
    Цi                     .   S r SSKJr  SSKJr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/J0r0J1r1J2r2J3r3J4r4J5r5J6r6J7r7J8r8J9r9J:r:J;r;J<r<J=r=J>r>J?r?J@r@JArAJBrBJCrCJDrDJErEJFrF  SSKGJHrH  SSKIJJrJ  SSKKJLrLJMrMJNrN  SSKOJPrP  \J" 5        V s/ s H  o R                  5       PM     sn u  rRrSrTrUrVrWrX\" \" \RS	\N5      \N" S
S5      S	\N5      rYS rZS r[S r\S r]S r^S r_S r`S raS rbS rcS rdS reS rfS rgS rhS riS rjS rkS rlS rmS  rnS! roS" rpS# rqS$ rrS% rsS& rtS' ruS( rvS) rwS* rxS+ ryS, rzS- r{S. r|S/ r}S0 r~S1 rS2 rS3 rS4 rS5 rS6 rS7 rS8 rS9 rS: rS; rS< rS= rS> rg?s  sn f )@z4Tests for dense recursive polynomials' arithmetics.     )GROUND_TYPES)
dup_normal
dmp_normal)@dup_add_termdmp_add_termdup_sub_termdmp_sub_termdup_mul_termdmp_mul_termdup_add_grounddmp_add_grounddup_sub_grounddmp_sub_grounddup_mul_grounddmp_mul_grounddup_quo_grounddmp_quo_grounddup_exquo_grounddmp_exquo_ground
dup_lshift
dup_rshiftdup_absdmp_absdup_negdmp_negdup_adddmp_adddup_subdmp_subdup_muldmp_muldup_sqrdmp_sqrdup_powdmp_powdup_add_muldmp_add_muldup_sub_muldmp_sub_muldup_pdivdup_premdup_pquo
dup_pexquodmp_pdivdmp_premdmp_pquo
dmp_pexquo
dup_rr_div
dmp_rr_div
dup_ff_div
dmp_ff_divdup_divdup_remdup_quo	dup_exquodmp_divdmp_remdmp_quo	dmp_exquodup_max_normdmp_max_normdup_l1_normdmp_l1_normdup_l2_norm_squareddmp_l2_norm_squared
dup_expand
dmp_expand)ExactQuotientFailed)f_polys)FFZZQQ)raises         c                     [        / [        5      n [        U [        S5      S[        5      [        / [        5      :X  d   e[        U [        S5      S[        5      [        S/[        5      :X  d   e[        U [        S5      S[        5      [        SS/[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        / SQ[        5      n [        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S	[        5      [        / S
Q[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        SS/[        5      :X  d   eg )Nr   rM   rL   rM   r   r   rM   rM   rM   )rM   rM   rL   )rM   rL   rM   )rL   rM   rM      )rM   rM   rM   rM      )rM   r   rM   rM   rM      )rM   r   r   rM   rM   rM      )rM   r   r   r   rM   rM   rM   )r   rI   r   fs    `/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/sympy/polys/tests/test_densearith.pytest_dup_add_termrZ   4   s   2rA2a5!R(Jr2,>>>>2a5!R(JsB,????2a5!R(J1vr,BBBB2a5!R(Jy",EEEE9b!A2a5!R(Jy",EEEE2a5!R(Jy",EEEE2a5!R(Jy",EEEE2a5!R(J|R,HHHH2a5!R(J,KKKK2a5!R(J7I2,NNNN	2a5!R&'<bAB B B 2b61b)ZA-CCCC    c                  z   [        [        S5      [        S5      [        S5      /[        S5      SS[        5      [        [        S5      [        S5      [        S5      /[        S5      S[        5      :X  d   e[        [        / /SS[        5      [        :X  d   e[        [        / /SS[
        5      [        :X  d   eg NrM   rL   r   rR   )r   rI   r   f_0F_0rJ    r[   rY   test_dmp_add_termra   L       A1r!u-r!uaB?beRUBqE*BqE1b9: : :bT1a,333bT1a,333r[   c                     [        / [        5      n [        U [        S5      S[        5      [        / [        5      :X  d   e[        U [        S5      S[        5      [        S/[        5      :X  d   e[        U [        S5      S[        5      [        SS/[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        / SQ[        5      n [        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / S	Q[        5      :X  d   e[        U [        S5      S
[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        SS/[        5      :X  d   eg )Nr   rM   rV   rL   )rV   r   r   rQ   )rM   rM   rV   )rM   rV   rM   )rV   rM   rM   rR   )rV   rM   rM   rM   rS   )rV   r   rM   rM   rM   rT   )rV   r   r   rM   rM   rM   rU   )rV   r   r   r   rM   rM   rM   )r   rI   r   rW   s    rY   test_dup_sub_termrd   S   s   2rA2a5!R(Jr2,>>>>2a5!R(JtR,@@@@2a5!R(JAw,CCCC2a5!R(Jz2,FFFF9b!A2a5!R(J{B,GGGG2a5!R(J{B,GGGG2a5!R(Jz2,FFFF2a5!R(J}b,IIII2a5!R(J7G,LLLL2a5!R(J7JB,OOOO	2a5!R&'=rBC C C 2a5!R(J1vr,BBBBr[   c                  z   [        [        S5      [        S5      [        S5      /[        S5      SS[        5      [        [        S5      [        S5      [        S5      /[        S5      S[        5      :X  d   e[        [        / /SS[        5      [        :X  d   e[        [        / /SS[
        5      [        :X  d   eg r]   )r	   rI   r   r^   r_   rJ   r`   r[   rY   test_dmp_sub_termrf   k   rb   r[   c                     [        / [        5      n [        U [        S5      S[        5      [        / [        5      :X  d   e[        SS/[        5      n [        U [        S5      S[        5      [        / [        5      :X  d   e[        / SQ[        5      n [        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / SQ[        5      :X  d   e[        U [        S5      S[        5      [        / S	Q[        5      :X  d   eg )
NrL   rR   rM   r   rM   rL   rR   rL   rS   rU   )rL   rS   rU   r   )rL   rS   rU   r   r   )rL   rS   rU   r   r   r   )r   rI   r
   rW   s    rY   test_dup_mul_termrj   r   s   2rA2a5!R(Jr2,>>>>Aq62A2a5!R(Jr2,>>>>9b!A2a5!R(Jy",EEEE2a5!R(J|R,HHHH2a5!R(J,KKKK2a5!R(J7I2,NNNNr[   c                     [        [        S5      [        S5      [        S5      /[        S5      SS[        5      [        [        S5      [        S5      [        S5      /[        S5      S[        5      :X  d   e[        / /[        S5      /SS[        5      / /:X  d   e[        [        S5      /// SS[        5      / /:X  d   e[        [        S5      [        S5      /[        S5      //[        S5      /SS[        5      [        S5      [        S5      /[        S5      // / /:X  d   e[        / /[        SS5      /SS[        5      / /:X  d   e[        [        SS5      /// SS[        5      / /:X  d   e[        [        SS5      [        SS5      /[        SS5      //[        SS5      /SS[        5      [        SS5      [        SS5      /[        SS5      // / /:X  d   eg )	NrM   rL   rR   r   rS   rU   rT      )r   rI   r
   rJ   r`   r[   rY   test_dmp_mul_termrm      s   A1r!u-r!uaB?beRUBqE*BqE1b9: : : r!ugq!R0RD888"Q%	2q!R0RD888"Q%A"Q%1BqE7Aq"E
Q%A"Q%"b)* * * r!Qxj!Q3t;;;"Q(b!Q3t;;;"Q(Bq!H-1az:R1XJ1bQ
Q)R2Y	"Q)b"56 6 6r[   c                      [         R                  " / SQ5      n [         R                  " / SQ5      n[        U [        S5      [         5      U:X  d   eg )NrM   rL   rR   rS   )rM   rL   rR      rS   )rI   mapr   rX   gs     rY   test_dup_add_groundrt      9    
|A
|A!RUB'1,,,r[   c                      [         R                  " S/S/S/S//5      n [         R                  " S/S/S/S//5      n[        U [        S5      S[         5      U:X  d   eg )NrM   rL   rR   rS   rp   )rI   rq   r   rr   s     rY   test_dmp_add_groundrw      s]    
aS1#s#$A
aS1#s#$A!RUAr*a///r[   c                      [         R                  " / SQ5      n [         R                  " / SQ5      n[        U [        S5      [         5      U:X  d   eg )Nro   )rM   rL   rR   r   rS   )rI   rq   r   rr   s     rY   test_dup_sub_groundry      ru   r[   c                      [         R                  " S/S/S/S//5      n [         R                  " S/S/S// /5      n[        U [        S5      S[         5      U:X  d   eg )NrM   rL   rR   rS   )rI   rq   r   rr   s     rY   test_dmp_sub_groundr{      s[    
aS1#s#$A
aS1#r"#A!RUAr*a///r[   c                  `   [        / [        5      n [        U [        S5      [        5      [        / [        5      :X  d   e[        / SQ[        5      n [        U [        S5      [        5      [        / [        5      :X  d   e[        U [        S5      [        5      [        / SQ[        5      :X  d   eg )NrL   rh   r   ri   )r   rI   r   rW   s    rY   test_dup_mul_groundr}      s    2rA!RUB':b"+====9b!A!RUB':b"+====!RUB':i+DDDDr[   c            
         [        [        [        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      ///:X  d   e[        [        [	        SS5      S[        5      [	        SS5      [	        SS5      [	        S	S5      /[	        SS5      //[	        S	S5      //[	        SS5      [	        S
S5      [	        SS5      /[	        SS5      [	        SS5      [	        SS5      /[	        SS5      ///:X  d   eg )NrL   rS   rU   rp   
      rM      rR   rT   )r   r^   rI   r_   rJ   r`   r[   rY   test_dmp_mul_groundr      s4   #r!ua,
Q%A1	A(
Q%	
Q%BB	 2a5"Q%A"7"Q%A1    #r!QxB/
Q)R2Y1b		*R2YK8
Q)
Q)R2Y1b		*R2Y1b	2Y-Q)	&4   r[   c                  (   [        [        S 5        [        / [        5      n [	        U [        S5      [        5      [        / [        5      :X  d   e[        / SQ[        5      n [	        U [        S5      [        5      U :X  d   e[	        U [        S5      [        5      [        / SQ[        5      :X  d   e[	        U [        S5      [        5      [        / SQ[        5      :X  d   e[        / SQ[
        5      n [	        U [        S5      [
        5      U :X  d   e[	        U [        S5      [
        5      [        S5      [        S5      [        S5      /:X  d   e[	        U [        S	5      [
        5      [        S
S	5      [        SS	5      [        SS	5      /:X  d   eg )Nc                  V    [        [        / SQ[        5      [        S5      [        5      $ Nrh   r   )r   r   rI   r`   r[   rY   <lambda>%test_dup_quo_ground.<locals>.<lambda>   s"    nZ A6qE2'r[   rR   rU   rL   rp   rM   rL   rR   rM   rS   )rL   r   rL   rS   rN   rU   rp   )rK   ZeroDivisionErrorr   rI   r   rJ   rW   s    rY   test_dup_quo_groundr      s6   
    	2rA!RUB':b"+====9b!A!RUB'1,,,!RUB':i+DDDD!RUB':i+DDDD9b!A!RUB'1,,,!RUB'BqE2a5"Q%+@@@@!RUB'Bq!HbAh1a+IIIIr[   c                     [        [        S 5        [        [        S 5        [        / [        5      n [        U [	        S5      [        5      [        / [        5      :X  d   e[        / SQ[        5      n [        U [	        S5      [        5      U :X  d   e[        U [	        S5      [        5      [        / SQ[        5      :X  d   e[        / SQ[        5      n [        U [        S5      [        5      U :X  d   e[        U [        S5      [        5      [        S5      [        S5      [        S5      /:X  d   e[        U [        S	5      [        5      [        S
S	5      [        SS	5      [        SS	5      /:X  d   eg )Nc                  V    [        [        / SQ[        5      [        S5      [        5      $ r   r   r   rI   r`   r[   rY   r   'test_dup_exquo_ground.<locals>.<lambda>   s#    &6z C8!ub'"r[   c                  V    [        [        / SQ[        5      [        S5      [        5      $ )Nrh   rR   r   r`   r[   rY   r   r      s#    (8 E:!ub)"r[   rR   r   rM   rL   r   rS   rN   rU   rp   )rK   r   rF   r   rI   r   rJ   rW   s    rY   test_dup_exquo_groundr      s$   
 " #
 !" # 	2rAAr!ub)ZB-????9b!AAr!ub)Q...Ar!ub)Z	2-FFFF9b!AAr!ub)Q...Ar!ub)beRUBqE-BBBBAr!ub)bAh1a"Q(-KKKKr[   c                  h   [        S/S/S//S[        5      n [        U [        S5      S[        5      U :X  d   e[        U [        S5      S[        5      [        S/S/S//S[        5      :X  d   e[        [        U [        S5      S[        5      S[        5      [        S// S//S[        5      :X  d   eg NrU   rL   rp   rM   rR   rS   )r   rI   r   rW   s    rY   test_dmp_quo_groundr      s    QC!qc?Ar*A!RUAr*a///	2a5!R&aS1#2>? ? ? n	2a5!RR!$.R!~q"$EF F Fr[   c                      [        S/S/S//S[        5      n [        U [        S5      S[        5      U :X  d   e[        U [        S5      S[        5      [        S/S/S//S[        5      :X  d   eg r   )r   rI   r   rW   s    rY   test_dmp_exquo_groundr     su    QC!qc?Ar*AAr!ua,111	2a5!R&aS1#2>? ? ?r[   c                  f    [        / S[        5      / :X  d   e[        S/S[        5      / SQ:X  d   eg )NrR   rM   rM   r   r   r   )r   rI   r`   r[   rY   test_dup_lshiftr   	  s2    b!R B&&&qc1b!\111r[   c                  f    [        / S[        5      / :X  d   e[        / SQS[        5      S/:X  d   eg )NrR   r   rM   )r   rI   r`   r[   rY   test_dup_rshiftr     s2    b!R B&&&lAr*qc111r[   c                     [        / [        5      / :X  d   e[        [        S5      /[        5      [        S5      /:X  d   e[        [        S5      /[        5      [        S5      /:X  d   e[        [        S5      [        S5      [        S5      /[        5      [        S5      [        S5      [        S5      /:X  d   e[        / [        5      / :X  d   e[        [        SS5      /[        5      [        SS5      /:X  d   e[        [        SS5      /[        5      [        SS5      /:X  d   e[        [        SS5      [        SS5      [        SS5      /[        5      [        SS5      [        SS5      [        SS5      /:X  d   eg )NrM   rN   rV   rL   rR   )r   rI   rJ   r`   r[   rY   test_dup_absr     sE   2r?b   BF8R RUG+++BrF8R RUG+++BrFBqE2a5)2.2a5"Q%A2GGGG2r?b   B1I;#1az111Br1I;#1az111	BBq!HbAh'-13Aq2a8R1X0NO O Or[   c                     [        [        S5      /S[        5      [        S5      /:X  d   e[        [        SS5      /S[        5      [        SS5      /:X  d   e[        / //S[        5      / //:X  d   e[        [        S5      ///S[        5      [        S5      ///:X  d   e[        [        S5      ///S[        5      [        S5      ///:X  d   e[        / //S[        5      / //:X  d   e[        [        SS5      ///S[        5      [        SS5      ///:X  d   e[        [        SS5      ///S[        5      [        SS5      ///:X  d   eg NrV   r   rM   rL   r   rN   	   )r   rI   rJ   r`   r[   rY   test_dmp_absr      s>   BrF8Q#1w...Br1I;2&2a8*444RD61b!rdV+++beWI;2&RUG9+555bfXJ<B'beWI;666RD61b!rdV+++bAhZL>1b)1azl^;;;bQi[M?Ar*Aq
|n<<<r[   c                     [        / [        5      / :X  d   e[        [        S5      /[        5      [        S5      /:X  d   e[        [        S5      /[        5      [        S5      /:X  d   e[        [        S5      [        S5      [        S5      /[        5      [        S5      [        S5      [        S5      /:X  d   e[        / [        5      / :X  d   e[        [        SS5      /[        5      [        SS5      /:X  d   e[        [        SS	5      /[        5      [        SS	5      /:X  d   e[        [        SS5      [        SS5      [        SS5      /[        5      [        SS5      [        SS5      [        SS5      /:X  d   eg )
NrM   rV   r   rN   rL   rR   r   )r   rI   rJ   r`   r[   rY   test_dup_negr   -  sL   2r?b   BqE7BBrF8+++BrF8R RUG+++BrFBqE2a5)2.2a5"R&"R&2IIII2r?b   Bq!H:r"r"ayk111Br1I;#1az111B
A1a"Q($%')-/1Xr"ay"R),LM M Mr[   c                     [        [        S5      /S[        5      [        S5      /:X  d   e[        [        SS5      /S[        5      [        SS5      /:X  d   e[        / //S[        5      / //:X  d   e[        [        S5      ///S[        5      [        S5      ///:X  d   e[        [        S5      ///S[        5      [        S5      ///:X  d   e[        / //S[        5      / //:X  d   e[        [        SS5      ///S[        5      [        SS5      ///:X  d   e[        [        SS5      ///S[        5      [        SS5      ///:X  d   eg r   )r   rI   rJ   r`   r[   rY   test_dmp_negr   :  s>   BrF8Q#1w...Br1I;2&2a8*444RD61b!rdV+++beWI;2&RVH:,666bfXJ<B'beWI;666RD61b!rdV+++bAhZL>1b)2q	{m_<<<bQi[M?Ar*Aq
|n<<<r[   c            	         [        / / [        5      / :X  d   e[        [        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      /[        S5      /[        5      [        S5      /:X  d   e[        [        S5      [        S5      /[        S5      /[        5      [        S5      [        S5      /:X  d   e[        [        S5      /[        S5      [        S5      /[        5      [        S5      [        S5      /:X  d   e[        [        S5      [        S5      [        S5      /[        S5      [        S5      [        S5      /[        5      [        S5      [        S5      [        S5      /:X  d   e[        / / [        5      / :X  d   e[        [        SS5      // [        5      [        SS5      /:X  d   e[        / [        SS5      /[        5      [        SS5      /:X  d   e[        [        SS	5      /[        SS	5      /[        5      [        SS5      /:X  d   e[        [        SS	5      /[        SS5      /[        5      [        SS	5      /:X  d   e[        [        SS5      [        SS5      /[        S5      /[        5      [        SS5      [        S
S5      /:X  d   e[        [        S5      /[        SS5      [        SS5      /[        5      [        SS5      [        S
S5      /:X  d   e[        [        SS5      [        SS5      [        SS5      /[        SS5      [        SS5      [        SS5      /[        5      [        SS5      [        SS5      [        SS5      /:X  d   eg )NrM   rL   rR   rp   r   r         rS   rT   rN   )r   rI   rJ   r`   r[   rY   test_dup_addr   G  s8   2r2"$$$BqE7B#1w...21w#1w...BqE7RUGR(RUG333BqE7RUGR(RUG333BqE2a5>BqE7B/BqE2a5>AAABqE7RUBqENB/BqE2a5>AAABqE2	qEUBqE2b6*B046qE2b62b63JK K K 2r2"$$$Bq!H:r2&2a8*44421az2&2a8*444Bq!H:1az2.2a8*<<<Bq!H:1az2.2a8*<<<Bq!HbAh'"Q%"5"Q(Bq!H9MMMMBqE7R1Xr!Qx0"5"Q(Bq!H9MMMMBq!HbAh1a1B	15!QxB4$%')-/1Xr"ay"R),LM M Mr[   c                     [        [        S5      [        S5      /[        S5      /S[        5      [        [        S5      [        S5      /[        S5      /[        5      :X  d   e[        [        SS5      [        SS5      /[        S5      /S[        5      [        [        SS5      [        SS5      /[        S5      /[        5      :X  d   e[        / /// //S[        5      / //:X  d   e[        [        S5      //// //S[        5      [        S5      ///:X  d   e[        / //[        S5      ///S[        5      [        S5      ///:X  d   e[        [        S5      ///[        S5      ///S[        5      [        S5      ///:X  d   e[        [        S5      ///[        S5      ///S[        5      [        S5      ///:X  d   e[        / /// //S[        5      / //:X  d   e[        [        SS5      //// //S[        5      [        SS5      ///:X  d   e[        / //[        SS5      ///S[        5      [        SS5      ///:X  d   e[        [        SS5      ///[        SS5      ///S[        5      [        SS5      ///:X  d   e[        [        SS5      ///[        SS5      ///S[        5      [        SS5      ///:X  d   eg )NrM   rL   r   rR   rN   )r   rI   r   rJ   r`   r[   rY   test_dmp_addr   a  s   BqE2a5>BqE7Ar2A1A,- - -Bq!HbAh'"Q%!R8Aq2a8$r!ugr23 3 3 RD6RD61b)rdV333beWI;"2.RUG9+===RD6beWI;2.RUG9+===beWI;2a5'Q3"Q%	{BBBbeWI;2a5'Q3"Q%	{BBBRD6RD61b)rdV333bAhZL>RD61b11azl^CCCRD6bAhZL>1b11azl^CCCbAhZL>bAhZL>1b91azl^KKKbAhZL>bAhZL>1b91azl^KKKr[   c            	      x   [        / / [        5      / :X  d   e[        [        S5      // [        5      [        S5      /:X  d   e[        / [        S5      /[        5      [        S5      /:X  d   e[        [        S5      /[        S5      /[        5      / :X  d   e[        [        S5      /[        S5      /[        5      [        S5      /:X  d   e[        [        S5      [        S5      /[        S5      /[        5      [        S5      [        S5      /:X  d   e[        [        S5      /[        S5      [        S5      /[        5      [        S5      [        S5      /:X  d   e[        [        S5      [        S5      [        S5      /[        S5      [        S5      [        S5      /[        5      [        S5      [        S	5      [        S
5      /:X  d   e[        / / [        5      / :X  d   e[        [        SS5      // [        5      [        SS5      /:X  d   e[        / [        SS5      /[        5      [        SS5      /:X  d   e[        [        SS5      /[        SS5      /[        5      / :X  d   e[        [        SS5      /[        SS5      /[        5      [        SS5      /:X  d   e[        [        SS5      [        SS5      /[        S5      /[        5      [        SS5      [        SS5      /:X  d   e[        [        S5      /[        SS5      [        SS5      /[        5      [        SS5      [        SS5      /:X  d   e[        [        SS5      [        SS5      [        SS5      /[        SS5      [        SS5      [        SS5      /[        5      [        SS5      [        S	S5      [        S
S5      /:X  d   eg )NrM   rV   rL   rR   rp   r   r   r   rN   rT   )r   rI   rJ   r`   r[   rY   test_dup_subr   t  s+   2r2"$$$BqE7B#1w...21w#2x///BqE7RUGR(B...BqE7RUGR(RVH444BqE2a5>BqE7B/BqE2a5>AAABqE7RUBqENB/BrFBrF3CCCCBqE2	qEUBqE2b6*B046rFBrFBrF3KL L L 2r2"$$$Bq!H:r2&2a8*44421az2&2b!9+555Bq!H:1az2."444Bq!H:1az2.2b!9+===Bq!HbAh'"Q%"5"Q(Br1I9NNNNBqE7R1Xr!Qx0"5"R)R1X9NNNNBq!HbAh1a1B	15!QxB4$%')-/AY2q	2b!9,MN N Nr[   c                     [        [        S5      [        S5      /[        S5      /S[        5      [        [        S5      [        S5      /[        S5      /[        5      :X  d   e[        [        SS5      [        SS5      /[        S5      /S[        5      [        [        SS5      [        SS5      /[        S5      /[        5      :X  d   e[        / /// //S[        5      / //:X  d   e[        [        S5      //// //S[        5      [        S5      ///:X  d   e[        / //[        S5      ///S[        5      [        S5      ///:X  d   e[        [        S5      ///[        S5      ///S[        5      [        S5      ///:X  d   e[        [        S5      ///[        S5      ///S[        5      [        S5      ///:X  d   e[        / /// //S[        5      / //:X  d   e[        [        SS5      //// //S[        5      [        SS5      ///:X  d   e[        / //[        SS5      ///S[        5      [        SS5      ///:X  d   e[        [        SS5      ///[        SS5      ///S[        5      [        SS5      ///:X  d   e[        [        SS5      ///[        SS5      ///S[        5      [        SS5      ///:X  d   eg )NrM   rL   r   rR   rV   rN   )r   rI   r   rJ   r`   r[   rY   test_dmp_subr     s   BqE2a5>BqE7Ar2A1A,- - -Bq!HbAh'"Q%!R8Aq2a8$r!ugr23 3 3 RD6RD61b)rdV333beWI;"2.RUG9+===RD6beWI;2.RVH:,>>>beWI;2a5'Q3"Q%	{BBBbeWI;2a5'Q3"R&
|CCCRD6RD61b)rdV333bAhZL>RD61b11azl^CCCRD6bAhZL>1b12q	{m_DDDbAhZL>bAhZL>1b91azl^KKKbAhZL>bAhZL>1b92q	{m_LLLr[   c                  l   [        [        S5      [        S5      [        S5      /[        S5      [        S5      [        S5      /[        S5      [        S5      /[        5      [        S5      [        S5      [        S5      [        S5      /:X  d   e[        [        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      //:X  d   eg )NrM   rL   rR   r   rN   rT   rS   )r&   rI   r'   r`   r[   rY   test_dup_add_mulr     s    1r!ube,r!ubeRU.C1r!u~r#')!ubeRUBqE&BC C CA1A0BqE7RUBqEN2KA"Q%!1b*/1!ug1r!u~1rRSu~-VW W Wr[   c                  l   [        [        S5      [        S5      [        S5      /[        S5      [        S5      [        S5      /[        S5      [        S5      /[        5      [        S5      [        S5      [        S5      [        S5      /:X  d   e[        [        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      //:X  d   eg )	NrM   rL   rR   r   r   rV   r   )r(   rI   r)   r`   r[   rY   test_dup_sub_mulr     s   1r!ube,r!ubeRU.C1r!u~r#')"vr"vr"vr!u&EF F FA1A0BqE7RUBqEN2KA"Q%!1b*/1"vhBB8H2b6SUVWSX/-Z[ [ [r[   c                     [        / / [        5      / :X  d   e[        / [        S5      /[        5      / :X  d   e[        [        S5      // [        5      / :X  d   e[        [        S5      /[        S5      /[        5      [        S5      /:X  d   e[        [        S5      /[        S5      /[        5      [        S5      /:X  d   e[        / / [        5      / :X  d   e[        / [        SS5      /[        5      / :X  d   e[        [        SS5      // [        5      / :X  d   e[        [        SS5      /[        SS5      /[        5      [        SS5      /:X  d   e[        [        SS5      /[        SS5      /[        5      [        SS	5      /:X  d   e[        / S
Q[        5      n [        / SQ[        5      n[        / SQ[        5      n[        X[        5      U:X  d   e[        X[        5      U:X  d   e[        / SQ[        5      n [        / SQ[        5      n[        X [        5      U:X  d   e[	        S5      n[        U" S5      U" S5      /U" S5      U" S5      /U5      U" S5      U" S5      /:X  d   e[        / SQ[        5      n[        / SQ[        5      n[        / SQ[        5      n[        XE[        5      U:X  d   e[        / SQ[        5      n[        / SQ[        5      n[        / SQ[        5      n[        XE[        5      U:X  d   eg )NrM   rT   rN   #   rL   rS   rR   rl   1   )rR   r   r   rU   rM   rL   )rS   r   rM   r   )	r   r   rR      rS   r   rM   rL   r   rL   r   r   rM   rN   	rS   r   r   rS      r   rM   r   r   rU   )O   rV   N   r       r   rL      I   *   U   M   S   r   _   %   r   r   C      L   rL   F   r   A   9   r   r   a   Y   !   r   Q   r   <   +      ,      r   r   r   rR   5      r   B   rM   r   b   r   rU   rp   r   r      r      r   7   r   D   r   T   ^   -   r   \   r  r  r   rp   K   r   [   r   "   r   r   r   r   r   rU   r      r   :   r      r   r   rN   r   r   r  r   r   r   r   rT   3   r   r!  r   r   r   r   R   r   r   r  r  r   r$  r  r  r&  ?   r   r   rU   r  r   rR   rR   .   r  >   X   r   r&  rV   r   H   r   r  r*  r   r   r  r   r  r  r   r  r   d   r  r   r   r   r7  4   V   r   r   r   r   r   r   r   r   r%  (\  r   r   rM   Z   r   r   r      r  r   2   r   r      rM   r   r   r   J   P   r   r   r   )   r      r*  r   r   E   r   r  r
  r   r   r   r  r   r   r   r  r-  r  r6  r  r   r   r   r7  r   r&  r   r   r'  r  r   r   r/  rT   r<  r  r   r&  r(  r  r   r  r  0   r   r   r   r   r   r   r  r   =   r   r3  r   rF  r   r   r   rL   rU   r   r"  r  rN  r   r  rP  rV   rJ  `   r   r   r   8   r  r4  r+  rT  r>  r*  r   r   r  r   r  r   r   r   rF  (   r   r   r   r7  r  r   r/  '   r$  r   r   W   @   r   r  r   rl   r,  r  r   r	  r   6   rU  r   rU   r;  r,  rP  r   r[  r   r  r  r   r   r   r  r   rJ  r  $   r   rT   r>  r&  rF  r9  r=  r   ir   r
  r   r  rS   rW  r\  r   r   r   r   r   r  rJ  r8  r   r   r)  r  r^  r   r   rL  r  r   r   rG  r#  r1  r4  rA  r   r5  r  r   r   r<  r"  r$  r;  r   r   rW  r  &   r   r`  r7  r   r   r[  r*  r'  r      r   r   r  r  r:  r   r  r   r   r   rB  r^  rM  r(  rA  rA  r<  r0  r   r3  r^  r   r   r  r   r   r   r  r   rM   r   r
  rp   rp   rS  r   r   r   rM  r   r  r&  r   r   rE  rE  rT   r   r   r(  rX  r   rT   r   r\  r   rD  r#  r^  r   r   rI  r  r   rB  r  r  r   r-  rZ  r  r"  r   r'  r/  r   r   r9  r   r<  r   r   r   rb  r   r   r-  r  r   r  r
  ra  r  r   r  r  r%  r   r   r   r7  rp   r/  r   r  r   (C  i  ii`  ii  i-  iA  iigiiY  ii_  iOi.  iin%  i0$  io  i[  i	J  i5'  i\ii*  ii?i  i*  iizi?  iDz  i`  i|  i  i  ii  i=  is  i  i|  i  ivki}i%  rd  iQi  i`iHii4  iw  i%  i3Uii,  ii  ii  iY  i}i|idi"li޷iiti\ioiiiNb  iiM  i2  iMiiKl  i#iiiiwN  i$iZi  iQ  i9i%}  5ig  ivF  i;if|  ii4ii0  ib  i&Mi^  i'iHi>iiTiߟirH  iuii'  ixiciL  iilg  iiU  i  ip  iXi  i  i0  i5i,  i iCi7  i  ibi/ i_  iYir  i  iM6  iiS  ii|d i  iY ii ii  iPi#i<  iii  i+  ii  i  iiii9i0|iiibiE  itiy  ii:  id  i ii iii  iwi% iW i  iiiiHxii*Fi[iiuUi+iieiy;  izi+  ii<i  i  i/8  iiihihsi  ii, iPi  i#  ibcii3  i*  iI6i&  i6/  iij ioiiѶiI  i?  i)  iii)  iii  iN  ii i߷  i  iϱ  ii<D  i!i1 iiwiix  isw i!  i]  ii}  i[  i  iiyai  io  i1zi'aidaimiVi  iiԔ i iiiIviJ
  i/  i iVK  ixii&i$c  iy`i"i4i  iOij  ii  i}i3  i4i\i i i  iri^ialiH
ii  ii i]  i.  iv  i  i  ii  i!ii  i^N iii
igi!  ivre  iZ  i'  i  iZiini2 i~  i  iRiorili  iiia  i  iii71  i\ih  i  iiƺ  ii0  ii(ioifi  ii+i i3i" i+G  i8 ii_ iD  i%}ii  imi i9  i=Ri0*  ii2i  iYV  it  ii5  i  i  i.!  i$  ii>{  ii  i1iiK  iO  i'ii{i}i  i_ii	i;  i  iiI  ig  iI  iifiDii  i2  i!陏iE  iiiiii`  is  i* i  iJiiWii.i]  iiܧ  i  i(q  iizi"_  i\ih  i  iiSiiOQii/iii{  iY  iiii4  i"  iw iI  i  i i  i.  iM\iO  ii  (iDie  i  iat  iz  iIio  iF  iO  i$  iS  iƔiOii^iYii*  iiSif  i9  iy  ini&  iii3.  i*iiw i_  iiwii	OiA#  [ioui]+  iv-  iq  i  i\i$  io5  i  i6  ii?  i   iWisiziAi&  iw  io  i7O  iiiyiii^  iC  ie  i'ii9i<i$X  ii  i-  in  iiiiix}  iiK,  i{ii  i i%iWrh  iU  ild  i   i  ii  iQ  iN  iX  i-  i3  i	  ii7iEii8i  iiiirii  i	  i  ii|)r   rI  r  rJ  r   r   r	  r   r   r  rX  rB  r   r  r   r  r   rS   r  rU   r   r   r   r   i/   r(  r  r9  r   r   r   r@  rF  rJ  rY  r   r   r  r=  rV   rV  r   r   r
  r  r   r3  rF  r   r	  r   r  rH  r-  r   r   r   ir   r  rR  rI  r>  rM   G   rS   r   rM  rS   r  r<  r  rT   rM  r'  r2  r   r  r   r  r   rM  rI  r  rj  r   r   rX  r   r"  r   r   r   r   r(  rb  r   r=  r)  r4  rT  r  r   rV  rS  r%  rL  r   r  r  r   r%  rb  r   r   r   rA  r   r   rR   r^  rM  r   rJ  r   r   r  r   r   rH  r2  r:  r   rL  r  r6  r   r3  rZ  r:  r
  r   r2  r   r  r   r   r   ;   r   c   r   r   r  r0  r   r   rM   r#  r  rC  r   r<  r   r   r   rY  r)  r   r   r   r  rU  r_  rG  rX  r   r   r-  r   r!  r  r   r  rR  rZ  rl  r4  r   r   rI  r   r   r  rI  rS   r   r   rS  r-  r   r   r  r  r  r   r6  r  r  rL  r  r   r   r7  r;  r  rT  r   rR   rU  r   r   r/  r   r   r   rD  rW  r!  r   r   r'  r'  rR  r   r   rM  r   rM  r   r  r   (+  r8  r2  r   r   r   r3  r-  r   r  rH  r   rT  ra  r   r   r   r
  r   r  r*  r   r   r>  r   rB  r  r"  rS   rj  r   r   r   rl  rB  r1  rm  r"  rH  rY  r   r0  r   rY  rl  r   rL  r  r   rW  r  rS   r  r3  r  r  rR  r   rR      rT  r]  r   r  r   rU   r   r   rV  r   r6  r\  r   rl  r   r   r[  r   r^  rE  r   r>  r   r  r   r   r   r   r   r   rk  r   r*  rQ  rT  r!  rp   rV   rT  r   r  r  r   r^  rk  r   r   r   r5  rm  r8  r_  rT   r[  r   rL  rN  r   r  r7  r  r   r:  rX  r	  r   rM   r   rc  r8  r   r  rR   r   r4  r   r+  rK  r   r   r  r   r   r   rT   r   r   ]   r   r  r>  rB  r   rq  rm  r;  r  r*  r   r   r  rS  r  r   r  rq  r   r   r   ro  r   r   r.  r  r   r`  rE  r   r9  r  r>  r   r   rj  r  r,  r   r5  r   r;  r  r  r   r   r   rU   r  r   r   rl   r   rq  r   r#  r&  r6  r>  r   r=  rl  rY  r   r   ro  r   r  rK  rO  rP  r?  r   rT   r   rn  r  r   r-  r  r   r   r  r  r)  ra  r   r6  r;  rA  rM   r  r   r%  r   rM  r=  r1  r   r   r]  ra  r   rS  r  r   rA  r   r>  r  r   r   r$  rP  r#  rR   r   r  rL   rN  r   r   r   r  r  r   r   r;  r   rS   r:  r   r=  r8  r#  rb  r   rA  rl  r   rm  r*  r  rp  rK  r   r   r   r^  rc  r   r   (  i  i$  i4iiiil  iii6  iA  i?,  idiiC  i+R  iii>  i  iis"  iD  i'  i  ii!  ii  ic  i5&  i/     i=I  iiik  i;ii1  i  ii/L  ii  ivi  i$\  iƐiu  i  ii[.i?iir  i  iV  iii8  iwii<  i  iS;  i:iiibi  i\  iViiA  ibI  i/  i^`  iy  i  ikii  ivii)Q  iL  iP  iڃ  iiUi}  i  iяi0ii5  i|-  iD  i(i\  ii  iQ  i  ii  iix`i`M  iHiZ  i  iqb  iG$  il  ii%  i6i3  i<  i  i_N  i  i-  ij  ivimi6  iʀ  i2ik  ios  iv igiXli(i   i  iˎi(i  iPiSi  iŒ  iii{iiU|igiizD  i  i
  iU$ib  iiiMiC ii\Ri i9  iia(  iN  iuiS)i  i  i8H  ir  i%  iid  i0 iii  i	  i5iiA iei  i  i  i0iʷ  i	f  i![i4 ii	  iipq  i]iHix[  ii?Si@YiiM  i  iw=  i,  i ifiJ  i9  i  ii@  ih i  i  i i  i iiiFiwi'  in i"  iG  iJ  iBr  iR!  i  ii<iiiT  i   izsi5 iii{  iiii**  iia  i  i6i wiy it  iM  i+ioiWiDid ihijisii.  iv  iS\i/]iNz  iNm  iH  i@  iJ  i(iۂ  iu  ii]  iz  ii\  i=i&iieiiri  i%i9iyw  i!  iJ  iiY iH   i-ci_i i
2  ii ii  i\i i^  i: i4  i&  i  i@i  iiiS i.i  iJo  i= iT  i i
  ivi  ip  ibi=  i6  i/  iPi9  iw  i;@iiGq  i  i  iiii)  imGi,  i*  iiiW  ii&  isiaiiu  i  i  i;  i iT  i
iS3 iUi5  i,  i6i.i-ii  iXi~iii  i1i8  ikin  iWdi{rg  i|D i:iǙifIi1  i  isiqiu  i2i  iX  iӉi3iVii  i9ig7  ii-i  i7i  ii i.  i  i`  i  i  i  iR  iii§i{  im i^  iiiiH  iYF  ii1  iiisO  i  ii.iiG  i=  i  i;  iLb  iHip(  iqi  iT  ii)i i}iiˁ  i  iR  i,i^h  iݯi)  i  r;  i^  iuiii  i  iABicC  i>in  iii  iim  iib  iii  ii[n  iitiiѝiI  iiyi5iC  iio~ip  iiiDB  i	i[i"7  i7ii  ii-i  iD  iPrf  iL&  iiu
  io  iii\  ii  i0  i4"  itiwii  iR  iiO  iii	  i{.  i  i
iX  iQ   is+  i\i  iniv/  iti  is  iJi	  i)r    rI   rJ   r   rH   )rX   rs   hKp1p2ress          rY   test_dup_mulry    s   2r2"$$$21w#r)))BqE7B#r)))BqE7RUGR(RUG333BqE7RUGR(RVH4442r2"$$$21az2&",,,Bq!H:r2&",,,Bq!H:1az2.2a8*<<<Bq!H:1az2.2b":,>>>%r*A<$A126A1!!!1!!!?B'A126A1!!!
1AAaD!A$<!A$!q1adAaD\AAA	 ; =?
@B 
 I* KM+
NB,  =z {=C~ 22#%%%	 8 :<
=B  
 A$ CE%
FB&  8/p 13q84Ct 22#%%%r[   c                     [        [        S5      /[        S5      /S[        5      [        [        S5      /[        S5      /[        5      :X  d   e[        [        SS5      /[        SS5      /S[        5      [        [        SS5      /[        SS5      /[        5      :X  d   e[        / /// //S[        5      / //:X  d   e[        [        S5      //// //S[        5      / //:X  d   e[        / //[        S5      ///S[        5      / //:X  d   e[        [        S5      ///[        S5      ///S[        5      [        S5      ///:X  d   e[        [        S5      ///[        S5      ///S[        5      [        S5      ///:X  d   e[        / /// //S[        5      / //:X  d   e[        [        SS5      //// //S[        5      / //:X  d   e[        / //[        SS5      ///S[        5      / //:X  d   e[        [        SS5      ///[        SS5      ///S[        5      [        SS5      ///:X  d   e[        [        SS5      ///[        SS5      ///S[        5      [        SS5      ///:X  d   e[	        S5      n [        U " S5      /U " S5      //U " S5      /U " S	5      //SU 5      U " S5      /U " S	5      //:X  d   eg )
NrT   rN   r   rR   rL   rM   r   rU   rS   )r!   rI   r    rJ   rH   ru  s    rY   test_dmp_mulr|    s   BqE7RUGQ+A"Q%"%& & &Bq!H:1az1b1Aq
R1XJ+, , , RD6RD61b)rdV333beWI;"2.B4&888RD6beWI;2.B4&888beWI;2a5'Q3"Q%	{BBBbeWI;2a5'Q3"Q%	{BBBRD6RD61b)rdV333bAhZL>RD61b1rdV;;;RD6bAhZL>1b1rdV;;;bAhZL>bAhZL>1b91b	{m_LLLbAhZL>bAhZL>1b91b	{m_LLL
1A
A$!A$AaD6AaD6*Aq278tfqtf5EF F Fr[   c                     [        / [        5      / :X  d   e[        [        S5      /[        5      [        S5      /:X  d   e[        [        S5      [        S5      /[        5      [        S5      [        S5      [        S5      /:X  d   e[        / [        5      / :X  d   e[        [        SS5      /[        5      [        SS5      /:X  d   e[        [        SS5      [        SS5      /[        5      [        SS5      [        SS5      [        SS5      /:X  d   e[        / SQ[        5      n [        U [        5      [        / SQ[        5      :X  d   e[	        S5      n[        U" S5      U" S5      /U5      U" S5      U" S	5      /:X  d   eg )
NrL   rS   rM   rR   r   r   r   rU   rN   )r"   rI   rJ   r   rH   )rX   ru  s     rY   test_dup_sqrr~    sA   2r?b   BqE7BBqE7***BqE2a5>2&2a5"Q%A*????2r?b   Bq!H:r"r!Qxj000Bq!HbAh',Aq2a8R1X0NNNN?B'A1b>Z(FKKKK
1AAaD!A$<#!ad|333r[   c                  F   [        [        S5      [        S5      /S[        5      [        [        S5      [        S5      /[        5      :X  d   e[        / //S[        5      / //:X  d   e[        [        S5      ///S[        5      [        S5      ///:X  d   e[        / //S[        5      / //:X  d   e[        [        SS5      ///S[        5      [        SS5      ///:X  d   e[	        S5      n [        U " S5      /U " S5      //SU 5      U " S5      /U " S5      //:X  d   eg )	NrM   rL   r   rS   rR   r   rU   rN   )r#   rI   r"   rJ   rH   r{  s    rY   test_dmp_sqrr    s   BqE2a5>1b)A1#$ $ $ RD61b!rdV+++beWI;2&RUG9+555RD61b!rdV+++bAhZL>1b)1azl^;;;
1AQqTFQqTF#Q*!v!v.>>>>r[   c                  ^   [        / S[        5      [        S5      /:X  d   e[        / S[        5      [        S5      /:X  d   e[        / S[        5      / :X  d   e[        / S[        5      / :X  d   e[        [        S5      /S[        5      [        S5      /:X  d   e[        [        S5      /S[        5      [        S5      /:X  d   e[        [        S5      /S[        5      [        S5      /:X  d   e[        [        S5      /S[        5      [        S5      /:X  d   e[        [        S5      /S[        5      [        S5      /:X  d   e[        [        S5      /S[        5      [        S5      /:X  d   e[        [        SS5      /S[        5      [        SS5      /:X  d   e[        [        SS5      /S[        5      [        SS5      /:X  d   e[        [        SS5      /S[        5      [        SS5      /:X  d   e[        [        SS5      /S[        5      [        SS5      /:X  d   e[        [        SS5      /S[        5      [        SS5      /:X  d   e[        [        SS5      /S[        5      [        SS5      /:X  d   e[        / SQ[        5      n [        U S[        5      [        S/[        5      :X  d   e[        U S[        5      [        / SQ[        5      :X  d   e[        U S[        5      [        / S	Q[        5      :X  d   e[        U S[        5      [        / S
Q[        5      :X  d   eg )Nr   rM   rN   rR      r   rL   r   )rp   r   r   r   r  r   rU   r  i&  rM   r      iW  )r$   rI   rJ   r   rW   s    rY   test_dup_powr    s   2q""Q%(((2q""Q%(((2q"###2q"###BqE7Ar"r!ug---BqE7Ar"r!ug---BqE7Ar"r!ug---BqE7Ar"r!ug---BqE7Ar"r!ug---BqE7Ar"r$xj000Bq!H:q"%"Q(333Bq!H:q"%"Q(333Bq!H:q"%"Q(333Bq!H:q"%"Q(333Bq!H:q"%"Q(333Bq!H:q"%"T6*:);;;;?B'A1a
A3 33331a
?B ????1a
+I2 NNNN1a
92!? ? ? ?r[   c                     [        / /SS[        5      [        S5      //:X  d   e[        / /SS[        5      [        S5      //:X  d   e[        / /SS[        5      / /:X  d   e[        / /SS[        5      / /:X  d   e[        [        S5      //SS[        5      [        S5      //:X  d   e[        [        S5      //SS[        5      [        S5      //:X  d   e[        [        S5      //SS[        5      [        S5      //:X  d   e[        [        SS5      //SS[        5      [        SS5      //:X  d   e[        [        SS5      //SS[        5      [        SS5      //:X  d   e[        [        SS5      //SS[        5      [        SS5      //:X  d   e[        / SQ[        5      n [        U SS[        5      [	        U S[        5      :X  d   eg )	Nr   rM   rN   rR   r  r  r   rL   )r%   rI   rJ   r   r$   rW   s    rY   test_dmp_powr    s   B4Ar"1wi///B4Ar"1wi///B4Ar"rd***B4Ar"rd***RUG9aB'RUG9444RUG9aB'RUG9444RUG9aB'RUG9444R1XJ<Ar*1azl:::R1XJ<Ar*1azl:::R1XJ<Ar*40@/A.BBBB?B'A1aB71a#4444r[   c                    ^^ [        / SQ[        5      m[        / SQ[        5      m[        SS/[        5      n [        SS/[        5      n[        TT[        5      X4:X  d   e[        TT[        5      U :X  d   e[	        TT[        5      U:X  d   e[        [        UU4S j5        [        / SQ[        5      m[        / SQ[        5      m[        SS/[        5      n [        SS/[        5      n[        TT[        5      X4:X  d   e[        TT[        5      U :X  d   e[	        TT[        5      U:X  d   e[        [        UU4S j5        g )	NrR   rM   rM   rT   rT   r   rM   rl   r   r8  o   c                  &   > [        T T[        5      $ N)r-   rI   rr   s   rY   r   test_dup_pdiv.<locals>.<lambda>
      
1a(<r[   c                  &   > [        T T[        5      $ r  )r-   rJ   rr   s   rY   r   r    r  r[   )r   rI   r*   r,   r+   rK   rF   rJ   qrrX   rs   s     @@rY   test_dup_pdivr    s   <$A:r"AB8R AB9b!AAq"!'''Aq""""Aq""""
 <=<$A:r"AB8R AB9b!AAq"!'''Aq""""Aq""""
 <=r[   c                    ^^ [        S// / SQ/S[        5      m[        S/SS//S[        5      m[        S/SS//S[        5      n [        / SQ/S[        5      n[        TTS[        5      X4:X  d   e[        TTS[        5      U :X  d   e[	        TTS[        5      U:X  d   e[        [        UU4S j5        [        S// / SQ/S[        5      m[        S/SS//S[        5      m[        S/SS//S[        5      n [        / S	Q/S[        5      n[        TTS[        5      X4:X  d   e[        TTS[        5      U :X  d   e[	        TTS[        5      U:X  d   e[        [        UU4S
 j5        g )NrM   rP   rV   r   rL   r   r   c                  (   > [        T TS[        5      $ NrM   r1   rI   rr   s   rY   r   test_dmp_pdiv.<locals>.<lambda>$      
1aB(?r[   rL   r   )rp   r   r   c                  (   > [        T TS[        5      $ r  r  rr   s   rY   r   r  0  r  r[   )r   rI   r.   r0   r/   rK   rF   r  s     @@rY   test_dmp_pdivr    sc   QCY'B/AQC"a>1b)AQC!Q=!R(AI;2&AAq!R QF***Aq!R A%%%Aq!R A%%%
 ?@QCY'B/AQC"a>1b)AQC!Q=!R(AI;2&AAq!R QF***Aq!R A%%%Aq!R A%%%
 ?@r[   c                      [        [        S 5        [        / SQ[        5      n [        / SQ[        5      n/ U p2[	        X[        5      X#4:X  d   eg )Nc                  (    [        / SQ/ [        5      $ Nrh   )r2   rI   r`   r[   rY   r   !test_dup_rr_div.<locals>.<lambda>4      jB&Cr[   r  r  )rK   r   r   rI   r2   rX   rs   r  r  s       rY   test_dup_rr_divr  3  sD    
CD<$A:r"AqqaBA6)))r[   c                  t   [        [        S 5        [        S// / SQ/S[        5      n [        S/SS//S[        5      n[        S/SS//S[        5      n[        / SQ/S[        5      n[	        XS[        5      X#4:X  d   e[        S// / SQ/S[        5      n [        S/SS//S[        5      n[        S/SS//S[        5      n[        / SQ/S[        5      n[	        XS[        5      X#4:X  d   e[        S// / SQ/S[        5      n [        S/SS//S[        5      n/ /U p2[	        XS[        5      X#4:X  d   eg )	Nc                  2    [        SS/S/// /S[        5      $ NrM   rL   rR   )r3   rI   r`   r[   rY   r   !test_dmp_rr_div.<locals>.<lambda>?      j1a&1#a&Lr[   rM   rP   rV   r   r  rL   r   )rK   r   r   rI   r3   r  s       rY   test_dmp_rr_divr  >  s?   
LMQCY'B/AQC"a>1b)AQC!Q=!R(AI;2&AaAr"qf,,,QCY'B/ARD1a&>1b)ARD2q'?Ar*AI;2&AaAr"qf,,,QCY'B/AQC"a>1b)A4qaAr"qf,,,r[   c                      [        [        S 5        [        / SQ[        5      n [        / SQ[        5      n[        SS5      [        SS5      /n[        SS5      [        S	S5      /n[	        X[        5      X#4:X  d   eg )
Nc                  (    [        / SQ/ [        5      $ r  )r4   rJ   r`   r[   rY   r   !test_dup_ff_div.<locals>.<lambda>Z  r  r[   r  r  rR   rT   r   r>  r8  r  )rK   r   r   rJ   r4   r  s       rY   test_dup_ff_divr  Y  si    
CD<$A:r"A	Aq2b":A	BRR[!AaBA6)))r[   c                     [         S:w  a  g SSKJn   SSKJn  U" 5       nU " SS5      U " SS5      /nU " SS5      /n[        X4SU5      U " SS5      U " SS	5      // 4:X  d   eU " SS5      U " SS5      U " SS	5      U " SS
5      /nU " SS5      U " SS5      U " SS5      /n[        X4SU5      U " SS5      U " SS5      /U " SS5      U " SS5      /4:X  d   eg )Ngmpy2r   )mpq)GMPYRationalFieldrM   rR   rL   rU   rS   rT   rV   r   rN   r   r   r   )r   r  r  sympy.polys.domainsr  r5   )r  r  ru  rX   rs   s        rY   test_dup_ff_div_gmpy2r  d  s    w5A	Qq3q8A	Qq
AaAq!s1QxQq&:B%????	Qq3q8S1Xs1Qx0A	RC!Hc"Qi(AaAq!s2ay#b)&<s1Ry#cRT+>V%WWWWr[   c                  z   [        [        S 5        [        S// / SQ/S[        5      n [        S/SS//S[        5      n[        SS5      /[        SS5      [        SS5      //n[        SS5      [        SS5      [        SS5      //n[	        XS[        5      X#4:X  d   e[        S// / SQ/S[        5      n [        S/SS//S[        5      n[        SS5      /[        SS5      [        SS5      //n[        SS5      [        SS5      [        SS5      //n[	        XS[        5      X#4:X  d   e[        S// / SQ/S[        5      n [        S/SS//S[        5      n[        SS5      /[        SS5      [        SS5      //n[        SS5      [        SS5      [        SS5      //n[	        XS[        5      X#4:X  d   eg )Nc                  2    [        SS/S/// /S[        5      $ r  )r5   rJ   r`   r[   rY   r   !test_dmp_ff_div.<locals>.<lambda>u  r  r[   rM   rP   rV   r   rL   r   )rK   r   r   rJ   r5   r  s       rY   test_dmp_ff_divr  t  s   
LMQCY'B/AQC"a>1b)A
Q(bAh1a)*A
Q(Bq!HbAh	'(AaAr"qf,,,QCY'B/ARD1a&>1b)A
R)r"ay"Q(+,A
Q(Bq!HbAh	'(AaAr"qf,,,QCY'B/AQC"a>1b)A
Q(bAh1a)*A
Q(Bq!HbAh	'(AaAr"qf,,,r[   c                    ^^ / SQ/ SQ/ SQSS/4u  mmp[        TT[        5      X4:X  d   e[        TT[        5      U :X  d   e[        TT[        5      U:X  d   e[	        [
        UU4S j5        / SQ/ SQS	S
// SQ4u  mmp[        TT[        5      X4:X  d   e[        TT[        5      U :X  d   e[        TT[        5      U:X  d   e[	        [
        UU4S j5        g )NrT   rS   rR   rL   rM   rh   rT   r"  r   r  rM   c                  &   > [        T T[        5      $ r  r9   rI   rr   s   rY   r   test_dup_div.<locals>.<lambda>      	!Q(;r[   )rT   rS   rR   rL   rM   r   )rM   rL   r   r   r   rT   r"  )rl   rL   r   r]  c                  &   > [        T T[        5      $ r  r  rr   s   rY   r   r    r  r[   )r6   rI   r8   r7   rK   rF   r  s     @@rY   test_dup_divr    s     )Z"a@JAq!1a&&&1a!!!1a!!!
 ;<#_q"g?OOJAq!1a&&&1a!!!1a!!!
 ;<r[   c                    ^^ / SQ/ SQ/ SQSS/4u  mmp[        TTS[        5      X4:X  d   e[        TTS[        5      U :X  d   e[        TTS[        5      U:X  d   e[	        [
        UU4S j5        S///S//S/// //S///4u  mmp[        TTS[        5      X4:X  d   e[        TTS[        5      U :X  d   e[        TTS[        5      U:X  d   e[	        [
        UU4S	 j5        g )
Nr  rh   r  r  rM   r   c                  (   > [        T TS[        5      $ )Nr   r=   rI   rr   s   rY   r   test_dmp_div.<locals>.<lambda>      	!Q2(>r[   rL   c                  (   > [        T TS[        5      $ )NrL   r  rr   s   rY   r   r    r  r[   )r:   rI   r<   r;   rK   rF   r  s     @@rY   test_dmp_divr    s     )Z"a@JAq!1aBA6)))1aB1$$$1aB1$$$
 >?3%QC51#,"1#7JAq!1aBA6)))1aB1$$$1aB1$$$
 >?r[   c                      [        / [        5      S:X  d   e[        S/[        5      S:X  d   e[        / SQ[        5      S:X  d   eg )Nr   rM   rM   rS   rL   rR   rS   )r>   rI   r`   r[   rY   test_dup_max_normr    sC    B1$$$R A%%%b)Q...r[   c                      [        / //S[        5      S:X  d   e[        S///S[        5      S:X  d   e[        [        S[        5      S:X  d   eg )NrL   r   rM   rU   )r?   rI   r^   r`   r[   rY   test_dmp_max_normr    sQ    "2&!+++1#B'1,,,Q#q(((r[   c                      [        / [        5      S:X  d   e[        S/[        5      S:X  d   e[        / SQ[        5      S:X  d   eg )Nr   rM   r  r   )r@   rI   r`   r[   rY   test_dup_l1_normr    sC    r2!###sB1$$$|R(B...r[   c                      [        / //S[        5      S:X  d   e[        S///S[        5      S:X  d   e[        [        S[        5      S:X  d   eg )NrL   r   rM   rA  )rA   rI   r^   r`   r[   rY   test_dmp_l1_normr    sQ    vq"%***!w2&!+++sAr"b(((r[   c                      [        / [        5      S:X  d   e[        S/[        5      S:X  d   e[        / SQ[        5      S:X  d   eg )Nr   rM   r  r   )rB   rI   r`   r[   rY   test_dup_l2_norm_squaredr    sC    r2&!+++sB'1,,,|R0B666r[   c                      [        / //S[        5      S:X  d   e[        S///S[        5      S:X  d   e[        [        S[        5      S:X  d   eg )NrL   r   rM   r  )rC   rI   r^   r`   r[   rY   test_dmp_l2_norm_squaredr    sQ    vq"-222!w2.!333sAr*c111r[   c            	          [        S[        5      S/:X  d   e[        / SQSS// SQ4[        5      [        / SQ[        SS// SQ[        5      [        5      :X  d   eg )Nr`   rM   rh   rL   )rN   rT   rS   rR   )rD   rI   r    r`   r[   rY   test_dup_expandr    sY    b"!$$$y1a&,7<	7Aq6<<bAB B Br[   c                      [        SS[        5      S//:X  d   e[        S/S/S//S/S//S/S/S/S//4S[        5      [        S/S/S//[        S/S//S/S/S/S//S[        5      S[        5      :X  d   eg )Nr`   rM   rL   rR   rN   rT   rS   )rE   rI   r!   r`   r[   rY   test_dmp_expandr    s    b!R aSE)))aS1#!qc
aS1#sQC4HI1bQ!qcA31#sqcA3AC6R"!"#R	)) ) )r[   N)__doc__sympy.external.gmpyr   sympy.polys.densebasicr   r   sympy.polys.densearithr   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   sympy.polys.polyerrorsrF   sympy.polys.specialpolysrG   r  rH   rI   rJ   sympy.testing.pytestrK   to_denser^   f_1f_2f_3f_4f_5f_6r_   rZ   ra   rd   rf   rj   rm   rt   rw   ry   r{   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   ry  r|  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rW   s   0rY   <module>r     s   : ,                > - * * '<CI$GIqjjlI$G !S#sCcZQ+R1Xq"=D04C04O"6"-0-0EJ,L,F?2
2

O
=
M
=M4L&N4M&W[`&FF04$??@5(>4A4*-6	*X -8=$@$/)/)72B)a %Hs   :F