ry   ztest_cholesky.<locals>.<lambda>$  r  rm   c                  8    t        d      j                  d      S r  r  rl   rm   rn   ry   ztest_cholesky.<locals>.<lambda>%  s    |,<=FFQVFW rm   )rN   r)   r  r1   r
   r  r   r  r  r   r2   )r   r  s     rn   test_choleskyr    sk   
!BC
:BC
:FG
:BC
:QRAE1:v&'0050AV	a!ea1a&M" F# # # # A	

U
#AAAd1gIaK 012222QSS5A::78A	

Aqss7a<<:::	9j9::::BqD!ac'"QqS!R!V$4q1Q3wQ6KLMA::< FI1ay1q5!Q-+P$QQQQ
!HI
:HI
:LM
:HI
:WX!a%V,-666G6	a!ea1a&S" L# # # #%&A	

U
#AAAd1gIaK 012222QSS5A::=>A	

Aqss7a<<:::	9j9::::q"Q$AaC(1Q326*:Q1Wb1fb<QRSA::<69q!Qi!a%A"GHHHHrm   c            	         t        dd      } t        t        |       t        |       g      }t	        |j                  d            dk(  sJ |j                  d      t        t        |       dz  t        |       dz  z   t        dd            k(  sJ t        dt        dd      gg      }|j                         t        d	t        d
d      z   t        j                        k(  sJ |j                  t              t        |      k(  sJ |j                  t               t        |      k(  sJ t        ddgddgg      }|j                  d      dk(  sJ |j                  d      dk(  sJ |j                  d      dk(  sJ t        d      j                  d      t        d      j                  d      cxk(  rdk(  sJ  J |j                  t              dk(  sJ t        dt        t        g| t        j                  t         gg      }|j                  d      t!        t        dd      dt#        t              dz  z  z   t        dz  z   | dz  z         k(  sJ t        g dddt        dd      gg      }|j                  d      t!        t        dd      t!        d      dz  z         k(  sJ |j                  d      t        j$                  u sJ |j                  d      t!        d      dz  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 ]  }t)        d      j                  |      t        j$                  u sJ |D ]H  }	|D ]A  }
|	j                  |      |
j                  |      z   |	|
z   j                  |      z
  }|dk\  rAJ  J ||||fD ]D  }t+        ||z  j                  |      t#        |      |j                  |      z  z
        }|dk(  rDJ   t        dddt&        z  z
  dg      }t        t        j                  dt&        z  dg      }t        g d      }t        ddt&        g      }t        t-        d      t        dd      dg      }|||||g}t        dd      }ddddt        j.                  t        j0                  t        fD ]  }|dkD  r.t        g d      j                  |      t        j$                  u sJ |dk\  rf|D ]a  }	|D ]Z  }
|	j                  |      |
j                  |      z   |	|
z   j                  |      z
  }t+        |dk\        t        j2                  u rZJ  c |ddddt        j.                  t        j0                  fv s|D ]D  }	t+        ||	z  j                  |      t#        |      |	j                  |      z  z
        }|dk(  rDJ   t        ddg d      }|j                  d      dk(  sJ y )Nr^   Tr  r   r   r   r   r   r  r   r   r  r   	frobeniusfro%   )r   r   r   r  i  r   iI3 r   alpha)r  r   r  r   )r   r   r   g      Y@r   )	r   r   r   r  r   r   r   r   r   )r   r1   r   r   r&   normr   r   r   r  r   maxr  r5   r_   r   r   r   r  r
   r>   r%   r   InfinityNegativeInfinitytrue)r^   r   r   r  r+  r1  r  r  orderr  r  difr   rZ   r[   r\   r]   es                     rn   test_matrix_normr  5  s    	sAAA AAFF1I!###66":SVRZ#a&"*4hq"oFFFF 	HQN#$%A668s2A.777766":Q662#;#a&    	AA A66!9>>66":??66+!###r7<<?c"gll2.3!3333366":?? 	Aq	Aqvvs+,-AFF5M8B?Qs1vqy[02q581a4?@A B A 	
Q8B?345A66!9Xc1-UA=>>>>66":66+$s)A+---
 	AA AAQ !AQB!Q !AAB !A	
Aq!A7&E Qx}}U#qvv--- 	"A "vve}qvve}4ULL'(q!"	" Q1 	AE!G>>%0J./ 0C!8O8	$ 	1qs7B A!Q A|A1ayAhq#.23A	
Aq!QA7&EQB

A,>,>C  19)$))%0AFF:::A: 8 8A66%=166%=8QU+,C#C1H-77788 Q2r1::q/A/ABB  a~~e4Z!&&-/ 1 2axx  & 	q!23A66!9??rm   c                     t        dd      t        d      } d| d<   t        dd      | d<   | j                         d	k(  sJ | d
<   | j                         t	        dt                    t        t        dd      t                    z  k(  sJ t        t              t              gt               t              gg      }|j                         t        fdt        dd      t        j                  t        dd      t        dz  t        t        t        dd      z  fD              sJ t        g       j                         dk(  sJ y )Nr^   Tr  r   r   r   r   r   r   r   r   c              3      K   | ]<  }t        d       j                  j                  |      j                                > yw)      ?N)r	   
epsilon_eqr  rr  )r   valMcr^   s     rn   r   z(test_condition_number.<locals>.<genexpr>  s9      QuRy##BGGAsO$9$9$;< Qs   AAr   r   r   r   r   )r   r5   r   condition_numberr   r   r   r1   r   r   r   r   r  r   )r   r   r  r^   s     @@rn   test_condition_numberr    s-   sAAAAdGq"oAdG3&&&AdG3r3q6?S!R#a&5Q#QQQQQQ CF7CF"345A	
			B Q	!Q!R"Q$Bx1~<MOQ Q Q Q ":&&(A---rm   c                      t        d      } t        d      }| | d d d d f   k(  sJ | | d d d d f   k7  rJ | |k(  rJ | |k7  sJ | dk7  sJ | dk(  rJ t        d      }t        d      }||k(  sJ ||k7  rJ y )N)r   rJ  r   r   r   ))r   r   r   )r   r   r   )r   r   r   r   )r5  r   r   )r1   r2   )r   r  r+  r1  s       rn   test_equalityr    s    01A01A!Q$<<AadG|Av:6M67N7Bw; 	67A01A6M6Av:vrm   c                      t        d      j                  t        g dg            t        g dg dg dg dg      k(  sJ y )Nr   )r   r   r   r5  r   r   )r5   rH  r1   rl   rm   rn   test_col_joinr    s@    q6??69+./	 	  rm   c                      t        g dg      } t        dd      D ]^  }g d}|j                  |d       t        t	        d      j                  ||       j                  d      j                               |k(  r^J  y )Nr   r   r   r=  r   r5  r   r   r   )r1   r   insertrJ   r5   rJ  rE  r  )r4rw   r  s      rn   test_row_insertr    so    		B2q\ F	As1v((B/33A6==?@AEEEFrm   c                      t        g d      } t        dd      D ]^  }g d}|j                  |d       t        t	        d      j                  ||       j                  d      j                               |k(  r^J  y )Nr  r=  r   r   r   r   r   )r1   r   r  rJ   r>   rM  rD  r  )c4rw   r  s      rn   test_col_insertr    sm    			B2q\ H	AuQx**1b155a8??ABaGGGHrm   c                  8   t        ddg      j                         t        t        dd      t        dd      g      k(  sJ t        g d      j                         t        g d      k(  sJ t        g d      } | j                  d       t        g d      k(  sJ y )Nr   r   r   r   )r   r   g0.++c                 >     | j                   dd      j                  S )Nr   T)r|   chop)rr  is_zeror  s    rn   ry   z!test_normalized.<locals>.<lambda>  s    2D199 rm   ru  )r1   rb  r   r   s    rn   test_normalizedr    s    1a&>$$&AA/01 1 1 )'')VI->>>> 	}A<<9  			  rm   c                  H    t        d       dk(  sJ t        d       dk(  sJ y )Nc                  4    t        d      j                         S r  r5   print_nonzerorl   rm   rn   ry   z$test_print_nonzero.<locals>.<lambda>  s    3q6//1 rm   z[X  ]
[ X ]
[  X]
c                  6    t        d      j                  d      S )Nr   .r  rl   rm   rn   ry   z$test_print_nonzero.<locals>.<lambda>  s    3q6//4 rm   z[.  ]
[ . ]
[  .]
)rK   rl   rm   rn   test_print_nonzeror    s8    12     45     rm   c                     t        j                  d      t        d      k(  sJ t        j                  d      t        d      k(  sJ t        dd      t        dddgdz        k(  sJ t        ddgddgg      } t        ddgddgg      }t        D ]v  }|j                  d      }| |k(  sJ | t        d|      k(  sJ t        |      |k(  sJ |j                  d      }||k(  sJ |t        d|      k(  sJ t        |      |k(  rvJ  y )Nr   r   r   r   r   r   r  )r1   r5   r>   r8   r   r   )rw   r`   r   r   s       rn   test_zeros_eyer    s   ::a=CF"""<<?eAh&&&1:1qc"f----AA AAA A GGAJAvvCsO###Aw#~~IIaLAvvE!%%%%Aw#~~rm   c                     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(  sJ t        t        dgddgg      j                  d k(  sJ t        t        dgddgg      j                  d k(  sJ t        t        dgddgg      j                  d k(  sJ t        t        dgddgg      j                  dk(  sJ t        dd      } t        | dgddgg      j                  dk(  sJ y )	Nr   r   r   r   FrZ   T)nonzero)	r1   is_zero_matrixr>   r5   r^   r2   r/   r0   r   ry  s    rn   test_is_zeror    sL   8""""Aq6Aq6"#2222A;%%%%1v$$$$Aq6Aq6"#22d:::!Q!Q()88D@@@QFQF+,;;tCCC 1a&1a&!12AATIIIAq6Aq6"#22e;;;sD!AAq6Aq6"#22e;;;rm   c                  J   t         dz  } t        |       }t        |        }t        |       }t        |        }t        |       }t        |        }||z  t	        d      z  t	        d      k(  sJ ||z  t	        d      z  t	        d      k(  sJ ||z  t	        d      z  t	        d      k(  sJ |j                         ddt        |       z  z   k(  sJ |j                         ddt        |       z  z   k(  sJ |j                         ddt        |       z  z   k(  sJ t        d      t	        d      k(  sJ t        d      t	        d      k(  sJ t        d      t	        d      k(  sJ t        j                  g dt         dz        }t        j                  g dt         dz        }t        j                  g dt         dz        }	t        t          dz        |j                         k(  sJ t        t          dz        |j                         k(  sJ t        t          dz        |	j                         k(  sJ t        t         dz        |j                         k(  sJ t        t         dz        |j                         k(  sJ t        t         dz        |	j                         k(  sJ y )Nr   r   r   r   r5  r   r   )r   r<   r;   r:   r5   r8  r   rY   from_axis_angleto_rotation_matrixrC   rD   rE   )
thetar3_plusr3_minusr2_plusr2_minusr1_plusr1_minusq1q2q3s
             rn   test_rotation_matricesr  	  sf   qDEG% HG% HG% HGCF"c!f,,,GCF"c!f,,,GCF"c!f,,, ==?a!CJ,....==?a!CJ,....==?a!CJ,.... Q<3q6!!!Q<3q6!!!Q<3q6!!! 
	#	#IrAv	6B		#	#IrAv	6B		#	#IrAv	6BrTAX""7"7"9999rTAX""7"7"9999rTAX""7"7"99992"b&;&;&====2"b&;&;&====2"b&;&;&====rm   c                     t        t        d      d         dk(  sJ t        t        d            t        d      k(  sJ t        t        d        t        t        d            dk(  sJ t        t        d            dk(  sJ y )Nvectorr   z	vector[4]r]   c                      t        d      d   S )Nr]   r   r*   rl   rm   rn   ry   z%test_DeferredVector.<locals>.<lambda>+	  s    ~c226 rm   testzDeferredVector('test'))strr+   r   rN   r  reprrl   rm   rn   test_DeferredVectorr  (	  sx    ~h'*+{:::>#&'>#+>>>>
:67~c"#s***v&'+CCCCrm   c                  0    t        t        d            rJ y )Nr  )rL   r+   rl   rm   rn    test_DeferredVector_not_iterabler  /	  s    s+,,,,rm   c                  &    t        t        d        y )Nc                  *    t        t        d            S )Nr  )r1   r+   rl   rm   rn   ry   z,test_DeferredVector_Matrix.<locals>.<lambda>3	  s    f^C%89 rm   )rN   r  rl   rm   rn   test_DeferredVector_Matrixr
  2	  s    
99:rm   c            
         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z   | d      dz  g      gk(  sJ t        |j                  |j                  g      t        ddddg      t        dd | d      dz   | d      dz  g      gk(  sJ t        t        ddg      t        ddg      gd      t        dt	        d      z  dz  t	        d      dz  g      t        t	        d       dz  dt	        d      z  dz  g      gk(  sJ t        t        dg            }t        |      t        dgg      gk(  sJ y )Nr   r   r   r   r   Tr   )r   r1   r.   r  r   r#   )r  r  r  r  s       rn   test_GramSchmidtr  5	  s}   A	1q!f	B	1q!f	BBx 	1q!f	vaQqT!VQrU1W,=>?@ @ @bdd|$	1q!f	vaQqT!VQrU1W,=>?@ @ @ 1v1v7>$r(
2tBx{+,b	"aRjm,-C/ / / / 	&!+Aq>fqcUm_,,,rm   c                  T    t        g dd      dk(  sJ t        g ddd      dk(  sJ y )Nr  r   r   F)zero)r3   rl   rm   rn   test_casoratianr  F	  s.    lA&!+++lAE2a777rm   c                      t               t        dd      z  j                  dk(  sJ t        dd      t        dd      z  t        dd      k(  sJ t        dd      t        dd      z  t               k(  sJ y )Nr   r   )r   r   )r1   r>   r   rl   rm   rn   test_zero_dimension_multiplyr  K	  si    HU1a[ ''6111A;uQ{"eAqk111A;uQ{"fh...rm   c                  v    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(  sJ t        t         fd       t        t         fd       y )Nr   r   r   r   r   c                       dd d f   S r  rl   r   s   rn   ry   z'test_slice_issue_2884.<locals>.<lambda>W	  s    qAw rm   c                       d   S )Nr  rl   r   s   rn   ry   z'test_slice_issue_2884.<locals>.<lambda>X	  s    qw rm   )r1   r   r  rN   r  r   s   @rn   test_slice_issue_2884r  Q	  s    q!U1XAQT7fq!fX&&&&RU8v1vh''''QT7fq!fX&(((((QU8v1vh')))))
:'
:'rm   c                      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 y )Nr   r   r   r   r   )r>   r   r1   rl   rm   rn   test_slice_issue_3401r  [	  sK    A;q"u##v---A;q!tq!R 0000rm   c                     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(  sJ | ddd f   t        ddgg      k(  sJ t        dd	gg      | ddd f<   | dd d f   t        g d
g      k(  sJ ddgg| ddd f<   | dd d f   t        g dg      k(  sJ d| d<   | d d d df   t        g d      k(  sJ g d| d<   | d d df   t        g d      k(  sJ t        g d      | d<   | d d df   t        g d      k(  sJ t        g d      | d<   | d d df   t        g d      k(  sJ y )Nr   r   r   r   r   rA  r   r   r   )r   r   r   +   )r   rA  r     r   )r  r   r   rN  )r>   r1   r2   )r  s    rn   test_copyinr  `	  s   aAAaDQT7fY''''Q4199Q7qc>>AdGT7b==QU8vAwi((((1vhAaeHQT7fi[))))RzAaeHQT7fk]++++AdGQU8vj))))AdGQT7fY''''YAdGQT7fY''''9%AdGQT7fY''''rm   c                  &    t        ddgddgg      j                         t        ddgddgg      dfk(  sJ t        t        d        t        g dt        ddgdt        dgg       t         j                         d          j                  k7  sJ  j                         d   t        d      k7  sJ  j                  t        	      d   t        d      k7  sJ t        t         fd
       t        t         fd       t        t         fd       y )Nr   r   r   )r   c                  @    t        ddgddgg      j                         S r   rD  rl   rm   rn   ry   z'test_invertible_check.<locals>.<lambda>{	  s!    v1v1v&67;;= rm   )r   r   r   r   r   r  c                  (     j                  d      S )Nr{  rp  r  r   s   rn   ry   z'test_invertible_check.<locals>.<lambda>	  s    quuEu2 rm   c                  (     j                  d      S )Nro  rp  r  r   s   rn   ry   z'test_invertible_check.<locals>.<lambda>	      quuDu1 rm   c                  (     j                  d      S )Nrx  rp  r  r   s   rn   ry   z'test_invertible_check.<locals>.<lambda>	  r!  rm   )	r1   rA  rN   r  r^   r4  r   r5   r$   r   s   @rn   test_invertible_checkr#  w	  s     Aq6Aq6"#((*v1v1v6F/G.NNNN
:=>
a!
a 	A
 qvvx{qvv%%% 668A;#a&   6686$Q'3q6111
:23
:12
:12rm   c                      t        d      \  } }| |z  }|j                  | t        g d            t        g d      |z  k(  sJ y )Nzx, y)r   r   r   )r   r  r1   )r^   r_   r  s      rn   test_issue_3959r%  	  s@    6?DAq	!A66!VI&'6)+<Q+>>>>rm   c                  B    t        t        ddgddgg            dk(  sJ y )Nr   r   r   r   zMatrix([[1, 2], [3, 4]]))r  r1   rl   rm   rn   test_issue_5964r'  	  s(    v1v1v&'(,FFFFrm   c                  p    t        d      \  } }t        t        | d|z  g|dz  | dz   gg            dk(  sJ y )Nx yr   r   z'Matrix([
[   x,   2*y],
[y**2, x + 3]]))r   r"   r1   )r^   r_   s     rn   test_issue_7604r*  	  sG    5>DAqAaC1a4Q-01234 4 4rm   c            
          t        d      j                  sJ t        d      j                         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                  sJ t        ddt        d            j                  rJ t        ddddd      j                  rJ t        dddddddd      j                  rJ y )	Nr   r5  r   )r   r   r  r   r   )r   r   )r   r   r  r   rO  )r5   is_Identityr  r>   r8   r1   r2   r   rl   rm   rn   test_is_Identityr-  	  s    q6q6 ,,,,Qx####Aw""""yk"....!AQa89EEEEAaq*6666Aa!34@@@@Aa!1A!NO[[[[[rm   c                     t        dd      j                  t        dd            dk(  sJ t        dd      j                  g d      dk(  sJ t        g d      j                  t        g d            dk(  sJ t        dddt        z  g      j                  t        t        ddt        z  g            dt        z   k(  sJ t        dddt        z  g      j                  t        t        ddt        z  g      d	      dt        z   k(  sJ t        dddt        z  g      j                  t        t        ddt        z  g      d
	      dt        z   k(  sJ t        dddt        z  g      j                  t        t        ddt        z  g      d
d      dt        z
  k(  sJ t        dddt        z  g      j                  t        ddt        z  dg      d
d      ddt        z  z   k(  sJ t        dddt        z  g      j                  t        ddt        z  dg      d
d      ddt        z  z
  k(  sJ t        t        dt        z  g      j                  t        t        dt        z  g      dd      dk(  sJ t        t        dt        z  g      j                  t        t        dt        z  g      d      dk(  sJ t	        t
        d        y )Nr   r   rN  r   r  r   r>  Fr  Tr  physicsr  conjugate_conventionr   r   r   rightr   left)r1  c                  V    t        ddg      j                  t        ddg      dd      S )Nr   r   r   r   Tr  r0  rZ  rl   rm   rn   ry   ztest_dot.<locals>.<lambda>	  s)    vq!f~11&!Q.Dgm1n rm   )r8   r[  r1   r
   rN   r  rl   rm   rn   test_dotr5  	  s   1:>>$q!*%***1:>>)$))))  	!23r9991a1+""61a1+#6726AAA1a1+""61a1+#6%"HBQRFRRR1a1+""61a1+#6$"G2PQ6QQQ1a1+""61a1+#6$]f"gkmpqkqqqq1a1+""61ac1+#6$]d"eijmnopmpipppp1a1+""61ac1+#6$]c"dhilmnolohoooo1ac(1Q3x 0EX^_ceeee1ac(1Q3x 0vNRSSSS
:norm   c            	         t        dd      \  } }}}}}t        d|||f| d|| f| | d| f| ||  dff      }t        d|  | | f| d|| f|| d|f||| dff      }|j                         j                  |      sJ t	        d      j                         j                  t        d            sJ |j                         j                         j                  |       sJ y )NzB_x B_y B_z E_x E_y E_zTr  r   r   )r   r1   dualequalsr5   r>   )B_xB_yB_zE_xE_yE_zFFds           rn   	test_dualrA  	  s   #*!$. Cc3ScC 
!cC4 
tC 
cTa 	 	A 
sdSD3$	S3$	sdq3	sSDQ	 
B 668??2q6;;=a)))668==?!!1"%%%rm   c                  ,   t        ddg      j                         du sJ t        dddt        dz  dt        z  z   dz   t        t        dz   dz   dt        t        z  t         t         t        z  dg	      } | j                         du sJ | j                  d      J | j                  d       J | d	    | d	<   | j                         J | d	    | d	<   | j	                         } | j                  d      du sJ d| d
<   | j                         du sJ y )Nr   r   Fr   r   Tr  c                     | S rt   rl   r  s    rn   ry   z%test_anti_symmetric.<locals>.<lambda>	  s    ! rm   r   r   )r1   is_anti_symmetricr^   r_   r   r   s    rn   test_anti_symmetricrE  	  s/   1a&>++-666q!aA!aa!eaZKAaC!aRT1MNA D(((.6664<<< whAdG (((whAdG	
A.$666AdG E)))rm   c                     t        d      } | j                  d      \  }}||j                  z  |j                  |z  cxk(  rt        |j                        k(  sJ  J | j                  dd      \  }}||j                  z  |j                  |z  cxk(  rt        |j                        k(  sJ  J ||z  |j                         z  | k(  sJ y )N)r   r   T)	normalize)rG  sort)r1   rk  r  r5   r   r  )r   r  rU   s      rn   #test_normalize_sort_diogonalizationrI  	  s     A==4=(DAqQSS5ACCE(S[(((((==4d=3DAqQSS5ACCE(S[(((((Q3quuw;!rm   c                  &    t        t        d        y )Nc                  6    t        g dt        ddg       g      S )Nr   r   r   r   rl   rm   rn   ry   z!test_issue_5321.<locals>.<lambda>	  s    vy&Ar2B&CD rm   )rN   r  rl   rm   rn   test_issue_5321rL  	  s    
:DErm   c            	         t        j                  t        d      dt        d      z        t        g dg dg      k(  sJ t        j                  t        d      dt        d      z        t        ddgddgddgddgg      k(  sJ t        } | j                   | t        d             | dt        d      z              t        g dg dg      k(  sJ y )Nr   )r   r   r   r   )r   r   r   r   r   r   )r1   hstackr5   vstackr2   r  s    rn   test_issue_5320rP  	  s    ==Q3q6*f6 /    ==Q3q6*f	
A	
A	
A	
A	6 /    C::c#a&k3qQx=1V= 6   rm   c                      t        dgg      } t        |       }t        j                  ||       t        ddgg      k(  sJ t        j                  ||       t        dgdgg      k(  sJ y r>  )r1   r   rN  rO  )r   AIms     rn   test_issue_11944rS  	  sb    uA
!*C==a FQF8$4444==a FQC!:$6666rm   c                     g d} g d}t        g d      }|j                  }fd}t        D ]   |       } |      } ||j                  |      |        ||j                  |j                        |        ||j                  j                  |j                        |        ||j                  j                  |      |        t	        t
        d        y )Nr   r   )r  r   r  c                 4    || k(  sJ t        |       k(  sJ y rt   )r   )r   r  r   s     rn   r  ztest_cross.<locals>.test	
  s    axxAw#~~rm   c                  X    t        ddddg      j                  t        ddddg            S r   rW  rl   rm   rn   ry   ztest_cross.<locals>.<lambda>
  s/    q!aV""6!QA#78 rm   )r1   r  r   rX  rN   r'   )rZ   r[   rE  rD  r  r   r  r   s          @rn   
test_crossrW  
  s    AA

C
%%C   FFQWWQZQWWQSS\3QSSYYqss^S!QSSYYq\3  : 9 :rm   c                  @   t        t        t        t        g      } t        t        t
        t        g      }| j                         |z  | j                  |      k(  sJ | j                         j                         sJ | j                         j                         | k(  sJ y rt   )r1   r^   r_   r`   rZ   r[   r\   hatrX  rD  vee)v1v2s     rn   test_hat_veer]  
  st    	Aq		B	Aq		B668b=BHHRL(((668%%'''668<<>Rrm   c                  &   t         dd  D ]V  } | j                  d      | j                  d      h}t        |      dk(  r#|j                         | j                  d      k(  rVJ  t         d d D ]#  } t	        | j                  d      t
              s#J  y )Nr  r   r   )r   r5   r4  popr   r   )r   r  s     rn   	test_hashr`  
  s    rs| 5WWQZ$1v{quuw#''!*4445 r{ 4cggaj(3334rm   c                  >     t         d    t        t         fd       y )Nr   c                  8    t         j                  d            S r>  )hashr5   r  s   rn   ry   z!test_issue_3979.<locals>.<lambda>+
  s    4
#3 rm   )r   rN   r2  r  s   @rn   test_issue_3979rd  &
  s     !*C
>34rm   c                      dt         gddgg} t        ddgt          dgg      }t        D ]  }| ||       j                         k(  rJ  y Nr   r   )r
   r1   r   adjoint)r  r  r   s      rn   test_adjointrh  .
  sW    q6Aq6
C
1a&A2q'"
#C )c#h&&(((()rm   c                      t        t        t        t              dz  t	        t              dz  z   gg            t        dgg      k(  sJ y )Nr   r   )r%   r/   r   r^   r   rl   rm   rn   test_simplify_immutablerj  4
  sE    Oc!fai#a&!)&;%<$=>?#aSE*+ + +rm   c                      t        dt              \  t        ddfd      } t        ddfd      }|j                        }|| k(  sJ y )NzF, Gr  r   c                      | |z         S rt   rl   )rw   rx   Gs     rn   ry   ztest_replace.<locals>.<lambda>:
      !AaC& rm   c                      | |z         S rt   rl   )rw   rx   r?  s     rn   ry   ztest_replace.<locals>.<lambda>;
  rn  rm   )r   r   r1   replace)Kr   Nr?  rm  s      @@rn   test_replacers  8
  sK    6x(DAqq!()Aq!()A			!QA6M6rm   c                     t        ddgt        ddt        z  z
  gg      } | j                         t        j                  t        d      t        j
                  t        hk(  sJ | j                  t              t        hk(  sJ y r   )r1   r^   atomsr   r  NegativeOner   r   s    rn   
test_atomsrw  @
  sb    AA!G%&A779qtAMM15555776?qc!!!rm   c            	        	 t        t        t        gt        t        gg      } t        | j                  d            t        | j                               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 ]f  }|j                  d      }||z  }||z  }t        ||z        |k(  sJ t        ||z        |k(  sJ |j                  |k(  sJ |j                  |k(  rfJ  |D ]o  }t        |j                  d            }||z  }||z  }t        ||z        |k(  sJ t        ||z        |k(  sJ |j                  |k(  sJ |j                  |k(  roJ  ddl	m
	 | j                  d      }| j                         }t        dt        dt        dt        di}t        	fdt        |j                  |      |j                  |            D              sJ y )NRDrp  r  h   i  r   r   r   )r   r   r   )r  r     EDr   )compi_ib,  i  ij  c              3   n   K   | ],  \  }} |j                         |j                                . y wrt   r{   )r   rw   rx   r}  s      rn   r   ztest_pinv.<locals>.<genexpr>m
  s0      
Aq 	QSSUACCE
rt  )r1   rZ   r[   r\   r]   r%   pinvr  r-  sympy.core.numbersr}  r   zipr  )
A1Asr   A_pinvAApApAr  wrepsr}  s
            @rn   	test_pinvr  F
  s   	!Q!Q 	!BBGG4G()Xbffh-???? 2s)dAYQ0
1
)\*
+
!Q.
B  t$&jqja A%%%f%///uu||uu||  !&&&-.&jqja A%%%f%///uu||uu|| (
tA
Avq%E1e4D 
taffTl3
 
 
 
rm   c            	          t        g dg dg dg dg dg dg      g} | D ]G  }|j                  d      }||z  }||z  }|j                  |k(  sJ d	 } ||j                  |      rGJ  y )
N)=   r   7   r  r   r   )>   `   U   r  r  r   )E   8   r  r   6   r   )r   r  [   )   r   r   )r   r  r   r   Z   r   )r   r   r   r   r   r   r|  rp  c                     | j                  t              }|D ci c]  }||j                          }}| |z
  j                  |      j                         }t	        d |D              S c c}w )Nc              3   8   K   | ]  }t        |      d k    yw)g|=Nr   r   r  s     rn   r   zXtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose.<locals>.<genexpr>
  s     ;!s1v~;s   )ru  r!   rr  r!  r   )M1r  rootofsr?  rootofs_approxdiff_approxs         rn   allclosezEtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose
  s`    hhv&G4;<qal<N<7,,^<BBDK;{;;; =s   A()r1   r  r-  )r  r   r  r  r  r  s         rn   3test_pinv_rank_deficient_when_diagonalization_failsr  s
  s    
 	#####  	!
B  $t$&jqjuu||	< s###-$rm   c                      t        dd      t        dd      z   t        ddg       k(  sJ t        dd      t        dd      z   t        ddg       k(  sJ y rf  )r8   r1   rl   rm   rn   test_issue_7201r  
  sR    1:Q
"fQ2&66661:Q
"fQ2&6666rm   c                      t         t        t        t        fD ]&  }  | t        gdgg      j
                  t        hk(  r&J  y r   )r/   r0   r1   r2   r^   free_symbolsr  s    rn   test_free_symbolsr  
  s=    3V\I 11#s}))aS0001rm   c                      	 ddl m  t	          g d            t	        g d      k(  sJ t	          g dg            t	        g dg      k(  sJ t	          g dg dg            t	        g dg dg      k(  sJ t	          t
        t        t        g            t	        t
        t        t        g      k(  sJ t        t         fd       t	          ddg        d	d
g      g      t	        ddgd	d
gg      k(  sJ t	          ddg      d	d
gg      t	        ddgd	d
gg      k(  sJ t	          g         g       g      t	        g       k(  sJ y# t        $ r t        d       Y ^w xY w)zSee issue 7465.r   array?NumPy must be available to test creating matrices from ndarraysr   rJ  c                  B    t          ddgddggddgddggg            S )	Nr   r   r   r   r   r   r   r   r   r  s   rn   ry   z#test_from_ndarray.<locals>.<lambda>
  s0    u1v1v.!Q!Q0@ABC rm   r   r   r   r   N)
numpyr  ImportErrorrQ   r1   r^   r_   r`   rN   NotImplementedErrorr  s   @rn   test_from_ndarrayr  
  sb   P %	"#vi'8888%$%)<<<<%I./0	9%&' ' '%Aq	"#vq!Qi'8888
CE5!Q=%A-01VaVaV<L5MMMM5!Q=1a&)*fq!fq!f5E.FFFF59eBi()VBZ777  PNOPs   E E('E(c                  ^   ddl m}  	 ddlm}m}  |  ddgddgg            }|d   dk(  sJ t        |      g d	k(  sJ t        t              5   |  ddgddgg            }d d d        |d   dk(  sJ t        |      g d	k(  sJ y # t
        $ r t        d       Y w xY w# 1 sw Y   @xY w)
Nr   
_matrixify)r  matrixzPNumPy must be available to test indexing matrixified NumPy ndarrays and matricesr   r   r   r   r  )
sympy.matrices.commonr  r  r  r  r  rQ   r   rM   PendingDeprecationWarning)r  r  r  r   s       rn   test_17522_numpyr  
  s    0a' 	51a&1a&)*+AQ41997l"""	2	3 1v1v1v./01Q41997l"""  a_`a1 1s   B	 B#	B B #B,c                      ddl m}  	 ddlm}  |  ddgddgg            }|d   d	k(  sJ t        |      g d
k(  sJ y # t        $ r t        d       Y Gw xY w)Nr   r  )r  zEmpmath must be available to test indexing matrixified mpmath matricesr   r   r   r         @)r  g       @r  r  )r  r  mpmathr  r  rQ   r   )r  r  r   s      rn   test_17522_mpmathr  
  sk    0V! 	6Aq6Aq6*+,AQ43;;7****  VTUV   ? AAc                      ddl m}  	 ddlm}  |  ddgddgg            }|d   dk(  sJ t        |      g d	k(  sJ y # t        $ r t        d       Y Gw xY w)
Nr   r  )
csr_matrixzJSciPy must be available to test indexing matrixified SciPy sparse matricesr   r   r   r   r  )r  r  scipy.sparser  r  rQ   r   )r  r  r   s      rn   test_17522_scipyr  
  sj    0[+ 	:1v1v./0AQ41997l"""  [YZ[r  c                      t        dt        gt         dgg      } | j                  sJ dt        z  | d<   | j                  du sJ t        | d<   | j                  J | d   t        z  | d<   | j                  du sJ y )Nr   r   r   Fr   r   )r1   r
   is_hermitianr^   ry  s    rn   test_hermitianr  
  s    A!Q !A>>>cAdG>>U"""AdG>>!!!gaiAdG>>U"""rm   c                      t        t        t        t        d      gg      } | d   dt        z  k7  sJ  | j                         t        dt        z  gg      k(  sJ y )NFr  r   r   )r1   r   r^   r  ry  s    rn   	test_doitr  
  sQ    Qq5)*+,AQ41Q3;;1668v!ug&&&rm   c                     t        g dg dg dg      } | j                  d       | t        g dg dg      k(  sJ t        g dg dg dg      }|j                  d       |t        g dg dg      k(  sJ t        g dg dg dg      }|j                  d       |t        g dg dg      k(  sJ t        g dg dg dg      t        t        fd	       t        g dg dg dg      t        t        fd
       t        g dg dg dg      } | j	                  d       | t        ddgddgddgg      k(  sJ t        g dg dg dg      }|j	                  d       |t        ddgddgddgg      k(  sJ t        g dg dg dg      t        t        fd       t        g dg dg dg      t        t        fd       y )Nr   r  r   r   r  )r   r   r   )r   r   r  r   c                  &     j                  d      S r   row_delr  s   rn   ry   z+test_issue_9457_9467_9876.<locals>.<lambda>
      qyy} rm   c                  (      j                   d      S Nr   r  rT   s   rn   ry   z+test_issue_9457_9467_9876.<locals>.<lambda>
      yqyy~ rm   r   r   r   r   c                  &     j                  d      S r   col_delr  s   rn   ry   z+test_issue_9457_9467_9876.<locals>.<lambda>   r  rm   c                  (      j                   d      S r  r  rT   s   rn   ry   z+test_issue_9457_9467_9876.<locals>.<lambda>  r  rm   )r1   r  rN   r  r  )r   rr  Or  rU   s      @@rn   test_issue_9457_9467_9876r  
  s   	9i01AIIaL	9-....	9i01AIIbM	9-....	9k23AIIbM	9-....	9i01A
:,-	9i01A
:-. 		9i01AIIaLAAA/0000	9i01AIIbMAAA/0000	9i01A
:,-	9i01A
:-.rm   c                  D   t        dd      \  } }t        d      \  }}t        d      }t        dd| ||t        g      }|| z  |z  | |z  |z  k7  sJ ||z  |z  ||z  |z  k(  sJ | |z  || z  k7  sJ ||z  ||z  k(  sJ || z  |z  t        || z  dgd|| z  gg      k(  sJ y )Nr)  F)commutativeza br   r   )r   r5   r1   r`   )r^   r_   rZ   r[   r   r  s         rn   test_issue_9422r    s    5e,DAq5>DAqAA	1q!Ql	#BQ3q5AaCE>>Q3q5AaCE>>R42a4<<R42a4<<Q3q5FQqS!Hq!A#h/0000rm   c                  2   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 ]K  \  }}|D ]A  }t        | |      }d
|v r ||      n |d|      }||k(  rt        |      t        |      k7  rAJ  M y )NrM  rF  )r   r   r   rJ  rH  r   r   r   r   joinrA  )r1   r  r  id)	r   rZ   r[   r\   opsr   opr  news	            rn   test_issue_10770r    s    r
A	z"F9$55A	z"AaDFF*A	|$fq!fq!f-=&>>Aa) 1Q 	1B2A B,!A$Ab!HC!832a5 000	11rm   c                  d   t        g dg dg dg      } | j                  g dg d      t        ddgdd	gd
dgg      k(  sJ | j                  g dg d      t        dgdgd
gg      k(  sJ | j                  g dg d      t        g dg      k(  sJ | j                  g dg d      t        g dg dg      k(  sJ | j                  g dg d      t        ddg       k(  sJ | j                  g dg d      t        ddg       k(  sJ | j                  g dg d      t        dgdgg      k(  sJ y )Nr   rJ  r  r   )TTFr   r   r   r   r   r   )TFF)TFT)FFFr   r   )FTF)r1   r   r   s    rn   test_issue_10658r    s8   	9i01A99Y 34AAA'() ) )99Y 45!qcA39PPPP99)959LLLL99()4	9%&' ' '99Y 56&Ar:JJJJ99*I6&Ar:JJJJ99(*>?aSz  rm   c                     t        ddt        d      z  z   dgdt        d      z  dz  dz   dt        d      z  dz  gg      } | j                         dk(  sJ t        ddt        d      z  t        z  z   dgdddt        d      z  t        z  z   gg      } t	        | j                         d	   t        ddddt        d      z  t        z  z   z  gd	d	gg      z
        t        dd      k(  sJ t        d
      \  }}}}}}}}}	}
}}t        ||||z  ||z  d	g||||z  ||z  d	g||||z  ||z  dg||||z  ||z  dg|	|
d|	z  |z  |	|z  z
  d|
z  |z  |
|z  z
  d	gg      } | j                         dk(  sJ y )Nr>  r   r   r   r   r  r   r   r   /a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1)r1   r   r  r
   r%   rA  r>   r   )r   axaybxbycxcydxdyexeyt0t1s                rn   !test_opportunistic_simplificationr  )  s    	aQi$r$q'z!|a'7DGA&FGHA668q== 	1T!W9Q;#Qr!DG)A+~$678AAFFHQK&1b!aQik/.B*CaV)L"MMNRWXY[\R]]]] +22c*d'Br"R2bBr"RBr"uRU1%r"RU2b5&;R2b5Bq<QSUVXY[\^Y^_abd_defRgiklnopqsostvovwyz|w|o|}~  @B  ~B  CE  ~E  FH  IK  FK  ~K  LM  iN  O  	PA668q==rm   c                     t        g dg dg      } | j                         d   t        g dg dg      z
  j                         dk  sJ t        g dg dg d	g      }t        g d
g dg dg      }t        g dg dg d	g      }|j                         |z
  j                         dk  sJ |j                         |z
  j                         dk  sJ y )N)g~jth?gRM@g(\M@)gDl)@gQgp=
cG@r   )r  r   r   )r   r  r  V瞯<)q7K<r  r   )      r   r   r   )r  r  r  )r                 @)r  r  r  )r   r  r  )r  r  g      )r1   rA  r  r  )mmm_mixedm_floatm_invs       rn   test_partial_pivotingr  9  s    
 $&;<=BGGIaL6#3#3#5 6 67;tvF F F o%%' (G ''') *G (((* +E
 KKME!'')E111KKME!'')E111rm   c                      t        g dg dg dg      } | j                  d       d   }t        g dg dg d	g      }||z
  }|j                         d
k  sJ |d   dk(  sJ y)z When doing numerical computations, all elements that pass
    the iszerofunc test should be set to numerically zero if they
    aren't already. )?皙gɿr   )皙r  gٿr   )r  r  g333333?r   c                     t        |       dk  S )Ng [n<r  r  s    rn   ry   z*test_iszero_substitution.<locals>.<lambda>X  s    Q rm   ru  r   )r  r   g4iҤIӿr   )r   r  glٲer   r  r  r  N)r1   rA  r  )r   m_rref	m_correctm_diffs       rn   test_iszero_substitutionr   Q  sr     	$%9:NOPAVV5V6q9F9:[\}~IiF;;=5   #;!rm   c            	         ddl m}  dt        t        t	        dd      z        z  t        t        t	        dd      z        t        d      z   z  }dt        d      z  t        t        t	        dd      z        dz  z  d	t        t        t	        dd      z        z  z   d
t        t        t	        dd      z        dz  z   z  } | dd      } | dt        d             } | ||      }t        |t        |      z
  |t        |      z
  g      }t        ||z
  ||z
  g      }t        t        ||z
        t        ||z
        g      }d }	|j                  d|	      dk(  sJ |j                  d|	      dk(  sJ |j                  d|	      dk(  sJ y )Nr   )Pointr   r  -   r   r  r   r   r   r   c                 <    t         | j                               dk  S )Ng#B;)r   r|   r  s    rn   ry   z"test_issue_11238.<locals>.<lambda>m  s    #cacce*u$ rm   T)r%   r  )	sympy.geometry.pointr  r   r   r   r   r1   r%   r  )
r  xxyyp1p2p0r  r  m3Zs
             rn   test_issue_11238r  _  s   *	
3r(2r""#	#SHR,<)<%=Q%G	HB
T!W*SHR,,-q0
02c"Xb"=M:M6N3N
NQSVYZ\]efhjl]mZmVnpqVqQq	rB	q!B	q47(	B	r"B	hrl"B"$56	7B	b"r'"	#B	"r'"HR"W$56	7B
 	%A77DQ7/144477DQ7/144477DQ7/1444rm   c                      t        ddg d      } | t        j                  z  }| |z   }t        D ]M  } ||      j	                         \  }}t        |      t        |       k(  sJ t        |      t        |       k(  rMJ  y )Nr   r  )r1   r   ImaginaryUnitr   as_real_imagr   )r  r  r  klsrZ   r[   s         rn   test_as_real_imagr  r  sx    	!I	B	AOO	B	bB #"g""$!Aw$r("""Aw$r("""#rm   c                      t        ddg d      } | j                         \  }}|d   t        dddg      k(  sJ |d   t        ddg d      k(  sJ y )Nr   r  r   r   r   )r   r   r   r   )r1   jordan_cells)r   r  Jcellss      rn   test_deprecatedr  |  s[    
 	q!23A IAv!9q!aS))))!9q!\2222rm   c                      ddl m}  t        g d      }t        g d      } | |d      t        g d      k(  sJ  | |d      t        g d      k(  sJ y )	Nr   )Mod)r   r   r   )r   r  r  r   )r   r   r   r   )r   r   r   )sympy.core.modr  r1   )r  r   r  s      rn   test_issue_14489r    sK    "zA}Aq!9y))))q!9y))))rm   c                      	 ddl m}  t	        ddgddgg      }  |t
              j                  j                  d	k(  sJ y # t        $ r t        d       Y Ow xY w)
Nr   r  r  r   r   r   r   )dtypefloat64)r  r  r  rQ   r1   floatr  name)r  r   s     rn   test_issue_14943r     s`    P 	1!u~A% &&++y888	  PNOPs   A AAc                  d    t        ddd      } t        d      }| d   dkD  }t        |      dk(  sJ y )Nr   r   rZ   r   r   zm[0, 0] > 0)rA   r   r  )r   rZ   s     rn   test_case_6913r"    s8    S!QAsA	$	Aq6]"""rm   c                  d    t        ddd      } t        d      }| j                  |      || ik(  sJ y )Nr   r   rZ   )rA   rH   match)r   rZ   s     rn   test_issue_11948r%    s3    S!QAS	A771:!Qrm   c                  b   t        dt        g      t        dt         g      g} t        j                  |  t        dgt        gg      t        dgt         gg      gk(  sJ t        dt        dg      t        t        dt         g      g} t        j                  |  t        dgt        gdgg      t        t        dz  gt        d      dz  gt         gg      gk(  sJ t        dt        gdt         gg      }|j	                         \  }}||j
                  z  t        j                  d      k(  sJ y )Nr   r   r   )r1   r
   orthogonalizer   QRdecompositionr-  r5   )vecsr   rU   r  s       rn   test_gramschmidt_conjugate_dotr*    s'   Aq6NFAr7O,D&	!qc
	VaSA2$K012 2 2 Aq!9vq!aRj12D&	!qcA3	 &1Q3%!A$q&QB4)@"ABC C C 1a&1qb'"
#C DAqqss7fjjm###rm   c                      t        t        ddd            } t        t        ddd            } | j                  |      }t        || d         }t        || d         }||d   k(  sJ |dk(  sJ y )NrZ   r   r   r[   r   r   )r1   rA   r[  r   )rZ   r[   r\   r]   r  s        rn   test_issue_8207r,    sr    |CA&'A|CA&'AaAQ$AQ$A$<<6M6rm   c            	         ddl m}  t        ddgddgg      j                  t	        t
        t        z        t
              t        t	        t              t	        dt        z        t	        t              z
  gdt	        dt        z        gg      k(  sJ t        ddgddgg      t        z  dz  j                  t        t
              t
              t        t        d      dz  t        d       dz  gt        d       dz  t        d      dz  gg      k(  sJ t        t        d        t        t        fd	       t        g d
g d
g dg dg      j                  t        t
              t
              j                         k(  sJ t        t        fd       t        ddgddgg      t        j                  t        t
              t
              dz        k(  sJ t        g dg dg dg      t        j                   | t
        d      t
              dz        k(  sJ t        g dg dg dg dg      j                  t        t
              t
              j                         k(  sJ t        g dg dg dg dg      j                  t        t
        t        z        t
              t        t        t        z  j                                     k(  sJ y )Nr   )nthrootr   r   r   r   r   c                  Z    t        d      j                  t        t              t              S r  )r>   analytic_funcr   r^   rl   rm   rn   ry   ztest_func.<locals>.<lambda>  s    a 6 6s1vq A rm   c                  X     t         z  j                  t        t               t               S rt   )r^   r0  r   r   s   rn   ry   ztest_func.<locals>.<lambda>  s    1 3 3CFA > rm   )r   r   r  r   )r   r   r   r   )r   r   r   r   c                  J     j                  t        t              t              S rt   )r0  r   r^   r   s   rn   ry   ztest_func.<locals>.<lambda>  s    Q ; rm   r  r   "   )r   r  r   )r   r   r  )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   r  )sympy.simplify.simplifyr.  r1   r0  r   r^   ra   r   r   r   rN   r  r   r%   r   )r.  r   s    @rn   	test_funcr5    sD   /A1vA??3qs8Q'6CFC!Hs1v<M3NQRTWXYZ[X[T\P]2^+____A1vAFQJ%%c!fa0FT!WQYaQR
<SW[\]W^V^_`V`bfghbijkbkUl;m4nnnn :AB
:>?}MNA??3q61%000
:;<R"b"#AAOODGQ/23q888[+67AAOOGAqM15q89Q>>>lL,GHA??3q61%000lL,GHA??3qs8Q'6(AaC99;2G+HHHHrm   z$Cannot create threads under pyodide.c                      d } t        d      5  t        j                  j                         5 }|j	                  |       }|j                         sJ 	 d d d        d d d        y # 1 sw Y   xY w# 1 sw Y   y xY w)Nc                  R    t         j                  d k(  sJ t        dgg      } | | z  } yr  )rF   stater1   r   s    rn   r  ztest_issue_19809.<locals>.f  s/    !''4///QC5MErm   T)rB   
concurrentfuturesThreadPoolExecutorsubmitresult)r  executorfutures      rn   test_issue_19809r@    sp     
T	 #224 	#__Q'F==?"?	## #	# 	## #s"   A0$A$A0$A-	)A00A9c                      t        t        t        g      } t        | t        ddft        ddf      t        t        j
                  gt        j
                  gg      k(  sJ y rf  )r1   r^   r_   r   r   r  r  s    rn   test_issue_23276rB    sT    1vAQAq	Aq!9-	
	
9 2   rm   c                  B   t        g dg dg dg dg      } | j                         }|d   t        g d      k(  sJ |d   t        g d      k(  sJ |d	   t        g d
      k(  sJ t        |      dk(  sJ t        j                  | g| j                         |k(  sJ y )Nr   r   r   r   r   r  r>  r   r   r  r   r   r   r   r   r   r   r   r_  r   r   )r   r  r   r   r   )r   r>  r   r   r   )r   r   r   r_  r   )rg   r\  r1   r4  rN  r   basiss     rn   test_columnspace_onerJ    s    00002 	3A
 MMOE8vm,,,,8vn----8vn----u:??==#U#//1U:::rm   c                      t        g dg dg dg dg      } | j                         }|d   t        g dg      k(  sJ |d   t        g dg      k(  sJ |d   t        g d	g      k(  sJ t        |      d
k(  sJ y )NrD  rE  rF  rG  r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )rg   rY  r1   r4  rH  s     rn   test_rowspacerL    s    00002 	3A
 JJLE8v/00008v/011118v/0000u:??rm   c                     t        g dg dg dg dg      } | j                         }|d   t        g d      k(  sJ |d   t        g d      k(  sJ t        d	 | |d   z  D              sJ t        d
 | |d   z  D              sJ y )NrD  rE  rF  rG  r   )r  r   r   r   r   r   )r   r   r   r   r   c              3   4   K   | ]  }|j                     y wrt   r  r  s     rn   r   z%test_nullspace_one.<locals>.<genexpr>       -Qqyy-   c              3   4   K   | ]  }|j                     y wrt   rO  r  s     rn   r   z%test_nullspace_one.<locals>.<genexpr>  rP  rQ  )rg   r`  r1   r   rH  s     rn   test_nullspace_onerS    s    00002 	3A
 KKME8v.////8v01111-!E!H*-----!E!H*----rm   c                  x   t        d      t        t        fd       t        t        fd       t        t        fd       t        t        fd       t        t        fd       t        t        fd       t        t        fd       t        t        fd	       t        t        fd
       t        t        fd       t        t        fd       t        t        fd       t        t        fd       j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  dddd      t	        g dg dg dg      k(  sJ j                  dddd      t	        g dg dg dg      k(  sJ j                  dddd       t	        g dg dg dg      k(  sJ t        d!ddgd"z        }  | j                  ddd      t	        d!ddgd"z        k(  sJ  | j                  ddd      t	        d!ddgd"z        k(  sJ  | j                  dddd      t	        d!ddgd"z        k(  sJ y )#Nr   c                  &     j                  d      S Nabcelementary_row_opr  s   rn   ry   ztest_row_op.<locals>.<lambda>      q2259 rm   c                  $     j                         S rt   rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>      q224 rm   c                  ,     j                  ddd      S )Nn->knr   rD  r  rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>       q227Q2G rm   c                  ,     j                  ddd      S )Nr_  r>  r   r`  rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>!      q227a2H rm   c                  ,     j                  ddd      S )Nn<->mr   r   row1row2rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>"      q2272K rm   c                  ,     j                  ddd      S )Nre  r   r   rf  rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>#  ri  rm   c                  ,     j                  ddd      S )Nre  r>  r   rf  rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>$      q227!2L rm   c                  ,     j                  ddd      S )Nre  r   r>  rf  rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>%      q2272L rm   c                  .     j                  dddd      S Nn->n+kmr   r   rg  rh  r  rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>&      q22911PQ2R rm   c                  .     j                  dddd      S )Nrq  r   r   rr  rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>'  rs  rm   c                  .     j                  dddd      S )Nrq  r>  r   r   rr  rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>(      q2292AQR2S rm   c                  .     j                  dddd      S )Nrq  r   r>  r   rr  rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>)      q22912QR2S rm   c                  .     j                  dddd      S rp  rX  rZ  s   rn   ry   ztest_row_op.<locals>.<lambda>*  rs  rm   r_  r   r   r  r   r   r   r5  r6  r`  )rg  r  re  rf  )rD  rh  rq  )r   r   r   )rD  r  rh  )rg  r  rh  r   r   )r}   rN   r  rY  r1   rq   rZ   r  s    @rn   test_row_opr{       qA
:9:
:45
:GH
:HI
:KL
:KL
:LM
:LM
:RS
:RS
:ST
:ST
:RS w1-Iy8Y1ZZZZw1-Iy8Y1ZZZZwA3vy)U^>_7````wQ!4	9V_?`8aaaaw1-Iy8Y1ZZZZwQQ769iYbBc;ddddwAA6&)YXaAb:ccccy!Q2fiT]=^6____ya11=T]_hHiAjjjjyqAA>&)U^`iIjBkkkk 	QA3q5)A1w1-1qc!e1DDDD1w1-1qc!e1DDDD1y!Q2fQA3q56IIIIrm   c                  x   t        d      t        t        fd       t        t        fd       t        t        fd       t        t        fd       t        t        fd       t        t        fd       t        t        fd       t        t        fd	       t        t        fd
       t        t        fd       t        t        fd       t        t        fd       t        t        fd       j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  ddd      t	        g dg dg dg      k(  sJ j                  dddd      t	        g dg dg dg      k(  sJ j                  dddd      t	        g dg dg dg      k(  sJ j                  dddd       t	        g dg dg dg      k(  sJ t        d!ddgd"z        }  | j                  ddd      t	        d!ddgd"z        k(  sJ  | j                  ddd      t	        d!ddgd"z        k(  sJ  | j                  dddd      t	        d!ddgd"z        k(  sJ y )#Nr   c                  &     j                  d      S rV  elementary_col_oprZ  s   rn   ry   ztest_col_op.<locals>.<lambda>B  r[  rm   c                  $     j                         S rt   r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>C  r]  rm   c                  ,     j                  ddd      S )Nr_  r   rE  r  r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>D  ra  rm   c                  ,     j                  ddd      S )Nr_  r>  r   r  r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>E  rc  rm   c                  ,     j                  ddd      S )Nre  r   r   col1col2r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>F  ri  rm   c                  ,     j                  ddd      S )Nre  r   r   r  r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>G  ri  rm   c                  ,     j                  ddd      S )Nre  r>  r   r  r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>H  rl  rm   c                  ,     j                  ddd      S )Nre  r   r>  r  r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>I  rn  rm   c                  .     j                  dddd      S Nrq  r   r   r  r  r  r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>J  rs  rm   c                  .     j                  dddd      S )Nrq  r   r   r  r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>K  rs  rm   c                  .     j                  dddd      S )Nrq  r>  r   r   r  r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>L  rv  rm   c                  .     j                  dddd      S )Nrq  r   r>  r   r  r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>M  rx  rm   c                  .     j                  dddd      S r  r  rZ  s   rn   ry   ztest_col_op.<locals>.<lambda>N  rs  rm   r_  r   r   r  r   r   r   r5  r6  r  )r  r  re  r  )rE  r  rq  )r   r   r   )rE  r  r  )r  r  r  r   r   )r}   rN   r  r  r1   rq   rz  s    @rn   test_col_opr  ?  r|  rm   c                     t        d      } t        d      }| j                  sJ |j                  sJ t        ddg       }|j                  sJ t        ddg d      }|j                  sJ t        ddg d      }|j                  rJ t	        d      }t        dd|ddg      }|j                  sJ t        dd||dg      }|j                  rJ t        ddg d      }|j                  rJ y )	Nr   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   r^   r   	r   r   r   r   r   r   r   r   r   )r   r}   
is_echelonrq   r   )zroidentrZ   r^   s       rn   test_is_echelonr  c  s    
1
C1E>>>Q2&A<<<Q#56A<<<Q#56A||sAQAq!9-A<<<QAq!9-A||Q#>?A|||rm   c                     t        d      } t        d      } | j                         | k(  sJ |j                         |k(  sJ t        ddg       }  | j                         | k(  sJ t        dddg      }  | j                         | k(  sJ fd}t        ddg d      } t	        dgdgdgg      g}t        | j                        D cg c]  }| |d d f    }} | j                         j                  sJ  || ||       t        ddg d      } g }t        | j                        D cg c]  }| |d d f    }} | j                         j                  sJ  || ||       t        ddg d	      } t	        t        d
d      gdgdgg      t	        t        dd      gdgdgg      g}t        | j                        D cg c]  }| |d d f    }} | j                         j                  sJ  || ||       t        ddg d      } t	        dgdgdgg      g}t        | j                        D cg c]  }| |d d f    }} | j                         j                  sJ  || ||       t        ddg d      } t	        dgdgdgg      t	        dgd
gdgg      g}t        | j                        D cg c]  }| |d d f    }} | j                         j                  sJ  || ||       t        ddg d      } t	        d
gdgdgg      g}t        | j                        D cg c]  }| |d d f    }} | j                         j                  sJ  || ||       y c c}w c c}w c c}w c c}w c c}w c c}w )Nr   r   r   r   c                     |D ]  }t        d |z  D              rJ  |D ]:  }t        d |D              rt        d |j                         z  D              s:J  y )Nc              3   4   K   | ]  }|j                     y wrt   rO  r   ra   s     rn   r   zCtest_echelon_form.<locals>.verify_row_null_space.<locals>.<genexpr>  s     6Qqyy6rQ  c              3   4   K   | ]  }|j                     y wrt   rO  r  s     rn   r   zCtest_echelon_form.<locals>.verify_row_null_space.<locals>.<genexpr>  s     ,Qqyy,rQ  c              3   4   K   | ]  }|j                     y wrt   rO  r  s     rn   r   zCtest_echelon_form.<locals>.verify_row_null_space.<locals>.<genexpr>  s     JQqyyJrQ  )r   r(  )r   r   nullsr   	a_echelons       rn   verify_row_null_spacez0test_echelon_form.<locals>.verify_row_null_space  sh     	7A6)A+6666	7 	KA,!,,J)AKKM2IJJJJ	Krm   r  r  )	r   r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   )	r   r}   rV  rq   r1   r   r   r  r   )rZ   r  r  r  rw   r   r  s         @rn   test_echelon_formr  ~  s   
 	AqA 1>>q   >>q   Q2&A1>>q   QA3'A1>>q   K 	Q#>?ATTT  E #166]+AadG+D+ I!T5) 	Q#>?AE"166]+AadG+D+ I!T5)Q#>?Ar1oVV  r1oVV 	E #166]+AadG+D+ I!T5) 	Q#>?AVVV  E #166]+AadG+D+ I!T5)Q#>?ASSS  TTT 	E #166]+AadG+D+ I!T5)Q#56ATSS  E #166]+AadG+D+ I!T5)y , , , , , ,s$   M&*M+M04M57M:*M?c                     t        ddg       } | j                  d      | k(  sJ t        dddg      } t        dddg      }| j                  d       |j                  d      cxk(  r| k(  sJ  J t        ddg d      } |j                  d      t        dgdgdgg      k(  sJ t        ddg d      } |j                  d      t        g dg      k(  sJ t        ddg d      } |j                  d      t        g d	g d
g dg      k(  sJ t        ddg d      }t        ddg d      }t        ddg d      }t        ddg d      } |j                  d       |j                  d      cxk(  r4 |j                  d      cxk(  r |j                  d      cxk(  r|k(  sJ  J t        d      } t	        d      }| j                  d      | k(  sJ  |j                  d      |k(  sJ t        g dg dg dg dg      } |j                         \  }}|t        g dg dg dg dg      k(  sJ |dk(  sJ t        t        dd      t        dd      ddgg dg dg dg      } |j                  d      t        dddt        dd      gdddt        d d      gdddt        d!d      gg d"g      k(  sJ t        d#      }t        dd|ddt        |      |dg      }t         |j                  d      ddt        |      | dz   z  |t        dd      z   |z   z  dddt        |      |z   dz   z  g      D ]  \  }	}
t        |	|
z
        j                  rJ  y )$Nr   F)pivotsr   r   r   r   r  )r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   r  )	r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r>  r   )r   r   r   r   r   r_  r   )r   r   r  r   r   r   r>  )r   r   r   r   r  r   r   )r   r>  r   r   r   r   r   )r   r   r   r   r   r   r   )r   r   r   r   r   r  r   )r   r   r   r   r   r   r   )r   r   r   r{  r   r  r  r  i   r>     r  r^   )rq   rA  r1   r}   r   r   r   r   r  r%   r  )r  rZ   r[   r\   r]   r`   r   pivot_offsetsr^   rw   rx   s              rn   	test_rrefr    s   Q2&A6661$$$QA3'AQA3'A6666166#7<1<<<<<Q9-A1666A3aS/#::::Q9-A16669+#6666Q#>?A1666%/%/%/+1 $2 2 2 2
 	Q#>?AQ#>?AQ#>?AQ#>?A166AFF% &AFF% & AFF% & %&& & & & &
 	qAA6661$$$1661$$$''''	) 	*A
  C&----	/ 0 0 0 0
 I%%%x2!QA!L0002 	3A 1666*+Q8C3E)F*+QHR4E)F*+Q8C3E)F);	+= $> > > > 	sAQAq!T!Wa#;<AFAFF%(47QBF#a!Q&7%7!%;<1aa1q)+, '1 A&&&&'rm   c                     t        d      \  } }}}t        ddgddgddgddgg      }t        | |||g      }|j                  |      t        ddgddgddgddgg      t        d|z  |z   gd|z  dz  |dz  z
  g| g|gg      fk(  sJ y )Nr  r   r   r   r   r   r  )r   r1   rref_rhs)rZ   r[   r\   r]   r   r  s         rn   test_rref_rhsr    s    #JAq!QAAAA/0A1a|A::a=VFFFF	%  
1qMqSUQqS[MMM	 	   rm   c            	         t        g dg dg dg dg dg dg      j                  ddd	
      } j                  dd	dd      }j                  dd	d      }| d	d d f   t        g dg      k(  sJ |d	d d f   t        g dg      k(  sJ |d	d d f   t        g dg      k(  sJ t        t        fd       t        t        fd       t        t        fd       y )N)r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r  )r   r   r   r>  )r   r   r   r   re  r   r   rf  rq  r   r=  rr  r_  r`  )r   r   r   r  )r  r  r   r   c                  ,     j                  ddd      S )Nre  r   r   rf  rX  r+  s   rn   ry   z"test_issue_17827.<locals>.<lambda>>  ri  rm   c                  ,     j                  ddd      S )Nr_  r   r   r`  rX  r  s   rn   ry   z"test_issue_17827.<locals>.<lambda>?  ra  rm   c                  .     j                  dddd      S )Nrq  r   r   r   rr  rX  r  s   rn   ry   z"test_issue_17827.<locals>.<lambda>@  rv  rm   )r1   rY  rN   r  )r1  r   r?  r+  s      @rn   test_issue_17827r  -  s     	A 	
G!!4A	IAA<A	Ga0AQT7fl^,,-,QT7fm_--.-QT7fo.//0/
:KL
:GH
:STrm   c                     t        ddgt        ddt        z  z
  gg      } | j                         dk(  sJ t        ddt        dd            }|j                         dk(  sJ t	        d      }|j                         dk(  sJ y )Nr   r   r   r   r   )r1   r^   r  r   r>   )r   r|   r  s      rn   	test_rankr  B  st    AA!G%&A668q==q!U1b\"A668q==aA668q==rm   c                     t        d      \  } }}}}}}}}}	}
}t        | || |
z  ||
z  dg||||
z  ||
z  dg||||
z  ||
z  dg||||
z  ||
z  dg||	d|z  |z  ||
z  z
  d|	z  |z  |	|
z  z
  dgg      }|j                         dk(  sJ y )Nr  r   r   r   r   )r   r1   r  )r  r  r  r  r  r  r  r  r  r  r  r  r   s                rn   test_issue_11434r  J  s    AB 3BBBBBBRB2q)RB2q)RB2q)RB2q)R2b2b5!B$r'BrE/1=	? 	@A
 668q==rm   c            
         t        d      \  } }t        d| z  dddgd| z  d| z  dz
  ddgdd| z  d| z  |z
  dz
  dgdd| |z   dgg      }t        dddd| dz  | | z
  z  z  gdddd| | | z
  z  z  gdddd| | z
  z  gg d	g      }d
}|j                         \  }}t        ||z
        t	        |j
                   k(  sJ ||k(  sJ y )Nz
nu, lambdar   r   r   r   r  r   r   r  r   )r   r1   rA  r%   r>   r   )nulambr   expected_reducedexpected_pivotsreducedr  s          rn   test_rank_regression_from_sor  T  s!    |$HBBA:B$2	A:QrTBrET>A#5:BIr:< 	=A 1aBED52:,>)?@ !1aArD52:,?@ !1aTEBJ@@B C  OffhOGV$w./5!''?BBB_$$$rm   c                      t        g dg dg dg dg      } | t        j                  d      t        z  z
  }|j                         dk(  sJ |dz  j                         dk(  sJ |dz  j                         dk(  sJ y )Nri  r  r  r  r   r   r   )r1   r5   r
   r  )r   r  s     rn   test_issue_15872r  h  sn    o~|LMA	FJJqMAA668q==qD;;=AqD;;=Arm   (Q  r  concurrent.futuresr9  collections.abcr   sympy.core.addr   sympy.core.functionr   r   r   r  r   r	   r
   r   r   r   r   r   sympy.core.powerr   sympy.core.singletonr   sympy.core.symbolr   r   sympy.core.sympifyr   $sympy.functions.elementary.complexesr   &sympy.functions.elementary.exponentialr   r   (sympy.functions.elementary.miscellaneousr   r   r   (sympy.functions.elementary.trigonometricr   r   r   sympy.integrals.integralsr   sympy.polys.polytoolsr   r    sympy.polys.rootoftoolsr!   sympy.printing.strr"   sympy.sets.setsr#   r4  r$   r%   sympy.simplify.trigsimpr&   sympy.matrices.exceptionsr'   r(   r)   sympy.matrices.matrixbaser+   sympy.matrices.determinantr,   sympy.matrices.utilitiesr-   sympy.matricesr.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   
sympy.corerG   rH   (sympy.functions.special.tensor_functionsrI   sympy.utilities.iterablesrJ   rK   rL   sympy.utilities.exceptionsrM   sympy.testing.pytestrN   rO   rP   rQ   rR   rS   sympy.assumptionsrU   sympy.tensor.arrayrV   $sympy.tensor.array.array_derivativesrW   sympy.matrices.expressionsrX   sympy.algebrasrY   r  rZ   r[   r\   r]   r^   r_   r`   ra   r   r  rb   rc   sympy.matrices.matricesrd   re   rg   rq   r}   r   r   r   r   r   r   r   r   r   r  r  r  r  r!  r,  r3  r8  r;  rB  rF  rJ  rN  rT  rW  rZ  r]  ra  rd  rg  rl  rt  ry  r|  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r"  r&  r)  r.  r3  r9  r;  rH  rL  rQ  rZ  r\  rn  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.  r2  r5  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
  r  r  r  r  r  r  r#  r%  r'  r*  r-  r5  rA  rE  rI  rL  rP  rS  rW  r]  r`  rd  rh  rj  rs  rw  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r   r"  r%  r*  r,  r5  r@  rB  rJ  rL  rS  r{  r  r  r  r  r  r  r  r  r  r  rl   rm   rn   <module>r     s     $  6 6 L L L   " / & 4 = E E D D / 2 * # % 8 ,  4 C .L L L L L L L 8 " C @ @ 6: :  $ @ - % , , , <2G
H B E  ^_o 
  ~@P 
@6
+
!+
&
9)XJ6Z^JB?_*JX_
%
'
 
6%
;
5
8GP
y
	8$
)&$<<<<<K&d&K0L2^FD+84P1$
:<7Mt 8!"AG2" "$$-:&>9$"*)  
.	*F!@.6&8G$1&3@E!P
1H%V&&'"$4.L)2
!$;6z"IG
O*4(nP!%IPZz.&"FH $<">JD-;-"8
/(1
(.3(?G4\p&(*&F"7:& 4 5 5)+"*
Z "$ "$J718$# 	+	##'
/8	1	1 205&#3*9# 
$I< :;# <#;.!JH!JH6\*~>'BU*%(Mi 
 s   0QQ&Q#&Q0