
    Цir                       S SK r S SKrS SKJr  S SKJr  S SKJrJ	r	J
r
  S SKJrJrJrJrJrJrJrJr  S SKJr  S SKJr  S SKJrJr  S S	KJr  S S
KJr  S SKJ r J!r!  S SK"J#r#J$r$J%r%  S SK&J'r'J(r(J)r)  S SK*J+r+  S SK,J-r-J.r.  S SK/J0r0  S SK1J2r2  S SK3J4r4  S SK5J6r6J7r7  S SK8J9r9  S SK:J;r;J<r<J=r=  S SK>J?r?  S SK@JArA  S SKBJCrC  S SKDJErEJFrFJGrGJHrHJIrIJJrJJKrKJLrLJMrMJNrNJOrOJPrPJQrQJRrRJSrSJTrTJUrUJVrVJWrWJXrXJYrYJZrZJ[r[J\r\  S SKBJ]r]  S SK^J_r_J`r`  S SKaJbrb  S SKcJdrdJereJfrf  S SKgJhrh  S SKiJjrjJkrkJlrlJmrmJnrnJoro  S S KpJqrq  S S!KrJsrs  S S"KtJuru  S S#KvJwrw  S S$KxJyry  S S%KzJ{r{J|r|J}r}J~r~JrJrJrJr  \H\I\F\G4rS S&KJrJr  S S'KJrJr  \o" 5           " S( S)\\\5      rSSS5        \o" 5           " S* S+\\\5      rSSS5        S, rS- rS. rS/ rS0 rS1 rS2 rS3 rS4 rS5 rS6 rS7 rS8 rS9 rS: rS; rS< rS= rS> rS? rS@ rSA rSB rSC rSD rSE rSF rSG rSH rSI rSJ rSK rSL rSM rSN rSO rSP rSQ rSR rSS rST rSU rSV rSW rSX rSY rSZ rS[ rS\ rS] rS^ rS_ rS` rSa rSb rSc rSd rSe rSf rSg rSh rSi rSj rSk rSl rSm rSn rSo rSp rSq rSr rSs rSt rSu rSv rSw rSx rSy rSz rS{ rS| rS} rS~ rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS Gr S GrS GrS GrS GrS GrS GrS GrS GrS Gr	S Gr
S GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS Gr \kS 5       Gr!S Gr"S Gr#S Gr$S Gr%S Gr&\lS 5       Gr'S Gr(S Gr)S Gr*S Gr+S Gr,S Gr-S Gr.S Gr/S Gr0S Gr1S Gr2S Gr3S Gr4S Gr5S Gr6S Gr7S Gr8S Gr9S Gr:S Gr;S Gr<S Gr=S Gr>S Gr?S Gr@\n" S5      S 5       GrAS GrBS GrCS GrDS GrES GrFS GrGS GrHS GrIS GrJS GrKS GrLS GrMS GrNS GrOS GrPg! , (       d  f       GN= f! , (       d  f       GN= f)    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                       \ rS rSrSrg)SubspaceOnlyMatrixC    N__name__
__module____qualname____firstlineno____static_attributes__ri       a/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/sympy/matrices/tests/test_matrices.pyrg   rg   C       rp   rg   c                       \ rS rSrSrg)ReductionsOnlyMatrixH   ri   Nrj   ri   rp   rq   rt   rt   H   rr   rp   rt   c                     [        X S 5      $ )Nc                     [        X:H  5      $ N)intijs     rq   <lambda> eye_Reductions.<locals>.<lambda>M   s
    3qv;rp   rt   ns    rq   eye_Reductionsr   L   s    &>??rp   c                     [        X S 5      $ )Nc                     gNr   ri   rz   s     rq   r}   "zeros_Reductions.<locals>.<lambda>Q   s    1rp   r   r   s    rq   zeros_Reductionsr   P   s    n55rp   c                  2   [        [        5       GH  u  pUR                  SS5      nUR                  S:X  a!  [	        S UR                   5       5      (       d   eUR
                  S:X  a  [        UR
                  5      [        L d   eUR                  S:X  a  [        UR                  5      [        L d   eU S-  (       d0  [        UR                  5       5      [        [        [        4;   d   eM  [        UR                  5       5      [        L a  GM   e   g )N      )r   r   c              3   D   #    U  H  n[        U5      [        L v   M     g 7frx   )typery   ).0r{   s     rq   	<genexpr>test_args.<locals>.<genexpr>X   s     (IAaCs    )	enumerateclassesr>   shapeallrowsr   ry   colsflatlisttuplerG   todokdict)r   clsms      rq   	test_argsr   T   s    G$IIaOww& S(I(I%I%IIIvv{tAFF|s222vv{tAFF|s2221u>dE5%9999	?d*** %rp   c                     [         [        4 HJ  n U R                  SS5      n[        5          UR                  nS S S 5        WUR                  5       :X  a  MJ   e   [        [        4 HJ  n U R                  SS5      n[        5          UR                  nS S S 5        WUR                  5       :X  a  MJ   e   g ! , (       d  f       N= f! , (       d  f       N:= fNr   r   )
r1   r/   r>   rS   _matr   r2   r0   _smatr   )r   r   matsmats       rq   test_deprecated_mat_smatr   a   s    &IIaO#%&&C &affh	 '
 22IIaO#%77D &qwwy   	 3 &%
 &%s   B6C6
C	
C	c                      [        SS[        [        /5      n U [        -  [        SS[        [        -  [        [        -  /5      :X  d   eg N   r   )r1   r^   r_   r`   )vs    rq   test_divisionr   n   s;    q!aVAQ3&A!QqSz****rp   c            	      J  ^ ^ [        / SQ[        [        [        /S[        -  S[        [        -  //5      m T T -   [        / SQS[        -  S[        -  S[        -  /S[        -  SS[        -  [        -  //5      :X  d   e[        SSSS/5      m[	        [
        U U4S j5        g )	Nr   r   r   r   i)r         r   ir   c                     > T T-   $ rx   ri   r   r   s   rq   r}   test_sum.<locals>.<lambda>w   s	    q1urp   )r1   r^   r_   r`   rN   r'   r   s   @@rq   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
:}%rp   c                      [        SSS[        /5      n [        SSS[        [        5      /5      n[        U 5      U:X  d   eg )Nr   r   r   )r1   r^   r   absr   s     rq   test_absr   y   s:    q!b!WAq!aQ[!Aq6Q;;rp   c                      [        S5      n [        S5      nX-   U R                  " U5      s=:X  a  [        SS/SS//5      :X  d   e   eg )N)r   r   r   r   r   )r   r   r   r   r   r   )r1   addrZ   r[   s     rq   test_additionr   ~   sY      	A
 	  	A
 5AEE!H8AA'7 888888rp   c            
         [         [        4 GH  n U " SS[        S5      5      nXS S 2S S 24   :X  d   eUSS S 24   [        SS/ SQ5      :X  d   eUS S 2S4   [        / SQ5      :X  d   eUSS/S S 24   [        / SQ/ SQ/5      :X  d   eUSS/S4   USS/S/4   :X  d   eUSSS/4   US/SS/4   :X  d   eUS S 2SS/4   [        SS/SS	/S
S//5      :X  d   eUS   S:X  d   eUSS2S S 24   [        / SQ/ SQ/5      :X  d   eUS S 2SS24   [        SS/SS	/S
S//5      :X  d   eUS S S2S4   USS/S4   :X  d   eUSS S S24   USSS/4   :X  d   eU " SS[        S5      5      nU/ SQS S 24   [        / SQ/ SQ/ SQ/ SQ/ SQ/5      :X  d   eUS S 2/ SQ4   [        / SQ/ SQ/ SQ/5      :X  a  GM   e   [        R                  " S5      nSUS'   SUS'   S	US'   UR                  " SS/S/5      [        S/S//5      :X  d   eUR                  " SS// SQ5      [        / SQ/ SQ/5      :X  d   eUR                  " / SQ/ SQ5      [        / SQ/ SQ/ SQ/ SQ/5      :X  d   eg )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     rq   test_fancy_index_matrixr      s   l#aE!Ha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, %  	 + $4 	1AAdGAdGAdG99aVaS!VCC-	 &
 
 
 
 99aVY'63 ,    99\<0F	< 5   rp   c                  |  ^^ [        S5      m[        S5      mTT-  n U S   S:X  d   eU S   S:X  d   eU S   S:X  d   eU S	   S:X  d   eU S
   S:X  d   eU S   S:X  d   e [        S5        U S   S:X  d   eU S   S:X  d   eU S   S:X  d   eU S	   S:X  d   eU S
   S:X  d   eU S   S:X  d   e [        TU 5      nUTR                  " U 5      :X  d   eUS   S:X  d   eUS   S:X  d   eUS   S:X  d   eUS	   S:X  d   eUS
   S:X  d   eUS   S:X  d   e[        [        UU4S j5        T[        S5      -  n [        U [         5      (       d   eU S   [        :X  d   eU S   S[        -  :X  d   eU S   S[        -  :X  d   eU S	   S:X  d   e[        T-  nX:X  d   eST-  n [        U [         5      (       d   eU S   S:X  d   eU S   S:X  d   eU S   S:X  d   eU S	   S:X  d   e [        S5        [        U [         5      (       d   eU S   S:X  d   eU S   S:X  d   eU S   S:X  d   eU S	   S:X  d   e [        [        S/S[        //5      nUS-  U:X  d   e[        [        [        /SS//5      nUS-  [        [        [        /[        [        //5      :X  d   eg ! [         a     GNf = f! [         a     Nf = f)N)r   r   r   r   r   r   r   r   r   r   r   r   r   r   r      r   r   r   z	c = a @ br   c                     > [        T T5      $ rx   )r7   r   s   rq   r}   %test_multiplication.<locals>.<lambda>   s    :1a@rp   r^   r   r   
      z	c = 5 @ b)r1   evalSyntaxErrorr7   multiply_elementwiserN   r'   r   
isinstancer^   r   r   )r\   hc2r   rZ   r[   s       @@rq   test_multiplicationr      sP     	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$   !J &J. 
J+*J+.
J;:J;c                  p  ^^^^ [        [        S 5        [        n [        SS/SS//5      mTS-  S S  U " S5      S-  U " S	5      S-  U " S
5      S-  U " S5      S-  /:X  d   eTS-  S S  / SQ:X  d   e[        / SQ/ SQ/ SQ/5      mTS-  S S  / SQ:X  d   eTS-  [	        S5      :X  d   eTS-  T:X  d   e[        S//5      S-  S   SS-  :X  d   e[	        S5      S-  [	        S5      :X  d   e[        SS/SS//5      [        S5      -  [        SS/SS//5      :X  d   e[        SS/SS//5      mT[        R                  -  S S  / SQ:X  d   e[        SS/SS//5      mT[        R                  -  S-  T:X  d   e[        SS/SS//5      [        R                  -  [        SS/[        R                  S//5      :X  d   e[        SS/SS//5      S -  [        SS/S S//5      :X  d   eSS!KJ	m  [        S[        /SS//5      T-  [        S[        T-  /SS//5      :X  d   e[        [        [        /S[        //5      T-  [        [        T-  [        [        TS-
  -  -  T-  /S[        T-  //5      :X  d   e[        [        T-  [        TS-
  -  T-  [        T-  TS-  -  [        T-  T-  -
  S[        S-  -  -  /S[        T-  [        TS-
  -  T-  /SS[        T-  //5      (       d   e[        [        SS/S[        S/SS[        //5      T-  [        [        T-  [        TS-
  -  T-  S/S[        T-  S/SS[        T-  //5      :X  d   e[        SS/SS//5      mTR                  [        S5      5      TR                  S5      :X  d   e[        S//5      mTS-  [        S"//5      s=:X  a5  TR                  [        S5      5      s=:X  a  TR                  S5      :X  d   e   e[        / S#Q/ S$Q/ S%Q/ S&Q/ S'Q/5      m[        [        U4S( j5        [        [        S) 5        [        / S*Q/ S+Q/ S,Q/5      mTS--  [        / S,Q/ S,Q/ S,Q/5      :X  d   e[        [        U4S. j5        [        [        U4S/ j5        [        SS/SS//5      mTS--  [        S0S1/S2S3//5      :X  d   e[        / S+Q/ S+Q/ S+Q/5      mTS--  [        / S+Q/ S+Q/ S+Q/5      :X  d   e[        / S*Q/ S+Q/ S+Q/5      mTS--  [        / S+Q/ S+Q/ S+Q/5      :X  d   e[!        S4S5S69m[#        TT-  [$        5      (       d   e[!        S4S5S5S79m[        [        UU4S8 j5        [!        S4S5S5S99mTT-  [        ['        ST5      ['        ST5      ['        ST5      * ['        ST5      -
  S-   /S['        ST5      S['        ST5      -
  // S+Q/5      :X  d   eTTS-   -  [        / S+Q/ S+Q/ S+Q/5      :X  d   e[        [        U4S: j5        [        / S+Q/ S;Q/ S<Q/5      mTS=-  [        / S>Q/ S?Q/ S@Q/5      :X  d   eTS=-  TS-  :X  d   e[        / S*Q/ SAQ/ S,Q/5      m[!        S45      mTT-  mTR)                  TS5      R+                  5       TS-  :X  d   e[        [        UU4SB j5        TT-  TST-  -  :X  d   e[        / S,Q/ S,Q/ S,Q/5      m[!        S4S5S5SC9mTT-  T:X  d   e[!        S4S5S5S99mTT-  [-        ST-  ST-  ST-  5      :X  d   eTT-  R)                  TS5      [	        S5      :X  d   eTT-  R)                  TS5      [/        S5      :X  d   e[        / SDQ/ SEQ/ SFQ/5      mTSG-  [-        SHSHSH5      :X  d   eT[0        -  [-        S[0        -  S[0        -  S[0        -  5      :X  d   e[        / S*Q/ S+Q/ S+Q/5      m[        [        U4SI j5        [        [        U4SJ j5        [        [        R                  [        R                  /[        R                  [        R                  //5      mT[        R                  -  T:X  d   e[        SS/SS//5      mT[        R                  -  [        [        R                  [        R                  /S[        R                  -  S[        R                  -  //5      :X  d   eg )KNc                      [        S5      S-  $ Nr   r   r1   ri   rp   rq   r}   test_power.<locals>.<lambda>  s    ):rp   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   > T R                  [        S5      5      $ Nr   )_matrix_pow_by_jordan_blocksr   r   s   rq   r}   r   /  s     > >qu Erp   c                  T    [        SS/SS//5      R                  [        S5      5      $ )Nr   r   )r1   r   r   ri   rp   rq   r}   r   2  s(    AA'7 8 U UVWX[V\ ]rp   r   r   r   r   r   r   r         $@c                     > T S-  $ N @ri   As   rq   r}   r   5  	    q#vrp   c                  "   > T [        SS5      -  $ r   r   r   s   rq   r}   r   6      q(1a.0rp   ihiO<iv0ir   T)integer)r   negativec                     > T T-  $ rx   ri   )r   r   s   rq   r}   r   @  s	    q!trp   )r   nonnegativec                  "   > T [        SS5      -  $ r   r   r   s   rq   r}   r   G  r   rp   )r   r   r   )r   r   r   g      @)   ru   Y   )i#        )i<  i  iI  r   r   r   c                  D   > T R                  TS5      R                  5       $ )N)subsdoit)Anr   s   rq   r}   r   O  s    rwwq"~224rp   )r   positiver   r   r   )r   r   r   r   r   r   r   gd%%@c                     > T S-  $ r   ri   r   s   rq   r}   r   ^  r   rp   c                     > T [         -  $ rx   r
   r   s   rq   r}   r   _  s	    q!trp   )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    @@@@rq   
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
:~&
:|$ 166166"234Aaff9>>A1vAaff9!&&!&&!1AaffHah3G HIIIIrp   c            
         [        S[        -   S[        -
  /S[        -
  S[        -   //5      n [        S5         U R                  5       R	                  5       [        [        S[        -  5      [        S5      -   S-  [        S[        -  5      * [        S5      -   S-  /[        S[        -  5      * [        S5      -   S-  [        S[        -  5      [        S5      -   S-  //5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nr   Tr   )r1   r^   rB   r   r   r   s    rq   $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!&;<+> $? ? 	? ? 
		s   B2C55
Dc                     [        S[        -   S[        -
  /S[        -
  S[        -   //5      n [        S5         U R                  5       u  pX-  UR	                  5       -  (       d   e S S S 5        g ! , (       d  f       g = fNr   T)r1   r^   rB   jordan_forminvr   PJs      rq   $test_issue_17247_expression_blowup_2r%  m  s_    1ac
QqS!A#J'(A	T	}}s1557{{ 
		s   /A22
B c            	      F   [        S[        -   S[        -
  /S[        -
  S[        -   //5      n [        S5         U S-  [        S[        S-  -  S-   SS[        S-  -  -
  /SS[        S-  -  -
  S[        S-  -  S-   //5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nr   Tr   l                )r1   r^   rB   r  s    rq   $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                      [        [        S5      5      n [        S5         U S-  [        [        S5      5      :X  d   e S S S 5        g ! , (       d  f       g = f)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    rq   $test_issue_17247_expression_blowup_4r)  z  sb    8 	q K L 	MA 
T	"uq "H  I J J 	J J 
		s   A
Ac                     [        SSS 5      n [        S5         U R                  S5      [        [        S-  SS[
        -  -
  [        S-  -  -   S[
        -  [        S-  -  -   [        S	S
9:X  d   e S S S 5        g ! , (       d  f       g = f)Nr   c                 $    SSX-   -  [         -  -   $ Nr   r   r  rz   s     rq   r}   6test_issue_17247_expression_blowup_5.<locals>.<lambda>      !rQSk!m"3rp   Tr^   r   $   r   EXdomain)r1   rB   charpolyr    r^   r
   r  s    rq   $test_issue_17247_expression_blowup_5r5    so    q!34A	T	zz#(1a42!8QT/+ABqDAI+MqY]"^^^^ 
		s   AA;;
B	c            	          [        SS[        S5       V s/ s H  n [        U -   PM     sn 5      n[        S5         UR	                  S5      S:X  d   e S S S 5        g s  sn f ! , (       d  f       g = f)Nr   @   Tbareissr   r1   r   r^   rB   detr{   r   s     rq   $test_issue_17247_expression_blowup_6r<    sZ    q!5":.:aac:./A	T	uuY1$$$ 
	 /		   AA!!
A/c                      [        SSS 5      n [        S5         U R                  S5      S:X  d   e S S S 5        g ! , (       d  f       g = f)Nr   c                 $    SSX-   -  [         -  -   $ r,  r  rz   s     rq   r}   6test_issue_17247_expression_blowup_7.<locals>.<lambda>  r.  rp   T	berkowitzr   )r1   rB   r:  r  s    rq   $test_issue_17247_expression_blowup_7rB    s<    q!34A	T	uu[!Q&&& 
		s	   <
A
c            	          [        SS[        S5       V s/ s H  n [        U -   PM     sn 5      n[        S5         UR	                  S5      S:X  d   e S S S 5        g s  sn f ! , (       d  f       g = f)Nr   r7  Tlur   r9  r;  s     rq   $test_issue_17247_expression_blowup_8rE    sY    q!5":.:aac:./A	T	uuT{a 
	 /		r=  c                  (   [        SS[        S5       V s/ s H  n [        U -   PM     sn 5      n[        S5         UR	                  5       [        / SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/5      S4:X  d   e S S S 5        g s  sn f ! , (       d  f       g = f)Nr   r7  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   rrefr;  s     rq   $test_issue_17247_expression_blowup_9rL    s    q!5":.:aac:./A	T	vvxF********$, - /56 6 	6 6 
	 /		s   A>:B
Bc                      [        SSS 5      n [        S5         U R                  SS5      S:X  d   e S S S 5        g ! , (       d  f       g = f)Nr   c                 $    SSX-   -  [         -  -   $ r,  r  rz   s     rq   r}   7test_issue_17247_expression_blowup_10.<locals>.<lambda>  r.  rp   Tr   )r1   rB   cofactorr  s    rq   %test_issue_17247_expression_blowup_10rQ    s>    q!34A	T	zz!Q1$$$ 
		s	   =
Ac                      [        SSS 5      n [        S5         U R                  5       [        SSS/S-  5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nr   c                 $    SSX-   -  [         -  -   $ r,  r  rz   s     rq   r}   7test_issue_17247_expression_blowup_11.<locals>.<lambda>  r.  rp   Tr   r0  )r1   rB   cofactor_matrixr  s    rq   %test_issue_17247_expression_blowup_11rV    sK    q!34A	T	  "fQA3r6&:::: 
		s   &A


Ac                      [        SSS 5      n [        S5         U R                  5       SSS[        -  SSS0:X  d   e S S S 5        g ! , (       d  f       g = f)Nr   c                 $    SSX-   -  [         -  -   $ r,  r  rz   s     rq   r}   7test_issue_17247_expression_blowup_12.<locals>.<lambda>  r.  rp   Tr   r   r   )r1   rB   	eigenvalsr
   r  s    rq   %test_issue_17247_expression_blowup_12r[    sJ    q!34A	T	{{}AqsAq! 4444 
		s   $A
Ac            
         [        SS[        -
  [        S-   S[        -
  /S[        -
  [        S-   S[        S-   /SS[        -
  [        S-   S[        -
  /SSS[        -
  S//5      n U R                  5       nUS   SS[        / SQ5      /4:X  d   eUS   S   [        [        S5      [        S-
  -  -
  S-   :X  d   eUS   S   S:X  d   eUS   S   S   R	                  SSS9[        [        * [        S5      [        S-
  -  -   S-
  [        S-
  -  /S[        -  [        S-  S[        -  -
  S-   -  [        S-   [        [        S5      [        S-
  -  -
  S-   -  [        S-  S[        -  -
  S-   -  -   /[        * [        S5      [        S-
  -  -   S-
  [        S-
  -  /S//5      :X  d   eUS   S   [        [        S5      [        S-
  -  -   S-   :X  d   eUS   S   S:X  d   eUS   S   S   R	                  SSS9[        [        * [        S5      [        S-
  -  -
  S-
  [        S-
  -  /S[        -  [        S-  S[        -  -
  S-   -  [        S-   [        [        S5      [        S-
  -  -   S-   -  [        S-  S[        -  -
  S-   -  -   /[        * [        S5      [        S-
  -  -
  S-
  [        S-
  -  /S//5      :X  d   eg )	Nr   r   r   )r   r   r   r   FT)deepnumerrG  )r1   r^   
eigenvectsr   r   )r   evs     rq   %test_issue_17247_expression_blowup_13ra    s   Aq1ua!e$	
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 :   rp   c                     [        SSS[        -   S[        -
  /S-  S[        -
  S[        -   /S-  -   S-  5      n [        S5         U R                  5       [        [        S-   S[        -
  [        S-   S[        -
  [        S-   S[        -
  [        S-   S[        -
  /SS[        -  SS[        -  SS[        -  SS[        -  // SQ/ SQ/ SQ/ SQ/ SQ/ SQ/5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nr   r   r   Tr   rJ  )r1   r^   rB   echelon_formr  s    rq   %test_issue_17247_expression_blowup_14rd    s    q!qsAaCjlac1Q3Z\1145A	T	~~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 
		s   BC''
C5c                     [        SSS[        -   S[        -
  /S-  S[        -
  S[        -   /S-  -   S-  5      n [        S5         U R                  5       [        [        S-   S[        -
  [        S-   S[        -
  [        S-   S[        -
  [        S-   S[        -
  //5      [        SS[        -  SS[        -  SS[        -  SS[        -  //5      /:X  d   e S S S 5        g ! , (       d  f       g = f)Nr   r   r   Tr   )r1   r^   rB   rowspacer  s    rq   %test_issue_17247_expression_blowup_15rg    s   q!qsAaCjlac1Q3Z\1145A	T	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 
		s   BC  
C.c                  6   [        SSS[        -   S[        -
  /S-  S[        -
  S[        -   /S-  -   S-  5      n [        S5         U R                  5       [        [        S-   /S[        -
  /[        S-   /S[        -
  /[        S-   /S[        -
  /[        S-   /S[        -
  //5      [        S[        -
  /[        S-   /S[        -
  /[        S-   /S[        -
  /[        S-   /S[        -
  /[        S-   //5      /:X  d   e S S S 5        g ! , (       d  f       g = f)Nr   r   r   T)r1   r^   rB   columnspacer  s    rq   %test_issue_17247_expression_blowup_16rj    s   q!qsAaCjlac1Q3Z\1145A	T	}}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 
		s   B;D


Dc                     [        SS[        S5       V s/ s H  n [        U -   PM     sn 5      n[        S5         UR	                  5       [        S/S/S/S/S/S/S/S//5      [        S/S/S/S/S/S/S/S//5      [        S	/S
/S/S/S/S/S/S//5      [        S/S/S/S/S/S/S/S//5      [        S/S/S/S/S/S/S/S//5      [        S/S/S/S/S/S/S/S//5      /:X  d   e S S S 5        g s  sn f ! , (       d  f       g = f)Nr   r7  Tr   r  r   r   r   r   rG  r   rH  r   r/  r   )r1   r   r^   rB   	nullspacer;  s     rq   %test_issue_17247_expression_blowup_17rn  	  sV   q!5":.:aac:./A	T	{{}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 
	 /		s   C7B3C<<
D
c                      [        SSS[        -   S[        -
  /S-  S[        -
  S[        -   /S-  -   S-  5      n [        S5         U R                  5       (       a   e S S S 5        g ! , (       d  f       g = f)Nr   r   r   T)r1   r^   rB   is_nilpotentr  s    rq   %test_issue_17247_expression_blowup_18rq    sd    q!qsAaCjlac1Q3Z\1145A	T	>>##### 
		s   A''
A5c                      [        [        S5      5      n [        S5         U R                  5       (       a   e S S S 5        g ! , (       d  f       g = f)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    rq   %test_issue_17247_expression_blowup_19rt    sI    q a b 	cA
 
T	&&((((( 
		s   A
Ac                     [        [        S-   S[        -
  SS/S[        -
  [        S-   S[        S-   /SS[        -
  [        S-   S/SSS[        S-   //5      n [        S5         U R                  5       [        SSS[        S-   [        S-
  -  // SQ/ SQ/ SQ/5      [        / SQSS[        -  SS/SS[        S-   S/SSS[        S-   //5      4:X  d   e S S S 5        g ! , (       d  f       g = f)	Nr   r   T)r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r1   r^   rB   diagonalizer  s    rq   %test_issue_17247_expression_blowup_20ry  "  s   UQU#UQUQU#	
QUQU#	
QU#	% 	&A
 
T	}}6AAA''''	+) $*
 "!"!QU"!AE"	$ %	#& 	& 		& 	& 
		s   #A1C
C,c                      [        [        S5      5      n [        S5         U R                  SS9[        [        S5      5      :X  d   e S S S 5        g ! , (       d  f       g = f)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    rq   %test_issue_17247_expression_blowup_21r  4  a    q c d 	eA
 
T	uuDu!VA /: -; &< < 	< < 
		   (A
A c                      [        [        S5      5      n [        S5         U R                  SS9[        [        S5      5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nr{  TLUr}  r  r  r  s    rq   %test_issue_17247_expression_blowup_22r  A  r  r  c                      [        [        S5      5      n [        S5         U R                  SS9R	                  5       [        [        S5      5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nr{  TADJr}  r  )r1   r   rB   r!  r   r  s    rq   %test_issue_17247_expression_blowup_23r  N  sj    q c d 	eA
 
T	uuEu"))+va 9: 7; 0< < 	< < 
		s   6A  
A.c                      [        [        S5      5      n [        S5         U R                  SS9[	        [        S5      5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nr{  TCHr}  r  r2   r   rB   r!  r1   r  s    rq   %test_issue_17247_expression_blowup_24r  [  sa    Q c d 	eA
 
T	uuDu!VA /: -; &< < 	< < 
		r  c                      [        [        S5      5      n [        S5         U R                  SS9[	        [        S5      5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nr{  TLDLr}  r  r  r  s    rq   %test_issue_17247_expression_blowup_25r  h  sa    Q c d 	eA
 
T	uuEu"fQ 0: .; '< < 	< < 
		r  c                      [        [        S5      5      n [        S5         U R                  5       S:X  d   e S S S 5        g ! , (       d  f       g = f)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    rq   %test_issue_17247_expression_blowup_26r  u  sC    q z { 	|A 
T	vvx1}} 
		   A
Ac            	         [        SS[        -
  [        S-   S[        -
  /S[        -
  [        S-   S[        S-   /SS[        -
  [        S-   S[        -
  /SSS[        -
  S//5      n [        S5         U R                  5       u  pUR	                  5       [        [        S5      5      R	                  5       :X  d   eU[        [        S5      5      :X  d   e S S S 5        g ! , (       d  f       g = f)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      rq   %test_issue_17247_expression_blowup_27r    s    Aq1ua!e$	
QA1a!e$Aq1ua!e$A1q5!$	& 	'A
 
T	}}xxzVA 'o %p q rx  rx  rz	z 	z z
 F1 I J K K 	K K 
		s   1A#C
C,c                      [        [        S5      5      n [        S5         U R                  5       [        S5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nr{  Ta  [
            sqrt(14609315/131072 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) + 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2 + sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 + sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2),
            sqrt(14609315/131072 - sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))/2 - sqrt(64789115132571/2147483648 - 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3) - 76627253330829751075/(35184372088832*sqrt(64789115132571/4294967296 + 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)) + 2*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3))) - 3546944054712886603889144627/(110680464442257309696*(25895222463957462655758224991455280215303/633825300114114700748351602688 + sqrt(1213909058710955930446995195883114969038524625997915131236390724543989220134670)*I/22282920707136844948184236032)**(1/3)))/2)])r1   r   rB   singular_valuesr  s    rq   %test_issue_17247_expression_blowup_28r    s]    q c d 	eA
 
T	  "a )c 'd d 	d d 
		s    A


Ac                      [        [        S5      5      n [        S5         U R                  5       S:X  d   e S S S 5        g ! , (       d  f       g = f)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    rq   test_issue_16823r    sC    q F G 	HA 
T	vvx1}} 
		r  c                  r   [        / SQS[        S5      -   S[        S5      -   S[        S5      -
  [        S5      * S-
  SSSSS/	SS[        S5      -  -   SS[        S5      -  -
  SS[        S5      -  -
  SS[        S5      -  -   SSSSS/	S	[        S5      -  S-
  SS
[        S5      -  -
  SS
[        S5      -  -   SS
[        S5      -  -   SSSSS
/	SS[        S5      -  -
  S[        S5      -  S-   S[        S5      -  S-   SS[        S5      -  -
  SSSSS/	SS
[        S5      -  -   SS
[        S5      -  -   S	[        S5      -  S-
  SS
[        S5      -  -
  SSSSS
/	S	S[        S5      -  -   S	S[        S5      -  -
  S	S[        S5      -  -
  S	S[        S5      -  -   SSSSS/	S[        S5      -
  [        S5      * S-
  S[        S5      -   S[        S5      -   SSSSS/	/5      n [        S5         U R                  5       [        SSSSSSSS[	        S5      S-  /	SSSSSSSS[	        S5      * S-  /	SSSSSSSS[	        S5      S-  /	SSSSSSSS[	        S5      * S-  /	/ SQSSSSSSSS[	        S5      * S-  /	/ SQSSSSSSSS[	        S5      * S-  /	/5      S4:X  d   e S S S 5        g ! , (       d  f       g = f)N)	r   r   r   r   r   r   r   r   r   r   r   r   rH  rl  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   rI  )r1   r   rB   rK  r   r  s    rq   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	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 
		s   .B0J((
J6c            	      
   [        [        S 5        [        [        S 5        [        [        S 5        [        [        5         S[        S5      S'   S S S 5        [        5       [        / 5      s=:X  a#  [        / /5      s=:X  a  [        SS/ 5      :X  d   e   e[	        5          [        S/S	//5      R                  5       S/S	//:X  d   e S S S 5        [	        5          [        S/S	//5      R                  R                  5       S//S	//:X  d   e S S S 5        [        S//5      n [	        5          [        R                  U S
'   S S S 5        [        [        S/SS//5      nUnUR                  UR                  :X  d   eUR                  S:X  d   eUS S  [        SSS/:X  d   e[        SS[        SSS/5      nUnUR                  UR                  :X  d   eUR                  S:X  d   eUS S  [        SSS/:X  d   eX:X  d   e[        U5      U:X  d   e[        SS[        SS5      5      n[        SS[        SS5      5      n[        XE/5      nUR                  S:X  d   eUR                  S:X  d   eUS S  / SQ:X  d   e[        [        S5      5      [        S5      :X  d   e[        [        [        S5      5      5      [        [        S5      5      :X  d   e[        U5      UR                  " 5       :X  d   e[        [        U5      5      [        U5      R!                  5       :X  d   eU[        U5      Ld   e[#        SS5      [#        SS5      S-  /[#        SS5      S-  [#        SS5      S-  //n[        U5      n U [        / SQ/ SQ/ SQ/ SQ/ SQ/5      :X  d   eU R                  5       U:w  d   e[        USS9R                  5       U:X  d   e[%        SSS5      n[#        S5      U/n[        U5      [        SS/SS/US
   US   /US   US   //5      :X  d   e[	        5          [        USS9R                  5       U V	s/ s H  o/PM     sn	:X  d   e S S S 5        [        [#        S5      [#        S5      /5      [        [#        S5      /5      :X  d   e[        [        S 5        [        [        S 5        [        SS/SS//5      n [        U S/5      n
U
[        SS/SS/SS//5      :X  d   eg ! , (       d  f       GN= f! , (       d  f       GN@= f! , (       d  f       GN= f! , (       d  f       GN= fs  sn	f ! , (       d  f       N= f)Nc                  .    [        SS[        S5      5      $ )Nr      )r1   r   ri   rp   rq   r}   test_creation.<locals>.<lambda>  s    vaE"I6rp   c                      [        SS/ 5      $ )Nr   r   r   ri   rp   rq   r}   r    s    vaR0rp   c                      [        S5      S   $ r   r   ri   rp   rq   r}   r    s    vf~a0rp   r   r   r   r   r   )r   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    [        [        S5      [        SS5      /5      $ )Nr   r   r   r1   r8   ri   rp   rq   r}   r        vtAwQ
&;<rp   c                  B    [        [        S5      [        SS5      /5      $ )Nr   r   r   r  ri   rp   rq   r}   r    r  rp   )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   r{   M2s              rq   test_creationr    s   
:67
:01
:01	
	vq 
 8vbzEVRD\EVAq"5EEEEEE		!T{m$++-A3+>>> 
"		!T{m$&&--/aSED6?BBB 
"uA		!**$ 
" 	AA A	A66QVV66Q;;Q4Aq!Q<q!aAq\"A	A66QVV66Q;;Q4Aq!Q<6M6!9>>
AuQ{
#C
AuQ|
$CzA66Q;;66Q;;Q4....#a&>SV###?3q623s1v7NNNN1!1111/!$%);)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	"    
 
 	!cE*113S7ISS7IIII 
" 47DG$%a	)::::
:<=
:<= 	AA A	F	B!Q!Q!Q01111Q 
	
 
"	!	!	! 
"	!h 8J 
"	!sN   S3#(T3T1T)'U T;U 3
T
T
T&)
T8;U  
Uc                  $   [         R                  " S[        SS5      [        SS5      S-  [        SS5      S-  [        SS5      S-  [        SS5      S-  [        SS5      S-  [        SS5      S-  5      [        / SQ/ SQ/ S	Q/ S
Q/5      :X  d   eg )Nr   r   r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )r1   	irregularr8   ri   rp   rq   test_irregular_blockr    s    AtAay$q)A+tAay{Qq	!T!AYq[$q)A+tAay{<?E	G @  rp   c                  4   [         R                  [         R                  [        [        -  [         R
                  /[        [        [        [        S-  /[        [         R                  * [        [        -  S//n [        U 5      nUR                  5       U :X  d   eg )Nr   r   )	r   Oner  r^   r_   Zeror`   r1   r  )lstr   s     rq   test_tolistr  &  sc    EE1661Q3'!Q1a41quufac1:M
NCsA88:rp   c                  $   [        SS5      R                  5       [        SS5      :X  d   e[        SS5      R                  5       [        [        SS5      5      :X  d   e[        SS5      R                  5       [        [        SS5      5      :X  d   eg Nr   r   )r>   r  r  r/   ri   rp   rq   test_as_mutabler  ,  su    A;!!#uQ{222A;##%q!)EEEEA;##%q!)EEEErp   c                     [        S5      n U S S2S S24   [        S5      :X  d   eU SS2SS24   [        S5      :X  d   e[        SSS 5      nUSS S 24   [        SSS5      :X  d   eUSS2S4   [        SSS5      :X  d   e[        / S	Q/ S
Q/ SQ/ SQ/5      nUS S 2S4   [        SS/ SQ5      :X  d   eUSS 2S S 24   [        / SQ/ SQ/5      :X  d   eg )Nr   r   r   r   c                 
    X-   $ rx   ri   rz   s     rq   r}   test_slicing.<locals>.<lambda>7      15rp   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r      r         r   r   )r   r   r  r   r  )r5   r>   r1   )m0m1m2s      rq   test_slicingr  2  s    	QBbqb"1"f:Qac1Q3h<58###	1(	)Bad8vaI....ac1f:1f----	|^=MN	OBae9q!^4444bc1f:1A BCCCCrp   c                     [        S5      n [        S5      U SS2SS24'   U [        S5      :X  d   e[        S5      U S S2S S24'   U [        S5      :X  d   e[        SSS5      U S S 2S4'   U [        S5      :X  d   e[        S5      U S S 2S S 24'   U [        S5      :X  d   e/ SQU S S 2S S 24'   U [        S5      :X  d   eSS/U S S2S4'   U [        S	5      :X  d   eg )
Nr   r   )r   r   r   r   r  r   r   r   r   rw  r   r   r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   r  r   r   r   r   r   r   r  r   r  r  r      ))r   r   r   r   )r   r   r   r   r  r  )r>   r5   r1   r   s    rq   test_submatrix_assignmentr  @  s$   aAa&Aac1Q3hK & ' ' ' ' AAbqb"1"fIA;;Q<(AadG & ' ' ' ' AhAadGa==MAadG * + + + + 1vAbqb!eH * + + + +rp   c                  j  ^  [        SSS 5      m T R                  / SQSS/5      [        SS/ SQ5      :X  d   eT R                  SS// S	Q5      [        SS/ S
Q5      :X  d   eT R                  [        S5      [        S5      5      T :X  d   e[        [        U 4S j5        [        [        U 4S j5        g )Nr   r   c                     U S-  U-   $ Nr   ri   rz   s     rq   r}   test_extract.<locals>.<lambda>]  s    !A#'rp   )r   r   r   r   r   r   )r   r   r   r   r   r   r  )r   r   r   r   r   r  c                  ,   > T R                  S/S/5      $ )Nr   r   r   r   s   rq   r}   r  a      qyy!qc2rp   c                  ,   > T R                  S/S/5      $ r  r  r   s   rq   r}   r  b  r  rp   )r1   r   r   rN   r  r   s   @rq   test_extractr  \  s    q!)*A99YA'6!Q8K+LLLL99aVY'6!Q8K+LLLL99U1XuQx(A---
:23
:23rp   c                      [        S5      n U R                  SS5      [        SSS5      :X  d   e[        SSS 5      nUR                  SS5      [        S5      :X  d   eUR                  SS	5      [        S
5      :X  d   eg )Nr   r   r   )	r   r   r   r   r   r   r   r   r   r   c                 
    X-   $ rx   ri   rz   s     rq   r}   test_reshape.<locals>.<lambda>h  r  rp   )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     rq   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Orp   c                      [        S5      n U R                  S 5      [        S5      S-  :X  d   eU R                  S 5      [        S5      :X  d   eg )Nr   c                     SU -  $ Nr   ri   r^   s    rq   r}    test_applyfunc.<locals>.<lambda>p  s    !A#rp   r   c                     gr   ri   r  s    rq   r}   r  q  s    !rp   )r5   	applyfuncr>   )r  s    rq   test_applyfuncr  n  sE    	QB<<&#a&(222<<$a000rp   c            	         [        [        [        [        -   -  S/[        [        -   [        -  [        -  [        [        [        [        [        -   -  -   -  //5      n U R                  5       nU[        [        [        -  [        S-  -   S/[        [        S-  -  [        [        S-  -  -   [        [        -  [        [        S-  -  -   [        S-  -   //5      :X  d   e[	        SSS9n[        [        [        U-  5      /5      R                  SS9[        [        U5      [        [        U5      -  -   /5      :X  d   e[        / SQ/ SQ/ S	Q/5      R                  5       [        S
S
[        SS5      // SQ/ SQ/5      :X  d   eg )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      rq   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!"#$ $ $ 9j)4599;v	
Ax1~G @   rp   c            	      :   [        [        [        5      S-  [        [        S-  5      /[        [        S-  5      [        [        5      S-  -  [        [        S-  5      [        [        5      S-  -  //5      n U R                  [        R                  " [        5      [        R                  " [        5      -  5      nU[        [        S-  [        [        5      /[        S-  [        [        5      -  [        S-  [        [        5      -  //5      :X  d   eU R                  [        R                  " [        5      [        R                  " [        5      -  5      nU[        [        S-  [        /[        [        S-  -  [        S-  [        -  //5      :X  d   eU R                  [        R                  " [        5      [        R                  " [        5      -  5      nU[        [        S-  [        * /[        * [        S-  -  [        S-  * [        -  //5      :X  d   eg r  )
r1   r   r^   r   r_   refinerU   r  r  r  r  s     rq   test_refiner    st   	#a&!)T!Q$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9rp   c            	      j   [        SS5      n [        SSSS9n U [        SSSS9:X  d   e[        SSSS5      n [        SSSS9n U [        SSSS9:X  d   eU R                  5       nUR                  " 5         X:X  d   e[        R                  " S5      nU [        SSUS9:X  d   eS	 H(  nS
 H  n[        USXBS9n X R
                  :X  a  M   e   M*     [        SSSS9n Sn[        U R                  S   5       H3  n[        U R                  S   5       H  nXU4   S:X  d  M  US-  nM     M5     US:X  d   eg )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_countr{   r|   s           rq   test_randomr    sD   1aA1aa A
1aa((((1aC A11-A
115555	AJJL6M6
--
C
137777 $G44KA8O8 % 
 	21b)AJ1771:qwwqz"AAw!|a
 #  rp   c                    ^^ [        S5      n U R                  5       [        S5      :X  d   eU R                  SS9[        S5      :X  d   eU R                  SS9[        S5      :X  d   eU R                  SS9[        S5      :X  d   eU R                  SS9[        S5      :X  d   eU R                  SS9[        S5      :X  d   e[        / SQ/ S	Q/ S
Q/5      n U R                  5       nX-  [        S5      :X  d   eU R                  SS9U:X  d   eU R                  SS9U:X  d   eU R                  SS9U:X  d   eU R                  SS9U:X  d   eU R                  SS9U:X  d   e[        / SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ S Q/ S!Q/ S"Q/ S#Q/ S$Q/5      nUR                  S%S9U-  [        UR                  S&   5      :X  d   e[        mT" / S'Q/ S(Q/ S)Q/5      m[        UU4S* jS+R                  5        5       5      (       d   e[        mT" / S'Q/ S(Q/ S)Q/5      m[        UU4S, jS+R                  5        5       5      (       d   eg )-Nr   r  r}  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   \   >#    U  H!  n[        TR                  U5      5      TL v   M#     g 7frx   r   r!  r   sr   r   s     rq   r   test_inverse.<locals>.<genexpr>  $     L.KtAEE!H~$.K   ),zGE ADJ LU CH LDL QRc              3   \   >#    U  H!  n[        TR                  U5      5      TL v   M#     g 7frx   r  r  s     rq   r   r    r  r  )r5   r!  r1   r   r/   r   splitr0   )r   AinvAAr   r   s      @@rq   test_inverser"    sq   AA557c!f555Q'''555#a&(((555Q'''555#a&(((555Q'''	 	A 557D6S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L
C\ 	A L.C.I.I.KLLLLLrp   c                     [        SS[        S-  [        -  S[        S-  -  [        [        -  -   /5      n [        [        /nU R                  U5      [        S[        -  [        -  [        S-  /[        S[        -  [        -   //5      :X  d   e[        SS[        [        S-  [        S-  -  /5      n U R                  U5      [        SS/S[        -  [        S-  -  [        S-  S-  [        S-  -  //5      :X  d   e[        S-  [        -  n[        [        /n[	        X!5      [        S[        -  S[        -  /S[        -  S//5      :X  d   e[        S-  [        S-  -  n[	        X!5      [        S[        S-  -  S[        -  [        S-  -  /S[        -  [        S-  -  S[        S-  -  [        -  //5      :X  d   e[
        [        [        S-  -  -   n[        S-  S[        S-  -  -   n[        SS[        -  /S[        -  S[        -  //5      nU[	        U[        [        [        /5      5      :X  d   eU[	        U[        [        [        /5      R                  5      :X  d   e[	        U[        [        4U/5      [        SS[        S-  -  S[        -  /S[        S-  -  S[        -  S[        -  /S[        -  S[        -  S//5      :X  d   eg )Nr   r   r   r   r   r   )r1   r^   r_   jacobianr6   r`   r  )Lsymsfganss        rq   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1v!QqSzAaC8&<====	1QT	A1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. '       rp   c                     [        [        [        5      [        [        5      /[        5      [        [        5      S-  [        [        5      S-  -   :X  d   e[        [	        [        5      [	        S[        -  5      /[        5      [	        S[        -  5      :X  d   e[        [	        [        5      [        /[        5      [	        [        5      [        [	        [        5      -  -
  :X  d   e[        S[        [        S-  /[        5      S:X  d   eS[	        [        5      -  [        [        5      -  [        -  S[        [        5      -  [	        [        5      -  [        S-  -  -   S[	        [        5      -  [        [        5      -  [        -  -
  [	        [        5      [        [        5      -  [        S-  -  -
  [	        [        5      [        [        5      -  [        S-  -  -   n [        [	        [        5      [        [        5      [        S-  /[        5      R                  5       U :X  d   e[        [	        [        5      [        [        5      [        S-  /[        SS9R                  5       U :X  d   e[        S-  * [        [        5      S-  -  [        S-  [        [        5      S-  -  -
  S[        -  [        [        5      S-  -  -
  S[        -  [        [        5      S-  -  -
  n[        [        [        5      [        [        5      [        S-  /[        5      R                  5       U:X  d   e[        [        [        5      [        [        5      [        S-  /[        SS9R                  5       U:X  d   e[        / [        5      S:X  d   eg )Nr   r   r   r/  r   rA  r}  )r=   r   r^   r   r   r   )w1w2s     rq   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   rp   c                     [        S[        /[        S//5      R                  [        S5      [        SS/SS//5      :X  d   e[        [        S/[        [        -   S//5      R                  [        S/[        S//5      [        SS/SS//5      :X  d   e[        [        S/[        [        -   S//5      R                  [        S4[        S4/5      [        SS/SS//5      :X  d   e[        [        S/[        [        -   S//5      R                  [        S[        S05      [        SS/SS//5      :X  d   e[        [        [        -  /5      R                  [        [        S-
  [        [        S-
  0SS	9[        [        S-
  [        S-
  -  /5      :X  d   e[         H9  n [        SS
/S
S//5      U R                  S5      R                  SS5      :X  a  M9   e   g )Nr   r   r   r   r   r  r   T)simultaneousr   )r1   r^   r  r_   r   r5   r   s    rq   	test_subsr2    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 !" " " 1v1v&'3771:??1a+@@@@ rp   c                     [        S[        /[        S//5      R                  [        S05      [        SS/SS//5      :X  d   e[        [        S/[        [        -   S//5      R                  [        S[        S05      [        SS/SS//5      :X  d   e[         H:  n [        SS/SS//5      U R                  S5      R                  SS05      :X  a  M:   e   g )	Nr   r   r   r   r   r  r   r   )r1   r^   xreplacer_   r   r5   r1  s    rq   test_xreplacer5  %  s    Aq6Aq6"#,,aV4AA ! ! !Aq6AE1:&'00!RB@Q"a!"# # #1v1v&'3771:+>+>1v+FFFF rp   c                  
   [        S5      n [        S5      n[        S[        -  S[        -  -   [        [        [        -  -   [        -  /U" [        5      [        U" [        5      -  -   U" [        5      -  SSU -  [        U [        -  5      U -  -
  -  [        -  //5      nUR                  5         U[        [        [        -   [        [        -  -  S[        -   /S[        -   SSS[        [        U -  5      -  -
  [        U -  -  -  //5      :X  d   eS[        -   S-  n[        U//5      nUR                  5         U[        U//5      :X  d   eUR                  [        S9  U[        UR                  [        S9//5      :X  d   eg )Nr   r'  r   r   )ratio)	r   r   r1   r^   r_   r   r   r%   r   )r   r'  r   eqs       rq   test_simplifyr9  -  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1rp   c                     [        / SQ/ SQ/5      n U R                  [        SS/SS/SS/SS/SS/SS/SS/S	S	/S
S
/SS//
5      :X  d   eU R                  R                  U :X  d   eU R                  U R                  5       :X  d   eg )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    rq   test_transposer<  >  s    ..0 	1A33&QFFFFFFFFFF	% 	& 	& 	& 	& 3355A::33!++-rp   c                     [        S[        S// SQ/5      n U R                  [        SS/[        S/SS//5      :X  d   eU R                  [        S[        * S// SQ/5      :X  d   eU R                  U R	                  5       :X  d   eU R
                  U R                  R                  :X  d   eU R
                  [        SS/[        * S/SS//5      :X  d   eg )Nr   r   )r   r   r   r   r   )r1   r
   r  C	conjugateHr  s    rq   test_conjugaterA  O  s    Aq	 	A 33&1a&a&a&" # # # # 33&1qb!*$& ' ' ' '33!++-33!##%%<<33&Aq'2q'q'# $ $ $ $rp   c            
      $   [        [        S 5        [        S[        [        [        /SS[        [        /SSS[        // SQ/5      n U R                  [        / SQ[        * SSS/[        * [        * SS/[        * [        * [        S//5      :X  d   eg )Nc                  ,    [        S5      R                  $ r  )r5   Dri   rp   rq   r}   !test_conj_dirac.<locals>.<lambda>b  s    3q688rp   r   r   rw  r  r   )rN   AttributeErrorr1   r
   rD  r  s    rq   test_conj_diracrG  a  s    
>+,Aq!Aq!Aq! 	A
 33&*2A*2r2*2rAr*, - - - -rp   c                  X    [        / SQ/ SQ/ SQ/5      n U R                  5       S:X  d   eg )Nr   r   r   r   r   r   )r   r   r   r  r1   tracer  s    rq   
test_tracerM  o  s-    	 	A 779??rp   c                  ^    [        [        SS/S[        S//5      n U R                  S:X  d   eg )Nr   r  )r1   r^   r_   r   r  s    rq   
test_shaperO  v  s4    Aq	Aq	 	A77frp   c                     [        [        SS/S[        S//5      n U R                  SS 5        U [        [        SS/S[        S-   S//5      :X  d   eU R	                  SS 5        U [        [        S-   SS/S[        -   [        S-   S//5      :X  d   eU R                  S5      [        [        S-   SS//5      :X  d   eU R                  S5      nSUS'   U S   [        S-   :X  d   eU SS S	24   nSUS'   U S   [        S-   :X  d   eU R                  S5      nU[        [        S-   S[        -   /5      :X  d   eSUS'   U S   [        S-   :X  d   eU S S 2S4   nSUS'   U S   [        S-   :X  d   eg )
Nr   r   c                     X-   S-   $ Nr   ri   )rr|   s     rq   r}   !test_col_row_op.<locals>.<lambda>  s
    QUQYrp   r   r   c                     U [         U-  -   $ rx   )r_   )r\   r|   s     rq   r}   rT    s    QAXrp   *   r   r   )r1   r^   r_   row_opcol_oprowcol)r   r1c1s      rq   test_col_row_opr]  |  s   Aq	Aq	 	AHHQ&'1AE1' ( ( ( ( HHQ%&QAq)QAq)+ , , , ,
 558vAq!}o....	
qBBqET7a!e	
1crc6BBqET7a!e	
qBQA''''BqET7a!e	
1a4BBqET7a!erp   c                      [        / SQ/ SQ/5      n U R                  SS5        U S   S:X  d   eU S   S:X  d   eU S   S	:X  d   eg )
Nr   r   r   r   r   r   r   r   r   r   r   )r1   row_multr  s    rq   test_row_multra    sS     	AJJqOS6R<<S6Q;;S6R<<rp   c                      [        / SQ/ SQ/ SQ/5      n U R                  SSS5        U S   S:X  d   eU S	   S
:X  d   eU S   S:X  d   eg )Nr   r_  r   r   r   r   r   r   r   r   r   r   r   r   r   )r1   row_addr  s    rq   test_row_addrf    s[     	A IIa!S6Q;;S6Q;;S6Q;;rp   c                  $   [         S S  H  n U R                  S5      nUR                  SSS 5        X" / SQ/ SQ/ SQ/5      :X  d   eU R                  S5      S-  nS	US
'   UR                  SSS 5        U  X" / SQ/ SQ/ SQ/5      :X  a  M   e   g )Nr   r   r   r   c                     U SU-  -   $ r  ri   r   us     rq   r}   !test_zip_row_op.<locals>.<lambda>      AaCrp   rI  r   r   r   r   r   r   c                     U SU-  -   $ r  ri   ri  s     rq   r}   rk    rl  rp   )r   r   r   )r   r   r   r  )r   r5   
zip_row_op)r   r   s     rq   test_zip_row_oprp    s    r{GGAJ	Q/0C""$ % % 	% % GGAJqL$	Q/0!C##% & & 	& & rp   c                      [        / SQ5      n [        / SQ5      n[        / SQ5      nU S;  d   eU S;  d   eU S:w  d   eX:X  d   eX:w  d   eg )Nr   )r   r   r   ri   )r   r   r   )r   rZ   r[   s      rq   test_issue_3950rr    sU    yAyAyARS6M66M66M6rp   c                  h    " S S5      n  " S S5      nU " 5       nU" 5       n[        / SQ5      nXC   S:X  d   eSXC'   US   S:X  d   e[        / SQ/ S	Q/5      nXBU4   S
:X  d   eUSU4   S
:X  d   eXBS4   S
:X  d   eSXBU4'   US   S:X  d   eS
USU4'   US   S
:X  d   eSXBS4'   US   S:X  d   eg )Nc                       \ rS rSrS rSrg)test_issue_3981.<locals>.Index1i  c                     grR  ri   selfs    rq   	__index__)test_issue_3981.<locals>.Index1.__index__      rp   ri   Nrk   rl   rm   rn   ry  ro   ri   rp   rq   Index1ru        	rp   r}  c                       \ rS rSrS rSrg)test_issue_3981.<locals>.Index2i  c                     gr  ri   rw  s    rq   ry  )test_issue_3981.<locals>.Index2.__index__  r{  rp   ri   Nr|  ri   rp   rq   Index2r    r~  rp   r  r   r   r   r   r_  r   r   r   r   r   r   )r}  r  index1index2r   s        rq   test_issue_3981r    s       XFXFyA9>>AIQ4199	9%&AV^!!!QY<1QY<1AfnT7a<<AaiLT7a<<AaiLT7a<<rp   c                    ^  [        [        S5      S/5      m [        U 4S j[        S5       5       5      (       d   e[        U 4S j[        S5       5       5      (       d   e[        U 4S j[        S5       5       5      (       d   eg )Nr   r   c              3   t   >#    U  H-  nTR                   " 5       U   TU   R                  5       :H  v   M/     g 7frx   evalfr   r{   rZ   s     rq   r   test_evalf.<locals>.<genexpr>  s*     >Xqwwy|qtzz|+Xs   58r   c              3   x   >#    U  H/  nTR                   " S 5      U   TU   R                  S 5      :H  v   M1     g7fr   Nr  r  s     rq   r   r    s.     @x!qwwqz!}!

1-x   7:c              3   x   >#    U  H/  nTR                   " S 5      U   TU   R                  S 5      :H  v   M1     g7fr  r   r  s     rq   r   r    s.     8x!qss1vayAaDFF1I%xr  )r1   r   r   r   rZ   s   @rq   
test_evalfr    sf    Q|A>U1X>>>>>@uQx@@@@@8uQx88888rp   c                  X   [        [        [        /[        [        //5      n U R                  " 5       SL d   e[        / SQ/ SQ/5      n U R                  " 5       SL d   e[        / SQSS[        S//5      n U R                  " 5       SL d   e[        S[        S	//5      n U R                  " 5       SL d   e[        / S
Q/5      n U R                  " 5       SL d   e[        S/[        /S	//5      n U R                  " 5       SL d   e[        S/S/S	//5      n U R                  " 5       SL d   eg )NTr  r  Fr   r   r   r   r   r   r   )r1   r^   is_symbolicr  s    rq   test_is_symbolicr    s   AA A==?d"""l+,A==?e###q!Ql+,A==?d"""Aq	{A==?d"""	{A==?e###aS1#A==?d"""aS1#A==?e###rp   c                      [        / SQ/5      n U R                  SL d   e[        S/S/S//5      n U R                  SL d   e[        SS5      n U R                  SL d   eg )Nr   Tr   r   r   Fr   )r1   is_upperr>   r  s    rq   test_is_upperr    se    	{A::aS1#A::aA::rp   c                      [        / SQ/5      n U R                  SL d   e[        S/S/S//5      n U R                  SL d   eg )Nr   Fr   r   r   T)r1   is_lowerr  s    rq   test_is_lowerr    sH    	{A::aS1#A::rp   c                      [        SS/ SQ5      n U R                  " 5       (       d   e[        SS/SS//5      n U R                  " 5       (       a   e[        / 5      n U R                  " 5       (       d   eg )Nr   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r1   rp  r  s    rq   test_is_nilpotentr    sj    q!EFA>>AA A~~r
A>>rp   c                     Su  p[        X5      nUR                  " S5        S[        X5      -  nX#:X  d   eUR                  UR                  s=:X  a  S:X  d   e   eUR                  UR                  s=:X  a  S:X  d   e   eUR
                  UR
                  s=:X  a  S:X  d   e   e[        S5      [        SS5      :X  d   e[        S5      [        SS5      :X  d   e[        SS5      [        SSS/S-  5      :X  d   e[        SS5      [        SSS/S-  5      :X  d   eUR                  " S5        U[        X5      :X  d   eg )N)r   r   r   r   r   r   r   r   )r>   fillr8   r   r   r   r1   )r   r   rZ   r[   s       rq   test_zeros_ones_fillr    s)   DAaAFFAK	DJA6M666QVV q     66QVV q     77agg''''''8uQ{"""7d1aj   A;&As1u----1:1qc!e,,,,FF1Iarp   c                      [        S5      n U [        5       :X  d   e[        SS5      n U R                  S:X  d   eU R                  S:X  d   e[        SS5      n U R                  S:X  d   eU R                  S:X  d   eg )Nr   r   )r>   r1   r   r   r  s    rq   test_empty_zerosr  +  so    aA==aA66Q;;66Q;;aA66Q;;66Q;;rp   c                     [        [        S-  [        [        -  /[        [        [        5      -  [        [	        [        5      -  //5      n U R
                  " [        5      [        S[        -  [        /[        [        5      [	        [        5      //5      :X  d   e[        [        [        * [        S-  /[        [        5      S[        -  [        [        * 5      -
  [        S[        -  -   //5      R                  [        [        5      [        [        [        * [        /[        S[        //5      :X  d   e[        [        [        5      S-
  [        -  S[        -  [        [        -  -   [        [        -  /S[        -  [        [        5      [        [        [        S-   5      5      //5      R                  [        S5      [        / SQ[        S[        S5      //5      :X  d   eU R                  " [        5      [        [        SS5      [        S-  -  [        [        S-  -  S-  /[        S-  [        [        5      -  S-  [        S-  [	        [        5      -  S-  //5      :X  d   eg )Nr   r   r   )r   r   r   r   )r1   r^   r_   r   r   r   r   limitr   r   r   r   r  s    rq   test_issue_3749r  6  s   AqsaAh#a&123A66!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?+,- - - ;;q>V	!Q1	a1fQh'	
Ac!fQ1SVA&%( ) ) ) )rp   c                      [        S5      n U R                  SS5        S H'  nU R                  US S9U R                  SS9:X  a  M'   e   g )	Nr   r   r   )r|  r  c                     U S:H  $ r   ri   r  s    rq   r}   %test_inv_iszerofunc.<locals>.<lambda>J  s    arp   )r~  
iszerofuncr  r}  )r5   col_swapr!  )r   r~  s     rq   test_inv_iszerofuncr  F  sQ    AAJJq!uuF/?u@EEE  	    rp   c                  $   [        S5      u  p[        U [        U5      -  U [        U5      -  /5      n[        X/5      nUR	                  U5      nXBR	                  UR
                  5      :X  d   eXBR
                  R	                  U5      :X  d   eXBR
                  R	                  UR
                  5      :X  d   eUR
                  [        UR                  S   5      -  U-  nUR                  [        5      nU[        SS/SU S-  //5      :X  d   eg )Nrho,phir   r   r   )
r   r1   r   r   r$  r  r5   r   r  r&   )rhophiXYr$  r(  s         rq   test_jacobian_metricsr  N  s    y!HCCHc#c(l+,AzA	

1A

133q!!!!qss####	C
OAA	HAACF,----rp   c                  :   [        S5      u  p[        U [        U5      -  U [        U5      -  U S-  /5      n[        X/5      n[        [        U5      U * [        U5      -  /[        U5      U [        U5      -  /SU -  S//5      nUR	                  U5      U:X  d   eg )Nr  r   r   )r   r1   r   r   r$  )r  r  r  r  r$  s        rq   test_jacobian2r  [  s    y!HCCHc#c(lCF34AzA	SC4C=!	SCCL!cEq! 	A
 ::a=Arp   c                     [        [        [        [        -   [        -   5      [        [        [        -   [        -   5      [        [        [        -   [        -   5      /5      n [        [        [        [        /5      n[        SS5       H  n[        SS5       Ho  nU S U2S S 24   nUS U2S S 24   nUR                  U5      nUR                  U:X  d   eUR                  U:X  d   e[        U5       H  nUS S 2U4   U:X  a  M   e   Mq     M     g Nr   r   )	r1   r   r^   r_   r`   r   r$  r   r   )r  r  r{   r|   X_sliceY_slicer$  ks           rq   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')))   rp   c                    ^ ^ [        [        [        [        -   [        -   5      [        [        [        -   [        -   5      /[        [        [        -   [        -   5      [        [        [        -   [        -   5      //5      m [        [        U 4S j5        T SS S 24   m [        [        [        /[        [        //5      m[        [        U U4S j5        [        [        U 4S j5        g )Nc                  V   > T R                  [        [        [        [        /5      5      $ rx   r$  r1   r^   r_   r`   r  s   rq   r}   (test_nonvectorJacobian.<locals>.<lambda>x  s    ajjAq	):;rp   r   c                  &   > T R                  T5      $ rx   )r$  r  r  s   rq   r}   r  {  s    ajjmrp   c                  d   > T R                  [        [        [        /[        [        //5      5      $ rx   r  r  s   rq   r}   r  |  s     ajj1a&1a&0B)CDrp   )r1   r   r^   r_   r`   rN   	TypeErrorr  s   @@rq   test_nonvectorJacobianr  u  s    QUQYQUQY0QUQYQUQY02 	3A
9;<	!Q$AAA A
9+,
9DErp   c                      [        SS/SS//5      n U R                  5       nUR                  S:X  d   e[        S5       H  nX   US-   :X  a  M   e   g Nr   r   r   r   )r1   vecr   r   )r   m_vecr{   s      rq   test_vecr    sV    AA AEEGE::??1Xx1q5    rp   c                     [        SS/SS//5      n U R                  5       nUR                  S:X  d   e[        S5       H  nX   US-   :X  a  M   e   U R                  SS9nUS   S:X  d   e[        S[        [        [
        -   -  /[
        [        -  [        S-  -   S//5      n U R                  SS9nUS   [
        [        -  [        S-  -   :X  d   e[        S[        [        [
        -   -  /[
        [        -  S//5      n U R                  SSS9nUS   [
        [        -  :X  d   e[        [        S 5        [        [        S	 5        [        [        S
 5        [        [        S 5        g )Nr   r   r   F)diagonalr   )r  check_symmetryc                  :    [        SS//5      R                  5       $ r  r1   vechri   rp   rq   r}   test_vech.<locals>.<lambda>      v1vh/446rp   c                  @    [        SS/SS//5      R                  5       $ r  r  ri   rp   rq   r}   r        v1v1v&67<<>rp   c                  :    [        SS//5      R                  5       $ r  r  ri   rp   rq   r}   r    r  rp   c                  @    [        SS/SS//5      R                  5       $ r  r  ri   rp   rq   r}   r    r  rp   )	r1   r  r   r   r^   r_   rN   r'   r  )r   m_vechr{   s      rq   	test_vechr    sH   AA AVVXF;;!1XyA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
:>?rp   c                     ^  [        / SQ5      [        / SQ5      :X  d   eSSS//m [        [        U 4S j5        [        T SS9[        / SQ5      :X  d   eg )Nr   r   r   r   c                     > [        T 5      $ rx   )r4   r   s   rq   r}   test_diag.<locals>.<lambda>  s	    tAwrp   F)strict)r4   r1   rN   r  r   s   @rq   	test_diagr    sK    	?fY////	
AsA
:'% F9$5555rp   c                  F   [        SS/SS//5      n [        S[        /[        S//5      n[        S[        S/[        S[        /[        [        [        //5      nU R                  " 5       U /:X  d   eUR                  " 5       U/:X  d   eUR                  " 5       U/:X  d   eg Nr   r   r   )r1   r^   r_   r`   get_diag_blocksrZ   r[   r\   s      rq   test_get_diag_blocks1r    s    AA AAA AAq	Aq!9q!Qi01A1#%%%1#%%%1#%%%rp   c                     [        SS/SS//5      n [        S[        /[        S//5      n[        S[        S/[        S[        /[        [        [        //5      n[	        XU5      R                  5       XU/:X  d   e[	        XU5      R                  5       XU/:X  d   e[	        XU5      R                  5       XU/:X  d   e[	        X"U5      R                  5       X"U/:X  d   eg r  )r1   r^   r_   r`   r4   r  r  s      rq   test_get_diag_blocks2r    s    AA AAA AAq	Aq!9q!Qi01Aa=((*qQi777a=((*qQi777a=((*qQi777a=((*qQi777rp   c                     [        SS/SS//5      n [        S[        /[        S//5      n[        S[        S/[        S[        /[        [        [        //5      n[	        XU5      nUR                  SS9[	        U R
                  " 5       UR
                  " 5       UR
                  " 5       5      :X  d   e[	        XU5      nUR                  SS9[	        U R
                  " 5       UR
                  " 5       UR
                  " 5       5      :X  d   e[	        XU5      nUR                  SS9[	        U R
                  " 5       UR
                  " 5       UR
                  " 5       5      :X  d   e[	        X XX 5      nUR                  SS9[	        U R
                  " 5       U R
                  " 5       UR
                  " 5       U R
                  " 5       UR
                  " 5       U R
                  " 5       5      :X  d   eUR                  SSS9[	        U R
                  " SS9U R
                  " SS9UR
                  " SS9U R
                  " SS9UR
                  " SS9U R
                  " SS95      :X  d   eg )	Nr   r   r   T)try_block_diagr  )r  r~  r}  )r1   r^   r_   r`   r4   r!  )rZ   r[   r\   r   s       rq   test_inv_blockr    s   AA AAA AAq	Aq!9q!Qi01AQ1A555%aeegquuw)HHHHQ1A555%aeegquuw)HHHHQ1A555%aeegquuw)HHHHQ1A555%	!%%'1557AEEGQUUW*> > > >55U53t	UQUU%0!%%u2E	UQUU%0!%%u2E8G G G Grp   c                  f   [        [        S 5        [        [        S 5        [        [	        S5      5      [        S5      :X  d   e[        [        S5      5      [        S5      :X  d   e[        [        S 5        [        [	        S5      5      [        S5      :X  d   e[        [        S5      5      [        S5      :X  d   e[        [        S 5        [        [	        S5      [        S5      5      [        SS5      :X  d   e[        [        S 5        [        [        S 5        [        [        S	 5        g
)z[
Check that matrix dimensions can be specified using any reasonable type
(see issue 4614).
c                      [        SS5      $ )Nr   r   r>   ri   rp   rq   r}   $test_creation_args.<locals>.<lambda>  s
    uQ|rp   c                      [        SSSS5      $ Nr   r   r   r   r  ri   rp   rq   r}   r    s    eAq!Q/rp   r   c                      [        S5      $ N      @r  ri   rp   rq   r}   r    s    uRyrp   c                      [        S5      $ r  r5   ri   rp   rq   r}   r    s    s2wrp   r   c                      [        S5      $ Nr   r   ri   rp   rq   r}   r    s    fQirp   c                      [        SS5      $ r   r   ri   rp   rq   r}   r    s
    fQlrp   c                      [        SS//5      $ r   r   ri   rp   rq   r}   r    s    vq1#h/rp   N)rN   r  r  r>   ry   r   r5   r8   ri   rp   rq   test_creation_argsr    s    
 :+,
9/0Q=E!H$$$a(((
:()s1v;#a&   wqz?c!f$$$
:'A
#tAqz111
9'(
9*+
:/0rp   c                     [        SS/ SQ5      n U R                  5       (       a   eU R                  5       (       d   eU R                  SS9(       d   e[        SS/ SQ5      n U R                  5       (       d   e[        SSS5      n U R                  5       (       d   eU R                  5       (       d   e[        SS/ SQ5      n U [        SSS5      :X  d   e[        SS[	        SS5      5      n U R                  5       (       a   eU R                  5       (       d   e[        S	5      n U R                  5       (       d   e[        S
5      n U R                  5       (       d   e[        SSS[
        S-  S[
        -  -   S-   [        [
        S-   S-  SS[        SS/	5      n U R                  5       (       d   eU R                  SS9(       a   eU R                  5       R                  SS9(       d   eg )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    rq   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2rp   c                  x  ^ [        SS[        -   /S[        -
  S//5      mTR                  5       (       d   e[        SS/ SQ5      mTR                  5       (       a   eTR                  5       (       a   e[	        [
        U4S j5        [        SSS5      mTR                  5       u  pU [        S5      :X  d   eUT:X  d   e[        SS/ SQ5      mTR                  5       (       d   eTR                  5       (       d   eTR                  5       u  pU R                  5       T-  U -  U:X  d   e[        SS/ SQ5      mTR                  5       (       d   eTR                  5       (       d   eTR                  5       u  pU R                  5       T-  U -  U:X  d   eU [        S5      :X  d   eUT:X  d   e[        SS/ SQ5      mTR                  5       (       d   eTR                  5       u  pU R                  5       T-  U -  U:X  d   e[        SS/ S	Q5      mTR                  5       (       d   eTR                  5       u  pU R                  5       T-  U -  U:X  d   eU  H  nUR                  5       S   S:X  a  M   e   [        SS/ S
Q5      mTR                  5       (       d   eTR                  5       (       d   eTR                  5       u  pU R                  5       T-  U -  U:X  d   eU [        SS/SS//5      :X  d   e[        SS/ SQ5      mTR                  S5      (       a   e[	        [        U4S j5        TR                  5       (       d   eTR                  5       u  pU R                  5       T-  U -  U:X  d   e[        SS/ SQ5      mTR                  5       (       a   e[	        [        U4S j5        [        SS/ SQ5      mTR                  5       (       a   e[	        [        U4S j5        [        S5      u  p4pV[        SSX5XT/5      mTR                  5       (       d   eTR                  5       (       d   eg )Nr   r   r   r   r   r   r  r   r   c                  $   > T R                  5       $ rx   rx  r   s   rq   r}   &test_diagonalization.<locals>.<lambda>      rp   r  )r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   rG  r   r  r   )r   r   r   r   Tc                  &   > T R                  S5      $ )NTr  r   s   rq   r}   r  1  s    d 3rp   r   r   r   r   c                  $   > T R                  5       $ rx   r  r   s   rq   r}   r  9      rp   )	r   r   r   r  r   r   r   r  r   c                  $   > T R                  5       $ rx   r  r   s   rq   r}   r  =  r
  rp   a b c d)r1   r
   rs  r  rN   r)   r4   rx  r5   r!  as_numer_denomr  r(   r   )r#  rD  r{   rZ   r[   r\   r]   r   s          @rq   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""$$$$
;/0q!56A""$$$$
;/0 #JA!q!aA\"A>>    rp   c                     ^  [        SS/SS//5      m T R                  " 5       SL d   eST S'   T R                  " 5       SL d   e[        SS/SS//5      m T R                  " 5         ST S'   [        [        U 4S j5        g )Nr   r   Tr   Fc                  &   > T R                   " 5       $ rx   r  r  s   rq   r}   "test_issue_15887.<locals>.<lambda>P  s    rp   )r?   rs  rx  rN   r(   r  s   @rq   test_issue_15887r  F  s    QFQF+,A D(((AdG E)))QFQF+,AMMOAdG
;/0rp   c            	        ^ [        SS/ SQ5      m[        [        U4S j5        [        SS/ SQ5      m[        SS/ SQ5      n TR                  5       u  pX:X  d   eU TR	                  5       S   :X  d   e[        SS/ SQ5      m[        SS/ S	Q5      n TR                  5       u  pX:X  d   e[        SS/ S
Q5      m[        SS/ SQ5      n TR                  5       u  pX:X  d   e[        SS/ SQ5      m[        SS/ SQ5      n TR                  5       u  pX:X  d   e[        SS/ SQ5      m[        SS/ SQ5      n TR                  5       u  pX:X  d   e[        SS/ SQ5      m[        SS/ SQ5      n TR                  5       u  pX:X  d   e[        SS/ SQ5      mTR                  5       (       a   e[        SS/ SQ5      n TR                  5       u  pX:X  d   e[        [        SSS9[        SSS9/[        SSS9[        SSS9//5      mTR                  5       u  pUR                  5        H,  n[        U[        5      (       d  M  UR                  S:X  a  M,   e   g )Nr   r   r  c                  $   > T R                  5       $ rx   )r   r   s   rq   r}   "test_jordan_form.<locals>.<lambda>V  r  rp   )	r   r  r   r   ir   r   ir  )	r   r   r   r   r   r   r   r   r   r   	r   r   r   rG  r   r   r  r   r   )	r   r   r   r   r   r   r   r   r   )	r   r   r   r   rH  r   r   r/  )	r   r   r   r   r   r   r   r   r   )	r   rH  r   r   rl  r   r   r   )	r   r   r   r   r   r   r   r   r   r   )r   r   r  r   r   r   r   r   r   r   r  r   r   r   r   r   )r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r/  r   r   r   r   r   r  r  r/  r   r   r   r   )r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   r   r   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   rx  rs  r	   valuesr   _prec)Jmustr#  r$  termr   s       @rq   test_jordan_formr   S  sV   q!+,A
!89 	q!:;A1a56E==?DA::AMMOA&&&& 	q!23A 1a45E==?DA:: 	q!45A 1a78E==?DA:: 	q!34A1a45E==?DA::q!LMA1a  E
 ==?DA::q!LMA 1a ' (E ==?DA::q!JKA""$$$$1aIJE==?DA:: 	u,eES.IJ8CH%PUadJefh 	iA==?DA
dE""::$$$ rp   c            	      b   [        / SQ/ SQ/ SQ/ SQ/5      n SS[        -  -
  nSS[        -  -   n[        USSS/SUSS/SSUS/SSSU//5      n[        USSS/SUSS/SSUS/SSSU//5      nU R                  5       u  pVXc:X  d  Xd:X  d   e[        XV-  UR	                  5       -  5      U :X  d   eg )	N)r   r   r   r   )rG  r   r   r   )r   r   r   r   )r   r   rG  r   r   r   r   r   )r1   r
   r   r%   r!  )r   pqJmust1Jmust2r#  r$  s          rq   #test_jordan_form_complex_issue_9274r&    s        " 	#A 	
AaCA	AaCAaAq\Aq\Aq\Aq\# $F aAq\Aq\Aq\Aq\# $F ==?DA;!+%%ACK A%%%rp   c                      [        / SQ/ SQ/ SQ/ SQ/5      n U R                  5       u  pU[        / SQ/ SQ/ SQ/ SQ/5      :X  d   eU[        / S	Q/ SQ/ SQ/ SQ/5      :X  d   eg )
Nr  r  )r   r   r   r   rw  r   r   r   r   r  r  r  r  )r1   r   r"  s      rq   test_issue_10220r)    s     	A ==?DA$$$& ' ' ' ' $$$$	& ' ' ' 'rp   c                     [        / SQ/ SQ/ SQ/ SQ/5      n U R                  5       u  pUR                  5       [        [        * [        * S-  [        [        S-  /S[        -   SS[        -
  S/S[	        S5      * S-  [        S-  -
  S[	        S5      * S-  [        S-  -   // S	Q/5      :X  d   eU[        [        * SSS/S[        * SS/SS[        S/SSS[        //5      :X  d   eg )
Nrv  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$  s      rq   test_jordan_form_issue_15858r.    s    	 	A
 ]]_FQ88:R1"Q$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!	    rp   c                  <   [        S5      u  pn[        U* U -
  US-  X-   -  -   X-  X-   -  /X-  X-   -  U* US-  X-   -  -   //5      nUR                  [        5      nU[	        [        S-  X-  X -  -   SU-  U-  -   X-   -  [        -  -   X-  U -  X-   -  -   [        SS9:X  d   e[        U5      [        L d   e[        SS/SS//5      nUR                  5       UR                  [        5      s=:X  a!  [        [        S-  [        -
  S-
  5      :X  d   e   e[        SS/[        S//5      nUR                  [        5      nUR                  [        :w  d   eUR                  5       R                  UR                  [        5      [        S-  S[        -  -
  :X  d   eg )	Nz
UA K_i K_wr   zZZ(K_i,K_w,UA)r2  r   r   r   r   )
r   r1   r4  r^   r   r   r    genas_exprr  )UAK_iK_wr   r4  r"  s         rq   test_Matrix_berkowitz_charpolyr5    s   <(LBS#S!VSY//sw	7JKGSY/#Q	8J1JKM 	NA zz!}HQTSVcf_quSy039=a??
CI !*:	<< < < >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3rp   c            
         [        S5      n [        R                  " SU 5      nUR                  5       [        [	        U 5      //5      :X  d   e[        R                  " SU 5      nUR                  5       [        [	        U 5      [	        U 5      [	        U 5      S-  /S[	        U 5      [	        U 5      /SS[	        U 5      //5      :X  d   eg )Nlamdar   r   r   r   )r   r1   jordan_block_eval_matrix_exp_jblockr   lr   s     rq   test_exp_jordan_blockr<    s    wAAq!A$$&&3q6(*<<<<Aq!A$$&VSVSVAX&AA3q6N 	  rp   c            	         [        SS/SS//5      n [        [        S5      S[        S5      -  S-  S[        S5      -  S-  -   /S[        S5      //5      nU R                  5       U:X  d   e[        U 5      U:X  d   e[        SS/SS//5      n U R                  5       [        [        S/S[        //5      :X  d   e[        U 5      [        [        S/S[        //5      :X  d   e[        SS/SS//5      n U R                  5       [        [        [        S5      -  [        * [	        S5      -  /[        [	        S5      -  [        [        S5      -  //5      :X  d   eg )	Nr   r   r   r  rG  r   r   r   )r1   r   r   r   r   )r   m_exps     rq   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Krp   c                    ^ [        S5      n [        R                  " SU 5      mTR                  5       [        [	        U 5      //5      :X  d   e[        R                  " SU 5      mTR                  5       [        [	        U 5      SU -  SSU S-  -  -  SSU S-  -  -  /S[	        U 5      SU -  SSU S-  -  -  /SS[	        U 5      SU -  /SSS[	        U 5      //5      :X  d   e[        / SQ/ S	Q/ S
Q/5      m[        [        U4S j5        g )Nr7  r   r   r   r   r   r   r   r   r	  c                  $   > T R                  5       $ rx   )r   r   s   rq   r}   test_log.<locals>.<lambda>  s    rp   )r   r1   r8  _eval_matrix_log_jblockr   rN   r(   r:  s    @rq   test_logrD    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
 ;(rp   c                  >   [        [        [        4S45      n U R                  [        5      (       d   eU R                  [        5      (       a   eU R                  [
        5      (       d   eU R                  [        S5      n U R                  [        5      (       a   eg )Nr  r   )r1   r^   r_   hasr`   r   r  r   s    rq   test_hasrG     sm    A A5588O8uuQxx<55===	q!AuuQxx<xrp   c            	          [        S5      n [        SSU [        U 5      S-  [        U 5      S-  -   [        R
                  /5      n[        U5      u  p#pEU[        R
                  :X  d   eg )Nr^   r   r   r   )r   r1   r   r   r   r  r,   r^   columnpivot_offset	pivot_valpivot_assumed_nonzero
simplifieds         rq   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero1rO  *  s_     	sAAq1c!fai#a&!)3QVV<=F$V, ?L2rp   c            
          [        S5      n [        SSU [        U 5      S-  [        U 5      S-  -   U S-  -   [        U 5      S-  [        U 5      S-  -   /5      n[	        U[
        S9u  p#pEUS:X  d   eg )Nr^   r   r   r   simpfunc)r   r1   r   r   r,   r-   rI  s         rq   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero2rS  6  s~     	sAAqVQYs1vqy(A-VQYs1vqy(*+F
 	%Vi@ ?L2>>rp   c            
      f   [        S5      n [        SSU [        U 5      S-  [        U 5      S-  -   U -   [        U 5      S-  [        U 5      S-  -   /5      n[	        U[
        S9u  p#pE[        U5      S:X  d   eUS   S   S:X  d   eUS   S   SU -   :X  d   eUS   S   S:X  d   eUS   S   S:X  d   eg )Nr^   r   r   r   rQ  r   )r   r1   r   r   r,   r-   lenrI  s         rq   +test_find_reasonable_pivot_naive_simplifiesrV  E  s     	sAAqVQYs1vqy(*VQYs1vqy(*+F
 	%Vi@ ?L2 z?aa=q   a=qs"""a=q   a=q   rp   c                  V  ^ ^ [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [
        S 5        [        [        S	 5        [        [        S
 5        [        [        S 5        [        [        S 5        [        [
        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [
        S 5        [        [        S 5        [        [        S 5        [        [
        S 5        [        [        S 5        [        [
        S 5        [        [        S 5        [        [
        S 5        [        [
        S 5        [        [
        S  5        [        [        S! 5        [        [        S" 5        [        [        S# 5        [        [        S$ 5        [        [        S% 5        [        [        S& 5        [        [        S' 5        [        [        S( 5        [        S)5      m [        [        U 4S* j5        [        / S+Q/5      m[        / S,Q/ S-Q/ S.Q/5      m [        [        U U4S/ j5        [        / S,Q/ S-Q/ S.Q/5      m [        [        U U4S0 j5        g )1Nc                  "    [        SS/S//5      $ r   r   ri   rp   rq   r}   test_errors.<locals>.<lambda>X  s    v1vsm4rp   c                  $    [        SS//5      S   $ )Nr   r   )g333333?r   r   ri   rp   rq   r}   rY  Y      v1vh/7rp   c                  $    [        SS//5      S   $ )Nr   r   )r   g@r   ri   rp   rq   r}   rY  Z  r[  rp   c                      [        SSSS9$ )Nr   r   T)r\   r   )r9   ri   rp   rq   r}   rY  [  s    z!qDArp   c                  <    [        SS/5      R                  SS5      $ )Nr   r   r   r   )r1   r  ri   rp   rq   r}   rY  \  s    vq!f~55a;rp   c                  ^    [        SS/SS//5      R                  SS/[        SS/5      5      $ Nr   r   r   r   r   )r1   copyin_matrixri   rp   rq   r}   rY  ^  s/    AA'(661vvq!f~Nrp   c                  X    [        SS/SS//5      R                  SS/[        5       5      $ r`  )r1   copyin_listsetri   rp   rq   r}   rY  _  s1    fq!fq!f%56BBADurp   c                  @    [        / SQ/ SQ/5      R                  5       $ )Nr   )r   r   r   r1   r!  ri   rp   rq   r}   rY  a  s    I0F)G)K)K)Mrp   c                  \    [        SSSS/5      R                  [        SS/SS//5      5      $ r  )r1   row_joinri   rp   rq   r}   rY  c  s.    q!aV$--fq!fq!f5E.FGrp   c                  X    [        SS/5      R                  [        SS/SS//5      5      $ r  )r1   col_joinri   rp   rq   r}   rY  e  s)    FAq6N33FQFQF;K4LMrp   c                  X    [        S/5      R                  S[        SS/SS//5      5      $ r  )r1   
row_insertri   rp   rq   r}   rY  f  6    vqc{55a!B1vA :  rp   c                  X    [        S/5      R                  S[        SS/SS//5      5      $ r  )r1   
col_insertri   rp   rq   r}   rY  h  rm  rp   c                  8    [        SS/5      R                  5       $ r   rK  ri   rp   rq   r}   rY  j  s    A)=)=)?rp   c                  8    [        S/5      R                  S5      $ rR  )r1   r  ri   rp   rq   r}   rY  k  s    faSk33A6rp   c                  D    [        SS/SS//5      R                  SS5      $ Nr   r   r   r   r   )r1   minorri   rp   rq   r}   rY  l  s#    v1v1v&67==aCrp   c                  D    [        SS/SS//5      R                  SS5      $ rs  )r1   minor_submatrixri   rp   rq   r}   rY  m  s#    v1v1v&67GG1Mrp   c                  :    [        / SQ5      R                  S5      $ Nr   r   r1   crossri   rp   rq   r}   rY  n  s    fY/55a8rp   c                  :    [        / SQ5      R                  S5      $ rx  r1   dotri   rp   rq   r}   rY  o  s    fY/33A6rp   c                  P    [        / SQ5      R                  [        SS/5      5      $ )Nr   r   r   r|  ri   rp   rq   r}   rY  p  s    vi044VQF^Drp   c                  :    [        SS/5      R                  / 5      $ r   r|  ri   rp   rq   r}   rY  q  s    vq!f~11"5rp   c                  :    [        SS/5      R                  S5      $ )Nr   r   rZ   r|  ri   rp   rq   r}   rY  r  s    faVn005rp   c                  >    [        SS/5      R                  / SQ5      $ )Nr   r   r   r|  ri   rp   rq   r}   rY  s  s    vq!f~11)<rp   c                  8    [        / SQ5      R                  5       $ )Nr   )r1   r   ri   rp   rq   r}   rY  t  s    	):)>)>)@rp   c                  @    [        SS/SS//5      R                  5       $ r  )r1   
normalizedri   rp   rq   r}   rY  u      v1v1v&67BBDrp   c                  6    [        SS/5      R                  SS9$ )Nr   r   znot a methodr}  rf  ri   rp   rq   r}   rY  v  s    vq!f~111Hrp   c                  8    [        SS/5      R                  5       $ r   r1   
inverse_GEri   rp   rq   r}   rY  w      A)B)B)Drp   c                  @    [        SS/SS//5      R                  5       $ r   r  ri   rp   rq   r}   rY  x  r  rp   c                  8    [        SS/5      R                  5       $ r   r1   inverse_ADJri   rp   rq   r}   rY  y  s    A)C)C)Erp   c                  @    [        SS/SS//5      R                  5       $ r   r  ri   rp   rq   r}   rY  z  s    v1v1v&67CCErp   c                  8    [        SS/5      R                  5       $ r   )r1   
inverse_LUri   rp   rq   r}   rY  {  r  rp   c                  8    [        SS/5      R                  5       $ r   r  ri   rp   rq   r}   rY  |  s    A)D)D)Frp   c                  8    [        SS/5      R                  5       $ r   r1   r:  ri   rp   rq   r}   rY  }  s    A););)=rp   c                  >    [        SS/SS//5      R                  SS9$ )Nr   r   r   r   zNot a real methodr}  r  ri   rp   rq   r}   rY    s%    AA'(,,4G,Hrp   c                  J    [        / SQ/ SQ/ SQ/ SQ/5      R                  SS9$ )Nr  r  r  r  zNot functionr  r  ri   rp   rq   r}   rY    s*    l)+ ,,/C>C,JKrp   c                  J    [        / SQ/ SQ/ SQ/ SQ/5      R                  SS9$ )Nr  r  r  r  Fr  r  ri   rp   rq   r}   rY    s*    l)+ ,,/C5C,ABrp   c                  V    [        [        SS/SS//5      [        SS/SS//5      5      $ r  r6   r1   ri   rp   rq   r}   rY    s/    AA/0&1a&1a&9I2JKrp   c                  8    [        [        SS/SS//5      / 5      $ r  r  ri   rp   rq   r}   rY    s    wv1v1v.>'?Drp   c                  2    [        [        S5      S-  S5      $ )Nr^   r   rZ   )r6   r   ri   rp   rq   r}   rY    s    wvc{A~s;rp   c                      [        S5      S   $ )Nr   )r   r   r  ri   rp   rq   r}   rY        s1vd|rp   c                      [        S5      S   $ )Nr   )r   r   r  ri   rp   rq   r}   rY    r  rp   r  c                  &   > T R                  S5      $ )Nzmethod=LU_decomposition())r:  r  s   rq   r}   rY    s    quu%@Arp   )r   r   r   r   r   r   r   r   c                  (   > T R                  ST5      $ )Ng@)rl  r   Vs   rq   r}   rY    s    q||C3rp   c                  (   > T R                  ST5      $ )Ng)ro  r  s   rq   r}   rY    s    q||D!4rp   )rN   r  r  r'   r  r)   r1   r  s   @@rq   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5rp   c                     [        [        5       5      S:X  d   e[        [        SS//5      5      [        [        S/S//5      5      s=:X  a  S:X  d   e   e[        [        SSS 5      5      [        [        SSS 5      5      s=:X  a  S:X  d   e   e[        [        / SQ/ SQ/5      5      S:X  d   e[        S/5      [        S//5      :X  d   e[        5       (       a   e[        5       [        / 5      :X  d   eg )	Nr   r   r   c                     gr   ri   rz   s     rq   r}   test_len.<locals>.<lambda>  s    rp   c                     gr   ri   rz   s     rq   r}   r    s    arp   r   r   r   )rU  r1   ri   rp   rq   test_lenr    s    vx=Av1vh CaSz(:$;@q@@@@@vaN+,F1a()/-./ / / / /vy),-.!3331#;&1#-'''xx<8vbz!!!rp   c            
      0   [        SS[        4[        SS4SS[        S-  445      n U R                  [        5      [        [        S[        -  [        S-  S-  4[        [        -  S[        -  S[        -  4S[        -  S[        -  [        S-  S-  445      :X  d   eU R                  [        5      [        [        S[        -  [        [        -  4[        S-  S-  S[        -  S[        -  4S[        -  S[        -  [        [        S-  -  445      :X  d   eg )Nr   r   r   r   r   r   )r1   r^   r_   r   r   s    rq   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rp   c                      [        SS[        [        5      [        -  4[        SS4SS[        S-  S-   445      n U R	                  [        S5      [        S[        SS4S45      :X  d   eg )	Nr   r   r   r   r   r   )r   r   r   )r   r   r   )r1   r   r^   r_   r  r   s    rq   
test_limitr    sa    As1vax 1a)b!QTAX->?@A771a=FI1ay*#EFFFFrp   c            	      D   [        SS[        4[        SS4SS[        S-  S-   445      n [        U R	                  [        5      [        U 5      5      (       d   eU R	                  [        5      [        SSSSS[        -  445      :X  d   eU R	                  [        5      [        S	5      :X  d   e[	        U [        5      [        SSSSS[        -  445      :X  d   e[	        U [        5      [        S	5      :X  d   eU R                  5       n[        UR	                  [        5      [        U5      5      (       d   eUR	                  [        5      [        SSSSS[        -  445      :X  d   eUR	                  [        5      [        S	5      :X  d   e[	        U[        5      [        SSSSS[        -  445      :X  d   e[	        U[        5      [        S	5      :X  d   eU R	                  [        S
S9[        U [        S
S9:X  d   e[	        U [        S
S9[        U [        S
S9:X  d   eg )Nr   r   r   r   r   r   r   r   )r   rI  r   Fr  )	r?   r^   r_   r   r   r   r  r@   rW   )r   A_imms     rq   	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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Nrp   c                     [        [        [        /[        [        //5      n U R                  U 5      [        SS/SS//SS/SS///SS/SS//SS/SS////5      :X  d   e[        X 5      [        SS/SS//SS/SS///SS/SS//SS/SS////5      :X  d   eU R                  5       nUR                  U5      [        SS/SS//SS/SS///SS/SS//SS/SS////5      :X  d   e[        X5      [        SS/SS//SS/SS///SS/SS//SS/SS////5      :X  d   eU R                  [        5      [        SS/SS//5      :X  d   e[        [        [        /5      nU R                  U5      [        R                  " SSSS5      :X  d   eU R                  U 5      [        SS/SS//SS/SS///SS/SS//SS/SS////5      :X  d   eUR                  [        [        //5      nUR                  S:X  d   eU[        S/S//S/S///5      :X  d   e[        S5      nU" [        [        [        5      nUR                  [        [        [        //5      [        UR                  [        5      UR                  [        5      UR                  [        5      /5      :X  d   eUR                  [        [        [        /S45      [        UR                  [        S5      UR                  [        [        5      UR                  [        [        5      /UR                  [        [        5      UR                  [        S5      UR                  [        [        5      /UR                  [        [        5      UR                  [        [        5      UR                  [        S5      //5      :X  d   e[        [        5      [        [        5      -  nUR                  [        [        //5      [        [!        [        5      [        [        5      -  [        [        5      [        [        5      -  /5      :X  d   eUR                  [        [        [        445      [        [!        [        5      [        [        5      -  [        [        5      [        [        5      -  /5      :X  d   eUR                  [        [        [        445      [        [        [        5      * [        [        5      -  [!        [        5      [        [        5      -  /5      :X  d   eUR                  [        [        44[        [        //5      [        [!        [        5      [        [        5      -  [        [        5      * [        [        5      -  /[        [        5      [        [        5      -  [!        [        5      [        [        5      -  //5      :X  d   eUR                  [        5      R                  [        5      R                  [        5      UR                  [        [        [        44S5      S   :X  d   eUR                  [        5      R                  [        5      R                  [        5      UR                  [        [        [        44S5      S   :X  d   eUR                  [        [        [        //[        [        [        445      [        [        [        [        4 VVs/ s HB  n[        [        [        4 Vs/ s H"  oR                  U5      R                  U5      PM$     snPMD     snn5      :X  d   e[        R
                  " [#        [        [        //5      5      n	[%        U	[        5      (       d   eU	[#        SS//5      :X  d   e[        S-  R                  [#        [        [        //5      5      n	[%        U	[        5      (       d   eU	[#        S[        S-  -  S//5      :X  d   eg s  snf s  snnf )	Nr   r   r   )r   r   r   r'  r   r   rm  )r?   r^   r_   r`   ra   r   rV   r  rZ   r@   r[   r>   r   r   r   r   r   r1   r   )
r   r  BdBr'  fxyzexprr|   r{   ress
             rq   test_diff_by_matrixr    s    	QFQF+,A66!9!Q!Q 0Aq6Aq62BC1vPQSTvFVZ[]^Y_bcefagXhEijkkkk: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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,/5noqrtumv9wmvhiZ[]^`aYb:cYbTU99Q<;L;LQ;OYb:cmv9w3xxxx &&!Q!
"Cc/0000&1a&""""a4++fq!fX&
'Cc/0000&1QT61+'''' ;d9ws   _$)___c            	         ^  [        SS[        4[        SS4SS[        S-  S-   445      m [        [        U 4S j5        [        T S5      " [        5      [        SS	S
S
S[        -  445      :X  d   eg )Nr   r   r   r   r   c                     > T R                   $ rx   )nonexistantattributer   s   rq   r}   test_getattr.<locals>.<lambda>  s    1#9#9rp   r   r   r   r   )r1   r^   r_   rN   rF  getattrr   s   @rq   test_getattrr    sj    Aq	Aq!9r1adQh&789A
>9:1fa FIy1a1++N$OOOOrp   c                  H   [        / SQ/ SQ/ SQ/5      n U R                  (       d   eU R                  n U R                  (       d   eSU S'   U R                  SL d   e[        / SQ/ SQ/ SQ/5      n U R                  (       a   e[	        SS	5      n U R                  (       d   eg )
N)r   r   r   )r   r   r   r   r   )r   r   Fr  r   r   )r1   is_upper_hessenbergr  is_lower_hessenbergr>   r   s    rq   test_hessenbergr    s    	9i01A    	A    AeH  E)))	9i01A$$$$aA    rp   c            	      L   [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        S[        -   S4S45      R                  S	S
9[        [        S[        -   5      S/SS//5      :X  d   e[        S5      n U R                  S	S
9nU[        SS/SS[        S5      -  [        -  //5      :X  d   eXR                  -  U :X  d   e[        S5      n U R                  5       nXR                  -  U :X  d   eUR                  (       d   eU[        / SQ/ SQ/ SQ/5      :X  d   e[        SS[        -  SS[        -  -   4S[        -  SS[        -   4SS[        -  -
  S[        -
  S445      n U R                  5       R                  5       [        S[        SS4S[        -
  SS445      :X  d   e[        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        S[        -   S4S45      R                  S	S
9[        [        S[        -   5      S/SS//5      :X  d   e[        S5      n U R                  S	S
9nU[        SS/SS[        S5      -  [        -  //5      :X  d   eXR                  -  U :X  d   e[        S5      n U R                  5       nXR                  -  U :X  d   eUR                  (       d   eU[        / SQ/ SQ/ SQ/5      :X  d   e[        SS[        -  SS[        -  -   4S[        -  SS[        -   4SS[        -  -
  S[        -
  S445      n U R                  5       [        S[        SS4S[        -
  SS445      :X  d   eg )Nc                  4    [        S5      R                  5       $ Nr   r1   choleskyri   rp   rq   r}   test_cholesky.<locals>.<lambda>  s    )@)@)Brp   c                  4    [        S5      R                  5       $ Nr   )r   r   r  ri   rp   rq   r}   r        v&67@@Brp   c                  J    [        S[        -   S4S45      R                  5       $ Nr   r   r   )r1   r
   r  ri   rp   rq   r}   r    s    vAqz6&:;DDFrp   c                  4    [        S5      R                  5       $ N)r   r   )r   r   r  ri   rp   rq   r}   r    r  rp   c                  2    [        S5      R                  SS9$ Nr  F	hermitianr  ri   rp   rq   r}   r    s    v&67@@5@Qrp   r   r   r   Fr  r   r  r   r   ))   r   rH  )r   r   r   )rH  r   r  r  )r   r   r   )r   r   r   r   r  r   r  r  r   c                  4    [        S5      R                  5       $ r  r2   r  ri   rp   rq   r}   r  !  s    f)=)F)F)Hrp   c                  4    [        S5      R                  5       $ r  r  ri   rp   rq   r}   r  "      |,<=FFHrp   c                  J    [        S[        -   S4S45      R                  5       $ r  )r2   r
   r  ri   rp   rq   r}   r  #  s    |a!eQZ,@AJJLrp   c                  4    [        S5      R                  5       $ r  r  ri   rp   rq   r}   r  $  r  rp   c                  2    [        S5      R                  SS9$ r  r  ri   rp   rq   r}   r  %  s    |,<=FFQVFWrp   )rN   r)   r  r1   r
   r  r   r  r  r   r2   )r   r%  s     rq   test_choleskyr    sc   
!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SS5A::78A	

Ass7a<<:::	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SS5A::=>A	

Ass7a<<:::	9j9::::q"Q$AaC(1Q326*:Q1Wb1fb<QRSA::<69q!Qi!a%A"GHHHHrp   c            	      L   [        SSS9n [        [        U 5      [        U 5      /5      n[	        UR                  S5      5      S:X  d   eUR                  S5      [        [        U 5      S-  [        U 5      S-  -   [        SS5      5      :X  d   e[        S[        SS5      //5      nUR                  5       [        S	[        S
S5      -   [        R                  5      :X  d   eUR                  [        5      [        U5      :X  d   eUR                  [        * 5      [        U5      :X  d   e[        SS/SS//5      nUR                  S5      S:X  d   eUR                  S5      S:X  d   eUR                  S5      S:X  d   e[        S5      R                  S5      [        S5      R                  S5      s=:X  a  S:X  d   e   eUR                  [        5      S:X  d   e[        S[        [        /U [        R                  [        * //5      nUR                  S5      [!        [        SS5      S[#        [        5      S-  -  -   [        S-  -   U S-  -   5      :X  d   e[        / SQSS[        SS5      //5      nUR                  S5      [!        [        SS5      [!        S5      S-  -   5      :X  d   eUR                  S5      [        R$                  L d   eUR                  S5      [!        S5      S-  :X  d   e[        SS/SS//5      n[        SS/SS//5      n[        S[&        * /[&        S//5      n[        SS/SS//5      nX#XE/n[        SSS9nS H  n[)        S5      R                  U5      [        R$                  L d   eU HK  n	U HB  n
U	R                  U5      U
R                  U5      -   X-   R                  U5      -
  nUS:  a  MB   e   MM     X#XE4 HE  n[+        X|-  R                  U5      [#        U5      UR                  U5      -  -
  5      nUS:X  a  ME   e   M     [        SSS[&        -  -
  S/5      n[        [        R                  S[&        -  S/5      n[        / SQ5      n[        SS[&        /5      n[        [-        S5      [        SS5      S/5      nXUUU/n[        SSS9nSSSS[        R.                  [        R0                  [        4 GH  nUS:  a/  [        / SQ5      R                  U5      [        R$                  L d   eUS:  aj  U Hd  n	U H[  n
U	R                  U5      U
R                  U5      -   X-   R                  U5      -
  n[+        US:  5      [        R2                  L a  M[   e   Mf     USSSS[        R.                  [        R0                  4;   d  M  U HE  n	[+        Xy-  R                  U5      [#        U5      U	R                  U5      -  -
  5      nUS:X  a  ME   e   GM!     [        SS/ SQ5      nUR                  S5      S:X  d   eg )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>  rD  r%  r  orderr  r  difr   rZ   r[   r\   r]   es                     rq   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	
qA7&EQx}}U#qvv---Avve}qvve}4ULL'(q!   AEG>>%0J./ 0C!8O8   $ 	1qs7B A!Q A|A1ayAhq#.23A	
q!QA7&EQB

A,>,>C19)$))%0AFF:::A:A66%=166%=8U+,C#C1H-777   Q2r1::q/A/ABB~~e4Z!&&-/ 1 2axx  D& 	q!23A66!9??rp   c                    ^^ [        SSS9m[        S5      n SU S'   [        SS5      U S'   U R                  5       S	:X  d   eTU S
'   U R                  5       [	        S[        T5      5      [        [        SS5      [        T5      5      -  :X  d   e[        [        T5      [        T5      /[        T5      * [        T5      //5      nUR                  5       m[        UU4S j[        SS5      [        R                  [        SS5      [        S-  [        [        [        SS5      -  4 5       5      (       d   e[        / 5      R                  5       S:X  d   eg )Nr^   Tr  r   r   r   r   r   r   r   r   c              3      >#    U  H=  n[        S 5      R                  TR                  TU5      R                  5       5      v   M?     g7f)      ?N)r	   
epsilon_eqr  r  )r   valMcr^   s     rq   r   (test_condition_number.<locals>.<genexpr>  s@      QO BEuRy##BGGAsO$9$9$;<<Os   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     @@rq   test_condition_numberr    s3   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$Bx1~<MOQ Q Q Q Q ":&&(A---rp   c                      [        S5      n [        S5      nX S S 2S S 24   :X  d   eX S S 2S S 24   :w  a   eX:X  a   eX:w  d   eU S:w  d   eU S:X  a   e[        S5      n[        S5      nX#:X  d   eX#:w  a   eg )N)r   r_  r   r   r   ))r   r   r   )r   r   r   )r   r   r   r   )rI  r   r   )r1   r2   )r   r  r>  rD  s       rq   test_equalityr    s    01A01A!Q$<<adG|v:6M67N7Bw; 	67A01A6M6v:vrp   c                      [        S5      R                  [        / SQ/5      5      [        / SQ/ SQ/ SQ/ SQ/5      :X  d   eg )Nr   )r   r   r   rI  r   r   )r5   rj  r1   ri   rp   rq   test_col_joinr    s@    q6??69+./	 	  rp   c                      [        / SQ/5      n [        SS5       H_  n/ SQnUR                  US5        [        [	        S5      R                  X5      R                  S5      R                  5       5      U:X  a  M_   e   g )Nr   r   r   rG  r   rI  r   r   r   )r1   r   insertrJ   r5   rl  rZ  r  )r4r{   r;  s      rq   test_row_insertr    sf    		B2q\	As1v((/33A6==?@AEEE rp   c                      [        / SQ5      n [        SS5       H_  n/ SQnUR                  US5        [        [	        S5      R                  X5      R                  S5      R                  5       5      U:X  a  M_   e   g )Nr  rG  r   r   r   r   r   )r1   r   r  rJ   r>   ro  rY  r  )c4r{   r;  s      rq   test_col_insertr    sd    			B2q\	AuQx**1155a8??ABaGGG rp   c                  8   [        SS/5      R                  5       [        [        SS5      [        SS5      /5      :X  d   e[        / SQ5      R                  5       [        / SQ5      :X  d   e[        / SQ5      n U R                  S S9[        / SQ5      :X  d   eg )Nr   r   r   r   )r   r   g0.++c                 8    U R                   " SSS9R                  $ )Nr   T)r   chop)r  is_zeror  s    rq   r}   !test_normalized.<locals>.<lambda>  s    2D199rp   r  )r1   r  r   r   s    rq   test_normalizedr
    s    1a&>$$&AA/01 1 1 )'')VI->>>> 	}A<<9  			  rp   c                  L    [        S 5      S:X  d   e[        S 5      S:X  d   eg )Nc                  4    [        S5      R                  5       $ r  r5   print_nonzerori   rp   rq   r}   $test_print_nonzero.<locals>.<lambda>  s    3q6//1rp   z[X  ]
[ X ]
[  X]
c                  6    [        S5      R                  S5      $ )Nr   .r  ri   rp   rq   r}   r    s    3q6//4rp   z[.  ]
[ . ]
[  .]
)rK   ri   rp   rq   test_print_nonzeror    s8    12     45     rp   c                     [         R                  " S5      [        S5      :X  d   e[         R                  " S5      [        S5      :X  d   e[        SS5      [        SSS/S-  5      :X  d   e[        SS/SS//5      n [        SS/SS//5      n[         Hu  nUR                  S5      nX:X  d   eU [        SUS9:X  d   e[        U5      U:X  d   eUR                  S5      nX:X  d   eU[        SUS9:X  d   e[        U5      U:X  a  Mu   e   g )Nr   r   r   r   r   r   r1  )r1   r5   r>   r8   r   r   )r{   r`   r   r   s       rq   test_zeros_eyer    s   ::a=CF"""<<?eAh&&&1:1qc"f----AA AAA AGGAJvvCsO###Aw#~~IIaLvvE!%%%%Aw#~~ rp   c                     [        5       R                  (       d   e[        SS/SS//5      R                  (       d   e[        SS5      R                  (       d   e[        S5      R                  (       a   e[        [        S/SS//5      R                  S :X  d   e[        [        S/SS//5      R                  S :X  d   e[        [        S/SS//5      R                  S :X  d   e[        [        S/SS//5      R                  S :X  d   e[        [        S/SS//5      R                  S:X  d   e[        SSS9n [        U S/SS//5      R                  S:X  d   eg )	Nr   r   r   r   FrZ   T)nonzero)	r1   is_zero_matrixr>   r5   r^   r2   r/   r0   r   r  s    rq   test_is_zeror    sL   8""""Aq6Aq6"#2222A;%%%%1v$$$$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;;;rp   c                  h   [         S-  n [        U 5      n[        U * 5      n[        U 5      n[        U * 5      n[        U 5      n[        U * 5      nX!-  [	        S5      -  [	        S5      :X  d   eXC-  [	        S5      -  [	        S5      :X  d   eXe-  [	        S5      -  [	        S5      :X  d   eUR                  5       SS[        U 5      -  -   :X  d   eUR                  5       SS[        U 5      -  -   :X  d   eUR                  5       SS[        U 5      -  -   :X  d   e[        S5      [	        S5      :X  d   e[        S5      [	        S5      :X  d   e[        S5      [	        S5      :X  d   e[        R                  " / SQ[         S-  5      n[        R                  " / SQ[         S-  5      n[        R                  " / SQ[         S-  5      n	[        [         * S-  5      UR                  5       :X  d   e[        [         * S-  5      UR                  5       :X  d   e[        [         * S-  5      U	R                  5       :X  d   e[        [         7S-  5      UR                  5       :X  d   e[        [         7S-  5      UR                  5       :X  d   e[        [         7S-  5      U	R                  5       :X  d   eg )Nr   r   r   r   rI  r   r   )r   r<   r;   r:   r5   rL  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
             rq   test_rotation_matricesr&  	  s`   qDEG% HG% HG% HCF"c!f,,,CF"c!f,,,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&;&;&====rp   c                     [        [        S5      S   5      S:X  d   e[        [        S5      5      [        S5      :X  d   e[        [        S 5        [        [        S5      5      S:X  d   e[        [        S5      5      S:X  d   eg )Nvectorr   z	vector[4]r]   c                      [        S5      S   $ )Nr]   r   r*   ri   rp   rq   r}   %test_DeferredVector.<locals>.<lambda>+	  s    ~c226rp   testzDeferredVector('test'))strr+   r   rN   r  reprri   rp   rq   test_DeferredVectorr.  (	  sx    ~h'*+{:::>#&'>#+>>>>
:67~c"#s***v&'+CCCCrp   c                  :    [        [        S5      5      (       a   eg )Nr  )rL   r+   ri   rp   rq    test_DeferredVector_not_iterabler0  /	  s    s+,,,,,rp   c                  &    [        [        S 5        g )Nc                  *    [        [        S5      5      $ )Nr  )r1   r+   ri   rp   rq   r}   ,test_DeferredVector_Matrix.<locals>.<lambda>3	  s    f^C%89rp   )rN   r  ri   rp   rq   test_DeferredVector_Matrixr4  2	  s    
99:rp   c            
         [         n [        SSSS/5      n[        SSSS/5      n[        X/5      [        SSSS/5      [        SSU " S5      S-  U " S5      S-  /5      /:X  d   e[        UR                  UR                  /5      [        SSSS/5      [        SSU " S5      S-  U " S5      S-  /5      /:X  d   e[        [        SS/5      [        SS/5      /S5      [        S[	        S5      -  S-  [	        S5      S-  /5      [        [	        S5      * S-  S[	        S5      -  S-  /5      /:X  d   e[        [        S/5      5      n[        U5      [        S//5      /:X  d   eg )Nr   r   r   r   r   Tr   )r   r1   r.   r  r   r#   )r  r  r  r%  s       rq   test_GramSchmidtr6  5	  s{   A	1q!f	B	1q!f	Bx 	1q!f	vaQqT!VQrU1W,=>?@ @ @bdd|$	1q!f	vaQqT!VQrU1W,=>?@ @ @ 1v1v7>$r(
2tBx{+,b	"aRjm,-C/ / / / 	&!+Aq>fqcUm_,,,rp   c                  R    [        / SQS5      S:X  d   e[        / SQSSS9S:X  d   eg )Nr  r   r   F)zero)r3   ri   rp   rq   test_casoratianr9  F	  s.    lA&!+++lAE2a777rp   c                      [        5       [        SS5      -  R                  S:X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        5       :X  d   eg )Nr   r   )r   r   )r1   r>   r   ri   rp   rq   test_zero_dimension_multiplyr;  K	  si    HU1a[ ''6111A;uQ{"eAqk111A;uQ{"fh...rp   c                    ^  [        SS[        S5      5      m T SS S 24   [        SS//5      :X  d   eT SS S 24   [        SS//5      :X  d   eT S S 2S4   [        SS//5      R                  :X  d   eT S S 2S4   [        SS//5      R                  :X  d   e[        [        U 4S j5        [        [        U 4S j5        g )Nr   r   r   r   r   c                     > T SS S 24   $ r  ri   r   s   rq   r}   'test_slice_issue_2884.<locals>.<lambda>W	  s    qAwrp   c                     > T S   $ )Nr  ri   r   s   rq   r}   r>  X	  s	    qwrp   )r1   r   r  rN   r  r   s   @rq   test_slice_issue_2884r@  Q	  s    q!U1XAQT7fq!fX&&&&RU8v1vh''''QT7fq!fX&(((((QU8v1vh')))))
:'
:'rp   c                      [        SS5      S S 2S4   R                  S:X  d   e[        SS5      SS S 24   [        SS/ 5      :X  d   eg )Nr   r   r   r   r   )r>   r   r1   ri   rp   rq   test_slice_issue_3401rB  [	  sK    A;q"u##v---A;q!tq!R 0000rp   c                     [        SS5      n SU S'   U S S 2S4   [        / SQ5      :X  d   eU S   S:X  d   eU SS S/:X  d   eSU S'   U S   S:X  d   eU SSS 24   [        SS//5      :X  d   e[        SS	//5      U SSS 24'   U SS S 24   [        / S
Q/5      :X  d   eSS//U SSS 24'   U SS S 24   [        / SQ/5      :X  d   eSU S'   U S S 2S S24   [        / SQ5      :X  d   e/ SQU S'   U S S 2S4   [        / SQ5      :X  d   e[        / SQ5      U S'   U S S 2S4   [        / SQ5      :X  d   e[        / SQ5      U S'   U S S 2S4   [        / SQ5      :X  d   eg )Nr   r   r   r   r   rV  r   r   r   )r   r   r   +   )r   rV  rD     r   )rE  r   r   rc  )r>   r1   r2   )r  s    rq   test_copyinrF  `	  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''''rp   c                  .  ^  [        SS/SS//5      R                  5       [        SS/SS//5      S4:X  d   e[        [        S 5        [        / SQ[        SS/S[        S//5      m [        T R                  5       S   5      T R                  :w  d   eT R                  5       S   [        S5      :w  d   eT R                  [        S	9S   [        S5      :w  d   e[        [        U 4S
 j5        [        [        U 4S j5        [        [        U 4S j5        g )Nr   r   r   )r   c                  @    [        SS/SS//5      R                  5       $ r   rf  ri   rp   rq   r}   'test_invertible_check.<locals>.<lambda>{	  s    v1v1v&67;;=rp   )r   r   r   r   r   r  c                  "   > T R                  SS9$ )Nr  r}  r!  r   s   rq   r}   rI  	  s    quuEu2rp   c                  "   > T R                  SS9$ )Nr|  r}  rK  r   s   rq   r}   rI  	      quuDu1rp   c                  "   > T R                  SS9$ )Nr  r}  rK  r   s   rq   r}   rI  	  rM  rp   )	r1   rK  rN   r  r^   rU  r   r5   r$   r   s   @rq   test_invertible_checkrO  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2rp   c                      [        S5      u  pX-  nUR                  U [        / SQ5      5      [        / SQ5      U-  :X  d   eg )Nzx, y)r   r   r   )r   r  r1   )r^   r_   r  s      rq   test_issue_3959rQ  	  s<    6?DA	A66!VI&'6)+<Q+>>>>rp   c                  D    [        [        SS/SS//5      5      S:X  d   eg )Nr   r   r   r   zMatrix([[1, 2], [3, 4]]))r,  r1   ri   rp   rq   test_issue_5964rS  	  s(    v1v1v&'(,FFFFrp   c                  p    [        S5      u  p[        [        U SU-  /US-  U S-   //5      5      S:X  d   eg )Nx yr   r   z'Matrix([
[   x,   2*y],
[y**2, x + 3]]))r   r"   r1   )r^   r_   s     rq   test_issue_7604rV  	  sE    5>DAAaC1a4Q-01234 4 4rp   c            
      Z   [        S5      R                  (       d   e[        S5      R                  5       R                  (       d   e[        S5      R                  (       a   e[	        S5      R                  (       a   e[        / SQ/5      R                  (       a   e[        SSSSSS.5      R                  (       d   e[        SS[        S5      5      R                  (       a   e[        SSSSS.5      R                  (       a   e[        SSSSSSSS.5      R                  (       a   eg )	Nr   rI  r   )r   r   r  r   r   )r   r   )r   r   r  r   rd  )r5   is_Identityr  r>   r8   r1   r2   r   ri   rp   rq   test_is_IdentityrY  	  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[[[[[rp   c                  ~   [        SS5      R                  [        SS5      5      S:X  d   e[        SS5      R                  / SQ5      S:X  d   e[        / SQ5      R                  [        / SQ5      5      S:X  d   e[        SSS[        -  /5      R                  [        [        SS[        -  /5      5      S[        -   :X  d   e[        SSS[        -  /5      R                  [        [        SS[        -  /5      SS	9S[        -   :X  d   e[        SSS[        -  /5      R                  [        [        SS[        -  /5      S
S	9S[        -   :X  d   e[        SSS[        -  /5      R                  [        [        SS[        -  /5      S
SS9S[        -
  :X  d   e[        SSS[        -  /5      R                  [        SS[        -  S/5      S
SS9SS[        -  -   :X  d   e[        SSS[        -  /5      R                  [        SS[        -  S/5      S
SS9SS[        -  -
  :X  d   e[        [        S[        -  /5      R                  [        [        S[        -  /5      SSS9S:X  d   e[        [        S[        -  /5      R                  [        [        S[        -  /5      SS9S:X  d   e[	        [
        S 5        g )Nr   r   rc  r   r  r   rH  Fr  Tr  physicsr  conjugate_conventionr   r   r   rightr   left)r]  c                  P    [        SS/5      R                  [        SS/5      SSS9$ )Nr   r   r   r   Tr+  r\  r|  ri   rp   rq   r}   test_dot.<locals>.<lambda>	  s'    vq!f~11&!Q.Dgm1nrp   )r8   r}  r1   r
   rN   r  ri   rp   rq   test_dotrb  	  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$]c"dhilmnolohoooo1ac(1Q3x 0EX^_ceeee1ac(1Q3x 0vNRSSSS
:norp   c            	         [        SSS9u  pp#pE[        SX4U4U* SX!* 4U* U* SU 4U* X* S445      n[        SU * U* U* 4U SXT* 4X* SU4X$U* S445      nUR                  5       R                  U5      (       d   e[	        S5      R                  5       R                  [        S5      5      (       d   eUR                  5       R                  5       R                  U* 5      (       d   eg )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           rq   	test_dualrn  	  s   #*!$. CcC 
!c4 
tC 
Ta 	 	A 
sdSD3$	S$	dq3	SDQ	 
B 668??2q6;;=a))))668==?!!1"%%%%rp   c                  (   [        SS/5      R                  5       SL d   e[        SSS[        S-  S[        -  -   S-   [        [        S-   S-  * S[        [        -  [        * [        * [        -  S/	5      n U R                  5       SL d   eU R                  SS9b   eU R                  S S9b   eU S	   * U S	'   U R                  5       b   eU S	   * U S	'   U R	                  5       n U R                  SS9SL d   eSU S
'   U R                  5       SL d   eg )Nr   r   Fr   r   Tr  c                     U $ rx   ri   r  s    rq   r}   %test_anti_symmetric.<locals>.<lambda>	  s    !rp   r   r   )r1   is_anti_symmetricr^   r_   r   r   s    rq   test_anti_symmetricrs  	  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)))rp   c                     [        S5      n U R                  SS9u  pXR                  -  UR                  U-  s=:X  a  [        UR                  5      :X  d   e   eU R                  SSS9u  pXR                  -  UR                  U-  s=:X  a  [        UR                  5      :X  d   e   eX-  UR                  5       -  U :X  d   eg )N)r   r   T)	normalize)ru  sort)r1   rx  r  r5   r   r!  )r   r#  rU   s      rq   #test_normalize_sort_diogonalizationrw  	  s     A==4=(DASS5ACCE(S[(((((==4d=3DASS5ACCE(S[(((((3quuw;!rp   c                  &    [        [        S 5        g )Nc                  6    [        / SQ[        SS/ 5      /5      $ )Nr   r   r   r   ri   rp   rq   r}   !test_issue_5321.<locals>.<lambda>	  s    vy&Ar2B&CDrp   )rN   r  ri   rp   rq   test_issue_5321r{  	  s    
:DErp   c            	         [         R                  " [        S5      S[        S5      -  5      [        / SQ/ SQ/5      :X  d   e[         R                  " [        S5      S[        S5      -  5      [        SS/SS/SS/SS//5      :X  d   e[        n U R                  U " [        S5      5      U " S[        S5      -  5      5      [        / SQ/ SQ/5      :X  d   eg )Nr   )r   r   r   r   )r   r   r   r   r   r   )r1   hstackr5   vstackr2   r1  s    rq   test_issue_5320r  	  s    ==Q3q6*f6 /    ==Q3q6*f	
A	
A	
A	
A	6 /    C::c#a&k3qQx=1V= 6   rp   c                      [        S//5      n [        U 5      n[         R                  " X5      [        SS//5      :X  d   e[         R                  " X5      [        S/S//5      :X  d   eg rR  )r1   r   r}  r~  )r   AIms     rq   test_issue_11944r  	  s^    uA
!*C== FQF8$4444== FQC!:$6666rp   c                    ^ / SQn / SQn[        / SQ5      nUR                  nU4S jn[         H  mT" U 5      nT" U5      nU" UR                  U5      U5        U" UR                  UR                  5      U5        U" UR                  R                  UR                  5      U5        U" UR                  R                  U5      U5        M     [	        [
        S 5        g )Nr   r   )r  r   r  c                 6   > X:X  d   e[        U 5      T:X  d   eg rx   )r   )r   r)  r   s     rq   r+  test_cross.<locals>.test	
  s    xxAw#~~rp   c                  X    [        SSSS/5      R                  [        SSSS/5      5      $ r   ry  ri   rp   rq   r}   test_cross.<locals>.<lambda>
  s*    q!aV""6!QA#78rp   )r1   r  r   rz  rN   r'   )rZ   r[   rZ  rY  r+  r   r  r   s          @rq   
test_crossr  
  s    AA

C
%%C FFQWWQZQWWQSS\3QSSYYqss^S!QSSYYq\3  : 9 :rp   c                  N   [        [        [        [        /5      n [        [        [
        [        /5      nU R                  5       U-  U R                  U5      :X  d   eU R                  5       R                  5       (       d   eU R                  5       R                  5       U :X  d   eg rx   )r1   r^   r_   r`   rZ   r[   r\   hatrz  rr  vee)v1v2s     rq   test_hat_veer  
  sw    	Aq		B	Aq		B668b=BHHRL(((668%%''''668<<>Rrp   c                  <   [         SS   HY  n U R                  S5      U R                  S5      1n[        U5      S:X  a%  UR                  5       U R                  S5      :X  a  MY   e   [         S S  H)  n [	        U R                  S5      [
        5      (       d  M)   e   g )Nr  r   r   )r   r5   rU  popr   r   )r   r  s     rq   	test_hashr  
  s    rs|WWQZ$1v{quuw#''!*444  r{cggaj(3333 rp   c                  @   ^  [         S   m [        [        U 4S j5        g )Nr   c                  8   > [        T R                  S5      5      $ rR  )hashr5   r1  s   rq   r}   !test_issue_3979.<locals>.<lambda>+
  s    4
#3rp   )r   rN   rF  r1  s   @rq   test_issue_3979r  &
  s     !*C
>34rp   c                      S[         /SS//n [        SS/[         * S//5      n[         H  nX" U 5      R                  5       :X  a  M   e   g Nr   r   )r
   r1   r   adjoint)r  r)  r   s      rq   test_adjointr  .
  sR    q6Aq6
C
1a&A2q'"
#Cc#h&&(((( rp   c                      [        [        [        [        5      S-  [	        [        5      S-  -   //5      5      [        S//5      :X  d   eg )Nr   r   )r%   r/   r   r^   r   ri   rp   rq   test_simplify_immutabler  4
  sE    Oc!fai#a&!)&;%<$=>?#aSE*+ + +rp   c                     ^^ [        S[        S9u  mm[        SSU4S j5      n [        SSU4S j5      nUR                  TT5      nX :X  d   eg )NzF, Gr1  r   c                    > T" X-   5      $ rx   ri   )r{   r|   Gs     rq   r}   test_replace.<locals>.<lambda>:
      !AC&rp   c                    > T" X-   5      $ rx   ri   )r{   r|   rl  s     rq   r}   r  ;
  r  rp   )r   r   r1   replace)Kr   Nrl  r  s      @@rq   test_replacer  8
  sI    6x(DAqq!()Aq!()A			!QA6M6rp   c                     [        SS/[        SS[        -  -
  //5      n U R                  5       [        R                  [        S5      [        R
                  [        1:X  d   eU R                  [        5      [        1:X  d   eg r   )r1   r^   atomsr   r  NegativeOner   r   s    rq   
test_atomsr  @
  sb    AA!G%&A779qtAMM15555776?qc!!!rp   c            	        ^	 [        [        [        /[        [        //5      n [        U R                  SS95      [        U R                  5       5      :X  d   e[        SS/SS/SS//5      [        / S	Q/ S
Q/5      [        [        [        /5      /nU Hd  nUR                  SS9nX#-  nX2-  n[        XB-  5      U:X  d   e[        XS-  5      U:X  d   eUR                  U:X  d   eUR                  U:X  a  Md   e   U Hm  n[        UR                  SS95      nX#-  nX2-  n[        XB-  5      U:X  d   e[        XS-  5      U:X  d   eUR                  U:X  d   eUR                  U:X  a  Mm   e   SSK	J
m	  U R                  SS9nU R                  5       n[        S[        S[        S[        S0n[        U	4S j[        UR                  U5      UR                  U5      5       5       5      (       d   eg )NRDr}  r  h   i  r   r   r   )r   r   r   )r  rE     EDr   )compi_ib,  i  ij  c              3   r   >#    U  H,  u  pT" UR                  5       UR                  5       5      v   M.     g 7frx   r   )r   r{   r|   r  s      rq   r   test_pinv.<locals>.<genexpr>m
  s0      
3DA 	QSSUACCE3s   47)r1   rZ   r[   r\   r]   r%   pinvr!  r@  sympy.core.numbersr  r   zipr  )
A1Asr   A_pinvAApApAr#  wrepsr  s
            @rq   	test_pinvr  F
  s   	!Q!Q 	!BBGG4G()Xbffh-???? 2s)dAYQ0
1
)\*
+
!Q.
B t$jj A%%%%///uu||uu||  !&&&-.jj A%%%%///uu||uu||  (
tA
Avq%E1e4D 
taffTl3
 
 
 
 
rp   c            	          [        / SQ/ SQ/ SQ/ SQ/ SQ/ SQ/5      /n U  HI  nUR                  SS9nX-  nX!-  nUR                  U:X  d   eS	 nU" UR                  U5      (       a  MI   e   g )
N)=   r  7   r  r  r   )>   `   U   r  r  r   )E   8   rE  r   6   r   )r   r  [   )   r  r   )r   r  r   r   Z   r   )r   r   r   r   r   r   r  r}  c                     U R                  [        5      nU Vs0 s H  o3UR                  5       _M     nnX-
  R                  U5      R                  5       n[	        S U 5       5      $ s  snf )Nc              3   >   #    U  H  n[        U5      S :  v   M     g7f)g|=Nr   r   r  s     rq   r   Xtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose.<locals>.<genexpr>
  s     ;{!s1v~{s   )r  r!   r  r4  r   )M1r  rootofsrS  rootofs_approxdiff_approxs         rq   allcloseEtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose
  s]    hhv&G4;<GqlGN<7,,^<BBDK;{;;; =s   A))r1   r  r@  )r  r   r  r  r  r  s         rq   3test_pinv_rank_deficient_when_diagonalization_failsr  s
  s    
 	#####  	!
B t$jjuu||	< s####- rp   c                      [        SS5      [        SS5      -   [        SS/ 5      :X  d   e[        SS5      [        SS5      -   [        SS/ 5      :X  d   eg r  )r8   r1   ri   rp   rq   test_issue_7201r  
  sR    1:Q
"fQ2&66661:Q
"fQ2&6666rp   c                      [         [        [        [        4 H(  n U " [        /S//5      R
                  [        1:X  a  M(   e   g r   )r/   r0   r1   r2   r^   free_symbolsr  s    rq   test_free_symbolsr  
  s9    3V\I1#s}))aS000 Jrp   c                    ^   SSK Jm   [	        T " / SQ5      5      [	        / SQ5      :X  d   e[	        T " / SQ/5      5      [	        / SQ/5      :X  d   e[	        T " / SQ/ SQ/5      5      [	        / SQ/ SQ/5      :X  d   e[	        T " [
        [        [        /5      5      [	        [
        [        [        /5      :X  d   e[        [        U 4S j5        [	        T " SS/5      T " S	S
/5      /5      [	        SS/S	S
//5      :X  d   e[	        T " SS/5      S	S
//5      [	        SS/S	S
//5      :X  d   e[	        T " / 5      T " / 5      /5      [	        / 5      :X  d   eg! [         a    [        S5         GNgf = f)zSee issue 7465.r   array?NumPy must be available to test creating matrices from ndarraysr   r_  c                  B   > [        T " SS/SS//SS/SS///5      5      $ )	Nr   r   r   r   r   r   r   r   r   r  s   rq   r}   #test_from_ndarray.<locals>.<lambda>
  s.    u1v1v.!Q!Q0@ABCrp   r   r   r   r   N)
numpyr  ImportErrorrQ   r1   r^   r_   r`   rN   NotImplementedErrorr  s   @rq   test_from_ndarrayr  
  sb   P %	"#vi'8888%$%)<<<<%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 E10E1c                  r   SSK Jn    SSKJnJn  U " W" SS/SS//5      5      nUS   S:X  d   e[        U5      / S	Q:X  d   e[        [        5         U " W" SS/SS//5      5      nS S S 5        US   S:X  d   e[        U5      / S	Q:X  d   eg ! [
         a    [        S5         Nf = f! , (       d  f       NH= f)
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       rq   test_17522_numpyr  
  s    0a' 	51a&1a&)*+AQ41997l"""	2	3v1v1v./0 
4Q41997l"""  a_`a 
4	3s   B B(B%$B%(
B6c                      SSK Jn    SSKJn  U " W" SS/SS//5      5      nUS   S	:X  d   e[        U5      / S
Q:X  d   eg ! [         a    [        S5         NJf = f)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      rq   test_17522_mpmathr  
  sk    0V! 	6Aq6Aq6*+,AQ43;;7****  VTUV   A AAc                      SSK Jn    SSKJn  U " W" SS/SS//5      5      nUS   S:X  d   e[        U5      / S	Q:X  d   eg ! [         a    [        S5         NJf = f)
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      rq   test_17522_scipyr  
  sj    0[+ 	:1v1v./0AQ41997l"""  [YZ[r  c                     [        S[        /[        * S//5      n U R                  (       d   eS[        -  U S'   U R                  SL d   e[        U S'   U R                  b   eU S   [        -  U S'   U R                  SL d   eg )Nr   r   r   Fr   r   )r1   r
   is_hermitianr^   r  s    rq   test_hermitianr  
  s    A!Q !A>>>cAdG>>U"""AdG>>!!!gaiAdG>>U"""rp   c                      [        [        [        [        SS9//5      n U S   S[        -  :w  d   eU R                  " 5       [        S[        -  //5      :X  d   eg )NFr  r   r   )r1   r   r^   r  r  s    rq   	test_doitr  
  sO    Qq5)*+,AQ41Q3;;668v!ug&&&rp   c                    ^^ [        / SQ/ SQ/ SQ/5      n U R                  S5        U [        / SQ/ SQ/5      :X  d   e[        / SQ/ SQ/ SQ/5      nUR                  S5        U[        / SQ/ SQ/5      :X  d   e[        / SQ/ SQ/ SQ/5      nUR                  S5        U[        / SQ/ SQ/5      :X  d   e[        / SQ/ SQ/ SQ/5      m[        [        U4S	 j5        [        / SQ/ SQ/ SQ/5      m[        [        U4S
 j5        [        / SQ/ SQ/ SQ/5      n U R	                  S5        U [        SS/SS/SS//5      :X  d   e[        / SQ/ SQ/ SQ/5      nUR	                  S5        U[        SS/SS/SS//5      :X  d   e[        / SQ/ SQ/ SQ/5      m[        [        U4S j5        [        / SQ/ SQ/ SQ/5      m[        [        U4S j5        g )Nr   r  r   r   r  )r   r   r   )r   r   r  r   c                  &   > T R                  S5      $ r   row_delr#  s   rq   r}   +test_issue_9457_9467_9876.<locals>.<lambda>
      qyy}rp   c                  (   > T R                   " S5      $ Nr   r  rT   s   rq   r}   r  
      qyy~rp   r   r   r   r   c                  &   > T R                  S5      $ r   col_delr  s   rq   r}   r     r   rp   c                  (   > T R                   " S5      $ r  r  rT   s   rq   r}   r    r  rp   )r1   r  rN   r  r  )r   r  Or#  rU   s      @@rq   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
:-.rp   c                  ,   [        SSS9u  p[        S5      u  p#[        S5      n[        SSXU[        /5      nX-  U-  X-  U-  :w  d   eX2-  U-  X#-  U-  :X  d   eX-  XP-  :w  d   eX%-  XR-  :X  d   eX-  U-  [        X-  S/SX-  //5      :X  d   eg )NrU  F)commutativeza br   r   )r   r5   r1   r`   )r^   r_   rZ   r[   r   r  s         rq   test_issue_9422r    s    5e,DA5>DAAA	1qQl	#B3q5ACE>>3q5ACE>>424<<424<<3q5FQS!Hq!#h/0000rp   c                  :   [        / 5      n SS/[        / SQ5      4nSS/US   R                  4nSS/[        SS/SS	//5      4nXU4 HO  u  pEU HD  n[        X5      nS
U;   a  U" U5      OU" SU5      nX:X  a  [        U5      [        U5      :w  a  MD   e   MQ     g )Nro  rh  )r   r   r   rl  rj  r   r   r   r   joinrV  )r1   r  r  id)	r   rZ   r[   r\   opsr   opr'  news	            rq   test_issue_10770r    s    r
A	z"F9$55A	z"AaDFF*A	|$fq!fq!f-=&>>A)BA B,!A$Ab!HC832a5 000  rp   c                  r   [        / SQ/ SQ/ SQ/5      n U R                  / SQ/ SQ5      [        SS/SS	/S
S//5      :X  d   eU R                  / SQ/ SQ5      [        S/S/S
//5      :X  d   eU R                  / SQ/ SQ5      [        / SQ/5      :X  d   eU R                  / SQ/ SQ5      [        / SQ/ SQ/5      :X  d   eU R                  / SQ/ SQ5      [        SS/ 5      :X  d   eU R                  / SQ/ SQ5      [        SS/ 5      :X  d   eU R                  / SQ/ SQ5      [        S/S//5      :X  d   eg )Nr   r_  r  r   )TTFr   r   r   r   r   r   )TFF)TFT)FFFr   r   )FTF)r1   r   r   s    rq   test_issue_10658r    s8   	9i01A99Y 34AAA'() ) )99Y 45!qcA39PPPP99)959LLLL99()4	9%&' ' '99Y 56&Ar:JJJJ99*I6&Ar:JJJJ99(*>?aSz  rp   c                     [        SS[        S5      -  -   S/S[        S5      -  S-  S-   S[        S5      -  S-  //5      n U R                  5       S:X  d   e[        SS[        S5      -  [        -  -   S/SSS[        S5      -  [        -  -   //5      n [	        U R                  5       S	   [        SSSS[        S5      -  [        -  -   -  /S	S	//5      -
  5      [        SS5      :X  d   e[        S
5      u  pp4pVpxpp[        XX-  X+-  S	/X4X;-  XK-  S	/XVX[-  Xk-  S/XxX{-  X-  S/XSU	-  U-  X-  -
  SU
-  U-  X-  -
  S	//5      n U R                  5       S:X  d   eg )NrH  r   r   r   r   r  r   r   r   /a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1)r1   r   r  r
   r%   rK  r>   r   )r   axaybxbycxcydxdyexeyt0t1s                rq   !test_opportunistic_simplificationr$  )  s    	aQi$r$q'z!|a'7DGA&FGHA668q== 	1T!W9Q;#Qr!DG)A+~$678AAFFHQK&1b!aQik/.B*CaV)L"MMNRWXY[\R]]]] +22c*d'B"bB"ruRU1%rRU25&;R25q<QSUY[Y^_a_defRgikopqsostvovwyw|o|}~  @B  ~B  CE  ~E  FH  FK  ~K  LM  iN  O  	PA668q==rp   c                     [        / SQ/ SQ/5      n U R                  5       S   [        / SQ/ SQ/5      -
  R                  5       S:  d   e[        / SQ/ SQ/ S	Q/5      n[        / S
Q/ SQ/ SQ/5      n[        / SQ/ SQ/ S	Q/5      nUR                  5       U-
  R                  5       S:  d   eUR                  5       U-
  R                  5       S:  d   eg )N)g~jth?gRM@g(\M@)gDl)@gQgp=
cG@r   )r  r   r   )r   r  r  V瞯<)q7K<r  r   )      r   r   r   )r'  r  r  )r(                 @)r)  r)  r  )r   r(  r*  )r  r'  g      )r1   rK  r  r!  )mmm_mixedm_floatm_invs       rq   test_partial_pivotingr/  9  s    
 $&;<=BGGIaL6#3#3#5 6 67;tvF F F o%%' (G ''') *G (((* +E
 KKME!'')E111KKME!'')E111rp   c                      [        / SQ/ SQ/ SQ/5      n U R                  S S9S   n[        / SQ/ SQ/ S	Q/5      nX-
  nUR                  5       S
:  d   eUS   S:X  d   eg)zWhen doing numerical computations, all elements that pass
the iszerofunc test should be set to numerically zero if they
aren't already. )?皙gɿr   )皙r1  gٿr   )r2  r3  g333333?r   c                     [        U 5      S:  $ )Ng [n<r  r  s    rq   r}   *test_iszero_substitution.<locals>.<lambda>X  s    Qrp   r  r   )r  r   g4iҤIӿr   )r   r  glٲer   r  r&  r  N)r1   rK  r  )r   m_rref	m_correctm_diffs       rq   test_iszero_substitutionr9  Q  sp     	$%9:NOPAVV5V6q9F9:[\}~IF;;=5   #;!rp   c            	         SSK Jn   S[        [        [	        SS5      -  5      -  [        [        [	        SS5      -  5      [        S5      -   -  nS[        S5      -  [        [        [	        SS5      -  5      S-  -  S	[        [        [	        SS5      -  5      -  -   S
[        [        [	        SS5      -  5      S-  -   -  nU " SS5      nU " S[        S5      * 5      nU " X5      n[        U[        U5      -
  U[        U5      -
  /5      n[        X5-
  XE-
  /5      n[        [        X5-
  5      [        XE-
  5      /5      nS n	UR                  SU	S9S:X  d   eUR                  SU	S9S:X  d   eUR                  SU	S9S:X  d   eg )Nr   )Pointr   r  -   r   r  r   r   r   r   c                 <    [        U R                  " 5       5      S:  $ )Ng#B;)r   r   r  s    rq   r}   "test_issue_11238.<locals>.<lambda>m  s    #acce*u$rp   T)r%   r  )	sympy.geometry.pointr;  r   r   r   r   r1   r%   r  )
r;  xxyyp1p2p0r  r  m3Zs
             rq   test_issue_11238rG  _  sx   *	
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	"'"HRW$56	7B
 	%A77DQ7/144477DQ7/144477DQ7/1444rp   c                     [        SS/ SQ5      n U [        R                  -  nX-   n[         HO  nU" U5      R	                  5       u  pE[        U5      [        U 5      :X  d   e[        U5      [        U 5      :X  a  MO   e   g )Nr   r  )r1   r   ImaginaryUnitr   as_real_imagr   )r  r  rE  klsrZ   r[   s         rq   test_as_real_imagrL  r  so    	!I	B	AOO	B	B"g""$Aw$r("""Aw$r(""" rp   c                      [        SS/ SQ5      n U R                  5       u  pUS   [        SSS/5      :X  d   eUS   [        SS/ SQ5      :X  d   eg )Nr   r  r   r   r   )r   r   r   r   )r1   jordan_cells)r   r#  Jcellss      rq   test_deprecatedrP  |  sY    
 	q!23A IA!9q!aS))))!9q!\2222rp   c                      SSK Jn   [        / SQ5      n[        / SQ5      nU " US5      [        / SQ5      :X  d   eU " US5      [        / SQ5      :X  d   eg )	Nr   )Mod)r   r   r   )r   r  r  r   )r   r   r   r   )r   r   r   )sympy.core.modrR  r1   )rR  r   r  s      rq   test_issue_14489rT    sK    "zA}Aq!9y))))q!9y))))rp   c                       SSK Jn   [	        SS/SS//5      nW " U[
        S9R                  R                  S	:X  d   eg ! [         a    [        S5         NNf = f)
Nr   r  r  r   r   r   r   )dtypefloat64)r  r  r  rQ   r1   floatrV  name)r  r   s     rq   test_issue_14943rZ    s`    P 	1!u~A% &&++y888	  PNOPs   ? AAc                  f    [        SSS5      n [        S5      nU S   S:  n[        U5      S:X  d   eg )Nr   r   rZ   r   r   zm[0, 0] > 0)rA   r   r,  )r   rZ   s     rq   test_case_6913r\    s8    S!QAsA	$	Aq6]"""rp   c                  d    [        SSS5      n [        S5      nU R                  U5      X0:X  d   eg )Nr   r   rZ   )rA   rH   match)r   rZ   s     rq   test_issue_11948r_    s1    S!QAS	A771:!rp   c                  j   [        S[        /5      [        S[        * /5      /n [         R                  " U 6 [        S/[        //5      [        S/[        * //5      /:X  d   e[        S[        S/5      [        [        S[        * /5      /n [         R                  " U 6 [        S/[        /S//5      [        [        S-  /[        S5      S-  /[        * //5      /:X  d   e[        S[        /S[        * //5      nUR	                  5       u  p#X"R
                  -  [         R                  " S5      :X  d   eg )Nr   r   r   )r1   r
   orthogonalizer   QRdecompositionr@  r5   )vecsr   rU   r  s       rq   test_gramschmidt_conjugate_dotrd    s#   Aq6NFAr7O,D&	!qc
	VaSA2$K012 2 2 Aq!9vq!aRj12D&	!qcA3	 &1Q3%!A$q&QB4)@"ABC C C 1a&1qb'"
#C DAss7fjjm###rp   c                      [        [        SSS5      5      n [        [        SSS5      5      nU R                  " U5      n[        X S   5      n[        X0S   5      nX1S   :X  d   eUS:X  d   eg )NrZ   r   r   r[   r   r   )r1   rA   r}  r   )rZ   r[   r\   r]   r  s        rq   test_issue_8207rf    sj    |CA&'A|CA&'A	aAQ$AQ$A$<<6M6rp   c            	        ^ SSK Jn   [        SS/SS//5      mTR                  [	        [
        [        -  5      [
        5      [        [	        [        5      [	        S[        -  5      [	        [        5      -
  /S[	        S[        -  5      //5      :X  d   e[        SS/SS//5      m[        T-  S-  R                  [        [
        5      [
        5      [        [        S5      S-  [        S5      * S-  /[        S5      * S-  [        S5      S-  //5      :X  d   e[        [        S 5        [        [        U4S	 j5        [        / S
Q/ S
Q/ SQ/ SQ/5      mTR                  [        [
        5      [
        5      TR                  5       :X  d   e[        [        U4S j5        [        SS/SS//5      m[        TR                  [        [
        5      [
        5      S-  5      T:X  d   e[        / SQ/ SQ/ SQ/5      m[        TR                  U " [
        S5      [
        5      S-  5      T:X  d   e[        / SQ/ SQ/ SQ/ SQ/5      mTR                  [        [
        5      [
        5      TR                  5       :X  d   e[        / SQ/ SQ/ SQ/ SQ/5      mTR                  [        [
        [        -  5      [
        5      [        [        T[        -  R                  5       5      5      :X  d   eg )Nr   )nthrootr   r   r   r   r   c                  Z    [        S5      R                  [        [        5      [        5      $ r  )r>   analytic_funcr   r^   ri   rp   rq   r}   test_func.<locals>.<lambda>  s    a 6 6s1vq Arp   c                  X   > T [         -  R                  [        [         5      [         5      $ rx   )r^   rj  r   r   s   rq   r}   rk    s    1 3 3CFA >rp   )r   r   r  r   )r   r   r   r   )r   r   r   r   c                  J   > T R                  [        [        5      [        5      $ rx   )rj  r   r^   r   s   rq   r}   rk    s    Q ;rp   r  r   "   )r   r  r   )r   r   r  )r   r   r   r   )r   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.simplifyrh  r1   rj  r   r^   ra   r   r   r   rN   r  r   r%   r   )rh  r   s    @rq   	test_funcrp    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Hrp   z$Cannot create threads under pyodide.c                     S n [        S5         [        R                  R                  5        nUR	                  U 5      nUR                  5       (       d   e S S S 5        S S S 5        g ! , (       d  f       N= f! , (       d  f       g = f)Nc                  R    [         R                  S :X  d   e[        S//5      n X -  n gr  )rF   stater1   r   s    rq   r'  test_issue_19809.<locals>.f  s-    !''4///QC5MErp   T)rB   
concurrentfuturesThreadPoolExecutorsubmitresult)r'  executorfutures      rq   test_issue_19809r|    s`     
T	224__Q'F==??"? 5 
	44 
	s"   A:)A)A:)
A7	3A::
Bc                      [        [        [        /5      n [        U [        SS4[        SS45      [        [        R
                  /[        R
                  //5      :X  d   eg r  )r1   r^   r_   r   r   r  r  s    rq   test_issue_23276r~    sT    1vAQAq	Aq!9-	
	
9 2   rp   c                  N   [        / SQ/ SQ/ SQ/ SQ/5      n U R                  5       nUS   [        / SQ5      :X  d   eUS   [        / SQ5      :X  d   eUS	   [        / S
Q5      :X  d   e[        U5      S:X  d   e[        R                  " U /UQ76 R                  5       U:X  d   eg )Nr   r   r   r   r   r  rH  r   r   r  r   r   r   r   r   r   r   r   rl  r   r   )r   r  r   r   r   )r   rH  r   r   r   )r   r   r   rl  r   )rg   ri  r1   rU  r}  r   basiss     rq   test_columnspace_oner    s    00002 	3A
 MMOE8vm,,,,8vn----8vn----u:??==#U#//1U:::rp   c                      [        / SQ/ SQ/ SQ/ SQ/5      n U R                  5       nUS   [        / SQ/5      :X  d   eUS   [        / SQ/5      :X  d   eUS   [        / S	Q/5      :X  d   e[        U5      S
:X  d   eg )Nr  r  r  r  r   r   )r   r   r   r   r   r   )r   r   r   r   r   r   )rg   rf  r1   rU  r  s     rq   test_rowspacer    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:??rp   c                  "   [        / SQ/ SQ/ SQ/ SQ/5      n U R                  5       nUS   [        / SQ5      :X  d   eUS   [        / SQ5      :X  d   e[        S	 XS   -   5       5      (       d   e[        S
 XS   -   5       5      (       d   eg )Nr  r  r  r  r   )r  r   r   r   r   r   )r   r   r   r   r   c              3   8   #    U  H  oR                   v   M     g 7frx   r  r  s     rq   r   %test_nullspace_one.<locals>.<genexpr>       -*Qyy*   c              3   8   #    U  H  oR                   v   M     g 7frx   r  r  s     rq   r   r    r  r  )rg   rm  r1   r   r  s     rq   test_nullspace_oner    s    00002 	3A
 KKME8v.////8v01111-!!H*------!!H*-----rp   c                    ^ [        S5      m[        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S	 j5        [        [        U4S
 j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        TR                  SSS5      [	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSS5      [	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSS9[	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSS9[	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSS5      [	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSS9[	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSS9[	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSS5      [	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSSS9[	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSSS 9[	        / SQ/ SQ/ SQ/5      :X  d   e[        S!SS/S"-  5      n U R                  " SSS5      [	        S!SS/S"-  5      :X  d   eU R                  " SSS5      [	        S!SS/S"-  5      :X  d   eU R                  " SSSS5      [	        S!SS/S"-  5      :X  d   eg )#Nr   c                  &   > T R                  S5      $ Nabcelementary_row_opr  s   rq   r}   test_row_op.<locals>.<lambda>      q2259rp   c                  $   > T R                  5       $ rx   r  r  s   rq   r}   r        q224rp   c                  &   > T R                  SSSS9$ )Nn->knr   rY  r  r  r  s   rq   r}   r         q227Q2Grp   c                  &   > T R                  SSSS9$ )Nr  rH  r   r  r  r  s   rq   r}   r  !      q227a2Hrp   c                  &   > T R                  SSSS9$ )Nn<->mr   r   row1row2r  r  s   rq   r}   r  "      q2272Krp   c                  &   > T R                  SSSS9$ )Nr  r   r   r  r  r  s   rq   r}   r  #  r  rp   c                  &   > T R                  SSSS9$ )Nr  rH  r   r  r  r  s   rq   r}   r  $      q227!2Lrp   c                  &   > T R                  SSSS9$ )Nr  r   rH  r  r  r  s   rq   r}   r  %      q2272Lrp   c                  (   > T R                  SSSSS9$ Nn->n+kmr   r   r  r  r  r  r  s   rq   r}   r  &      q22911PQ2Rrp   c                  (   > T R                  SSSSS9$ )Nr  r   r   r  r  r  s   rq   r}   r  '  r  rp   c                  (   > T R                  SSSSS9$ )Nr  rH  r   r   r  r  r  s   rq   r}   r  (      q2292AQR2Srp   c                  (   > T R                  SSSSS9$ )Nr  r   rH  r   r  r  r  s   rq   r}   r  )      q22912QR2Srp   c                  (   > T R                  SSSSS9$ r  r  r  s   rq   r}   r  *  r  rp   r  r   r   r  r   r   r   rI  rJ  r  )r  r  r  r  )rY  r  r  )r   r   r   )rY  r  r  )r  r  r  r   r   )r   rN   r  r  r1   rt   rZ   r  s    @rq   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w1-1qc!e1DDDDw1-1qc!e1DDDDy!Q2fQA3q56IIIIrp   c                    ^ [        S5      m[        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S	 j5        [        [        U4S
 j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        [        U4S j5        TR                  SSS5      [	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSS5      [	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSS9[	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSS9[	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSS5      [	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSS9[	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSS9[	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSS5      [	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSSS9[	        / SQ/ SQ/ SQ/5      :X  d   eTR                  SSSSS 9[	        / SQ/ SQ/ SQ/5      :X  d   e[        S!SS/S"-  5      n U R                  " SSS5      [	        S!SS/S"-  5      :X  d   eU R                  " SSS5      [	        S!SS/S"-  5      :X  d   eU R                  " SSSS5      [	        S!SS/S"-  5      :X  d   eg )#Nr   c                  &   > T R                  S5      $ r  elementary_col_opr  s   rq   r}   test_col_op.<locals>.<lambda>B  r  rp   c                  $   > T R                  5       $ rx   r  r  s   rq   r}   r  C  r  rp   c                  &   > T R                  SSSS9$ )Nr  r   rZ  r  r  r  s   rq   r}   r  D  r  rp   c                  &   > T R                  SSSS9$ )Nr  rH  r   r  r  r  s   rq   r}   r  E  r  rp   c                  &   > T R                  SSSS9$ )Nr  r   r   col1col2r  r  s   rq   r}   r  F  r  rp   c                  &   > T R                  SSSS9$ )Nr  r   r   r  r  r  s   rq   r}   r  G  r  rp   c                  &   > T R                  SSSS9$ )Nr  rH  r   r  r  r  s   rq   r}   r  H  r  rp   c                  &   > T R                  SSSS9$ )Nr  r   rH  r  r  r  s   rq   r}   r  I  r  rp   c                  (   > T R                  SSSSS9$ Nr  r   r   r  r  r  r  r  s   rq   r}   r  J  r  rp   c                  (   > T R                  SSSSS9$ )Nr  r   r   r  r  r  s   rq   r}   r  K  r  rp   c                  (   > T R                  SSSSS9$ )Nr  rH  r   r   r  r  r  s   rq   r}   r  L  r  rp   c                  (   > T R                  SSSSS9$ )Nr  r   rH  r   r  r  r  s   rq   r}   r  M  r  rp   c                  (   > T R                  SSSSS9$ r  r  r  s   rq   r}   r  N  r  rp   r  r   r   r  r   r   r   rI  rJ  r  )r  r  r  r  )rZ  r  r  )r   r   r   )rZ  r  r  )r  r  r  r   r   )r   rN   r  r  r1   rt   r  s    @rq   test_col_opr  ?  r  rp   c                  (   [        S5      n [        S5      nU R                  (       d   eUR                  (       d   e[        SS/ 5      nUR                  (       d   e[        SS/ SQ5      nUR                  (       d   e[        SS/ SQ5      nUR                  (       a   e[	        S5      n[        SSUSS/5      nUR                  (       d   e[        SSX3S/5      nUR                  (       a   e[        SS/ SQ5      nUR                  (       a   eg )	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_echelonrt   r   )zroidentrZ   r^   s       rq   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A!9-A||Q#>?A|||rp   c                  Z  ^ [        S5      n [        S5      nU R                  " 5       U :X  d   eUR                  5       U:X  d   e[        SS/ 5      n U R                  " 5       U :X  d   e[        SSS/5      n U R                  " 5       U :X  d   eU4S jn[        SS/ SQ5      n [	        S/S/S//5      /n[        U R                  5       Vs/ s H  o@US S 24   PM     nnU R                  " 5       mTR                  (       d   eU" XU5        [        SS/ SQ5      n / n[        U R                  5       Vs/ s H  o@US S 24   PM     nnU R                  " 5       mTR                  (       d   eU" XU5        [        SS/ S	Q5      n [	        [        S
S5      /S/S//5      [	        [        SS5      /S/S//5      /n[        U R                  5       Vs/ s H  o@US S 24   PM     nnU R                  " 5       mTR                  (       d   eU" XU5        [        SS/ SQ5      n [	        S/S/S//5      /n[        U R                  5       Vs/ s H  o@US S 24   PM     nnU R                  " 5       mTR                  (       d   eU" XU5        [        SS/ SQ5      n [	        S/S/S//5      [	        S/S
/S//5      /n[        U R                  5       Vs/ s H  o@US S 24   PM     nnU R                  " 5       mTR                  (       d   eU" XU5        [        SS/ SQ5      n [	        S
/S/S//5      /n[        U R                  5       Vs/ s H  o@US S 24   PM     nnU R                  " 5       mTR                  (       d   eU" XU5        g s  snf s  snf s  snf s  snf s  snf s  snf )Nr   r   r   r   c                    > U H  n[        S TU-   5       5      (       a  M   e   U HF  n[        S U 5       5      (       a  M  [        S TUR                  5       -   5       5      (       d  MF   e   g )Nc              3   8   #    U  H  oR                   v   M     g 7frx   r  r   ra   s     rq   r   Ctest_echelon_form.<locals>.verify_row_null_space.<locals>.<genexpr>  s     6+Qyy+r  c              3   8   #    U  H  oR                   v   M     g 7frx   r  r  s     rq   r   r    s     ,!Qyy!r  c              3   8   #    U  H  oR                   v   M     g 7frx   r  r  s     rq   r   r    s     J2IQyy2Ir  )r   r;  )r   r   nullsr   	a_echelons       rq   verify_row_null_space0test_echelon_form.<locals>.verify_row_null_space  se    A6)A+66666 A,!,,,J)AKKM2IJJJJJ rp   r  r  )	r   r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   )	r   r   r   r   r   r   r   r   r   )r   r   r   r   r   r   )	r   r   rc  rt   r1   r   r   r  r   )rZ   r  r  r  r{   r   r  s         @rq   test_echelon_formr  ~  s   
 	AqA >>q   >>q   Q2&A>>q   QA3'A>>q   K 	Q#>?ATTT  E #166]+]adG]D+ I!5) 	Q#>?AE"166]+]adG]D+ I!5)Q#>?Ar1oVV  r1oVV 	E #166]+]adG]D+ I!5) 	Q#>?AVVV  E #166]+]adG]D+ I!5)Q#>?ASSS  TTT 	E #166]+]adG]D+ I!5)Q#56ATSS  E #166]+]adG]D+ I!5)y , , , , , ,s$   N5NNNN#N(c                     [        SS/ 5      n U R                  SS9U :X  d   e[        SSS/5      n [        SSS/5      nU R                  SS9UR                  " SS9s=:X  a  U :X  d   e   e[        SS/ SQ5      nUR                  " SS9[        S/S/S//5      :X  d   e[        SS/ SQ5      nUR                  " SS9[        / SQ/5      :X  d   e[        SS/ SQ5      nUR                  " SS9[        / S	Q/ S
Q/ SQ/5      :X  d   e[        SS/ SQ5      n[        SS/ SQ5      n[        SS/ SQ5      n[        SS/ SQ5      nUR                  " SS9UR                  " SS9s=:X  a1  UR                  " SS9s=:X  a  UR                  " SS9s=:X  a  U:X  d   e   e[        S5      n [	        S5      nU R                  SS9U :X  d   eUR                  " SS9U:X  d   e[        / SQ/ SQ/ SQ/ SQ/5      nUR                  " 5       u  pgU[        / SQ/ SQ/ SQ/ SQ/5      :X  d   eUS:X  d   e[        [        SS5      [        SS5      SS// SQ/ SQ/ SQ/5      nUR                  " SS9[        SSS[        SS5      /SSS[        S S5      /SSS[        S!S5      // S"Q/5      :X  d   e[        S#5      n[        SSUSS[        U5      US/5      n[        UR                  " SS9SS[        U5      U* S-   -  U[        SS5      -  * U-   -  SSS[        U5      U-   S-   -  /5       H#  u  p[        X-
  5      R                  (       a  M#   e   g )$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   rH  r   )r   r   r   r   r   rl  r   )r   r   r  r   r   r   rH  )r   r   r   r   r  r   r   )r   rH  r   r   r   r   r   )r   r   r   r   r   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   rH     r  r^   )rt   rK  r1   r   r   r   r   r   r  r%   r  )r  rZ   r[   r\   r]   r`   r   pivot_offsetsr^   r{   r|   s              rq   	test_rrefr    s   Q2&A6661$$$QA3'AQA3'A666166#7<1<<<<<Q9-A666A3aS/#::::Q9-A6669+#6666Q#>?A666%/%/%/+1 $2 2 2 2
 	Q#>?AQ#>?AQ#>?AQ#>?A66FF% &FF% & FF% & %&& & & & &
 	qAA6661$$$661$$$''''	) 	*A
 C&----	/ 0 0 0 0
 I%%%x2!QA!L0002 	3A 666*+Q8C3E)F*+QHR4E)F*+Q8C3E)F);	+= $> > > > 	sAQAq!T!Wa#;<AAFF%(47QBF#a!Q&7%7!%;<1aa1q)+, &&&&&,rp   c                  
   [        S5      u  pp#[        SS/SS/SS/SS//5      n[        XX#/5      nUR                  U5      [        SS/SS/SS/SS//5      [        SU-  U-   /SU-  S-  US-  -
  /U /U//5      4:X  d   eg )Nr  r   r   r   r   r   r  )r   r1   rref_rhs)rZ   r[   r\   r]   r   r  s         rq   test_rref_rhsr    s    #JA!AAAA/0Aa|A::a=VFFFF	%  
1qMqSUQqS[MMM	 	   rp   c            	        ^ [        / SQ/ SQ/ SQ/ SQ/ SQ/ SQ/5      mTR                  SSS	S
9n TR                  SS	SSS9nTR                  SS	SS9nU S	S S 24   [        / SQ/5      :X  d   eUS	S S 24   [        / SQ/5      :X  d   eUS	S S 24   [        / SQ/5      :X  d   e[        [        U4S j5        [        [        U4S j5        [        [        U4S j5        g )N)r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r  )r   r   r   rH  )r   r   r   r   r  r   r   r  r  r   rG  r  r  r  )r   r   r   r  )r  r  r   r   c                  &   > T R                  SSSS9$ )Nr  r   r   r  r  r>  s   rq   r}   "test_issue_17827.<locals>.<lambda>>  r  rp   c                  &   > T R                  SSSS9$ )Nr  r   r   r  r  r  s   rq   r}   r  ?  r  rp   c                  (   > T R                  SSSSS9$ )Nr  r   r   r   r  r  r  s   rq   r}   r  @  r  rp   )r1   r  rN   r  )rD  r   rl  r>  s      @rq   test_issue_17827r  -  s     	A 	
G!!4A	IAA<A	Ga0AQT7fl^,,-,QT7fm_--.-QT7fo.//0/
:KL
:GH
:STrp   c                  
   [        SS/[        SS[        -  -
  //5      n U R                  5       S:X  d   e[        SS[        SS5      5      nUR                  5       S:X  d   e[	        S5      nUR                  5       S:X  d   eg )Nr   r   r   r   r   )r1   r^   r  r   r>   )r   r   r"  s      rq   	test_rankr  B  st    AA!G%&A668q==q!U1b\"A668q==aA668q==rp   c                      [        S5      u  pp#pEpgpp[        XX
-  X-  S/X#X*-  X:-  S/XEXJ-  XZ-  S/XgXj-  Xz-  S/XSU-  U-  X-  -
  SU	-  U-  X-  -
  S//5      nUR                  5       S:X  d   eg )Nr  r   r   r   r   )r   r1   r  )r  r  r  r  r  r  r  r  r   r!  r"  r#  r   s                rq   test_issue_11434r  J  s    AB 3BBBBBBq)q)q)q)2b25!B$r'BE/1=	? 	@A
 668q==rp   c            
         [        S5      u  p[        SU -  SSS/SU -  SU -  S-
  SS/SSU -  SU -  U-
  S-
  S/SSX-   S//5      n[        SSSSU S-  U* U -
  -  -  /SSSSX* U -
  -  -  /SSSSU* U -
  -  // S	Q/5      nS
nUR                  5       u  pV[        X5-
  5      [	        UR
                  6 :X  d   eXd:X  d   eg )Nz
nu, lambdar   r   r   r   r  r   r   r  r   )r   r1   rK  r%   r>   r   )nulambr   expected_reducedexpected_pivotsreducedr  s          rq   test_rank_regression_from_sor  T  s    |$HBBA:B$2	A:QrTBrET>A#5:BIr:< 	=A 1aBED52:,>)?@ !1aAr52:,?@ !1aTEBJ@@B C  OffhOG$./5!''?BBB$$$rp   c                     [        / SQ/ SQ/ SQ/ SQ/5      n U [         R                  " S5      [        -  -
  nUR                  5       S:X  d   eUS-  R                  5       S:X  d   eUS-  R                  5       S:X  d   eg )Nrv  r+  r,  r-  r   r   r   )r1   r5   r
   r  )r   r  s     rq   test_issue_15872r  h  sn    o~|LMA	FJJqMAA668q==qD;;=AqD;;=Arp   (Q  r  concurrent.futuresru  collections.abcr   sympy.core.addr   sympy.core.functionr   r   r   r  r   r	   r
   r   r   r   r   r   sympy.core.powerr   sympy.core.singletonr   sympy.core.symbolr   r   sympy.core.sympifyr   $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#   ro  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   rt   r   r   r   r   r   r   r   r   r   r   r  r  r%  r'  r)  r5  r<  rB  rE  rL  rQ  rV  r[  ra  rd  rg  rj  rn  rq  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.  r2  r5  r9  r<  rA  rG  rM  rO  r]  ra  rf  rp  rr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r&  r)  r.  r5  r<  r?  rD  rG  rO  rS  rV  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
  r  r  r  r&  r.  r0  r4  r6  r9  r;  r@  rB  rF  rO  rQ  rS  rV  rY  rb  rn  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$  r/  r9  rG  rL  rP  rT  rZ  r\  r_  rd  rf  rp  r|  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  ri   rp   rq   <module>r$     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(+
Q: