
    Цi                       S SK rS SKrS SKJr  S SKJrJrJrJ	r	J
r
JrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJ r J!r!J"r"J#r#J$r$J%r%J&r&J'r'J(r(J)r)J*r*J+r+J,r,J-r-J.r.J/r/J0r0J1r1J2r2J3r3J4r4J5r5J6r6J7r7J8r8J9r9J:r:J;r;J<r<J=r=J>r>J?r?J@r@JArAJBrBJCrCJDrDJErEJFrFJGrGJHrHJIrIJJrJJKrK  S SKLJMrMJNrNJOrOJPrPJQrQJRrRJSrSJTrT  S SKUJVrVJWrW  S SKXJYrY  S SKZJ[r[J\r\J]r]  S SK^J_r_  S S	K`JaraJbrbJcrc  S S
KdJere  S SKfJgrgJhrhJiriJjrjJkrkJlrl  S SKmJnrnJoro  S SKpJqrq  \\%\\4rr\\%4rs\\4rtS ruS rvS rwS rxS ryS rzS r{S r|S r}S r~S rS rS rS rS rS rS rS rS  rS! rS" rS# rS$ rS% rS& rS' rS( rS) rS* rS+ rS, rS- rS. rS/ rS0 rS1 rS2 rS3 rS4 rS5 rS6 rS7 rS8 rS9 rS: rS; rS< rS= rS> rS? rS@ rSA rSB rSC rSD rSE rSF rSG rSH rSI rSJ rSK rSL rSM rSN rSO rSP rSQ rSR rSS rST rSU rSV rSW rSX rSY rSZ rS[ rS\ rS] rS^ rS_ rS` rSa rSb rSc rSd rSe rSf rSg rSh rSi rSj rSk rSl rSm rSn rSo rSp rSq rSr rSs rSt rSu rSv rSw r\kSx 5       rSy rSz rS{ rS| rS} rS~ rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS Gr S GrS GrS GrS GrS GrS GrS GrS GrS Gr	S Gr
S GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS GrS Gr S Gr!S Gr"S Gr#S Gr$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r0S Gr1S Gr2S Gr3S Gr4S Gr5S Gr6\kS 5       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@S 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rO\j" S5      S 5       GrPS GrQg)    N)Hashable)FAbsAddArrayDeferredVectorEExpr	FiniteSetFloatFunctionGramSchmidtIImmutableDenseMatrixImmutableMatrixImmutableSparseMatrixIntegerKroneckerDeltaMatPowMatrixMatrixSymbolMaxMinMutableDenseMatrixMutableSparseMatrixPolyPowPurePolyQ
QuaternionRationalRootOfSSparseMatrixSymbolTupleWildbanded
casoratiancosdiagdiffexpexpandeyehessian	integratelogmatrix_multiply_elementwisenanonesoopi
randMatrix	rot_axis1	rot_axis2	rot_axis3rot_ccw_axis1rot_ccw_axis2rot_ccw_axis3signsimpsimplifysinsqrtsstrsymbolssympifytantrigsimp	wronskianzeroscancel)abcdtxyz)
NumberKindUndefinedKind)_find_reasonable_pivot_naive)MatrixErrorNonSquareMatrixError
ShapeError)
MatrixKind)_dotprodsimp_state	_simplifydotprodsimp)ArrayDerivative)ignore_warningsraisesskipskip_under_pyodideslowwarns_deprecated_sympy)captureiterable)versionc                     [        SS/ SQ5      n U R                  S:X  d   eU R                  S:X  d   eU S   S:X  d   eU S   S:X  d   e[        U 5      / SQ:X  d   e[        U SS S 24   5      / SQ:X  d   e[        U S S 2S4   5      SS/:X  d   e[        U S S 2S S 24   5      [        U 5      :X  d   eU S S 2S S 24   U :X  d   e[        U 5      U :X  d   e[        / SQ/ SQ/5      U :X  d   e[        / SQ/ SQ45      U :X  d   e[        SS/5      U :X  d   e[        S	5      U :X  d   e[        SS/SS
/SS//5      U :X  a   eg )N      )   rg   rh            ri   ri   rk   ri   rj   rk   rl   ri   rg   rh   )ro   rn   rj   rl   )r   rowscolslistrO   s    c/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/sympy/matrices/tests/test_matrixbase.pytest__MinimalMatrixru   #   sc   q!'(A66Q;;66Q;;Q4199T7a<<7((((!Q$=I%%%!Q$=QF"""!Q$=DG###QT7a<<!9>>9i()Q...9i()Q...9i()Q...()Q...AAA/0A5665    c                     [        SS/SS//5      R                  [        [        5      :X  d   e[        SS/SS//5      R                  [        [        5      :X  d   e[        SS/ 5      R                  [        [        5      :X  d   e[        [        //5      R                  [        [        5      :X  d   e[        S[        S//5      //5      R                  [        [
        5      :X  d   e[        S//5      R                  [        [        5      :X  d   e[        S[        S//5      //5      R                  [        [
        5      :X  d   eg Nri   rg   rh   rj   r   )r   kindrX   rR   rO   rS   r#    rv   rt   	test_kindr{   6   s   Aq6Aq6"#((Jz,BBBBAq6Aq6"#((Jz,BBBB!Q  Jz$::::A3%=J!7777Avse}%&',,
=0IIII!##z*'====!VaSE]+,-22j6OOOOrv   c                  N   [        S5      u  pp#[        X/X#//5      n[        X/X#//5      n[        X/X#//5      n[	        X/X#//5      nUR                  5       UR                  5       s=:X  a4  UR                  5       s=:X  a  UR                  5       s=:X  a
  XX#S.:X  d   e   eg )Nza:d)r   r   r   ri   ri   r   rm   )rC   r   r   r   r   todok)rJ   rK   rL   rM   m1m2m3m4s           rt   
test_todokr   @   s    JA!	aVaV,	-B	vv.	/B	qfqf-	.B	/	0B88: 5rxxz 5RXXZ 5q45 5 5 5 5rv   c                      [         R                  [         R                  [        [        -  [         R
                  /[        [        [        [        S-  /[        [         R                  * [        [        -  S//n [         R                  [         R                  [        [        -  [         R
                  [        [        [        [        S-  [        [         R                  * [        [        -  S/n[        SSU5      nUR                  5       U :X  d   eg )Nrg   rh   rj   )	r"   OneHalfrO   rP   ZerorQ   r   tolist)lstflat_lstms      rt   test_tolistr   J   s    EE1661Q3'!Q1a41quufac1:M
NCqvvqsAFFAq!QT1quufac1MHq!XA88:rv   c                      [        [        R                  S/S[        R                  /[        S//5      n S[        R                  0S[        R                  0S[        0S.nU R                  5       U:X  d   eg )Nr   ri   r   ri   rg   )r   r"   r   r   rO   todod)r   dicts     rt   
test_tododr   Q   s[    
QK!Q01A155zq!&&kq!f5D779rv   c                    ^  [        SS/ SQ5      m [        [        U 4S j5        [        [        U 4S j5        [        [        U 4S j5        [        [        U 4S j5        T R                  S5      T R                  S5      s=:X  a  [	        / S	Q/ S
Q/5      :X  d   e   eT R                  S5      T R                  S5      s=:X  a  [	        SS/SS/SS//5      :X  d   e   eT R                  S5      T R                  S5      s=:X  a  [	        / S	Q/ SQ/5      :X  d   e   eT R                  S5      T R                  S5      s=:X  a  [	        SS/SS/SS//5      :X  d   e   eg )Nrh   	ri   rg   rh   rj   rk   rl         	   c                  &   > T R                  S5      $ Nrk   row_deles   rt   <lambda>"test_row_col_del.<locals>.<lambda>Y       qyy|rv   c                  &   > T R                  S5      $ Nr   r   s   rt   r   r   Z       qyy}rv   c                  &   > T R                  S5      $ r   col_delr   s   rt   r   r   [   r   rv   c                  &   > T R                  S5      $ r   r   r   s   rt   r   r   \   r   rv   rg   ro   rn   ri   rj   rk   r   r   r   r   r   rl   r   )r   r^   
IndexErrorr   r   r   r   s   @rt   test_row_col_delr   W   s&   19:A
:+,
:,-
:+,
:,-99Q<199R=JFIy3I,JJJJJJ99Q<199R=LFQFQFQF3K,LLLLLL99Q<199R=JFIy3I,JJJJJJ99Q<199R=LFQFQFQF3K,LLLLLLrv   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 Nri   rg   rh   )r   rO   rP   rQ   get_diag_blocks)rJ   rK   rL   s      rt   test_get_diag_blocks1r   e   s    AA AAA AAq	Aq!9q!Qi01A1#%%%1#%%%1#%%%rv   c                     [        SS/SS//5      n [        S[        /[        S//5      n[        S[        S/[        S[        /[        [        [        //5      n[	        XU5      [	        XU5      [	        XU5      [	        X"U5      4u  p4pV[        UR
                  UR                  U5      n[        UR
                  UR                  U5      n[        UR
                  UR                  U5      n[        UR
                  UR                  U5      nUR                  5       XU/:X  d   eUR                  5       XU/:X  d   eUR                  5       XU/:X  d   eUR                  5       X"U/:X  d   eg r   )r   rO   rP   rQ   r*   rp   rq   r   )rJ   rK   rL   ABCDs          rt   test_get_diag_blocks2r   n   sA   AA AAA AAq	Aq!9q!Qi01AaAQ1tA!}d1mKJA!qvvqvvq!Aqvvqvvq!Aqvvqvvq!Aqvvqvvq!A1)+++1)+++1)+++1)+++rv   c                      [        SS/ SQ5      n U R                  S5      [        SS/ SQ5      :X  d   eU R                  S5      [        SS/ SQ5      :X  d   eg )Nrh   r   r   ri   ro   ri   rj   r   )r   rowcolr   s    rt   test_row_colr   ~   sO    q!01A558vaI....558vaI....rv   c                  ~    [        S5      R                  [        / SQ5      5      [        / SQ/ SQ/ SQ/5      :X  d   eg )Nrh   r   r   r   )ri   r   r   r   )r   ri   r   r   )r   r   ri   r   )r.   row_joinr   rz   rv   rt   test_row_joinr      s;    q6??6),-<! "" " "rv   c                      [        S5      R                  [        / SQ/5      5      [        / SQ/ SQ/ SQ/ SQ/5      :X  d   eg )Nrh   r   ri   r   r   r   ri   r   r   r   ri   )r.   col_joinr   rz   rv   rt   test_col_joinr      s@    q6??69+./9   rv   c                      [        / SQ/5      n [        SS5       HV  n/ SQnUR                  US5        [        S5      R	                  X5      R                  S5      R                  5       U:X  a  MV   e   g )Nrj   rj   rj   rk   r   rj   rh   r   )r   rangeinsertr.   
row_insertr   flat)r4ils      rt   test_row_insertr      sa    		B2q\	A1v  '++A.335::: rv   c                     [        / SQ5      n [        SS5       HV  n/ SQnUR                  US5        [        S5      R	                  X5      R                  S5      R                  5       U:X  a  MV   e   [        S5      R	                  S[        S	S	/S	S	/S	S	/S	S	/S	S	/S	S	//5      5      [        / S
Q/ SQ/ SQ/ SQ/ SQ/ SQ/5      :X  d   eg )Nr   r   rk   r   r   r   rj   rh   r   rl   rg   )ri   r   r   rg   rg   r   r   r   )r   ri   r   rg   rg   r   r   r   )r   r   ri   rg   rg   r   r   r   )r   r   r   rg   rg   ri   r   r   )r   r   r   rg   rg   r   ri   r   )r   r   r   rg   rg   r   r   ri   )r   r   r   rH   
col_insertr   r   r.   )c4r   r   s      rt   test_col_insertr      s    			B2q\	AQx""1)--a05571<<< 
 q6QAAAAAQRTUPV'W XY++++++- .. . .rv   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 )Nrj   rh   c                     U S-  U-   $ Nrh   rz   r   js     rt   r   test_extract.<locals>.<lambda>       !A#'rv   )r   ri   rh   r   ri   rg   )r   ri   rh   rj   r   
   r   r   rg   )r   r   rg   r   r      c                  ,   > T R                  S/S/5      $ )Nrj   r   extractr   s   rt   r   r          qyy!qc2rv   c                  ,   > T R                  S/S/5      $ )Nr   rh   r   r   s   rt   r   r      r   rv   )r   r   r   r^   r   r   s   @rt   test_extractr      s    q!)*A99YA'6!Q8K+LLLL99aVY'6!Q8K+LLLL99U1XuQx(A---
:23
:23rv   c                    ^^ [        SSS 5      m[        SSS 5      mTTR                  T5      :X  d   eTR                  TTT5      [         R                  " TTT5      s=:X  a  [        / SQ/ SQ/ SQ/ SQ/5      :X  d   e   e[        [        UU4S	 j5        [         R                  " 5       [        5       :X  d   e[         R                  " S
S
5      n [         R                  " S
S5      n[         R                  " S
S5      n[         R                  " S
S5      n[         R                  " XX#5      mTR
                  S
:X  a  TR                  S:X  d   eg )Nrj   rh   c                     U S-  U-   $ r   rz   r   s     rt   r   test_hstack.<locals>.<lambda>   r   rv   c                     U S-  U-   $ r   rz   r   s     rt   r   r          1Q37rv   )	r   ri   rg   r   ri   rg   r   ri   rg   )	rh   rj   rk   rh   rj   rk   rh   rj   rk   )	rl   r   r   rl   r   r   rl   r   r   )	r   r   r   r   r   r   r   r   r   c                  (   > T R                  T T5      $ N)hstackr   r   s   rt   r   r          qxx2rv   r   ri   rg   rl   )r   r   r^   rW   rH   rp   rq   )M1M2M3M4r   r   s       @@rt   test_hstackr      s   q!)*A	1*	+B88Aq!aA 6 4&1111	B3 ;4 4 4 4 4 4
 :./==?fh&&& 
a	B	a	B	a	B	a	Bbb%A66Q;166Q;&&;rv   c                    ^ ^ [        SSS 5      m [        SSS 5      mT T R                  T 5      :X  d   eT R                  T T T 5      [         R                  " T T T 5      s=:X  a4  [        / 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      :X  d   e   e[        [        U U4S	 j5        [         R                  " 5       [        5       :X  d   eg )
Nrj   rh   c                     U S-  U-   $ r   rz   r   s     rt   r   test_vstack.<locals>.<lambda>   r   rv   c                     U S-  U-   $ r   rz   r   s     rt   r   r      r   rv   r   rh   rj   rk   rl   r   r   r   r   r   c                  (   > T R                  T T5      $ r   )vstackr   s   rt   r   r      r   rv   )r   r   r^   rW   r   s   @@rt   test_vstackr     s    q!)*A	1*	+B88Aq!aA 6 .& + + + + + + + + + + + +B- ;. . . . . . :./==?fh&&&rv   c                  8   [        [        [        4S45      n U R                  [        5      (       d   eU R                  [        5      (       a   eU R                  [
        5      (       d   e[        S[        4S45      n U R                  [        5      (       a   eg )Nrg   rh   rg   )r   rO   rP   hasrQ   r$   r   s    rt   test_hasr     sq    A A5588O8uuQxx<55===A AuuQxx<xrv   c                     [        S5      n [        SSSS/5      R                  5       SL d   e[        SSSU S-  SU -  -   S-   [        U S-   S-  * SU [        -  [        * U * [        -  S/	5      nUR                  5       SL d   eUR                  SS9b   eUR                  S	 S9b   e[        SSU V s/ s H  o R                  " 5       PM     sn 5      nUR                  SS9SL d   e[        SS[
        R                  /[        U5      SS  -    V s/ s H  o R                  " 5       PM     sn 5      nUR                  5       SL d   eg s  sn f s  sn f )
NrO   rg   ri   Frh   r   Tr?   c                     U $ r   rz   rs   s    rt   r   (test_is_anti_symmetric.<locals>.<lambda>       !rv   )rC   r   is_anti_symmetricrP   r-   r"   r   rr   )rO   r   s     rt   test_is_anti_symmetricr     sU   A!QA113u<<<q!aA!aa!eaZKAaC!aRT1MNA D(((.6664<<<q!!,!Qhhj!,-A.$666q!155'DGABK*?@*?Qhhj*?@AA E))) -@s   4E	Ec                  r   [        S[        /[        * S//5      n U R                  (       d   e[        S[        -  [        /[        * S//5      n U R                  SL d   e[        [        [        /[        * S//5      n U R                  b   e[        [        S/[        * S//5      n U R                  SL d   eg )Nri   rg   Fr   r   is_hermitianrO   rJ   s    rt   test_is_hermitianr     s    A!Q !A>>>1aA2q'"#A>>U"""A!Q !A>>!!!A!Q !A>>U"""rv   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 )NTri   rg   rh   rj   rk   rl   r   r   Frk   rl   r   ri   rh   ro   rg   )r   rO   is_symbolicr  s    rt   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###rv   c                      [        S/S//5      n [        SS/SS//5      nU R                  (       a   eUR                  (       d   eg Nri   rg   )r   	is_squarer   s     rt   test_is_squarer    sC    aSzA	!Q!Q 	!B{{?<<<rv   c                      [        SS/ SQ5      n U R                  5       (       d   e[        SS/ SQ5      n U R                  5       (       a   eg )Nrg   r   ri   ri   r   r   ri   r   ri   )r   is_symmetricr   s    rt   test_is_symmetricr     sG    q!\"A>>q!\"A~~rv   c                  F   [        / SQ/ SQ/ SQ/5      n U R                  (       d   e[        SS/ SQ5      n U R                  (       d   e[        SS/ SQ5      n U R                  SL d   eU R                  SL d   e[        / SQ/ SQ/ SQ/5      n U R                  (       a   eg )	Nrh   rj   ri   rg   rj   rk   r   rh   )	rh   rg   r   rj   rj   ri   ri   rk   rg   )	rh   rg   r   rj   rj   ri   ri   rk   rg   Frh   ri   rg   )r   is_upper_hessenbergis_lower_hessenbergr  s    rt   test_is_hessenbergr'     s    	9i01A    q!01A    q!12A  E)))  E)))	9i01A$$$$$rv   c            
          [        [        SS/ SQ5      R                  5       5      1 Sk:X  d   e[        SSS9n [        [        SSU SSS/5      R                  5       5      U S1:X  d   eg )	Nrg   r   ri   rg   rh   >   ri   rg   rh   rO   Trealr   ri   )setr   valuesr$   rs   s    rt   test_valuesr.  -  sv    vaL 

&( ! ! !sAvaQ1aL 

&(1v  rv   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   rk   ri   rg   r   ri   rg   )r   r   Tr   	conjugateHMs    rt   test_conjugater6  5  s    Aq	 	A 33&1a&a&a&" # # # # 33&1qb!*$& ' ' ' '33!++-33!##%%<<33&Aq'2q'q'# $ $ $ $rv   c                      [        [        [        [        SS9//5      n U S   S[        -  :w  d   eU R                  " 5       [        S[        -  //5      :X  d   eg )NFevaluater   rg   )r   r   rO   doitr  s    rt   	test_doitr;  G  sO    QE*+,-AQ41Q3;;668v!ug&&&rv   c                    ^  [        SS[        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 )Nrg   ri   rk   rl   c              3   t   >#    U  H-  nTR                   " 5       U   TU   R                  5       :H  v   M/     g 7fr   evalf.0r   rJ   s     rt   	<genexpr>test_evalf.<locals>.<genexpr>O  s*     >Xqwwy|qtzz|+Xs   58c              3   x   >#    U  H/  nTR                   " S 5      U   TU   R                  S 5      :H  v   M1     g7frg   Nr>  r@  s     rt   rB  rC  P  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rE  nr@  s     rt   rB  rC  Q  s.     8x!qss1vayAaDFF1I%xrF  )r   rA   allr   r  s   @rt   
test_evalfrK  M  sj    q!d1gq\"A>U1X>>>>>@uQx@@@@@8uQx88888rv   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 )NF, Gclsrg   c                    > T" X-   5      $ r   rz   r   r   Gs     rt   r   test_replace.<locals>.<lambda>V      !AC&rv   c                    > T" X-   5      $ r   rz   r   r   Fs     rt   r   rS  W  rT  rv   rC   r   r   replace)Kr5  NrW  rR  s      @@rt   test_replacer\  T  sI    6x(DAqq!()Aq!()A			!QA6M6rv   c            	        ^^ [        S[        S9u  mm[        SSU4S j5      n U R                  TTS5      u  pU[        SSU4S j5      :X  d   eUT" S5      T" S5      T" S5      T" S5      T" S5      T" S5      0:X  d   eg )	NrM  rN  rg   c                    > T" X-   5      $ r   rz   rV  s     rt   r   "test_replace_map.<locals>.<lambda>^  rT  rv   Tc                    > T" X-   5      $ r   rz   rQ  s     rt   r   r_  `  s    !AC&rv   r   ri   rX  )r5  r[  rM   rW  rR  s      @@rt   test_replace_mapra  \  s    6x(DAqq!()A99Q4 DAq!011111qtQqT1Q41qt4444rv   c                  d  ^^  SSK JmJn   [        SS/SS//5      mT" SS/SS//5      nW " T" T5      U5      (       d   eU " T" TSS	9U5      (       d   e[        [        S
5      R                  S5      S   5      S:  a  [        [        UU4S j5        g g ! [         a    [	        S5         Nf = f)Nr   )arrayarray_equal?NumPy must be available to test creating matrices from ndarraysri   rg   rh   rj   Tcopynumpy.c                     > T" T SS9$ )NFrf  rz   )r   rc  s   rt   r   'test_numpy_conversion.<locals>.<lambda>m  s    %"6rv   )rh  rc  rd  ImportErrorr_   r   intre   splitr^   	TypeError)rd  np_arrayr   rc  s     @@rt   test_numpy_conversionrq  c  s    P, 	1!u~AqeaU^$HuQx****uQT*H5555
77!!#&q)*a/y67 0  PNOPs   B B/.B/c                  \   [        SS/SS//5      n X R                  S5      s=:X  a  U R                  S5      :X  d   e   eU R                  S5      U R                  S5      s=:X  a&  U R                  S5      s=:X  a  [        S5      :X  d   e   eU R                  S5      U R                  S	5      s=:X  a&  U R                  S
5      s=:X  a  [        S5      :X  d   e   eU R                  5       U R                  S5      s=:X  a&  U R                  S5      s=:X  a  [        S5      :X  d   e   eg )Nri   rg   rh   rj   r   r   rl   ))rj   rh   rg   ri   r   r   ))rg   rj   ri   rh   )rh   ri   )rj   rg   )r   rot90r  s    rt   
test_rot90ry  o  s    AA A
(aggaj(((((771:N
Nf=M6NNNNNN771:N
Nf=M6NNNNNN779Nqwwr{Nf=M6NNNNNNrv   c                  4   [        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g )
Nri   rj   rk   rg   r   r   rv  T)simultaneous)r   rO   subsrP   rz   rv   rt   	test_subsr}  w  s   Aq6Aq6"#((A.&1a&1a&9I2JJJJAq6AE1:&',,q"g2w-?@B7RG$%& & &Aq6AE1:&',,q"g2w-?@B7RG$%& & &Aq6AE1:&',,aQ^<B7RG$%& & &AaC5'?AE1a!e 44HQUQUO$%&' ' 'rv   c                  $  ^ [        SS/ SQ5      m[        [        U4S j5        [        [        U4S j5        TR                  " SS/SS//5      n TR
                  " SS/SS//5      U s=:X  a  [        / S	Q/ S
Q/ SQ/5      :X  d   e   eTR                  " SS/SS//5      n TR
                  " SS/SS//SS9U s=:X  a  [        / SQ/ SQ/ SQ/5      :X  d   e   eTR                  " SS/SS//SS9n TR
                  " SS/SS//SSS9U s=:X  a  [        / SQ/ SQ/ SQ/5      :X  d   e   eTR
                  " / SQ5      [        / S	Q/ S
Q/ SQ/5      :X  d   eSSKJn  TR
                  " U" / SQ5      5      [        / S	Q/ S
Q/ SQ/5      :X  d   eg )Nrh   rj   )ri   rg   rh   rj   rk   rl   r   r   r   r   r      c                  .   > T R                   " SS//5      $ )Nr   rk   )permuter  s   rt   r   test_permute.<locals>.<lambda>  s    qyy1a&2rv   c                  :   > T R                   " [        S5      5      $ )NrO   )r  r$   r  s   rt   r   r    s    qyy5rv   r   rg   ri   r  r   r   r   r  r  rq   )orientation)rg   rh   ri   rj   )rl   r   rk   r   )r   r   r   r  backward)	direction)r  r  )rh   ri   rg   rj   )r   rk   rl   r   )r   r   r   r  )ri   rg   r   rh   )Permutation)	r   r^   r   
ValueErrorpermute_rowsr  permute_colssympy.combinatoricsr  )rK   r  rJ   s     @rt   test_permuter    s   q!<=A
:23
:56	AA'(A99q!fq!f%&! >v,;,;,;7= 0> > > > > >
 	
AA'(A99q!fq!f%6:a ."+++$- .. . . . . 	
AA':>A99q!fq!f%6ZPTU ."+++$- .. . . . . 99\"f,;,;,;.= '> > > >
 099[./6,;,;,;;= 4> > > >rv   c                  D   [        / SQ/ SQ/ SQ/ SQ/5      n U R                  S5      nU[        / SQ/ SQ/ SQ/ SQ/5      :X  d   eU R                  S5      nU[        / SQ/ SQ/ SQ/ SQ/5      :X  d   eU R                  5       nU[        / SQ/ SQ/ SQ/ SQ/5      :X  d   eg )Nri   ri   ri   ri   rg   r   r   ri   ri   r   r   r   ri   r   r   r   r   r   )r   ri   ri   ri   )r   upper_triangular)r   Rs     rt   test_upper_triangularr    s    	 	A 	
1A$$$$	     	
2A$$$$	     	
A$$$$	    rv   c                  D   [        / SQ/ SQ/ SQ/ SQ/5      n U R                  5       nU[        / SQ/ SQ/ SQ/ SQ/5      :X  d   eU R                  S5      nU[        / SQ/ SQ/ SQ/ SQ/5      :X  d   eU R                  S5      nU[        / SQ/ SQ/ SQ/ SQ/5      :X  d   eg )Nr  ri   r   r   r   ri   ri   r   r   ri   ri   ri   r   rg   r   r  )r   lower_triangularr   Ls     rt   test_lower_triangularr    s    $$$$	 	A 	
A$$$$	& ' ' ' ' 	
1A$$$$	     	
2A$$$$	    rv   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 )	Nro   rg   rg   rj   rl   rj   ri   c                     > T T-   $ r   rz   r   rI  s   rt   r   test_add.<locals>.<lambda>  	    q1urv   r   rO   rP   rQ   r^   rW   r  s   @@rt   test_addr        	Aq!9qsC1o67Aq5FI!QqS!A#1dAaCE8JKLLLLq!aVA
:}%rv   c                  2   [        SS/SS//5      n U R                  " S5      [        :X  d   eU R                  " S5      [        :X  d   e [	        S5         [	        S5        g ! [
         a     N[         a     N$f = f! [
         a     g [         a     g f = f)Nri   rg   rh   rj   z2 @ aza @ 2)r   
__matmul__NotImplemented__rmatmul__evalSyntaxErrorro  r  s    rt   test_matmulr    s    AA A<<?n,,,==~---WW      s0   A# A> #
A;/	A;:A;>
B
	BBc                       " S S[         5      n [        SS/SS//5      nU " 5       nX!-  [        USU-  /SU-  SU-  //5      :X  d   eX-  [        USU-  /SU-  SU-  //5      :X  d   eg)zX
Test that if explicitly specified as non-matrix, mul reverts
to scalar multiplication.
c                        \ rS rSrSrSrSrSrg)test_non_matmul.<locals>.fooi  Frm   rz   N)__name__
__module____qualname____firstlineno__	is_Matrixis_MatrixLikeshape__static_attributes__rz   rv   rt   foor    s    	rv   r  ri   rg   rh   rj   N)r	   r   )r  r   rK   s      rt   test_non_matmulr  	  s    
d 
 	AA AA3&1ac(QqS!A#J/00003&1ac(QqS!A#J/0000rv   c                  N    [        SSSS/5      n U * [        SSSS/5      :X  d   eg )Nri   rg   r   r   r   rH  s    rt   test_negr    s1    q!aVA21r2h''''rv   c                  P    [        SSSS/5      n X -
  [        SSSS/5      :X  d   eg )Nri   rg   r   r  rH  s    rt   test_subr    s1    q!aVA5F1a!Q((((rv   c            	          [        SSSS/5      n U S-  [        SS[        R                  [        S5      S-  /5      :X  d   eg r  )r   r"   r   rH  s    rt   test_divr  #  s@    q!aVAQ3&A!Q/0000rv   c                  L   [        [        R                  " SS5      5      / SQ:X  d   e[        [        R                  " S5      5      / SQ:X  d   e[        [        R                  " S5      5      [        :X  d   e[        [        R                  " S[        S95      [        :X  d   eg )Nrg   ri   r   r   ri   rN  )rr   r   r.   typerz   rv   rt   test_eyer  (  st    

1a !\111

1,...

1&(((

1&)*f444rv   c                     [        [        R                  " SS5      5      / SQ:X  d   e[        [        R                  " S5      5      / SQ:X  d   e[        R                  " SS5      [        / SQ/ SQ/5      :X  d   e[        [        R                  " S5      5      [        :X  d   e[        [        R                  " S[        S95      [        :X  d   eg )Nrg   r  rh   ri   ri   ri   rN  )rr   r   r4   r  rz   rv   rt   	test_onesr  /  s    Aq!"l222A<///;;q!	9'= >>>>A6)))A6*+v555rv   c                     [        [        R                  " SS5      5      / SQ:X  d   e[        [        R                  " S5      5      / SQ:X  d   e[        R                  " SS5      [        / SQ/ SQ/5      :X  d   e[        [        R                  " S5      5      [        :X  d   e[        [        R                  " S[        S95      [        :X  d   eg )Nrg   r  rh   r   rN  )rr   r   rH   r  rz   rv   rt   
test_zerosr  7  s    Q"#|333Q L000<<1I(>!????Q F***QF+,666rv   c                  	  ^ ^^^ [         R                  m[        SS/SS//5      m [        S[        /[        S//5      m[        S[        S/[        S[        /[        [        [        //5      mT" T TT5      [        / SQ/ SQSSS[        SS/SS[        SSS/SSSSS[        /SSSS[        S//5      :X  d   eT" T TT5      [        / SQ/ SQSSS[        SSS/SS[        SSSS/SSSSS[        S/SSSS[        S[        /SSSS[        [        [        //5      :X  d   eT" T TT5      [        / SQ/ SQSSS[        SSS/SS[        S[        SS/SS[        [        [        SS/SSSSSS[        /SSSSS[        S//5      :X  d   e[        [        [        [        /5      m [        SS/SS	//5      m[        S
S//5      mT" T STT5      [        [        SSSSS/[        SSSSS/[        SSSSS// SQ/ SQ/ SQ/ SQ/5      :X  d   e[        [        U UUU4S j5        T" S5      [        S//5      :X  d   eT" SSS9[        SS/SS//5      :X  d   eT" SSS9[        SS/SS//5      :X  d   eT" SSSS9[        SS/SS/SS//5      :X  d   eT" SS/6 [        SS/SS//5      :X  d   eT" [        SS/5      5      [        S/S//5      :X  d   eT" SSS/S	/SS9T" S/SS/S	//SS9s=:X  a  [        SS/SS/S	S//5      :X  d   e   e[        T" S5      5      [         :X  d   e[        T" S[         S95      [         :X  d   e[         R                  " / SQ5      [         R                  " SSS5      :X  d   e[         R                  " / SQSS9R                  S:X  d   e[         R                  " / SQ/5      R                  S:X  d   e[         R                  " / SQ/SS9R                  S:X  d   e[         R                  " / SQ//5      R                  S:X  d   e[         R                  " [        SS5      SS5      [        / SQ/ SQ/5      :X  d   e[         R                  " [        SS5      SS5      [        SS/SS/SS/SS//5      :X  d   eg )Nri   rg   rh   )ri   rg   r   r   r   r   )rg   rh   r   r   r   r   r   )ri   rg   r   r   r   r   r   )rg   rh   r   r   r   r   r   rj   rk   rl   r   )r   r   r   r   r   r   )r   r   ri   rg   r   r   )r   r   rh   rj   r   r   )r   r   r   r   rk   rl   c                     > T" T STTSS9$ )Nr   rk   rp   rz   rJ   rK   rL   r*   s   rt   r    test_diag_make.<locals>.<lambda>l  s    tAq!QQ7rv   r  )rq   )rp   rq   F)unpackrN  ro   rw  rt  r   r   ri   r   )r   r   r   rg   )
r   r*   rO   rP   rQ   r^   r  r  r  r4   r  s   @@@@rt   test_diag_maker  ?  sQ   ;;DAA AAA AAq	Aq!9q!Qi01A1a=F	
Aq!Q	
Aq!Q	
Aq!Q	
Aq!Q$     1a=F	
Aq!Q1	
Aq!Q1	
Aq!Q1	
Aq!Q1	
Aq!Q1$     1a=F	
Aq!Q1	
Aq!Q1	
Aq!Q1	
Aq!Q1	
Aq!Q1$     	1ayAAA AAxA 1av	
Aq!Q	
Aq!Q	
Aq!Q'      :787fqcUm###?fq!fq!f%56666?fq!fq!f%56666"fq!fq!fq!f-E&FFFF!Q=F	
A	
A$     1v6	
	
+ $    QFAu-1#1vs#E26<	
A	
A	
A> 7    
 Q=F"""QF#$...;;y!V[[Aq%9999;;y/55???;;	{#))V333;;	{51776AAA;;}%++v555;;tAqz1a(F4 -    ;;tAqz1a(F	
A	
A	
A	
A	4 -   rv   c                    ^ [        SS[        S5      5      mTR                  5       n U TR                  S5      :X  d   e[        U 5      S:X  d   e[        TR                  S5      5      S:X  d   e[        TR                  S5      5      S:X  d   e[        TR                  S	5      5      S
:X  d   e[	        TR                  5       5      [	        T5      :X  d   e[        SSSS05      n[	        UR                  5       5      [	        U5      :X  d   e[	        T5      [	        U5      :w  d   e[        [        U4S j5        [        [        U4S j5        [        [        U4S j5        [        S	S5      n[        [        SUR                  -
  UR                  5       Vs0 s H  nU[        UR                  U5      5      _M      sn5      U:X  d   eg s  snf )Nrh   r   r   )r   rj   r   ri   ri   rk   r   )rh   r   rg   rg   rm   c                  &   > T R                  S5      $ r   diagonalr   s   rt   r   test_diagonal.<locals>.<lambda>  s    qzz!}rv   c                  &   > T R                  S5      $ )Nrv  r  r   s   rt   r   r    s    qzz"~rv   c                  .   > T R                  [        5      $ r   )r  r6   r   s   rt   r   r    s    qzz"~rv   )r   r   r  tupler  r#   r^   r  r4   r'   rp   rq   rr   )rM   sr5  r   r   s       @rt   test_diagonalr    s   q!U1XA	

A

18y   A6)))B F***A4'''

a(((QFA;'A

a(((7d1g
:,-
:-.
:-.Q
Aqx(*(A d1::a=))(* +./0 0 0 *s   %Gc                  |   [         R                  " SS5      [         R                  " SSS9s=:X  ai  [         R                  " SSS9s=:X  aO  [         R                  " SSSS9s=:X  a4  [         R                  " SSSS9s=:X  a  [        / SQ/ S	Q/ S
Q/5      :X  d   e   e[         R                  " SSSS9[        / SQ/ SQ/ SQ/5      :X  d   e[        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [         R                  " SSS9[         R                  " SSS9:X  d   eg )Nrh   rg   
eigenvalue)sizer  upper)band)r  eigenvalr  rg   ri   r   )r   rg   ri   r   lowerrg   r   r   r0  r   c                  .    [         R                  " S5      $ Nrg   r   jordan_blockrz   rv   rt   r   #test_jordan_block.<locals>.<lambda>  s    v2215rv   c                  0    [         R                  " SS5      $ )Ng      @rg   r  rz   rv   rt   r   r    s    v223:rv   c                  *    [         R                  " SS9$ )Nrg   r  r  rz   rv   rt   r   r    s    v22a@rv   c                  ,    [         R                  " SSS9$ )Nrg   rj   )r  r  r  rz   rv   rt   r   r    s    Fq"rv   )r  r  )r   r  r^   r  rz   rv   rt   test_jordan_blockr    s:   q!$(;(;A!(L ""a8""1ag6 ""q2
       q!'2f> 7       
 :56
::;
:@A
:"#
 A!4Q/0 0 0rv   c            	        ^ [        SS/SS//5      n U R                  [        S/S//5      5      [        S/S//5      /:X  d   eU R                  [        S/S//5      SS9[        S[        S5      -  S-  /[        S5      S-  //5      /:X  d   eU R                  [        S/S//5      [        S/S//5      5      [        S/S//5      [        [        S	S5      /[        S
S5      //5      /:X  d   eU R                  [        S/S//5      [        S/S//5      5      [        S/S//5      /:X  d   eU R                  [        S/S//5      5      / :X  d   e[        / SQ/ SQ/ SQ/5      n[        S/S//5      [        S/S//5      [        S/S//5      /mUR                  " T6 [        S/S//5      [        [        SS5      /[        SS5      //5      /:X  d   e[        / SQ5      [        / SQ5      [        / SQ5      /m[	        [
        U4S j5        [        / SQ5      [        / SQ5      [        / SQ5      /m[	        [
        U4S j5        g )Nri   rg   rh   rj   T	normalizerk   r   rl   r   )r   ri   r   )rh   rl   r   )r   rk   rg   r   r         r   ro   )ri   rj   rk   c                  0   > [         R                  " T SS06$ N	rankcheckTr   orthogonalizevecss   rt   r   $test_orthogonalize.<locals>.<lambda>      v33TJTJrv   rn   r   c                  0   > [         R                  " T SS06$ r  r  r  s   rt   r   r    r  rv   )r   r  rA   r    r^   r  )r   rI  r   s     @rt   test_orthogonalizer    s^   AA A??6A3*-.6A3*3E2FFFF??6A3*-?>	!DG)A+a,	-./ / /??6A3*-vtaSk/BC	!qc
	VhsA&6%7(1a.9I$JKLM M M??6A3*-vtaSk/BC	"s	  ??6A3*-."444	:y12ARD1#;"s!4frdRD\6JKD??D!	"s	fx2&7(2r:J9K%LMNO O O 9vi0&2CDD
:JK9vi0&2CDD
:JKrv   c                  d   [         R                  " S5      u  pU [        / SQ/ SQ/ SQ/5      :X  d   eU[        / SQ/ SQ/ SQ/5      :X  d   e[         R                  " S5      u  pU [        / SQ/ SQ/ S	Q/ S
Q/ SQ/ SQ/ SQ/5      :X  d   eU[        / SQ/ SQ/ SQ/ S
Q/ SQ/ SQ/ SQ/5      :X  d   eg )Nri   )r   ri   r   ri   r   ri   )r   ri   ri   )ri   ri   r   rh   )rv  ri   r   r   r   r   r   )ri   r   ri   r   r   r   r   )r   ri   r   ri   r   r   r   )r   r   ri   r   ri   r   r   )r   r   r   ri   ri   ri   r   )r   r   r   r   ri   rg   ri   )r   r   r   r   r   ri   rh   )rh   ri   r   r   r   r   r   )ri   rg   ri   r   r   r   r   )r   ri   ri   ri   r   r   r   )r   	wilkinson)wminuswpluss     rt   test_wilkinsonr
    s    $$Q'MFV * ) )+ , , , , F%%%' ( ( ( (
 $$Q'MFV 8 7 7 7 7 7         F11111113 4 4 4 4rv   c            	      @   [        S5      u  p[        SSSU -  U/5      nUR                  U S5      [        SS[        SS5      U/5      :X  d   e[        SS[	        U 5      U -  4USS4SSU S-  S-   445      nUR                  U S5      [        SUSS4S	45      :X  d   eg )
Nx yrg   ri   rk   rj   r   r   )ri   rj   ri   )r   rk   ri   )rC   r   limitr    r@   )rO   rP   r   r   s       rt   
test_limitr    s    5>DAq!ac1XA771a=F1a(1a.!)<====As1vax 1a)b!QTAX->?@A771a=FI1ay*#EFFFFrv   c                     ^ ^ [        / SQ/ SQ/ SQ/5      m / SQm[        [        U U4S j5        [        [        U U4S j5        g )Nro   rn   r   r  c                     > T T-  $ r   rz   r5  vs   rt   r   "test_issue_13774.<locals>.<lambda>  	    acrv   c                     > TT -  $ r   rz   r  s   rt   r   r    r  rv   )r   r^   ro  r  s   @@rt   test_issue_13774r     s-    	9i01AA
9k"
9k"rv   c                  F  ^^ [        S5      m[        S5      m[        [        S 5        [        [        U4S j5        [        [        U4S j5        [        [        UU4S j5        [        S5      u  pn[        R
                  " [        SU /T5      5      [	        U * /5      :X  d   e[        R
                  " [        SX/T5      5      [	        S	U * /SU* //5      :X  d   e[        R
                  " [        SX!U /T5      5      [	        S	S	U * /SS	U* /S	SU* //5      :X  d   eg )
NrO   rP   c                  .    [         R                  " S5      $ Nri   )r   	companionrz   rv   rt   r    test_companion.<locals>.<lambda>
  s    v//2rv   c                  F   > [         R                  " [        S/T 5      5      $ r  r   r  r   rs   s   rt   r   r    s    v//aS!=rv   c                  H   > [         R                  " [        SS/T 5      5      $ )Nrg   ri   r  rs   s   rt   r   r    s    v//aVQ@rv   c                  N   > [         R                  " [        T T-  T T/5      5      $ r   r  rO   rP   s   rt   r   r    s    v//QqS1a&0ABrv   zc0:3ri   r   )r$   r^   r  rC   r   r  r   )c0c1c2rO   rP   s      @@rt   test_companionr$    s   sAsA
:23
:=>
:@A
:BCJBBD!R!,-">>>D!Ra01RC1rc(#$% % %D!RR!45AsaRC[1a"+678 8 8rv   c            	      B   [        S5      u  pn[        XU/5      nUR                  [        XU// SQ5      5      nU[        S/S/S//5      :X  d   e[        X X U /X X U /X X U //5      nUR                  [        U /S/5      5      nU[        / SQ/ SQ/ SQ/5      :X  d   eg )Nzx, y zro   ri   rg   rh   )ri   ri   ri   ri   ri   )rC   r   r|  zip)rO   rP   rQ   r   r   s        rt   test_issue_10589r'    s    hGA!	q		B	aAY	*	+B!qcA3((((	!a1q/A!?C	DB	aS1#	B/?KLLLLrv   c                       " S S[         5      n [        SS/ SQ5      nU " SS/ SQ5      nX-  n[        X05      (       d   eU[        SS/SS//5      :X  d   eg )	Nc                   2    \ rS rSr\R
                  S-   rSrg)test_rmul_pr19860.<locals>.Fooi#  g{Gz?rz   N)r  r  r  r  r   _op_priorityr  rz   rv   rt   Foor*  #  s    )66=rv   r,  rg   r  r   r         )r   r   
isinstance)r,  rJ   rK   rL   s       rt   test_rmul_pr19860r0  "  sg    >" > 	q!\"AAq,A 	
AaB"b*++++rv   c                     ^ ^ [        SS/SS//5      m [        SS/SS//5      m[        [        U U4S j5        [        [        U U4S j5        g )Nri   rg   rh   rj   c                     > TT -   $ r   rz   r   r   s   rt   r   "test_issue_18956.<locals>.<lambda>4  	    a!erv   c                     > T T-   $ r   rz   r3  s   rt   r   r4  5  r5  rv   )r   r   r^   ro  r3  s   @@rt   test_issue_18956r7  1  sD    1v1vA1qe}A
9m$
9m$rv   c                       " S S[         5      n [        SSSS/5      nX" 5       :w  d   e " S SU 5      nX" 5       :X  d   eg )Nc                        \ rS rSrS rS rSrg)test__eq__.<locals>.Myi9  c              3      #    Sv   Sv   g 7fr  rz   selfs    rt   __iter__test__eq__.<locals>.My.__iter__:  s     GGs   
c                     [        U 5      U   $ r   )rr   )r=  r   s     rt   __getitem__"test__eq__.<locals>.My.__getitem__>  s    :a= rv   rz   N)r  r  r  r  r>  rA  r  rz   rv   rt   Myr:  9  s    		!rv   rC  rg   ri   c                       \ rS rSrS rSrg)test__eq__.<locals>.My_sympyiB  c                     [        U 5      $ r   r  r<  s    rt   _sympy_$test__eq__.<locals>.My_sympy._sympy_C  s    $<rv   rz   N)r  r  r  r  rG  r  rz   rv   rt   My_sympyrE  B  s    	 rv   rI  )objectr   )rC  rJ   rI  s      rt   
test__eq__rK  8  sL    !V ! 	q!aVA99 2   
??rv   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 )Nrh   rg   )rh   rg   c              3   D   #    U  H  n[        U5      [        L v   M     g 7fr   )r  rm  )rA  r   s     rt   rB  test_args.<locals>.<genexpr>L  s     (IAaCs    )	enumerateall_classesrH   r  rJ  rp   r  rm  rq   r   rr   r  r%   r   r   )rI  rO  r   s      rt   	test_argsrQ  H  s    K(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*** )rv   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Nrh   rg   )
r   r   rH   rb   _matr   r#   r   _smatr   )rO  r   matsmats       rt   test_deprecated_mat_smatrX  U  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 r  )r   rO   rP   rQ   )r  s    rt   test_divisionrZ  b  s;    q!aVAQ3&A!QqSz****rv   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 )	Nro   rg   r  r  rj   r  ri   c                     > T T-   $ r   rz   r  s   rt   r   test_sum.<locals>.<lambda>k  r  rv   r  r  s   @@rt   test_sumr^  g  r  rv   c                  *   [        SS/[        [        //5      n [        U 5      [        SS/[	        [        5      [	        [        5      //5      :X  d   e[        SSS[        /5      n [        SSS[	        [        5      /5      n[        U 5      U:X  d   eg )Nri   r   rg   rv  rh   )r   rO   rP   absr   r  s     rt   test_absra  n  s~    B!Q !Aq6VaVc!fc!f%567777q!b!WAq!aQ[!Aq6Q;;rv   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)ri   rg   rw  rc  )rh   r   rg   rj   rl   ri   )r   addrJ   rK   s     rt   test_additionrg  v  sY      	A
 	  	A
 5AEE!H8AA'7 888888rv   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 )Nrh   r   ri   r   r   r   r   rg   rj   rl   r   r}   )r   rg   ri   rg   ri   r   )rh   rk   rj   rk   rj   )rl   r   r   r   r   rc  r~   rg   r   )rg   rg   rg   r   )ri   r   ri   rg   )rg   r   ri   r   rg   r   r   r   )r   r   rh   r   )r   rj   r   rj   )r   r#   r   rH   r   )r5  rJ   s     rt   test_fancy_index_matrixrk    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, %  	 + $4 	1AAdGAdGAdG99aVaS!VCC-	 &
 
 
 
 99aVY'63 ,    99\<0F	< 5   rv   c                    ^^ [        S5      m[        S5      m[        [        UU4S j5        [        [        U4S j5        TT-  n U S   S:X  d   eU S   S:X  d   eU S	   S
:X  d   eU S   S
:X  d   eU S   S:X  d   eU S   S:X  d   eTT-  n U S   S:X  d   eU S   S:X  d   eU S	   S
:X  d   eU S   S
:X  d   eU S   S:X  d   eU S   S:X  d   e[	        TU 5      nUTR
                  " U 5      :X  d   eUS   S:X  d   eUS   S:X  d   eUS	   S:X  d   eUS   S
:X  d   eUS   S:X  d   eUS   S:X  d   e[        [        UU4S j5        T[        S5      -  n [        U [         5      (       d   eU S   [        :X  d   eU S   S[        -  :X  d   eU S	   S[        -  :X  d   eU S   S:X  d   e[        T-  nX:X  d   eST-  n [        U [         5      (       d   eU S   S:X  d   eU S   S:X  d   eU S	   S:X  d   eU S   S:X  d   e[        [        S/S[        //5      nUS-  U:X  d   e[        [        [        /SS//5      nUS-  [        [        [        /[        [        //5      :X  d   e[        [        SS5      5      n[        SS5      * n[        XUU/5      nUR                  U5      [        U/U/U//5      :X  d   eg )N)rc  rw  r   rl   rd  c                     > TT -  $ r   rz   rf  s   rt   r   %test_multiplication.<locals>.<lambda>  s	    qsrv   c                     > T 0 -  $ r   rz   r  s   rt   r   ro    s	    adrv   r}   r   r~   rg   r   rl   rm   ri     rs  r   rj   c                     > [        T T5      $ r   )r2   rf  s   rt   r   ro    s    :1a@rv   rO   rh   rk   r   r-  ri   )r   r^   rW   ro  r2   multiply_elementwiser$   r/  rO   r5   r3   r4   r    )	rL   hr#  r5  r   _hr   rJ   rK   s	          @@rt   test_multiplicationrv    s8     	A 	  	A
 :{#
9l#	!AT7a<<T7a<<T7a<<T7a<<T7b==T7a<<	AAT7a<<T7a<<T7a<<T7a<<T7b==T7a<<#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<<Q!R!"A6Q;;R1a&!"A6Vc3Z#s45555 	tAqzA
1a.B|A!!!$			0 )   rv   c                    ^ ^^^ [        [        S 5        [        SS/SS//5      m T S-  [        SS/SS	//5      :X  d   e[        / S
Q/ SQ/ SQ/5      m T S-  [        / SQ/ SQ/ SQ/5      :X  d   eT S-  [        S5      :X  d   eT S-  T :X  d   e[        S//5      S-  S   SS-  :X  d   e[        SS/SS//5      [	        S5      -  [        SS/SS//5      :X  d   e[        SS/SS//5      m T R                  SSS9T R                  SSS9:X  d   eT [	        S5      -  [        SS/SS//5      :X  d   e[        S5      S -  [        S5      :X  d   e[        SS/S!S"//5      m T [        R                  -  S S  / S#Q:X  d   e[        SS/S$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/ S0Q/ S1Q/5      m T S2-  [        / S1Q/ S1Q/ S1Q/5      :X  d   e[        [        U 4S3 j5        [        [        U 4S4 j5        [        S5S/SS//5      m T S2-  [        S6S7/S8S9//5      :X  d   e[        / S0Q/ S0Q/ S0Q/5      m T S2-  [        / S0Q/ S0Q/ S0Q/5      :X  d   e[        / S/Q/ S0Q/ S0Q/5      m T S2-  [        / S0Q/ S0Q/ S0Q/5      :X  d   e[!        S:S;S<9m[#        T T-  [$        5      (       d   e[!        S:S;S;S=9m[        [        U U4S> j5        [!        S:S;S;S?9mT T-  [        ['        ST5      ['        ST5      ['        ST5      * ['        ST5      -
  S-   /S['        ST5      S['        ST5      -
  // S0Q/5      :X  d   eT TS-   -  [        / S0Q/ S0Q/ S0Q/5      :X  d   e[        [        U 4S@ j5        [        / S0Q/ SAQ/ SBQ/5      m T SC-  [        / SDQ/ SEQ/ SFQ/5      :X  d   eT SC-  T S-  :X  d   e[        / S/Q/ SGQ/ S1Q/5      m [!        S:5      mT T-  mTR)                  TS5      R+                  5       T S-  :X  d   e[        [        UU4SH j5        TT-  T ST-  -  :X  d   e[        / S1Q/ S1Q/ S1Q/5      m [!        S:S;S;SI9mT T-  T :X  d   e[!        S:S;S;S?9mT T-  [-        ST-  ST-  ST-  5      :X  d   eT T-  R)                  TS5      [        S5      :X  d   eT T-  R)                  TS5      [/        S5      :X  d   e[        / SJQ/ SKQ/ SLQ/5      m T SM-  [-        SNSNSN5      :X  d   eT [0        -  [-        S[0        -  S[0        -  S[0        -  5      :X  d   e[        / S/Q/ S0Q/ S0Q/5      m [        [        U 4SO j5        [        [        U 4SP j5        [        [        R                  [        R                  /[        R                  [        R                  //5      m T [        R                  -  T :X  d   e[        SS/SS//5      m T [        R                  -  [        [        R                  [        R                  /S[        R                  -  S[        R                  -  //5      :X  d   eg )QNc                      [        S5      S-  $ Nrc  rg   r  rz   rv   rt   r   test_power.<locals>.<lambda>  s    ):rv   rg   rh   rj   rk   i  i  i,*  i7  )rg   ri   rh   )rj   rg   rj   )rl   r  ri   )i"  i     )i  i  ip  )i  i  i  r   ri   d   r}   r   r   r-  r.     cayleymethodmultiplyr   r     !   i 0   9   )rk   rg   rj   r   r   g      ?rH  i   )rh   r   r   r   rv  )r   rv  rv  r   rh   )r   rh   r   rh   r   )r   r   rh   r   rh   )rh   r   r   rh   r   c                  8   > T R                  [        S5      5      $ Nr   )_matrix_pow_by_jordan_blocksr"   r   s   rt   r   rz  %  s     > >qu Erv   c                  T    [        SS/SS//5      R                  [        S5      5      $ )Nri   rh   )r   r  r"   rz   rv   rt   r   rz  (  s(    AA'7 8 U UVWX[V\ ]rv   r   r   r         $@c                     > T S-  $ N @rz   r  s   rt   r   rz  +  	    q#vrv   c                  "   > T [        SS5      -  $ rS  r    r  s   rt   r   rz  ,      q(1a.0rv   r   ihiO<iv0irI  T)integer)r  negativec                     > T T-  $ r   rz   )r   rI  s   rt   r   rz  6  s	    q!trv   )r  nonnegativec                  "   > T [        SS5      -  $ rS  r  r  s   rt   r   rz  =  r  rv   )rh   r   ri   )rj   rh   ri   g      @)   H   Y   )i#        )i<  i  iI  r   r   r   c                  D   > T R                  TS5      R                  5       $ )Nr   )r|  r:  )AnrI  s   rt   r   rz  E  s    rwwq"~224rv   )r  positiver  )r   rg   r   r   r  gd%%@c                     > T S-  $ r  rz   r  s   rt   r   rz  T  r  rv   c                     > T [         -  $ r   r   r  s   rt   r   rz  U  s	    q!trv   )r^   rV   r   r.   r   powr"   r   	sympy.abcrI  rJ   rK   r  _eval_pow_by_recursionrU   r  r$   r/  r   r   r|  r:  r*   rH   r   )r   r  r   rI  s   @@@@rt   
test_powerr    s   
!:;AA Aa46D$<%89999	9j12Aa46?O_MNNNNa43q6>>a4199QC5MS $'1c6111Aq6Aq6"#WQZ/6Ar7RH:M3NNNN1qe}A55H5%r*)EEEEgaj=FQGb"X#67777q68s1v%%%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
:~&
:|$ 166166"234Aaff9>>A1vAaff9!&&!&&!1AaffHah3G HIIIIrv   c            
         [        S[        -   S[        -
  /S[        -
  S[        -   //5      n [        S5         U R                  5       R	                  5       [        [        S[        -  5      [        S5      -   S-  [        S[        -  5      * [        S5      -   S-  /[        S[        -  5      * [        S5      -   S-  [        S[        -  5      [        S5      -   S-  //5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nri   Trg   )r   rO   r[   r,   r-   r4  s    rt   $test_issue_17247_expression_blowup_1r  \  s    1ac
QqS!A#J'(A	T	uuw~~61Q3x#a& !#s1Q3xi#a&&8!%;<1Q3xi#a& !#s1Q3x#a&'8!&;<+> $? ? 	? ? 
		s   B2C55
Dc                     [        S[        -   S[        -
  /S[        -
  S[        -   //5      n [        S5         U R                  5       u  pX-  UR	                  5       -  (       d   e S S S 5        g ! , (       d  f       g = fNri   T)r   rO   r[   jordan_forminvr5  PJs      rt   $test_issue_17247_expression_blowup_2r  d  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)Nri   Tr|  l                )r   rO   r[   r4  s    rt   $test_issue_17247_expression_blowup_3r  k  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]])r   r"   r[   r4  s    rt   $test_issue_17247_expression_blowup_4r  s  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)Nrl   c                 $    SSX-   -  [         -  -   $ Nri   r   r  r   s     rt   r   6test_issue_17247_expression_blowup_5.<locals>.<lambda>      !rQSk!m"3rv   TrO   rk   $   rj   EXdomain)r   r[   charpolyr   rO   r   r4  s    rt   $test_issue_17247_expression_blowup_5r    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   r   r   rO   r[   detr   r5  s     rt   $test_issue_17247_expression_blowup_6r    sZ    q!5":.:aac:./A	T	uuY1$$$ 
	 /		   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)Nrl   c                 $    SSX-   -  [         -  -   $ r  r  r   s     rt   r   6test_issue_17247_expression_blowup_7.<locals>.<lambda>  r  rv   T	berkowitzr   )r   r[   r  r4  s    rt   $test_issue_17247_expression_blowup_7r    s<    q!34A	T	uu[!Q&&& 
		s	   <
A
c            	          [        SS[        S5       V s/ s H  n [        U -   PM     sn 5      n[        S5         UR	                  S5      S:X  d   e S S S 5        g s  sn f ! , (       d  f       g = f)Nr   r  Tlur   r  r  s     rt   $test_issue_17247_expression_blowup_8r    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   r  T)ri   r   r   r   rv  r   r   r  r   ri   rg   rh   rj   rk   rl   r   r   r   r   r   r   r   r   r   r~   )r   r   rO   r[   rrefr  s     rt   $test_issue_17247_expression_blowup_9r    s    q!5":.:aac:./A	T	vvxF********$, - /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)Nrl   c                 $    SSX-   -  [         -  -   $ r  r  r   s     rt   r   7test_issue_17247_expression_blowup_10.<locals>.<lambda>  r  rv   Tr   )r   r[   cofactorr4  s    rt   %test_issue_17247_expression_blowup_10r    s>    q!34A	T	zz!Q1$$$ 
		s	   =
Ac                      [        SSS 5      n [        S5         U R                  5       [        SSS/S-  5      :X  d   e S S S 5        g ! , (       d  f       g = f)Nrl   c                 $    SSX-   -  [         -  -   $ r  r  r   s     rt   r   7test_issue_17247_expression_blowup_11.<locals>.<lambda>  r  rv   Tr   r  )r   r[   cofactor_matrixr4  s    rt   %test_issue_17247_expression_blowup_11r    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)Nrl   c                 $    SSX-   -  [         -  -   $ r  r  r   s     rt   r   7test_issue_17247_expression_blowup_12.<locals>.<lambda>  r  rv   Tri   r   rj   )r   r[   	eigenvalsr   r4  s    rt   %test_issue_17247_expression_blowup_12r    sJ    q!34A	T	{{}AqsAq! 4444 
		s   $A
Ac            
         [        SS[        -
  [        S-   S[        -
  /S[        -
  [        S-   S[        S-   /SS[        -
  [        S-   S[        -
  /SSS[        -
  S//5      n U R                  5       nUS   SS[        / SQ5      /4:X  d   eUS   S   [        [        S5      [        S-
  -  -
  S-   :X  d   eUS   S   S:X  d   eUS   S   S   R	                  SSS9[        [        * [        S5      [        S-
  -  -   S-
  [        S-
  -  /S[        -  [        S-  S[        -  -
  S-   -  [        S-   [        [        S5      [        S-
  -  -
  S-   -  [        S-  S[        -  -
  S-   -  -   /[        * [        S5      [        S-
  -  -   S-
  [        S-
  -  /S//5      :X  d   eUS   S   [        [        S5      [        S-
  -  -   S-   :X  d   eUS   S   S:X  d   eUS   S   S   R	                  SSS9[        [        * [        S5      [        S-
  -  -
  S-
  [        S-
  -  /S[        -  [        S-  S[        -  -
  S-   -  [        S-   [        [        S5      [        S-
  -  -   S-   -  [        S-  S[        -  -
  S-   -  -   /[        * [        S5      [        S-
  -  -
  S-
  [        S-
  -  /S//5      :X  d   eg )	Nr   ri   rg   )r   r   r   ri   FT)deepnumerr   )r   rO   
eigenvectsrA   r-   )r5  evs     rt   %test_issue_17247_expression_blowup_13r    s   Aq1ua!e$	
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 :   rv   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   ri   rj   Tr   r  )r   rO   r[   echelon_formr4  s    rt   %test_issue_17247_expression_blowup_14r    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   ri   rj   Tr   )r   rO   r[   rowspacer4  s    rt   %test_issue_17247_expression_blowup_15r    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   ri   rj   T)r   rO   r[   columnspacer4  s    rt   %test_issue_17247_expression_blowup_16r    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   r  Tri   r   r   rg   rv  rh   r   rj   r   rk   r  rl   ru  )r   r   rO   r[   	nullspacer  s     rt   %test_issue_17247_expression_blowup_17r    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)Nrl   ri   rh   T)r   rO   r[   is_nilpotentr4  s    rt   %test_issue_17247_expression_blowup_18r    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)r   r"   r[   is_diagonalizabler4  s    rt   %test_issue_17247_expression_blowup_19r     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)	Nri   r   T)ri   r   r   r   r  r  rj  rg   )r   rO   r[   diagonalizer4  s    rt   %test_issue_17247_expression_blowup_20r   *  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GEr  v  [
            [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785],
            [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785],
            [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905],
            [0, 0, 0, -11328/952745 + 87616*I/952745]]r   r"   r[   r  r4  s    rt   %test_issue_17247_expression_blowup_21r  =  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  r4  s    rt   %test_issue_17247_expression_blowup_22r  K  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  )r   r"   r[   r  r-   r4  s    rt   %test_issue_17247_expression_blowup_23r  Y  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  r#   r"   r[   r  r   r4  s    rt   %test_issue_17247_expression_blowup_24r  g  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  r4  s    rt   %test_issue_17247_expression_blowup_25r  u  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]]Trj   r   r"   r[   rankr4  s    rt   %test_issue_17247_expression_blowup_26r    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   ri   Ta  [
            [    0,  4*x/(x**2 - 2*x + 1), -(-17*x**4 + 12*sqrt(2)*x**4 - 4*sqrt(2)*x**3 + 6*x**3 - 6*x - 4*sqrt(2)*x + 12*sqrt(2) + 17)/(-7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 + 8*x**3 - 2*x**2 + 8*x + 6*sqrt(2)*x - 5*sqrt(2) - 7), -(12*sqrt(2)*x**4 + 17*x**4 - 6*x**3 - 4*sqrt(2)*x**3 - 4*sqrt(2)*x + 6*x - 17 + 12*sqrt(2))/(7*x**4 + 5*sqrt(2)*x**4 - 6*sqrt(2)*x**3 - 8*x**3 + 2*x**2 - 8*x + 6*sqrt(2)*x - 5*sqrt(2) + 7)],
            [x - 1, x/(x - 1) + 1/(x - 1),                       (-7*x**3 + 5*sqrt(2)*x**3 - x**2 + sqrt(2)*x**2 - sqrt(2)*x - x - 5*sqrt(2) - 7)/(-3*x**3 + 2*sqrt(2)*x**3 - 2*sqrt(2)*x**2 + 3*x**2 + 2*sqrt(2)*x + 3*x - 3 - 2*sqrt(2)),                       (7*x**3 + 5*sqrt(2)*x**3 + x**2 + sqrt(2)*x**2 - sqrt(2)*x + x - 5*sqrt(2) + 7)/(2*sqrt(2)*x**3 + 3*x**3 - 3*x**2 - 2*sqrt(2)*x**2 - 3*x + 2*sqrt(2)*x - 2*sqrt(2) + 3)],
            [    0,                     1,                                                                                            -(-3*x**2 + 2*sqrt(2)*x**2 + 2*x - 3 - 2*sqrt(2))/(-x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x + 1 + sqrt(2)),                                                                                            -(2*sqrt(2)*x**2 + 3*x**2 - 2*x - 2*sqrt(2) + 3)/(x**2 + sqrt(2)*x**2 - 2*sqrt(2)*x - 1 + sqrt(2))],
            [1 - x,                     0,                                                                                                                                                                                               1,                                                                                                                                                                                             1]]a  [
            [0, 1,                       0,                       0],
            [0, 0,                       0,                       0],
            [0, 0, x - sqrt(2)*(x - 1) + 1,                       0],
            [0, 0,                       0, x + sqrt(2)*(x - 1) + 1]])r   rO   r[   r  r-   r"   r  s      rt   %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)])r   r"   r[   singular_valuesr4  s    rt   %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  r4  s    rt   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)	ri   ri   ri   ri   ri   r   ri   r   r   ri   rg   r   r   ru  r   r   rv  rh   r   rj   r  r  T)	r   r   r   r   ri   r   r   r   r   )	r   r   r   r   r   r   ri   r   r   r  )r   rA   r[   r  r"   r4  s    rt   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      $ )Nrk   r}  )r   r   rz   rv   rt   r   test_creation.<locals>.<lambda>  s    vaE"I6rv   c                      [        SS/ 5      $ )Nrk   r   r  rz   rv   rt   r   r&    s    vaR0rv   c                      [        S5      S   $ ry  r  rz   rv   rt   r   r&    s    vf~a0rv   rk   rc  rh   r   ri   r  r}   rg   r   r   r   rj   )ri   ri   rg   rg   rg   )rh   rh   rh   rj   rj   Fr8  r   r~   r   rm   c                  B    [        [        S5      [        SS5      /5      $ )Nrg   r   rh   r   r4   rz   rv   rt   r   r&  $      vtAwQ
&;<rv   c                  B    [        [        S5      [        SS5      /5      $ )Nrg   rh   r   r*  rz   rv   rt   r   r&  %  r+  rv   )rk   rl   rl   )r^   r  r   r   rb   r   r1  r"   EmptySetrO   rq   rp   r   r.   r   as_immutable
as_mutabler4   r   )r5  rJ   r   rK   c23c13rL   datr   r   r   s              rt   test_creationr3    s   
:67
:01
:01	
	vq 
 8vbzEVRD\EVAq"5EEEEEE		!T{m$++-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                  $   [         R                  " S[        SS5      [        SS5      S-  [        SS5      S-  [        SS5      S-  [        SS5      S-  [        SS5      S-  [        SS5      S-  5      [        / SQ/ SQ/ S	Q/ S
Q/5      :X  d   eg )Nrh   rg   ri   rj   rk   rl   r   )ri   rg   rg   rg   rh   rh   )rj   rg   rg   rg   rk   rk   )rl   rl   r   r   rk   rk   )r   	irregularr4   rz   rv   rt   test_irregular_blockr6  -  s    AtAay$q)A+tAay{Qq	!T!AYq[$q)A+tAay{<?E	G @  rv   c                     [        S5      n U S S2S S24   [        S5      :X  d   eU SS2SS24   [        S5      :X  d   e[        SSS 5      nUSS S 24   [        SSS5      :X  d   eUSS2S4   [        SSS5      :X  d   e[        / S	Q/ S
Q/ SQ/ SQ/5      nUS S 2S4   [        SS/ SQ5      :X  d   eUSS 2S S 24   [        / SQ/ SQ/5      :X  d   eg )Nrj   rh   rg   r   c                 
    X-   $ r   rz   r   s     rt   r   test_slicing.<locals>.<lambda>;      15rv   ri   r   r  r)  )rj   rk   rl   r   )r   r   r   r   )r        r-  r   )rh   r   r   r-  r   )r.   rH   r   )m0r   r   s      rt   test_slicingr>  6  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Crv   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 )
Nrj   rg   )r  r  r  r  ri   r  r   )r  )rg   ri   r   r   )rh   r   ri   r   )rj   r   r   ri   r  r  r  r;  r<  r-     ))r   rg   rh   rj   )r   rl   r   r   r  rA  )rH   r.   r   r   s    rt   test_submatrix_assignmentrC  D  s$   aAa&Aac1Q3hK & ' ' ' ' AAbqb"1"fIA;;Q<(AadG & ' ' ' ' AhAadGa==MAadG * + + + + 1vAbqb!eH * + + + +rv   c                      [        S5      n U R                  SS5      [        SSS5      :X  d   e[        SSS 5      nUR                  SS5      [        S5      :X  d   eUR                  SS	5      [        S
5      :X  d   eg )Nrh   ri   r   )	ri   r   r   r   ri   r   r   r   ri   rj   c                 
    X-   $ r   rz   r   s     rt   r   test_reshape.<locals>.<lambda>c  r:  rv   )r   r$  )rh   rj   rg   r   rg   rl   ))r   ri   rg   rh   ri   rg   )rh   rj   rg   rh   rj   rk   )r.   reshaper   r=  r   s     rt   test_reshaperI  `  s    	QB::ava,GHHHH	1(	)B::	1DEF F F::av&NOOOOrv   c                      [        S5      n U R                  S 5      [        S5      S-  :X  d   eU R                  S 5      [        S5      :X  d   eg )Nrh   c                     SU -  $ r  rz   rs   s    rt   r    test_applyfunc.<locals>.<lambda>k  s    !A#rv   rg   c                     gNr   rz   rs   s    rt   r   rL  l  s    !rv   )r.   	applyfuncrH   )r=  s    rt   test_applyfuncrP  i  sE    	QB<<&#a&(222<<$a000rv   c            	         [        [        [        [        -   -  S/[        [        -   [        -  [        -  [        [        [        [        [        -   -  -   -  //5      n U R                  5       nU[        [        [        -  [        S-  -   S/[        [        S-  -  [        [        S-  -  -   [        [        -  [        [        S-  -  -   [        S-  -   //5      :X  d   e[	        SSS9n[        [        [        U-  5      /5      R                  SS9[        [        U5      [        [        U5      -  -   /5      :X  d   e[        / SQ/ SQ/ S	Q/5      R                  5       [        S
S
[        SS5      // SQ/ SQ/5      :X  d   eg )Nrg   rh   rJ   Tr*  )complexr   )r   r   r   r   ri   )r   ri   r   r   )
r   rO   rP   r-   r$   r,   r   r)   r@   r    )r=  r   rJ   s      rt   test_expandrS  o  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!"#$ $ $ 9j)4599;v	
Ax1~G @   rv   c            	      :   [        [        [        5      S-  [        [        S-  5      /[        [        S-  5      [        [        5      S-  -  [        [        S-  5      [        [        5      S-  -  //5      n U R                  [        R                  " [        5      [        R                  " [        5      -  5      nU[        [        S-  [        [        5      /[        S-  [        [        5      -  [        S-  [        [        5      -  //5      :X  d   eU R                  [        R                  " [        5      [        R                  " [        5      -  5      nU[        [        S-  [        /[        [        S-  -  [        S-  [        -  //5      :X  d   eU R                  [        R                  " [        5      [        R                  " [        5      -  5      nU[        [        S-  [        * /[        * [        S-  -  [        S-  * [        -  //5      :X  d   eg r  )
r   r   rO   rA   rP   refiner   r+  r  r  rH  s     rt   test_refinerV    st   	#a&!)T!Q$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9rv   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 )Nrh   )seedrj   r      T)rX  	symmetric)rZ  prng)r   r   )r|  F      )rZ  percentr[  r   ri   r\  )minr^  r]  )r7   rg  r?   randomRandomr1  r   r  )r5  r"   rngr  r^  
zero_countr   r   s           rt   test_randomrd    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 $G44KA8O8 % 
 	21b)AJ1771:qwwqz"AAw!|a
 #  rv   c                    ^^ [        S5      n U R                  5       [        S5      :X  d   eU R                  SS9[        S5      :X  d   eU R                  SS9[        S5      :X  d   eU R                  SS9[        S5      :X  d   eU R                  SS9[        S5      :X  d   eU R                  SS9[        S5      :X  d   e[        / SQ/ S	Q/ S
Q/5      n U R                  5       nX-  [        S5      :X  d   eU R                  SS9U:X  d   eU R                  SS9U:X  d   eU R                  SS9U:X  d   eU R                  SS9U:X  d   eU R                  SS9U:X  d   e[        / SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ S Q/ S!Q/ S"Q/ S#Q/ S$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 )-Nrj   r
  r  r  r  r  QR)rg   rh   rk   )rh   rl   rg   )r   rh   rl   rh   )r   r   r   r   ri   r   r   ri   r   ri   ri   ri   r   r   r   ri   ri   r   r   r   r   ri   ri   r   r   )ri   r   ri   r   r   ri   r   r   ri   r   ri   r   ri   ri   ri   r   ri   ri   r   r   r   r   r   ri   r   )ri   ri   ri   ri   r   ri   r   r   ri   ri   r   r   r   ri   ri   ri   ri   r   r   ri   ri   r   r   ri   ri   )ri   r   r   r   r   r   ri   ri   r   r   ri   ri   ri   r   r   r   r   r   r   ri   r   r   ri   r   r   )ri   r   r   ri   ri   ri   r   ri   r   r   ri   r   r   ri   ri   ri   r   ri   r   r   r   ri   r   r   r   )ri   r   r   r   r   r   r   r   ri   ri   ri   r   ri   r   ri   ri   ri   ri   r   r   r   ri   ri   r   ri   )r   ri   ri   ri   r   r   r   r   ri   ri   ri   r   ri   r   ri   r   ri   r   ri   r   ri   r   r   ri   r   )ri   ri   r   r   r   ri   ri   r   r   ri   ri   r   ri   ri   r   ri   ri   r   ri   r   ri   ri   r   ri   ri   )r   r   ri   ri   ri   r   r   ri   ri   r   ri   ri   r   ri   r   r   r   r   r   r   ri   r   ri   r   ri   )ri   r   ri   ri   ri   r   ri   r   r   ri   ri   r   ri   ri   r   ri   ri   ri   ri   r   ri   ri   ri   r   r   )r   ri   ri   r   r   r   r   ri   ri   r   ri   r   ri   r   ri   ri   r   r   ri   r   r   r   ri   ri   r   )ri   r   r   ri   r   ri   r   ri   ri   r   r   ri   r   ri   r   ri   r   ri   r   ri   r   ri   ri   r   r   )r   ri   ri   r   r   ri   ri   r   r   ri   ri   r   ri   r   r   r   ri   r   r   ri   r   ri   ri   r   ri   )ri   ri   ri   r   ri   r   r   ri   r   r   ri   r   ri   ri   r   r   ri   ri   ri   r   ri   r   ri   ri   r   )r   ri   r   r   r   r   ri   ri   r   ri   ri   r   r   r   r   ri   r   ri   ri   ri   r   r   ri   r   r   )ri   ri   ri   ri   r   ri   ri   ri   ri   ri   ri   r   r   r   ri   r   ri   r   ri   r   r   ri   r   r   r   )r   r   r   ri   r   ri   ri   r   ri   r   r   r   r   r   ri   r   ri   ri   r   ri   r   ri   ri   r   ri   )r   ri   r   ri   r   r   r   r   ri   ri   ri   r   r   ri   ri   ri   r   r   ri   r   ri   ri   r   ri   ri   )ri   r   ri   ri   r   ri   r   ri   ri   r   ri   ri   ri   r   ri   r   r   r   r   ri   r   r   ri   r   ri   )r   r   r   ri   r   r   ri   ri   r   ri   ri   r   ri   r   ri   ri   r   r   r   r   r   r   r   r   r   )ri   r   r   r   r   ri   r   ri   r   r   ri   ri   r   ri   r   ri   ri   ri   ri   r   ri   ri   ri   ri   ri   )r   r   ri   ri   r   ri   r   r   r   ri   r   r   ri   r   r   ri   r   r   r   ri   r   ri   r   ri   ri   )r   r   r   r   r   ri   ri   ri   r   ri   ri   ri   r   r   r   ri   r   ri   ri   r   ri   ri   r   r   r   )r   r   ri   r   ri   ri   r   ri   ri   ri   r   r   ri   r   ri   r   r   ri   r   ri   r   r   r   r   r   )r   r   r   ri   ri   r   ri   ri   ri   r   r   ri   r   ri   r   ri   ri   r   ri   ri   ri   r   r   ri   r   BLOCKr   )r  1      )r   G   ^   );      A   c              3   \   >#    U  H!  n[        TR                  U5      5      TL v   M#     g 7fr   r  r  rA  r  rO  r   s     rt   rB  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r   rp  rq  s     rt   rB  rr    rs  rt  )r.   r  r   r  r   rJ  rn  r   )r   AinvAArO  r   s      @@rt   test_inverserx    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Lrv   c                     [        S5      u  pp#n[        S5      n[        SSSSSSU -  U-  SU-  U-  -
  SU -  SU-  -
  -  SU -  U-  SU -  SU-  -
  -  /SSSSSSU -  U-  SU-  U-  -   SU -  U-  SUS-  -  -
  -  S/SSU -  U-  SU-  U-  -
  SU -  SU-  -
  -  SU -  U-  SU -  SU-  -
  -  SSSS/SSU -  U-  SU-  U-  -   SU -  U-  SUS-  -  -
  -  SSSSS/SSSSU -  U-  SU-  U-  -
  SU -  SU-  -
  -  SU -  U-  SU -  SU-  -
  -  SS/SSSSU -  U-  SU-  U-  -   SU -  U-  SUS-  -  -
  -  SSS/SSU -  U-  U-  SU-  U -  SU-  U-  -
  -  SSU -  U-  U-  SU-  U -  SU-  U-  -
  -  SSU -  U-  U-  SU-  U -  SU-  U-  -
  -  S//5      nUR                  5       nXg-  [        S5      -
  R	                  [
        5      [        S5      :X  d   e[        S	 UR                  [        5       5       5      S
:  d   eg )Nz)Tau Tau_syn_in Tau_syn_ex C_m Tau_syn_gap__hr         ?       @      rg   r   c              3   8   #    U  H  n[        U5      v   M     g 7fr   r`  rA  fs     rt   rB  :test_inverse_symbolic_float_issue_26821.<locals>.<genexpr>       /!s1vv        @@)
rC   r   r  r.   rO  rI   rH   maxatomsr   )Tau
Tau_syn_in
Tau_syn_exC_mTau_syn_gaprz  r5  Mis           rt   'test_inverse_symbolic_float_issue_26821r    s   4;<g4h1CZk
%.C	
1QqCGCKJs 22SWS^5KLTRUXV`M`befibijmnxjxbxMyz	
1QqDHSLZ!33c#gj6HZYZ]IZ6Z[\_`	
CGCKJs**SWS^-CDT#XjEXZ]^aZabefpbpZpEqrstuvwxyz	
DHSLZ++c#gj.@ZQR]AR.RSTWXYZ[\]^_`	
1QCCOC//#c'#k/2IJ4PS8T_K_adehahilmxixaxKyz{|}~	
1QSS_S003s7;3Fs;XY>GY3YZ[^_`abc	T#Xj $c#gck#c'*2D&DEaSQ\H\]`H`befibijmbmnqrunu  wB  oB  cB  IC  DE  FJ  KN  FN  OY  FY  Z]  F]  _b  cf  _f  gj  _j  kn  or  kr  s}  k}  _}  F~  @  	A 	A 
BD3q6M$$V,a888 /rxx//#555rv   c                     [        S5      u  pp#n[        S5      n[        / SQSUS-  -  SU-  SSSSS// SQSSSUS-  -  SU-  SSS// S	QSSSSSUS-  -  SU-  S/S
U-  SS
U-  SS
U-  SSU -  //5      nXV-  R                  5       nUR                  U5      Xg-  -
  R	                  [
        5      [        S5      :X  d   e[        S UR                  [        5       5       5      S:  d   eg )Nz-Tau, Tau_syn_in, Tau_syn_ex, C_m, Tau_syn_gaprz  )r   r{  r   r   r   r   r   r   rg   r   r   )r   r   r   r{  r   r   r   )r   r   r   r   r   ri   r   ri   r   c              3   8   #    U  H  n[        U5      v   M     g 7fr   r  r  s     rt   rB  6test_matrix_exponential_issue_26821.<locals>.<genexpr>  r  r  r  )
rC   r   r,   r+   rO  rI   rH   r  r  r   )rJ   rK   rL   rM   r   rN   r5  Mes           rt   #test_matrix_exponential_issue_26821r    s    KLMA!A;	AqD"Q$aAQ1;;Q1a4AQ1;;QaAr!Q$w1;qSQAaCA1Q31bd; 	A #BGGAJ((0E!H<<< /rxx//#555rv   c                     [        SS[        S-  [        -  S[        S-  -  [        [        -  -   /5      n [        [        /nU R                  U5      [        S[        -  [        -  [        S-  /[        S[        -  [        -   //5      :X  d   e[        SS[        [        S-  [        S-  -  /5      n U R                  U5      [        SS/S[        -  [        S-  -  [        S-  S-  [        S-  -  //5      :X  d   e[        S-  [        -  n[        [        /n[	        X!5      [        S[        -  S[        -  /S[        -  S//5      :X  d   e[        S-  [        S-  -  n[	        X!5      [        S[        S-  -  S[        -  [        S-  -  /S[        -  [        S-  -  S[        S-  -  [        -  //5      :X  d   e[
        [        [        S-  -  -   n[        S-  S[        S-  -  -   n[        SS[        -  /S[        -  S[        -  //5      nU[	        U[        [        [        /5      5      :X  d   eU[	        U[        [        [        /5      R                  5      :X  d   e[	        U[        [        4U/5      [        SS[        S-  -  S[        -  /S[        S-  -  S[        -  S[        -  /S[        -  S[        -  S//5      :X  d   eg )Nri   rg   rj   rh   r   rl   )r   rO   rP   jacobianr/   rQ   r1  )r  symsr  ganss        rt   test_jacobian_hessianr    s   q!ad1fa1fqsl+,Aq6D::dv!Aq!t}q!A#'l&CDDDDq!aAad^$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. '       rv   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 )Nrg   rh   ri   r  rl   r  r  )rG   r)   rO   r@   r,   r-   )w1w2s     rt   test_wronskianr  1  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   rv   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 )	Nri   rj   rk   rg   r   r   rv  r   )r   rO   xreplacerP   rP  r.   rN  s    rt   test_xreplacer  B  s    Aq6Aq6"#,,aV4AA ! ! !Aq6AE1:&'00!RB@Q"a!"# # #1v1v&'3771:+>+>1v+FFFF rv   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[        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       [        [        [        -   [        [        -  -  S[        -   /S[        -   SSS[        [        U -  5      -  -
  [        U -  -  -  //5      :X  d   eS[        -   S-  n[        U//5      nUR                  5       [        U//5      :X  d   eUR                  [        S9[        UR                  [        S9//5      :X  d   e[        [        [        [        5      S-  [        [        5      S-  -   //5      5      [        S//5      :X  d   e[        SS/SS//5      nSUR                  5       -  R                  5       [        SS	5      :X  d   eg )
NrI  r  ri   rg   )ratior]  rh   rj   "   )r$   r   r   rO   rP   r)   r6   r?   r5   r   r@   tracer    )rI  r  r5  eqr   s        rt   test_simplifyr  K  s0   sAAQqS1Q3YQqSAHQ4!AaD&=!A$&QqS3q2v;q=-@(AB(FHJ 	KAJJL1q51q5/!a%I$%E1q1SAY;A.F+GIK L L L L
a%!BvAJJLvJJRJ2./01111sAAqS1Q3YQqSA@Q4!AaD&=!A$
QqS3q2v;q=%8 9B >@ 	A ::<6q51q5/!a%9E1q1SAY;A679#    
 a%!B"A::<6B4&>)))::B:6BKKbK,A+B*C#DDDDOc!fai#a&!)&;%<$=>?#aSE*+ + + 	Q!Q !AqwwyM##%!R888rv   c                     [        / SQ/ SQ/5      n U R                  [        SS/SS/SS/SS/SS/SS/SS/S	S	/S
S
/SS//
5      :X  d   eU R                  R                  U :X  d   eU R                  U R                  5       :X  d   eg )N)
ri   rg   rh   rj   rk   rl   r   r   r   r   ri   rg   rh   rj   rk   rl   r   r   r   r   )r   r1  	transposer4  s    rt   test_transposer  s  s    ..0 	1A33&QFFFFFFFFFF	% 	& 	& 	& 	& 3355A::33!++-rv   c            
      $   [        [        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                  $ r   )r.   r   rz   rv   rt   r   !test_conj_dirac.<locals>.<lambda>  s    3q688rv   ri   r   r  r  r   )r^   AttributeErrorr   r   r   r4  s    rt   test_conj_diracr    s    
>+,Aq!Aq!Aq! 	A
 33&*2A*2r2*2rAr*, - - - -rv   c                  X    [        / SQ/ SQ/ SQ/5      n U R                  5       S:X  d   eg )Nr   )r   rk   r   )r   r   r   r<  r   r  r4  s    rt   
test_tracer    s-    	 	A 779??rv   c                      [        SSSS/5      n U R                  S:X  d   e[        [        SS/S[        S//5      nUR                  S:X  d   eg )Nri   rg   r   rc  r  )r   r  rO   rP   )r   r5  s     rt   
test_shaper    sX    q!aVA77fAq	Aq	 	A77frv   c                     [        [        SS/S[        S//5      n U R                  SS 5        U [        [        SS/S[        S-   S//5      :X  d   eU R	                  SS 5        U [        [        S-   SS/S[        -   [        S-   S//5      :X  d   eU R                  S5      [        [        S-   SS//5      :X  d   eU R                  S5      nSUS'   U S   [        S-   :X  d   eU SS S	24   nSUS'   U S   [        S-   :X  d   eU R                  S5      nU[        [        S-   S[        -   /5      :X  d   eSUS'   U S   [        S-   :X  d   eU S S 2S4   nSUS'   U S   [        S-   :X  d   eg )
Nr   ri   c                     X-   S-   $ r  rz   )rr   s     rt   r   !test_col_row_op.<locals>.<lambda>  s
    QUQYrv   rg   rh   c                     U [         U-  -   $ r   )rP   )rL   r   s     rt   r   r    s    QAXrv   *   r}   r   )r   rO   rP   row_opcol_opr   r   )r5  r1r"  s      rt   test_col_row_opr    s   Aq	Aq	 	AHHQ&'1AE1' ( ( ( ( HHQ%&QAq)QAq)+ , , , ,
 558vAq!}o....	
qBBqET7a!e	
1crc6BBqET7a!e	
qBQA''''BqET7a!e	
1a4BBqET7a!erv   c                      [        / SQ/ SQ/5      n U R                  SS5        U S   S:X  d   eU S   S:X  d   eU S   S	:X  d   eg )
Nro   rn   ri   rh   r   r  r}   rc  rq  )r   row_multr4  s    rt   test_row_multr    sS     	AJJqOS6R<<S6Q;;S6R<<rv   c                      [        / SQ/ SQ/ SQ/5      n U R                  SSS5        U S   S:X  d   eU S	   S
:X  d   eU S   S:X  d   eg )Nro   rn   r  rg   r   rk   r}   rl   r   rj   r   rg   r   )r   row_addr4  s    rt   test_row_addr    s[     	A IIa!S6Q;;S6Q;;S6Q;;rv   c                     [          H  n U R                  S5      nUR                  SSS 5        X" / SQ/ SQ/ SQ/5      :X  d   eU R                  S5      S-  nS	US
'   UR                  SSS 5        U  X" / SQ/ SQ/ SQ/5      :X  a  M   e   g )Nrh   ri   r   c                     U SU-  -   $ r  rz   r  us     rt   r   !test_zip_row_op.<locals>.<lambda>      AaCrv   r   r  r   rg   r   r~   c                     U SU-  -   $ r  rz   r  s     rt   r   r    r  rv   )rg   r   r   )rj   r   r   r   )mutable_classesr.   
zip_row_op)rO  r5  s     rt   test_zip_row_opr    s    GGAJ	Q/0C""$ % % 	% % GGAJqL$	Q/0!C##% & & 	& & rv   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 )Nro   )rg   rg   rh   rz   )ri   ri   r  )r   rJ   rK   s      rt   test_issue_3950r    sU    yAyAyARS6M66M66M6rv   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r  rz   r<  s    rt   	__index__)test_issue_3981.<locals>.Index1.__index__      rv   rz   Nr  r  r  r  r  r  rz   rv   rt   Index1r        	rv   r  c                       \ rS rSrS rSrg)test_issue_3981.<locals>.Index2i  c                     gr  rz   r<  s    rt   r  )test_issue_3981.<locals>.Index2.__index__  r  rv   rz   Nr  rz   rv   rt   Index2r    r  rv   r  ro   rh   rk   rg   rn   rl   ri   rj   rc  r   r  )r  r  index1index2r   s        rt   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<<rv   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 )Nro   Tri   rg   rh   Frj   )r   is_upperrH   r  s    rt   test_is_upperr    se    	{A::aS1#A::aA::rv   c                      [        / SQ/5      n U R                  SL d   e[        S/S/S//5      n U R                  SL d   eg )Nro   Fri   rg   rh   T)r   is_lowerr  s    rt   test_is_lowerr    sH    	{A::aS1#A::rv   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 )Nrj   )r   rg   ri   rl   r   r   ri   rg   r   r   r   rh   r   r   r   r   ri   r   r   r  r  s    rt   test_is_nilpotentr    sj    q!EFA>>AA A~~r
A>>rv   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)rh   rk   rk   rh   rg   r   rl   ri   )rH   fillr4   rp   rq   r  r   )rI  r   rJ   rK   s       rt   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rv   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   rg   )rH   r   rp   rq   r  s    rt   test_empty_zerosr  9  so    aA==aA66Q;;66Q;;aA66Q;;66Q;;rv   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 )Nrg   ri   r   r  rh   )r   rO   rP   r@   r)   r+   r,   r  r5   r`  r0   r    r  s    rt   test_issue_3749r  D  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&%( ) ) ) )rv   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 )	Nrj   r   ri   )r  r
  c                     U S:H  $ rN  rz   rs   s    rt   r   %test_inv_iszerofunc.<locals>.<lambda>X  s    arv   )r  
iszerofuncr  r  )r.   col_swapr  )r   r  s     rt   test_inv_iszerofuncr  T  sQ    AAJJq!uuF/?u@EEE  	    rv   c                  $   [        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   ri   rg   )
rC   r   r)   r@   r  r1  r.   r  rO  rF   )rhophiXYr  r  s         rt   test_jacobian_metricsr  \  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,----rv   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  rg   r   )rC   r   r)   r@   r  )r  r  r  r  r  s        rt   test_jacobian2r  i  s    y!HCCHc#c(lCF34AzA	SC4C=!	SCCL!cEq! 	A
 ::a=Arv   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 Nri   rh   )	r   r,   rO   rP   rQ   r   r  rp   rq   )r  r  r   r   X_sliceY_slicer  ks           rt   test_issue_4564r  u  s    AEAIAEAIAEAI?@A1ayA1a[q!AAhGAhG  )A66Q;;66Q;;1XAw')))   rv   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      $ r   r  r   rO   rP   rQ   r  s   rt   r   (test_nonvectorJacobian.<locals>.<lambda>  s    ajjAq	):;rv   r   c                  &   > T R                  T5      $ r   )r  r  r  s   rt   r   r    s    ajjmrv   c                  d   > T R                  [        [        [        /[        [        //5      5      $ r   r
  r  s   rt   r   r    s     ajj1a&1a&0B)CDrv   )r   r,   rO   rP   rQ   r^   ro  r  s   @@rt   test_nonvectorJacobianr    s    QUQYQUQY0QUQYQUQY02 	3A
9;<	!Q$AAA A
9+,
9DErv   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 Nri   rh   rg   rj   )r   vecrq   r   )r   m_vecr   s      rt   test_vecr    sV    AA AEEGE::??1Xx1q5    rv   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 )Nri   rg   rh   Fr  r   )r  check_symmetryc                  :    [        SS//5      R                  5       $ r  r   vechrz   rv   rt   r   test_vech.<locals>.<lambda>      v1vh/446rv   c                  @    [        SS/SS//5      R                  5       $ r  r  rz   rv   rt   r   r        v1v1v&67<<>rv   c                  :    [        SS//5      R                  5       $ r  r  rz   rv   rt   r   r    r  rv   c                  @    [        SS/SS//5      R                  5       $ r  r  rz   rv   rt   r   r    r  rv   )	r   r  rq   r   rO   rP   r^   rW   r  )r   m_vechr   s      rt   	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
:>?rv   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 )Nro   ri   rg   rh   c                     > [        T 5      $ r   )r*   r   s   rt   r   test_diag.<locals>.<lambda>  s	    tAwrv   F)strict)r*   r   r^   r  r   s   @rt   	test_diagr'    sK    	?fY////	
AsA
:'% F9$5555rv   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 )	Nri   rg   rh   T)try_block_diagr  )r)  r  r  )r   rO   rP   rQ   r*   r  )rJ   rK   rL   r   s       rt   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rv   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      $ )Nrh   r   rH   rz   rv   rt   r   $test_creation_args.<locals>.<lambda>  s
    uQ|rv   c                      [        SSSS5      $ Nri   rg   rh   rj   r-  rz   rv   rt   r   r.    s    eAq!Q/rv   rh   c                      [        S5      $ N      @r-  rz   rv   rt   r   r.    s    uRyrv   c                      [        S5      $ r2  r.   rz   rv   rt   r   r.    s    s2wrv   rj   c                      [        S5      $ r   r  rz   rv   rt   r   r.    s    fQirv   c                      [        SS5      $ r  r  rz   rv   rt   r   r.    s
    fQlrv   c                      [        SS//5      $ r  r  rz   rv   rt   r   r.    s    vq1#h/rv   N)r^   r  ro  rH   rm  r   r.   r4   rz   rv   rt   test_creation_argsr9    s    
 :+,
9/0Q=E!H$$$a(((
:()s1v;#a&   wqz?c!f$$$
:'A
#tAqz111
9'(
9*+
:/0rv   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 )Nrg   r  Fr  r  ri   rh   )	ri   r   r   r   rg   r   r   r   rh   ))rk   r   rm  r}   )rk   r   r   )r   rl   r   r   )r   is_diagonalr  r*   rH   rO   rP   r-   r   s    rt   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2rv   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 )Nri   rg   rh   rv  ri   rv  r}  rh   r   c                  $   > T R                  5       $ r   r  r   s   rt   r   &test_diagonalization.<locals>.<lambda> 	      rv   r  )ri   r   r   rh   r  )	ri   rg   r   r   rh   r   rg   r   rg   r  r   )r   ri   r   r   Tc                  &   > T R                  S5      $ )NTrA  r   s   rt   r   rB  ,	  s    d 3rv   r   ri   r   r   c                  $   > T R                  5       $ r   rA  r   s   rt   r   rB  4	      rv   )	rv  ri   rv  r}  rh   r   rg   r   rj   c                  $   > T R                  5       $ r   rA  r   s   rt   r   rB  8	  rG  rv   za b c d)r   r   r  r  r^   rV   r*   r  r.   r  as_numer_denomr<  rU   rC   )r  r   r   rJ   rK   rL   rM   r   s          @rt   test_diagonalizationrJ    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""$$$$
;/0q!56A""$$$$
;/0 #JA!q!aA\"A>>    rv   c                     ^  [        SS/SS//5      m T R                  " 5       SL d   eST S'   T R                  " 5       SL d   e[        SS/SS//5      m T R                  " 5         ST S'   [        [        U 4S j5        g )Nr   ri   Tr   Fc                  &   > T R                   " 5       $ r   rA  r  s   rt   r   "test_issue_15887.<locals>.<lambda>K	  s    rv   )r   r  r  r^   rU   r  s   @rt   test_issue_15887rN  A	  s    QFQF+,A D(((AdG E)))QFQF+,AMMOAdG
;/0rv   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 )Nrh   rg   r?  c                  $   > T R                  5       $ r   )r  r   s   rt   r   "test_jordan_form.<locals>.<lambda>Q	  rC  rv   )	r   r  rl   r   ir   r  ir;  )	r   r   r   r   ri   r   r   r   ri   ri   	r   ri   r   r   rj   r   r   ri   rg   )	rg   ri   r   r   rg   r   r   r   rg   )	rg   rl   ri   ri   r   ri   rg   r  )	r   ri   r   r   r   r   r   r   r   )	rj   r   rg   rk   ru  rh   rl   rj   )	r   ri   r   r   r   r   r   r   ri   rj   )rl   rk   r   rv  rv  r   rh   rh   rg   ri   r   rv  r   ri   rk   rk   )rg   ri   r   r   r   rg   r   r   r   r   rg   ri   r   r   r   rg   )rl   rg   r  rv  rg   r   rl   rg   r   rU  r  r   r   rh   rj   )r   r   r   r   r   rg   ri   r   r   r   rg   r   r   r   r   rg   )rk   rj   rg   ri   r   ri   r   r   r   r   rh   r   ri   ri   r   rg   )ri   r   r   r   r   rg   r   r   r   r   rj   ri   r   r   r   rj   z1.0n   )	precisionz2.0z3.14159265358979323846264338327z4.0)
r   r^   rV   r  r  r  r   r-  r/  _prec)Jmustr  r  termr   s       @rt   test_jordan_formr[  N	  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""::$$$ rv   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)rg   rj   ri   r   )r   rg   r   ri   )r   r   rg   rj   )r   r   r   rg   rg   rj   ri   r   )r   r   r  r?   r  )r   pqJmust1Jmust2r  r  s          rt   #test_jordan_form_complex_issue_9274ra  	  s        " 	#A 	
AaCA	AaCAaAq\Aq\Aq\Aq\# $F aAq\Aq\Aq\Aq\# $F ==?DA;!+%%ACK A%%%rv   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  rE  r  r  )r   r  r  s      rt   test_issue_10220rc  	  s     	A ==?DA$$$& ' ' ' ' $$$$	& ' ' ' 'rv   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 )
Nr  )r   r   r   r   )r   r   r   r   )r   r   rg   ri   rg   r   r   ri   r  )r   r  r-   r   r"   )r   r  r  s      rt   test_jordan_form_issue_15858re  	  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!	    rv   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_wrg   zZZ(K_i,K_w,UA)r  ri   rh   r   rl   )
rC   r   r  rO   r   r  r   genas_exprr|  )UAK_iK_wr   r  r]  s         rt   test_Matrix_berkowitz_charpolyrl  	  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3rv   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lamdari   rh   rg   r   )r$   r   r  _eval_matrix_exp_jblockr,   r   r   s     rt   test_exp_jordan_blockrq  	  s    wAAq!A$$&&3q6(*<<<<Aq!A$$&VSVSVAX&AA3q6N 	  rv   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 )	Nrh   rj   r   r   r   rk   ri   r   )r   r,   r   r)   r@   )r   m_exps     rt   test_exprt  	  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Krv   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 )Nrn  ri   rj   r   rg   rh   r   r   r   r  c                  $   > T R                  5       $ r   )r1   r   s   rt   r   test_log.<locals>.<lambda>
  s    rv   )r$   r   r  _eval_matrix_log_jblockr1   r^   rU   rp  s    @rt   test_logry  
  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
 ;(rv   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 )NrO   rh   ri   rg   )r$   r   r)   r@   r"   r   rT   rO   columnpivot_offset	pivot_valpivot_assumed_nonzero
simplifieds         rt   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero1r  
  s_     	sAAq1c!fai#a&!)3QVV<=F$V, ?L2rv   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 )NrO   rh   ri   rg   simpfunc)r$   r   r)   r@   rT   rZ   r{  s         rt   :test_find_reasonable_pivot_naive_finds_guaranteed_nonzero2r  +
  s~     	sAAqVQYs1vqy(A-VQYs1vqy(*+F
 	%Vi@ ?L2>>rv   c            
      f   [        S5      n [        SSU [        U 5      S-  [        U 5      S-  -   U -   [        U 5      S-  [        U 5      S-  -   /5      n[	        U[
        S9u  p#pE[        U5      S:X  d   eUS   S   S:X  d   eUS   S   SU -   :X  d   eUS   S   S:X  d   eUS   S   S:X  d   eg )NrO   rh   ri   rg   r  r   )r$   r   r)   r@   rT   rZ   lenr{  s         rt   +test_find_reasonable_pivot_naive_simplifiesr  ;
  s     	sAAqVQYs1vqy(*VQYs1vqy(*+F
 	%Vi@ ?L2 z?aa=q   a=qs"""a=q   a=q   rv   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  rz   rv   rt   r   test_errors.<locals>.<lambda>O
  s    v1vsm4rv   c                  $    [        SS//5      S   $ )Nri   rg   )g333333?rk   r  rz   rv   rt   r   r  P
      v1vh/7rv   c                  $    [        SS//5      S   $ )Nri   rg   )ri   g@r  rz   rv   rt   r   r  Q
  r  rv   c                      [        SSSS9$ )Nrh   rj   T)rL   rZ  )r7   rz   rv   rt   r   r  R
  s    z!qDArv   c                  <    [        SS/5      R                  SS5      $ )Nri   rg   rj   rl   )r   rG  rz   rv   rt   r   r  S
  s    vq!f~55a;rv   c                  ^    [        SS/SS//5      R                  SS/[        SS/5      5      $ rx   )r   copyin_matrixrz   rv   rt   r   r  U
  s/    AA'(661vvq!f~Nrv   c                  X    [        SS/SS//5      R                  SS/[        5       5      $ rx   )r   copyin_listr,  rz   rv   rt   r   r  V
  s1    fq!fq!f%56BBADurv   c                  @    [        / SQ/ SQ/5      R                  5       $ )Nro   )rg   rh   r   r   r  rz   rv   rt   r   r  X
  s    I0F)G)K)K)Mrv   c                  \    [        SSSS/5      R                  [        SS/SS//5      5      $ r0  )r   r   rz   rv   rt   r   r  Z
  s.    q!aV$--fq!fq!f5E.FGrv   c                  X    [        SS/5      R                  [        SS/SS//5      5      $ r0  )r   r   rz   rv   rt   r   r  \
  s)    FAq6N33FQFQF;K4LMrv   c                  X    [        S/5      R                  S[        SS/SS//5      5      $ r0  )r   r   rz   rv   rt   r   r  ]
  6    vqc{55a!B1vA :  rv   c                  X    [        S/5      R                  S[        SS/SS//5      5      $ r0  )r   r   rz   rv   rt   r   r  _
  r  rv   c                  8    [        SS/5      R                  5       $ r  r  rz   rv   rt   r   r  a
  s    A)=)=)?rv   c                  8    [        S/5      R                  S5      $ r  )r   rO  rz   rv   rt   r   r  b
  s    faSk33A6rv   c                  D    [        SS/SS//5      R                  SS5      $ Nri   rg   rh   rj   rk   )r   minorrz   rv   rt   r   r  c
  s#    v1v1v&67==aCrv   c                  D    [        SS/SS//5      R                  SS5      $ r  )r   minor_submatrixrz   rv   rt   r   r  d
  s#    v1v1v&67GG1Mrv   c                  :    [        / SQ5      R                  S5      $ Nro   ri   r   crossrz   rv   rt   r   r  e
  s    fY/55a8rv   c                  :    [        / SQ5      R                  S5      $ r  r   dotrz   rv   rt   r   r  f
  s    fY/33A6rv   c                  P    [        / SQ5      R                  [        SS/5      5      $ )Nro   ri   rg   r  rz   rv   rt   r   r  g
  s    vi044VQF^Drv   c                  :    [        SS/5      R                  / 5      $ r  r  rz   rv   rt   r   r  h
  s    vq!f~11"5rv   c                  :    [        SS/5      R                  S5      $ )Nri   rg   rJ   r  rz   rv   rt   r   r  i
  s    faVn005rv   c                  >    [        SS/5      R                  / SQ5      $ )Nri   rg   ro   r  rz   rv   rt   r   r  j
  s    vq!f~11)<rv   c                  8    [        / SQ5      R                  5       $ )Nro   )r   r,   rz   rv   rt   r   r  k
  s    	):)>)>)@rv   c                  @    [        SS/SS//5      R                  5       $ r0  )r   
normalizedrz   rv   rt   r   r  l
      v1v1v&67BBDrv   c                  6    [        SS/5      R                  SS9$ )Nri   rg   znot a methodr  r  rz   rv   rt   r   r  m
  s    vq!f~111Hrv   c                  8    [        SS/5      R                  5       $ r  r   
inverse_GErz   rv   rt   r   r  n
      A)B)B)Drv   c                  @    [        SS/SS//5      R                  5       $ r  r  rz   rv   rt   r   r  o
  r  rv   c                  8    [        SS/5      R                  5       $ r  r   inverse_ADJrz   rv   rt   r   r  p
  s    A)C)C)Erv   c                  @    [        SS/SS//5      R                  5       $ r  r  rz   rv   rt   r   r  q
  s    v1v1v&67CCErv   c                  8    [        SS/5      R                  5       $ r  )r   
inverse_LUrz   rv   rt   r   r  r
  r  rv   c                  8    [        SS/5      R                  5       $ r  r  rz   rv   rt   r   r  s
  s    A)D)D)Frv   c                  8    [        SS/5      R                  5       $ r  r   r  rz   rv   rt   r   r  t
  s    A););)=rv   c                  >    [        SS/SS//5      R                  SS9$ )Nri   rg   rh   rj   zNot a real methodr  r  rz   rv   rt   r   r  v
  s%    AA'(,,4G,Hrv   c                  J    [        / SQ/ SQ/ SQ/ SQ/5      R                  SS9$ )Nr  r  r  rA  zNot functionr  r  rz   rv   rt   r   r  x
  s*    l)+ ,,/C>C,JKrv   c                  J    [        / SQ/ SQ/ SQ/ SQ/5      R                  SS9$ )Nr  r  r  rA  Fr  r  rz   rv   rt   r   r  {
  s*    l)+ ,,/C5C,ABrv   c                  V    [        [        SS/SS//5      [        SS/SS//5      5      $ r0  r/   r   rz   rv   rt   r   r  ~
  s/    AA/0&1a&1a&9I2JKrv   c                  8    [        [        SS/SS//5      / 5      $ r0  r  rz   rv   rt   r   r  
  s    wv1v1v.>'?Drv   c                  2    [        [        S5      S-  S5      $ )NrO   rg   rJ   )r/   r$   rz   rv   rt   r   r  
  s    wvc{A~s;rv   c                      [        S5      S   $ )Nrh   )rk   rg   r5  rz   rv   rt   r   r  
      s1vd|rv   c                      [        S5      S   $ )Nrh   )rg   rk   r5  rz   rv   rt   r   r  
  r  rv   r@  c                  &   > T R                  S5      $ )Nzmethod=LU_decomposition())r  r4  s   rt   r   r  
  s    quu%@Arv   )r   r   r   ro   rg   rh   rj   r   c                  (   > T R                  ST5      $ )Ng@)r   r5  Vs   rt   r   r  
  s    q||C3rv   c                  (   > T R                  ST5      $ )Ng)r   r  s   rt   r   r  
  s    q||D!4rv   )r^   r  r   rW   ro  rV   r   r  s   @@rt   test_errorsr  N
  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5rv   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   ri   rg   c                     grN  rz   r   s     rt   r   test_len.<locals>.<lambda>
  s    rv   c                     grN  rz   r   s     rt   r   r  
  s    arv   r   r   rl   )r  r   rz   rv   rt   test_lenr  
  s    vx=Av1vh CaSz(:$;@q@@@@@vaN+,F1a()/-./ / / / /vy),-.!3331#;&1#-'''xx<8vbz!!!rv   c            
         [        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[        SS[        [        /5      nUR                  [        5      [        SS[        S-  S-  [        [        -  /5      :X  d   eg )Nri   rj   rg   r   rk   rh   )r   rO   rP   r0   )r   r   s     rt   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q!aVA;;q>VAq1a461Q3-8888rv   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 )Nri   rj   rg   r   rk   r   r   r   )r   r   r   Fr8  )	r   rO   rP   r/  r+   r  r.  r   r\   )r   A_imms     rt   	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Nrv   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 )	Nri   r   rg   )rg   rg   ri   r  rh   r   r  )r   rO   rP   rQ   rN   r+   r   r.  rJ   r   rK   rH   r  r   r@   r,   r)   r   r/  )
r   r  r   dBr  fxyzexprr   r   ress
             rt   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   _$)___c            	         ^  [        SS[        4[        SS4SS[        S-  S-   445      m [        [        U 4S j5        [        T S5      " [        5      [        SS	S
S
S[        -  445      :X  d   eg )Nri   rj   rg   r   rk   c                     > T R                   $ r   )nonexistantattributer  s   rt   r   test_getattr.<locals>.<lambda>
  s    1#9#9rv   r+   r   r   r   )r   rO   rP   r^   r  getattrr  s   @rt   test_getattrr  
  sj    Aq	Aq!9r1adQh&789A
>9:1fa FIy1a1++N$OOOOrv   c                  H   [        / SQ/ SQ/ SQ/5      n U R                  (       d   eU R                  n U R                  (       d   eSU S'   U R                  SL d   e[        / SQ/ SQ/ SQ/5      n U R                  (       a   e[	        SS	5      n U R                  (       d   eg )
Nr"  r#  r   ri   )r   r   Fr$  rk   rg   )r   r%  r1  r&  rH   r  s    rt   test_hessenbergr  
  s    	9i01A    	A    AeH  E)))	9i01A$$$$aA    rv   c            	      L   [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        S[        -   S4S45      R                  S	S
9[        [        S[        -   5      S/SS//5      :X  d   e[        S5      n U R                  S	S
9nU[        SS/SS[        S5      -  [        -  //5      :X  d   eXR                  -  U :X  d   e[        S5      n U R                  5       nXR                  -  U :X  d   eUR                  (       d   eU[        / SQ/ SQ/ SQ/5      :X  d   e[        SS[        -  SS[        -  -   4S[        -  SS[        -   4SS[        -  -
  S[        -
  S445      n U R                  5       R                  5       [        S[        SS4S[        -
  SS445      :X  d   e[        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        [        S 5        [        S[        -   S4S45      R                  S	S
9[        [        S[        -   5      S/SS//5      :X  d   e[        S5      n U R                  S	S
9nU[        SS/SS[        S5      -  [        -  //5      :X  d   eXR                  -  U :X  d   e[        S5      n U R                  5       nXR                  -  U :X  d   eUR                  (       d   eU[        / SQ/ SQ/ SQ/5      :X  d   e[        SS[        -  SS[        -  -   4S[        -  SS[        -   4SS[        -  -
  S[        -
  S445      n U R                  5       [        S[        SS4S[        -
  SS445      :X  d   eg )Nc                  4    [        S5      R                  5       $ Nrc  r   choleskyrz   rv   rt   r   test_cholesky.<locals>.<lambda>  s    )@)@)Brv   c                  4    [        S5      R                  5       $ Nrc  )rh   rj   r  rz   rv   rt   r   r        v&67@@Brv   c                  J    [        S[        -   S4S45      R                  5       $ Nrk   r   r~   )r   r   r  rz   rv   rt   r   r    s    vAqz6&:;DDFrv   c                  4    [        S5      R                  5       $ Nr  )rk   ri   r  rz   rv   rt   r   r    r  rv   c                  2    [        S5      R                  SS9$ Nr  F	hermitianr  rz   rv   rt   r   r    s    v&67@@5@Qrv   rk   r   r~   Fr  ri   r  rg   rl   ))r  r-  r   )r-  rq  r   )r   r   r   r;  )rh   rh   r   )r   ri   rh   rj   r   r   r   r  rh   c                  4    [        S5      R                  5       $ r  r#   r  rz   rv   rt   r   r    s    f)=)F)F)Hrv   c                  4    [        S5      R                  5       $ r  r  rz   rv   rt   r   r        |,<=FFHrv   c                  J    [        S[        -   S4S45      R                  5       $ r  )r#   r   r  rz   rv   rt   r   r    s    |a!eQZ,@AJJLrv   c                  4    [        S5      R                  5       $ r  r  rz   rv   rt   r   r    r  rv   c                  2    [        S5      R                  SS9$ r  r  rz   rv   rt   r   r    s    |,<=FFQVFWrv   )r^   rV   r  r   r   r  rA   r1  r  r-   r#   r  s     rt   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$AaC(1Q326*:Q1Wb1fb<QRSA::<69q!Qi!a%A"GHHHHrv   c            	      L   [        SSS9n [        [        U 5      [        U 5      /5      n[	        UR                  S5      5      S:X  d   eUR                  S5      [        [        U 5      S-  [        U 5      S-  -   [        SS5      5      :X  d   e[        S[        SS5      //5      nUR                  5       [        S	[        S
S5      -   [        R                  5      :X  d   eUR                  [        5      [        U5      :X  d   eUR                  [        * 5      [        U5      :X  d   e[        SS/SS//5      nUR                  S5      S:X  d   eUR                  S5      S:X  d   eUR                  S5      S:X  d   e[        S5      R                  S5      [        S5      R                  S5      s=:X  a  S:X  d   e   eUR                  [        5      S:X  d   e[        S[        [        /U [        R                  [        * //5      nUR                  S5      [!        [        SS5      S[#        [        5      S-  -  -   [        S-  -   U S-  -   5      :X  d   e[        / SQSS[        SS5      //5      nUR                  S5      [!        [        SS5      [!        S5      S-  -   5      :X  d   eUR                  S5      [        R$                  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 )NrO   Tr*  rg   ri   r   rk   rh   r  r   rj   r   r   	frobeniusfro%   )ri   rg   rv  r;  i  r   iI3 r   alpha)r  rg   r   rv  )r   r   r   g      Y@r   )	ri   rh   r   r   r   r   rh   r   rl   )r$   r   r)   r@   rF   normr   r    r"   r   r5   r  r_  r.   rP   r6   rA   r`  r   r   rH   r?   r   InfinityNegativeInfinitytrue)rO   r  r   r   r   r   r  r
  orderr  r  difr5  rJ   rK   rL   rM   r   s                     rt   test_matrix_normr  *  s~    	sAAA AAFF1I!###66":SVRZ#a&"*4hq"oFFFF 	HQN#$%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??rv   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 )NrO   Tr*  rh   r   r}   ri   rg   rg   r|  rm   c              3      >#    U  H=  n[        S 5      R                  TR                  TU5      R                  5       5      v   M?     g7f)r{  N)r   
epsilon_eqr|  r?  )rA  valMcrO   s     rt   rB  (test_condition_number.<locals>.<genexpr>  s@      QO BEuRy##BGGAsO$9$9$;<<Os   AArk   rg   r   rj   r   )r$   r.   r    condition_numberr   r   r   r   r)   r@   rJ  r"   r   r6   )r   r5  r  rO   s     @@rt   test_condition_numberr    s3   sAAAAdGq"oAdG3&&&AdG3r3q6?S!R#a&5Q#QQQQQQ CF7CF"345A	
			B Q	!Q!R"Q$Bx1~<MOQ Q Q Q Q ":&&(A---rv   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)ro   rn   r   ))r   r   r   )rl   rk   rj   )rh   rg   ri   r   )r   r   r   )r   r#   )r   r   r   r   s       rt   test_equalityr    s    01A01A!Q$<<adG|v:6M67N7Bw; 	67A01A6M6v:vrv   c                  8   [        SS/5      R                  5       [        [        SS5      [        SS5      /5      :X  d   e[        / SQ5      R                  5       [        / SQ5      :X  d   e[        / SQ5      n U R                  S S9[        / SQ5      :X  d   eg )Nrh   rj   rk   r   )r   r   g0.++c                 8    U R                   " SSS9R                  $ )Nr   T)rI  chop)r?  is_zerors   s    rt   r   !test_normalized.<locals>.<lambda>  s    2D199rv   r  )r   r  r    r   s    rt   test_normalizedr"    s    1a&>$$&AA/01 1 1 )'')VI->>>> 	}A<<9  			  rv   c                  L    [        S 5      S:X  d   e[        S 5      S:X  d   eg )Nc                  4    [        S5      R                  5       $ r   r.   print_nonzerorz   rv   rt   r   $test_print_nonzero.<locals>.<lambda>  s    3q6//1rv   z[X  ]
[ X ]
[  X]
c                  6    [        S5      R                  S5      $ )Nrh   ri  r%  rz   rv   rt   r   r'    s    3q6//4rv   z[.  ]
[ . ]
[  .]
)rc   rz   rv   rt   test_print_nonzeror)    s8    12     45     rv   c                     [         R                  " S5      [        S5      :X  d   e[         R                  " S5      [        S5      :X  d   e[        SS5      [        SSS/S-  5      :X  d   e[        SS/SS//5      n [        SS/SS//5      n[         Hu  nUR                  S5      nX:X  d   eU [        SUS9:X  d   e[        U5      U:X  d   eUR                  S5      nX:X  d   eU[        SUS9:X  d   e[        U5      U:X  a  Mu   e   g )Nrh   rj   ri   r  r   rg   rN  )r   r.   rH   r4   rP  r  )r   rQ   rO  r   s       rt   test_zeros_eyer+    s   ::a=CF"""<<?eAh&&&1:1qc"f----AA AAA AGGAJvvCsO###Aw#~~IIaLvvE!%%%%Aw#~~ rv   c                     [        5       R                  (       d   e[        SS/SS//5      R                  (       d   e[        SS5      R                  (       d   e[        S5      R                  (       a   e[        [        S/SS//5      R                  S :X  d   e[        [        S/SS//5      R                  S :X  d   e[        [        S/SS//5      R                  S :X  d   e[        [        S/SS//5      R                  S :X  d   e[        [        S/SS//5      R                  S:X  d   e[        SSS9n [        U S/SS//5      R                  S:X  d   eg )	Nr   rh   rj   ri   FrJ   T)nonzero)	r   is_zero_matrixrH   r.   rO   r#   r   r   r$   r  s    rt   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;;;rv   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 )Nrh   ri   rg   r   r   r   r   )r6   r:   r9   r8   r.   r  r)   r   from_axis_angleto_rotation_matrixr;   r<   r=   )
thetar3_plusr3_minusr2_plusr2_minusr1_plusr1_minusq1q2q3s
             rt   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&;&;&====rv   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vectorrj   z	vector[4]rM   c                      [        S5      S   $ )NrM   r   )r   rz   rv   rt   r   %test_DeferredVector.<locals>.<lambda>  s    ~c226rv   testzDeferredVector('test'))strr   rD   r^   r   reprrz   rv   rt   test_DeferredVectorrE    sx    ~h'*+{:::>#&'>#+>>>>
:67~c"#s***v&'+CCCCrv   c                  :    [        [        S5      5      (       a   eg )Nr  )rd   r   rz   rv   rt    test_DeferredVector_not_iterablerG    s    s+,,,,,rv   c                  &    [        [        S 5        g )Nc                  *    [        [        S5      5      $ )Nr  )r   r   rz   rv   rt   r   ,test_DeferredVector_Matrix.<locals>.<lambda>  s    f^C%89rv   )r^   ro  rz   rv   rt   test_DeferredVector_MatrixrK    s    
99:rv   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 )Nri   rg   rh   rk   r   Tr   )r    r   r   r1  rA   r
   )r  r   r   r  s       rt   test_GramSchmidtrM    s{   A	1q!f	B	1q!f	Bx 	1q!f	vaQqT!VQrU1W,=>?@ @ @bdd|$	1q!f	vaQqT!VQrU1W,=>?@ @ @ 1v1v7>$r(
2tBx{+,b	"aRjm,-C/ / / / 	&!+Aq>fqcUm_,,,rv   c                  R    [        / SQS5      S:X  d   e[        / SQSSS9S:X  d   eg )Nr  ri   r   F)zero)r(   rz   rv   rt   test_casoratianrP  &  s.    lA&!+++lAE2a777rv   c                      [        5       [        SS5      -  R                  S:X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        5       :X  d   eg )Nr   rh   )r   rh   )r   rH   r  rz   rv   rt   test_zero_dimension_multiplyrR  +  si    HU1a[ ''6111A;uQ{"eAqk111A;uQ{"fh...rv   c                    ^  [        SS[        S5      5      m T SS S 24   [        SS//5      :X  d   eT SS S 24   [        SS//5      :X  d   eT S S 2S4   [        SS//5      R                  :X  d   eT S S 2S4   [        SS//5      R                  :X  d   e[        [        U 4S j5        [        [        U 4S j5        g )Nrg   rj   ri   rh   r   c                     > T SS S 24   $ r  rz   r   s   rt   r   'test_slice_issue_2884.<locals>.<lambda>7  s    qAwrv   c                     > T S   $ )Nr  rz   r   s   rt   r   rU  8  s	    qwrv   )r   r   r1  r^   r   r   s   @rt   test_slice_issue_2884rW  1  s    q!U1XAQT7fq!fX&&&&RU8v1vh''''QT7fq!fX&(((((QU8v1vh')))))
:'
:'rv   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   rh   r   r~   ri   )rH   r  r   rz   rv   rt   test_slice_issue_3401rY  ;  sK    A;q"u##v---A;q!tq!R 0000rv   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 )Nrh   ri   r   r   rj   r  rm   rk   rl   )ri   rk   rl   +   )ri   r  r[     r}   )r\  ri   r   r  )rH   r   r#   )r  s    rt   test_copyinr]  @  s   aAAaDQT7fY''''Q4199Q7qc>>AdGT7b==QU8vAwi((((1vhAaeHQT7fi[))))RzAaeHQT7fk]++++AdGQU8vj))))AdGQT7fY''''YAdGQT7fY''''9%AdGQT7fY''''rv   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 )Nri   rg   r   )r   c                  @    [        SS/SS//5      R                  5       $ r  r  rz   rv   rt   r   'test_invertible_check.<locals>.<lambda>[  s    v1v1v&67;;=rv   )r   r   r   r   rh   r  c                  "   > T R                  SS9$ )Nr  r  r  r   s   rt   r   r`  f  s    quuEu2rv   c                  "   > T R                  SS9$ )Nr  r  rb  r   s   rt   r   r`  g      quuDu1rv   c                  "   > T R                  SS9$ )Nr
  r  rb  r   s   rt   r   r`  h  rd  rv   )	r   r  r^   r  rO   r  rp   r.   r>   r   s   @rt   test_invertible_checkrf  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2rv   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)rh   rk   rh   )rC   r|  r   )rO   rP   r   s      rt   test_issue_3959rh  k  s<    6?DA	A66!VI&'6)+<Q+>>>>rv   c                  D    [        [        SS/SS//5      5      S:X  d   eg )Nri   rg   rh   rj   zMatrix([[1, 2], [3, 4]]))rC  r   rz   rv   rt   test_issue_5964rj  q  s(    v1v1v&'(,FFFFrv   c                  p    [        S5      u  p[        [        U SU-  /US-  U S-   //5      5      S:X  d   eg )Nr  rg   rh   z'Matrix([
[   x,   2*y],
[y**2, x + 3]]))rC   rB   r   r   s     rt   test_issue_7604rl  u  sE    5>DAAaC1a4Q-01234 4 4rv   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 )	Nrh   r   ri   )r}   rm   r  rg   rl   )r}   rm   )r}   rm   r  r~   r  )r.   is_Identityr.  rH   r4   r   r#   r   rz   rv   rt   test_is_Identityro  {  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[[[[[rv   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 )Nri   rh   r  ro   r<  rg   r   Fr  Tr;  physicsr  conjugate_conventionrj   rk   rl   rightr   left)rs  c                  P    [        SS/5      R                  [        SS/5      SSS9$ )Nri   rg   rh   rj   TrB  rr  r  rz   rv   rt   r   test_dot.<locals>.<lambda>  s'    vq!f~11&!Q.Dgm1nrv   )r4   r  r   r   r^   r  rz   rv   rt   test_dotrx    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$]c"dhilmnolohoooo1ac(1Q3x 0EX^_ceeee1ac(1Q3x 0vNRSSSS
:norv   c            	         [        SSS9u  pp#pE[        SX4U4U* SX!* 4U* U* SU 4U* X* S445      n[        SU * U* U* 4U SXT* 4X* SU4X$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   rh   )rC   r   dualequalsr.   rH   )B_xB_yB_zE_xE_yE_zrW  Fds           rt   	test_dualr    s   #*!$. CcC 
!c4 
tC 
Ta 	 	A 
sdSD3$	S$	dq3	SDQ	 
B 668??2q6;;=a))))668==?!!1"%%%%rv   c                  (   [        SS/5      R                  5       SL d   e[        SSS[        S-  S[        -  -   S-   [        [        S-   S-  * S[        [        -  [        * [        * [        -  S/	5      n U R                  5       SL d   eU R                  SS9b   eU R                  S S9b   eU S	   * U S	'   U R                  5       b   eU S	   * U S	'   U R	                  5       n U R                  SS9SL d   eSU S
'   U R                  5       SL d   eg )Nri   rg   Frh   r   Tr  c                     U $ r   rz   rs   s    rt   r   %test_anti_symmetric.<locals>.<lambda>  r  rv   rs  r}   )r   r  rO   rP   r-   r   s    rt   test_anti_symmetricr    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)))rv   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)rc  rs  Tr  )r  sort)r   r  r1  r.   rq   r  )r   r  r   s      rt   #test_normalize_sort_diogonalizationr    s     A==4=(DASS5ACCE(S[(((((==4d=3DASS5ACCE(S[(((((3quuw;!rv   c                  &    [        [        S 5        g )Nc                  6    [        / SQ[        SS/ 5      /5      $ )Nro   r   ri   r  rz   rv   rt   r   !test_issue_5321.<locals>.<lambda>  s    vy&Ar2B&CDrv   )r^   r  rz   rv   rt   test_issue_5321r    s    
:DErv   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 )Nrg   )ri   r   rg   r   )r   ri   r   rg   ri   r   )r   r   r.   r   r#   rN  s    rt   test_issue_5320r    s    ==Q3q6*f6 /    ==Q3q6*f	
A	
A	
A	
A	6 /    C::c#a&k3qQx=1V= 6   rv   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 r  )r   rD   r   r   )r   AIms     rt   test_issue_11944r    s^    uA
!*C== FQF8$4444== FQC!:$6666rv   c                    ^ / SQn / SQn[        / SQ5      nUR                  nU4S jn[         H  mT" U 5      nT" U5      nU" UR                  U5      U5        U" UR                  UR                  5      U5        U" UR                  R                  UR                  5      U5        U" UR                  R                  U5      U5        M     [	        [
        S 5        g )Nro   r   )r   rj   r   c                 6   > X:X  d   e[        U 5      T:X  d   eg r   )r  )r5  r  rO  s     rt   rB  test_cross.<locals>.test  s    xxAw#~~rv   c                  X    [        SSSS/5      R                  [        SSSS/5      5      $ r  r  rz   rv   rt   r   test_cross.<locals>.<lambda>  s*    q!aV""6!QA#78rv   )r   r1  rP  r  r^   rW   )rJ   rK   r   r   rB  r   r   rO  s          @rt   
test_crossr    s    AA

C
%%C FFQWWQZQWWQSS\3QSSYYqss^S!QSSYYq\3  : 9 :rv   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 r   )r   rO   rP   rQ   rJ   rK   rL   hatr  r  vee)v1v2s     rt   test_hat_veer    sw    	Aq		B	Aq		B668b=BHHRL(((668%%''''668<<>Rrv   c                  0   [          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   [         H)  n [        U R                  S5      [        5      (       d  M)   e   g r  )immutable_classesr.   r  popr  r/  r   )rO  r  s     rt   	test_hashr    ss     WWQZ$1v{quuw#''!*444 ! cggaj(3333 rv   c                      S[         /SS//n [        SS/[         * S//5      n[         H  nX" U 5      R                  5       :X  a  M   e   g Nr   ri   )r   r   rP  adjoint)r2  r  rO  s      rt   test_adjointr  
  sR    q6Aq6
C
1a&A2q'"
#Cc#h&&(((( rv   c                     [        SS/[        SS[        -  -
  //5      n U R                  5       [        R                  [        S5      [        R
                  [        1:X  d   eU R                  [        5      [        1:X  d   eg r  )r   rO   r  r"   r   NegativeOner$   r   s    rt   
test_atomsr    sb    AA!G%&A779qtAMM15555776?qc!!!rv   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  rh   rv  rk   )ri   r   r   )r   r\     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r   rH  )rA  r   r   r  s      rt   rB  test_pinv.<locals>.<genexpr>>  s0      
3DA 	QSSUACCE3s   47)r   rJ   rK   rL   rM   r?   pinvr  r3  sympy.core.numbersr  rJ  r&  r|  )
A1Asr   A_pinvAApApAr^  wrepsr  s
            @rt   	test_pinvr    s   	!Q!Q 	!BBGG4G()Xbffh-???? 2s)dAYQ0
1
)\*
+
!Q.
B t$jj A%%%%///uu||uu||  !&&&-.jj A%%%%///uu||uu||  (
tA
Avq%E1e4D 
taffTl3
 
 
 
 
rv   c            	          [        / SQ/ SQ/ SQ/ SQ/ SQ/ SQ/5      /n U  HI  nUR                  SS9nX-  nX!-  nUR                  U:X  d   eS	 nU" UR                  U5      (       a  MI   e   g )
N)=   r  7   r}  rj  r   )>   `   U   r  rB  r   )E   8   r\  rj   6   r   )r   r  [   )   rj  r   )r   r]  r   r  Z   r   )r   r   r   r   r   r   r  r  c                     U R                  [        5      nU Vs0 s H  o3UR                  5       _M     nnX-
  R                  U5      R                  5       n[	        S U 5       5      $ s  snf )Nc              3   >   #    U  H  n[        U5      S :  v   M     g7f)g|=Nr  )rA  r   s     rt   rB  Xtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclose.<locals>.<genexpr>e  s     ;{!s1v~{s   )r  r!   r?  r  rJ  )r   r   rootofsr  rootofs_approxdiff_approxs         rt   allcloseEtest_pinv_rank_deficient_when_diagonalization_fails.<locals>.allclosea  s]    hhv&G4;<GqlGN<7,,^<BBDK;{;;; =s   A))r   r  r3  )r  r   r  r  r  r  s         rt   3test_pinv_rank_deficient_when_diagonalization_failsr  D  s    
 	#####  	!
B t$jjuu||	< s####- rv   c                      [        SS5      [        SS5      -   [        SS/ 5      :X  d   e[        SS5      [        SS5      -   [        SS/ 5      :X  d   eg r  )r4   r   rz   rv   rt   test_issue_7201r  j  sR    1:Q
"fQ2&66661:Q
"fQ2&6666rv   c                      [         [        [        [        4 H(  n U " [        /S//5      R
                  [        1:X  a  M(   e   g rN  )r   r   r   r#   rO   free_symbolsr4  s    rt   test_free_symbolsr  o  s9    3V\I1#s}))aS000 Jrv   c                    ^   SSK Jm   [	        T " / SQ5      5      [	        / SQ5      :X  d   e[	        T " / SQ/5      5      [	        / SQ/5      :X  d   e[	        T " / SQ/ SQ/5      5      [	        / SQ/ SQ/5      :X  d   e[	        T " [
        [        [        /5      5      [	        [
        [        [        /5      :X  d   e[        [        U 4S j5        [	        T " SS/5      T " S	S
/5      /5      [	        SS/S	S
//5      :X  d   e[	        T " SS/5      S	S
//5      [	        SS/S	S
//5      :X  d   e[	        T " / 5      T " / 5      /5      [	        / 5      :X  d   eg! [         a    [        S5         GNgf = f)zSee issue 7465.r   rc  re  ro   rn   c                  B   > [        T " SS/SS//SS/SS///5      5      $ )	Nri   rg   rh   rj   rk   rl   r   r   r  r  s   rt   r   #test_from_ndarray.<locals>.<lambda>  s.    u1v1v.!Q!Q0@ABCrv   ri   rg   rh   rj   N)
rh  rc  rl  r_   r   rO   rP   rQ   r^   NotImplementedErrorr  s   @rt   test_from_ndarrayr  t  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)rc  matrixzPNumPy must be available to test indexing matrixified NumPy ndarrays and matricesri   rg   rh   rj   r  )
sympy.matrices.commonr  rh  rc  r  rl  r_   rr   r]   PendingDeprecationWarning)r  rc  r  r   s       rt   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 matricesri   rg   rh   rj         @)r{  r|  r3  r  )r  r  mpmathr  rl  r_   rr   )r  r  r   s      rt   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 matricesri   rg   rh   rj   r  )r  r  scipy.sparser  rl  r_   rr   )r  r  r   s      rt   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 )Nri   rg   r}   Fr   r~   r  r  s    rt   test_hermitianr    s    A!Q !A>>>cAdG>>U"""AdG>>!!!gaiAdG>>U"""rv   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 )Nro   r  r   ri   r   )rk   rl   r   r   r   c                  &   > T R                  S5      $ r  r   r  s   rt   r   +test_issue_9457_9467_9876.<locals>.<lambda>  r   rv   c                  (   > T R                   " S5      $ Nr  r   r   s   rt   r   r        qyy~rv   rh   rg   rj   rk   c                  &   > T R                  S5      $ r  r   r  s   rt   r   r    r   rv   c                  (   > T R                   " S5      $ r  r   r  s   rt   r   r    r  rv   )r   r   r^   r   r   )r5  r[  Or  r   s      @@rt   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
:-.rv   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 )Nr  F)commutativeza brg   r   )rC   r.   r   rQ   )rO   rP   rJ   rK   r5  r   s         rt   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0rv   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 )Nr   r   )r   rl   rh   r   r   ri   rg   rh   rj   joinr  )r   r1  r  id)	r5  rJ   rK   rL   opsr   opr  news	            rt   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  rv   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 )Nro   rn   r   r   )TTFri   rg   rj   rk   r   r   )TFF)TFT)FFFrh   r   )FTF)r   r   r  s    rt   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  rv   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 )Nr   rk   rg   ri   rh   rT  rj   rv  r   z/a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1)r   rA   r  r   r?   r  rH   rC   )r   axaybxbycxcydxdyexeyt0t1s                rt   !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+~$678AAFFHQK&1b!aQik/.B*CaV)L"MMNRWXY[\R]]]] +22c*d'B"bB"ruRU1%rRU25&;R25q<QSUY[Y^_a_defRgikopqsostvovwyw|o|}~  @B  ~B  CE  ~E  FH  FK  ~K  LM  iN  O  	PA668q==rv   c                     [        / SQ/ SQ/5      n U R                  5       S   [        / SQ/ SQ/5      -
  R                  5       S:  d   e[        / SQ/ SQ/ S	Q/5      n[        / S
Q/ SQ/ SQ/5      n[        / SQ/ SQ/ S	Q/5      nUR                  5       U-
  R                  5       S:  d   eUR                  5       U-
  R                  5       S:  d   eg )N)g~jth?gRM@g(\M@)gDl)@gQgp=
cG@r   )r{  r   r  )r   r{  r{  V瞯<)q7K<r{  rj   )r}  r   r   r   )r  r{  r  )r}                 @)r  r  r{  )r   r}  r  )r{  r  g      )r   r  r  r  )mmm_mixedm_floatm_invs       rt   test_partial_pivotingr    s    
 $&;<=BGGIaL6#3#3#5 6 67;tvF F F o%%' (G ''') *G (((* +E
 KKME!'')E111KKME!'')E111rv   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r   gٿr   )r!  r"  g333333?r   c                     [        U 5      S:  $ )Ng [n<r  rs   s    rt   r   *test_iszero_substitution.<locals>.<lambda>/  s    Qrv   r  r   )r{  r   g4iҤIӿr   )r   r{  glٲer   r  r  r  N)r   r  r  )r   m_rref	m_correctm_diffs       rt   test_iszero_substitutionr(  (  sp     	$%9:NOPAVV5V6q9F9:[\}~IF;;=5   #;!rv   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;  -   rh   rU  rg   r  rv  ri   c                 <    [        U R                  " 5       5      S:  $ )Ng#B;)r`  rI  rs   s    rt   r   "test_issue_11238.<locals>.<lambda>E  s    #acce*u$rv   T)r?   r  )	sympy.geometry.pointr*  rE   r6   r    rA   r   r?   r  )
r*  xxyyp1p2p0r   r   r   Zs
             rt   test_issue_11238r5  7  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$56	7B
 	%A77DQ7/144477DQ7/144477DQ7/1444rv   c                     [        SS/ SQ5      n U [        R                  -  nX-   n[         HO  nU" U5      R	                  5       u  pE[        U5      [        U 5      :X  d   e[        U5      [        U 5      :X  a  MO   e   g )Nrg   r  )r   r"   ImaginaryUnitrP  as_real_imagrr   )r   r   r   klsrJ   rK   s         rt   test_as_real_imagr:  K  so    	!I	B	AOO	B	B"g""$Aw$r("""Aw$r(""" rv   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 )Nrh   rR  ri   rg   r   )rg   ri   r   rg   )r   jordan_cells)r   r  Jcellss      rt   test_deprecatedr>  V  sY    
 	q!23A IA!9q!aS))))!9q!\2222rv   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   ri   rg   )r   r}  rS  rh   )rg   ri   rg   rj   )rg   r   ri   )sympy.core.modr@  r   )r@  r   r   s      rt   test_issue_14489rB  a  sK    "zA}Aq!9y))))q!9y))))rv   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  re  ri   rg   rh   rj   )dtypefloat64)rh  rc  rl  r_   r   floatrD  name)rc  r5  s     rt   test_issue_14943rH  j  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   ri   rJ   r}   r   zm[0, 0] > 0)r   r$   rC  )r   rJ   s     rt   test_case_6913rJ  u  s8    S!QAsA	$	Aq6]"""rv   c                  d    [        SSS5      n [        S5      nU R                  U5      X0:X  d   eg )Nr   rh   rJ   )r   r&   match)r   rJ   s     rt   test_issue_11948rM  |  s1    S!QAS	A771:!rv   c                  j   [        S[        /5      [        S[        * /5      /n [         R                  " U 6 [        S/[        //5      [        S/[        * //5      /:X  d   e[        S[        S/5      [        [        S[        * /5      /n [         R                  " U 6 [        S/[        /S//5      [        [        S-  /[        S5      S-  /[        * //5      /:X  d   e[        S[        /S[        * //5      nUR	                  5       u  p#X"R
                  -  [         R                  " S5      :X  d   eg )Nri   r   rg   )r   r   r  r"   QRdecompositionr3  r.   )r   rV  r   r  s       rt   test_gramschmidt_conjugate_dotrP    s#   Aq6NFAr7O,D&	!qc
	VaSA2$K012 2 2 Aq!9vq!aRj12D&	!qcA3	 &1Q3%!A$q&QB4)@"ABC C C 1a&1qb'"
#C DAss7fjjm###rv   c                      [        [        SSS5      5      n [        [        SSS5      5      nU R                  " U5      n[        X S   5      n[        X0S   5      nX1S   :X  d   eUS:X  d   eg )NrJ   rh   ri   rK   r}   r   )r   r   r  r+   )rJ   rK   rL   rM   r   s        rt   test_issue_8207rR    sj    |CA&'A|CA&'A	aAQ$AQ$A$<<6M6rv   c            	        ^ SSK Jn   [        SS/SS//5      mTR                  [	        [
        [        -  5      [
        5      [        [	        [        5      [	        S[        -  5      [	        [        5      -
  /S[	        S[        -  5      //5      :X  d   e[        SS/SS//5      m[        T-  S-  R                  [        [
        5      [
        5      [        [        S5      S-  [        S5      * S-  /[        S5      * S-  [        S5      S-  //5      :X  d   e[        [        S 5        [        [        U4S	 j5        [        / S
Q/ S
Q/ SQ/ SQ/5      mTR                  [        [
        5      [
        5      TR                  5       :X  d   e[        [        U4S j5        [        SS/SS//5      m[        TR                  [        [
        5      [
        5      S-  5      T:X  d   e[        / SQ/ SQ/ SQ/5      m[        TR                  U " [
        S5      [
        5      S-  5      T:X  d   e[        / SQ/ SQ/ SQ/ SQ/5      mTR                  [        [
        5      [
        5      TR                  5       :X  d   e[        / SQ/ SQ/ SQ/ SQ/5      mTR                  [        [
        [        -  5      [
        5      [        [        T[        -  R                  5       5      5      :X  d   eg )Nr   )nthrootri   rg   rh   rl   rj   c                  Z    [        S5      R                  [        [        5      [        5      $ r   )rH   analytic_funcr1   rO   rz   rv   rt   r   test_func.<locals>.<lambda>  s    a 6 6s1vq Arv   c                  X   > T [         -  R                  [        [         5      [         5      $ r   )rO   rV  r1   r  s   rt   r   rW    s    1 3 3CFA >rv   )r   r   r   rh   )r   ri   r   r   )r   r   r   ri   c                  J   > T R                  [        [        5      [        5      $ r   )rV  rA   rO   r  s   rt   r   rW    s    Q ;rv   r  r  r  )rh   r  rj   )r   r   r   )r   rk   r   rj  )ri   rg   r   r   )r   ri   rh   r   )r   r   ri   rh   )r   rg   ri   rl   )r   r   ri   rg   )r   r   r   rh   r  )sympy.simplify.simplifyrT  r   rV  r@   rO   rN   r6   r)   rA   r^   r  r,   r?   r-   )rT  r   s    @rt   	test_funcr[    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Hrv   z$Cannot create threads under pyodide.c                     S n [        S5         [        R                  R                  5        nUR	                  U 5      nUR                  5       (       d   e S S S 5        S S S 5        g ! , (       d  f       N= f! , (       d  f       g = f)Nc                  R    [         R                  S :X  d   e[        S//5      n X -  n gr  )rY   stater   r   s    rt   r  test_issue_19809.<locals>.f  s-    !''4///QC5MErv   T)r[   
concurrentfuturesThreadPoolExecutorsubmitresult)r  executorfutures      rt   test_issue_19809rg    s`     
T	224__Q'F==??"? 5 
	44 
	s"   A:)A)A:)
A7	3A::
Bc                      [        [        [        /5      n [        U [        SS4[        SS45      [        [        R
                  /[        R
                  //5      :X  d   eg r  )r   rO   rP   r0   r"   r   r4  s    rt   test_issue_23276ri    sT    1vAQAq	Aq!9-	
	
9 2   rv   (R  concurrent.futuresr`  r`  collections.abcr   sympyr   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   r  rJ   rK   rL   rM   rN   rO   rP   rQ   sympy.core.kindrR   rS   sympy.matrices.determinantrT   sympy.matrices.exceptionsrU   rV   rW   sympy.matrices.kindrX   sympy.matrices.utilitiesrY   rZ   r[   $sympy.tensor.array.array_derivativesr\   sympy.testing.pytestr]   r^   r_   r`   ra   rb   sympy.utilities.iterablesrc   rd   importlib.metadatare   rP  r  r  ru   r{   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r   r'  r.  r6  r;  rK  r\  ra  rq  ry  r}  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
  r  r  r$  r'  r0  r7  rK  rQ  rX  rZ  r^  ra  rg  rk  rv  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r!  r#  r3  r6  r>  rC  rI  rP  rS  rV  rd  rx  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r"  r'  r*  r9  r=  rJ  rN  r[  ra  rc  re  rl  rq  rt  ry  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r"  r)  r+  r/  r=  rE  rG  rK  rM  rP  rR  rW  rY  r]  rf  rh  rj  rl  ro  rx  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r(  r5  r:  r>  rB  rH  rJ  rM  rP  rR  r[  rg  ri  rz   rv   rt   <module>rv     s     $
( 
( 
( 
( 
( 
( 
( 
( 
( 
( 
( 
( 
( 
( 
( 
( 
( 
( - , , 5 C3 3 * O O @  8 &|_6KL<($&;< 7&P5M&, /";. 4'*'**#$" 
%$$'95
8O	'">HD@&21 (
)
1
567L^0(0>L,4BG#8 M,% 
+
!+
&9)XGT_JD?_*JZ_%' 6%;58GPy	8$)&&<<<<<K(d&K0L2^D+8P1&
:>7Mt6. 6 6* 8!"G&9P "-:& >*)  
.	*F!@.6G$1&3@E!P
1H%V&('$&4.L)2
 !&;6|"9O*4(nP!%IPZz.&" $<">JD-;-"8
/(1
(.3(?G4\p&(*&F$7:( 4)"*
Z "$ "$J7
1
8&#"	+	##/:	1	1"225(#3*9# $I< :;# <#rv   