
    sg                     *   d Z ddlmZ ddlmZmZ ddlmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZF ddlGmHZH ddlImJZJ ddlKmLZLmMZMmNZN ddlOmPZP  eJ       D  cg c]  } | j                          c} \  ZRZSZTZUZVZWZX e eeRd	eN       eNd
d      d	eN      ZYd ZZd Z[d Z\d Z]d Z^d Z_d Z`d Zad Zbd Zcd Zdd Zed Zfd Zgd Zhd Zid Zjd Zkd Zld Zmd  Znd! Zod" Zpd# Zqd$ Zrd% Zsd& Ztd' Zud( Zvd) Zwd* Zxd+ Zyd, Zzd- Z{d. Z|d/ Z}d0 Z~d1 Zd2 Zd3 Zd4 Zd5 Zd6 Zd7 Zd8 Zd9 Zd: Zd; Zd< Zd= Zd> Zy?c c} w )@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                     t        g t              } t        | t        d      dt              t        g t              k(  sJ t        | t        d      dt              t        dgt              k(  sJ t        | t        d      dt              t        ddgt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        g dt              } t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      d	t              t        g d
t              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        ddgt              k(  sJ y )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    T/var/www/html/venv/lib/python3.12/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                  t   t        t        d      t        d      t        d      gt        d      ddt              t        t        d      t        d      t        d      gt        d      dt              k(  sJ t        t        g gddt              t        k(  sJ t        t        g gddt
              t        k(  sJ y 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                     t        g t              } t        | t        d      dt              t        g t              k(  sJ t        | t        d      dt              t        dgt              k(  sJ t        | t        d      dt              t        ddgt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        g dt              } t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g d	t              k(  sJ t        | t        d      d
t              t        g dt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        ddgt              k(  sJ y )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                  t   t        t        d      t        d      t        d      gt        d      ddt              t        t        d      t        d      t        d      gt        d      dt              k(  sJ t        t        g gddt              t        k(  sJ t        t        g gddt
              t        k(  sJ y r]   )r	   rI   r   r^   r_   rJ   r`   r[   rY   test_dmp_sub_termrf   k   rb   r[   c                     t        g t              } t        | t        d      dt              t        g t              k(  sJ t        ddgt              } t        | t        d      dt              t        g t              k(  sJ t        g dt              } t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g dt              k(  sJ t        | t        d      dt              t        g d	t              k(  sJ y )
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                     t        t        d      t        d      t        d      gt        d      ddt              t        t        d      t        d      t        d      gt        d      dt              k(  sJ t        g gt        d      gddt              g gk(  sJ t        t        d      ggg ddt              g gk(  sJ t        t        d      t        d      gt        d      ggt        d      gddt              t        d      t        d      gt        d      gg g gk(  sJ t        g gt        dd      gddt              g gk(  sJ t        t        dd      ggg ddt              g gk(  sJ t        t        dd      t        dd      gt        dd      ggt        dd      gddt              t        dd      t        dd      gt        dd      gg g gk(  sJ y )	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                      t        j                  g d      } t        j                  g d      }t        | t        d      t               |k(  sJ y )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                      t        j                  dgdgdgdgg      } t        j                  dgdgdgdgg      }t        | t        d      dt               |k(  sJ y )NrM   rL   rR   rS   rp   )rI   rq   r   rr   s     rY   test_dmp_add_groundrw      s]    
aS1#s#$A
aS1#s#$A!RUAr*a///r[   c                      t        j                  g d      } t        j                  g d      }t        | t        d      t               |k(  sJ y )Nro   )rM   rL   rR   r   rS   )rI   rq   r   rr   s     rY   test_dup_sub_groundry      ru   r[   c                      t        j                  dgdgdgdgg      } t        j                  dgdgdgg g      }t        | t        d      dt               |k(  sJ y )NrM   rL   rR   rS   )rI   rq   r   rr   s     rY   test_dmp_sub_groundr{      s[    
aS1#s#$A
aS1#r"#A!RUAr*a///r[   c                  Z   t        g t              } t        | t        d      t              t        g t              k(  sJ t        g dt              } t        | t        d      t              t        g t              k(  sJ t        | t        d      t              t        g dt              k(  sJ y )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            
         t        t        t        d      dt              t        d      t        d      t        d      gt        d      ggt        d      ggt        d      t        d      t        d      gt        d      t        d      t        d      gt        d      gggk(  sJ t        t        t	        dd      dt              t	        dd      t	        dd      t	        d	d      gt	        dd      ggt	        d	d      ggt	        dd      t	        d
d      t	        dd      gt	        dd      t	        dd      t	        dd      gt	        dd      gggk(  sJ y )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                     t        t        d        t        g t              } t	        | t        d      t              t        g t              k(  sJ t        g dt              } t	        | t        d      t              | k(  sJ t	        | t        d      t              t        g dt              k(  sJ t	        | t        d      t              t        g dt              k(  sJ t        g dt
              } t	        | t        d      t
              | k(  sJ t	        | t        d      t
              t        d      t        d      t        d      gk(  sJ t	        | t        d	      t
              t        d
d	      t        dd	      t        dd	      gk(  sJ y )Nc                  V    t        t        g dt              t        d      t              S Nrh   r   )r   r   rI   r`   r[   rY   <lambda>z%test_dup_quo_ground.<locals>.<lambda>   s$    nZ A6qE2' r[   rR   rU   rL   rp   rM   rL   rR   rM   rS   )rL   r   rL   rS   rN   rU   rp   )rK   ZeroDivisionErrorr   rI   r   rJ   rW   s    rY   test_dup_quo_groundr      s6   
    	2rA!RUB':b"+====9b!A!RUB'1,,,!RUB':i+DDDD!RUB':i+DDDD9b!A!RUB'1,,,!RUB'BqE2a5"Q%+@@@@!RUB'Bq!HbAh1a+IIIIr[   c                     t        t        d        t        t        d        t        g t              } t        | t	        d      t              t        g t              k(  sJ t        g dt              } t        | t	        d      t              | k(  sJ t        | t	        d      t              t        g dt              k(  sJ t        g dt              } t        | t        d      t              | k(  sJ t        | t        d      t              t        d      t        d      t        d      gk(  sJ t        | t        d	      t              t        d
d	      t        dd	      t        dd	      gk(  sJ y )Nc                  V    t        t        g dt              t        d      t              S r   r   r   rI   r`   r[   rY   r   z'test_dup_exquo_ground.<locals>.<lambda>   s%    &6z C8!ub'" r[   c                  V    t        t        g dt              t        d      t              S )Nrh   rR   r   r`   r[   rY   r   z'test_dup_exquo_ground.<locals>.<lambda>   s%    (8 E:!ub)" r[   rR   r   rM   rL   r   rS   rN   rU   rp   )rK   r   rF   r   rI   r   rJ   rW   s    rY   test_dup_exquo_groundr      s$   
 " #
 !" # 	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                  b   t        dgdgdggdt              } t        | t        d      dt              | k(  sJ t        | t        d      dt              t        dgdgdggdt              k(  sJ t        t        | t        d      dt              dt              t        dgg dggdt              k(  sJ y 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                      t        dgdgdggdt              } t        | t        d      dt              | k(  sJ t        | t        d      dt              t        dgdgdggdt              k(  sJ y 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                  b    t        g dt              g k(  sJ t        dgdt              g dk(  sJ y )NrR   rM   rM   r   r   r   )r   rI   r`   r[   rY   test_dup_lshiftr   	  s2    b!R B&&&qc1b!\111r[   c                  b    t        g dt              g k(  sJ t        g ddt              dgk(  sJ y )NrR   r   rM   )r   rI   r`   r[   rY   test_dup_rshiftr     s2    b!R B&&&lAr*qc111r[   c                     t        g t              g k(  sJ t        t        d      gt              t        d      gk(  sJ t        t        d      gt              t        d      gk(  sJ t        t        d      t        d      t        d      gt              t        d      t        d      t        d      gk(  sJ t        g t              g k(  sJ t        t        dd      gt              t        dd      gk(  sJ t        t        dd      gt              t        dd      gk(  sJ t        t        dd      t        dd      t        dd      gt              t        dd      t        dd      t        dd      gk(  sJ y )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                     t        t        d      gdt              t        d      gk(  sJ t        t        dd      gdt              t        dd      gk(  sJ t        g ggdt              g ggk(  sJ t        t        d      gggdt              t        d      gggk(  sJ t        t        d      gggdt              t        d      gggk(  sJ t        g ggdt              g ggk(  sJ t        t        dd      gggdt              t        dd      gggk(  sJ t        t        dd      gggdt              t        dd      gggk(  sJ y 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                     t        g t              g k(  sJ t        t        d      gt              t        d      gk(  sJ t        t        d      gt              t        d      gk(  sJ t        t        d      t        d      t        d      gt              t        d      t        d      t        d      gk(  sJ t        g t              g k(  sJ t        t        dd      gt              t        dd      gk(  sJ t        t        dd	      gt              t        dd	      gk(  sJ t        t        dd      t        dd      t        dd      gt              t        dd      t        dd      t        dd      gk(  sJ y )
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                     t        t        d      gdt              t        d      gk(  sJ t        t        dd      gdt              t        dd      gk(  sJ t        g ggdt              g ggk(  sJ t        t        d      gggdt              t        d      gggk(  sJ t        t        d      gggdt              t        d      gggk(  sJ t        g ggdt              g ggk(  sJ t        t        dd      gggdt              t        dd      gggk(  sJ t        t        dd      gggdt              t        dd      gggk(  sJ y 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            	         t        g g t              g k(  sJ t        t        d      gg t              t        d      gk(  sJ t        g t        d      gt              t        d      gk(  sJ t        t        d      gt        d      gt              t        d      gk(  sJ t        t        d      gt        d      gt              t        d      gk(  sJ t        t        d      t        d      gt        d      gt              t        d      t        d      gk(  sJ t        t        d      gt        d      t        d      gt              t        d      t        d      gk(  sJ t        t        d      t        d      t        d      gt        d      t        d      t        d      gt              t        d      t        d      t        d      gk(  sJ t        g g t              g k(  sJ t        t        dd      gg t              t        dd      gk(  sJ t        g t        dd      gt              t        dd      gk(  sJ t        t        dd	      gt        dd	      gt              t        dd      gk(  sJ t        t        dd	      gt        dd      gt              t        dd	      gk(  sJ t        t        dd      t        dd      gt        d      gt              t        dd      t        d
d      gk(  sJ t        t        d      gt        dd      t        dd      gt              t        dd      t        d
d      gk(  sJ t        t        dd      t        dd      t        dd      gt        dd      t        dd      t        dd      gt              t        dd      t        dd      t        dd      gk(  sJ y )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$%')-/1Xr"ay"R),LM M Mr[   c                  |   t        t        d      t        d      gt        d      gdt              t        t        d      t        d      gt        d      gt              k(  sJ t        t        dd      t        dd      gt        d      gdt              t        t        dd      t        dd      gt        d      gt              k(  sJ t        g ggg ggdt              g ggk(  sJ t        t        d      gggg ggdt              t        d      gggk(  sJ t        g ggt        d      gggdt              t        d      gggk(  sJ t        t        d      gggt        d      gggdt              t        d      gggk(  sJ t        t        d      gggt        d      gggdt              t        d      gggk(  sJ t        g ggg ggdt              g ggk(  sJ t        t        dd      gggg ggdt              t        dd      gggk(  sJ t        g ggt        dd      gggdt              t        dd      gggk(  sJ t        t        dd      gggt        dd      gggdt              t        dd      gggk(  sJ t        t        dd      gggt        dd      gggdt              t        dd      gggk(  sJ y )NrM   rL   r   rR   rN   )r   rI   r   rJ   r`   r[   rY   test_dmp_addr   a  s   BqE2a5>BqE7Ar2A1A,- - -Bq!HbAh'"Q%!R8Aq2a8$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   t        g g t              g k(  sJ t        t        d      gg t              t        d      gk(  sJ t        g t        d      gt              t        d      gk(  sJ t        t        d      gt        d      gt              g k(  sJ t        t        d      gt        d      gt              t        d      gk(  sJ t        t        d      t        d      gt        d      gt              t        d      t        d      gk(  sJ t        t        d      gt        d      t        d      gt              t        d      t        d      gk(  sJ t        t        d      t        d      t        d      gt        d      t        d      t        d      gt              t        d      t        d	      t        d
      gk(  sJ t        g g t              g k(  sJ t        t        dd      gg t              t        dd      gk(  sJ t        g t        dd      gt              t        dd      gk(  sJ t        t        dd      gt        dd      gt              g k(  sJ t        t        dd      gt        dd      gt              t        dd      gk(  sJ t        t        dd      t        dd      gt        d      gt              t        dd      t        dd      gk(  sJ t        t        d      gt        dd      t        dd      gt              t        dd      t        dd      gk(  sJ t        t        dd      t        dd      t        dd      gt        dd      t        dd      t        dd      gt              t        dd      t        d	d      t        d
d      gk(  sJ y )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$%')-/AY2q	2b!9,MN N Nr[   c                  |   t        t        d      t        d      gt        d      gdt              t        t        d      t        d      gt        d      gt              k(  sJ t        t        dd      t        dd      gt        d      gdt              t        t        dd      t        dd      gt        d      gt              k(  sJ t        g ggg ggdt              g ggk(  sJ t        t        d      gggg ggdt              t        d      gggk(  sJ t        g ggt        d      gggdt              t        d      gggk(  sJ t        t        d      gggt        d      gggdt              t        d      gggk(  sJ t        t        d      gggt        d      gggdt              t        d      gggk(  sJ t        g ggg ggdt              g ggk(  sJ t        t        dd      gggg ggdt              t        dd      gggk(  sJ t        g ggt        dd      gggdt              t        dd      gggk(  sJ t        t        dd      gggt        dd      gggdt              t        dd      gggk(  sJ t        t        dd      gggt        dd      gggdt              t        dd      gggk(  sJ y )NrM   rL   r   rR   rV   rN   )r   rI   r   rJ   r`   r[   rY   test_dmp_subr     s   BqE2a5>BqE7Ar2A1A,- - -Bq!HbAh'"Q%!R8Aq2a8$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                  h   t        t        d      t        d      t        d      gt        d      t        d      t        d      gt        d      t        d      gt              t        d      t        d      t        d      t        d      gk(  sJ t        t        d      t        d      gt        d      ggt        d      gt        d      t        d      ggt        d      gt        d      ggdt              t        d      gt        d      t        d      gt        d      t        d      ggk(  sJ y )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                  h   t        t        d      t        d      t        d      gt        d      t        d      t        d      gt        d      t        d      gt              t        d      t        d      t        d      t        d      gk(  sJ t        t        d      t        d      gt        d      ggt        d      gt        d      t        d      ggt        d      gt        d      ggdt              t        d      gt        d      t        d      gt        d      t        d      ggk(  sJ y )	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                     t        g g t              g k(  sJ t        g t        d      gt              g k(  sJ t        t        d      gg t              g k(  sJ t        t        d      gt        d      gt              t        d      gk(  sJ t        t        d      gt        d      gt              t        d      gk(  sJ t        g g t              g k(  sJ t        g t        dd      gt              g k(  sJ t        t        dd      gg t              g k(  sJ t        t        dd      gt        dd      gt              t        dd      gk(  sJ t        t        dd      gt        dd      gt              t        dd	      gk(  sJ t        g d
t              } t        g dt              }t        g dt              }t        | |t              |k(  sJ t        || t              |k(  sJ t        g dt              } t        g dt              }t        | | t              |k(  sJ t	        d      }t         |d       |d      g |d       |d      g|       |d       |d      gk(  sJ t        g dt              }t        g dt              }t        g dt              }t        ||t              |k(  sJ t        g dt              }t        g dt              }t        g dt              }t        ||t              |k(  sJ y )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   r5  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  r4  r  r   r   r   r5  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   r1  r   rD  r   r   r   rL   rU   r   r   r  rL  r   r  rN  rV   rH  `   r   r   r   8   r  r2  r)  rR  r<  r(  r   r   r  r   r  r   r   r   rD  (   r   r   r   r5  r  r   r-  '   r"  r   r   W   @   r   r  r   rl   r*  r   r   r  r   6   rS  r   rU   r9  r*  rN  r   rY  r   r  r  r   r   r   r   r   rH  r  $   r   rT   r<  r$  rD  r7  r;  r   ir   r  r   r  rS   rU  rZ  r   r   r   r   r   r  rH  r6  r   r   r'  r  r\  r   r   rJ  r  r   r   rE  r!  r/  r2  r?  r   r3  r  r   r   r:  r   r"  r9  r   r   rU  r   &   r   r^  r5  r   r   rY  r(  r%  r      r   r   r	  r  r8  r   r  r   r   r   r@  r\  rK  r&  r?  r?  r:  r.  r   r1  r\  r  r   r  r   r   r   r  r   rM   r   r  rp   rp   rQ  r   r   r   rK  r   r  r$  r   r   rC  rC  rT   r   r   r&  rV  r   rT   r   rZ  r   rB  r!  r\  r   r   rG  r  r   r@  r  r  r   r+  rX  r  r   r   r%  r-  r   r   r7  r   r:  r   r   r   r`  r   r   r+  r  r   r  r  r_  r  r   r  r	  r#  r   r   r   r5  rp   r-  r   r  r   (C  i  ii`  ii  i-  iA  iigiiY  ii_  iOi.  iin%  i0$  io  i[  i	J  i5'  i\ii*  ii?i  i*  iizi?  iDz  i`  i|  i  i  ii  i=  is  i  i|  i  ivki}i%  rb  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$iZi  iQ  i9i%}  5ig  ivF  i;if|  ii4ii0  ib  i&Mi^  i'iHi>iiTiߟirF  iuii'  ixiciL  iilg  iiU  i  ip  iXi  i  i0  i5i,  i iCi7  i  ibi/ i_  iYir  i  iM6  iiS  ii|d i  iY ii ii  iPi#i<  iii  i+  ii  i  iiii9i0|iiibiE  itiy  ii:  id  i ii iii  iwi% iW i  iiiiHxii*Fi[iiuUi+iieiy;  izi+  ii<i  i  i/8  iiihihsi  ii, iPi  i#  ibcii3  i*  iI6i&  i6/  iij ioiiѶiI  i?  i)  iii)  iii  iN  ii i߷  i  iϱ  ii<D  i!i1 iiwiix  isw i!  i]  ii}  i[  i  iiyai  io  i1zi'aidaimiVi  iiԔ i iiiIviJ
  i/  i iVK  ixii&i$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rc  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%iWrf  iU  ild  i   i  ii  iQ  iN  iX  i-  i3  i	  ii7iEii8i  iiiirii  i	  i  ii|)r   rG  r  rH  r   r   r  r   r   r  rV  r@  r   r  r   r  r   rS   r  rU   r   r   r   r   i/   r&  r  r7  r   r   r   r>  rD  rH  rW  r   r   r  r;  rV   rT  r   r   r  r  r   r1  rD  r   r  r   r  rF  r+  r   r   r   ir   r  rP  rG  r<  rM   G   rS   r   rK  rS   r  r:  r   rT   rK  r%  r0  r   r  r   r  r   rK  rG  r  rh  r   r   rV  r   r   r   r  r   r   r&  r`  r   r;  r'  r2  rR  r  r   rT  rQ  r#  rJ  r   r  r  r   r#  r`  r   r   r   r?  r   r   rR   r\  rK  r   rH  r   r   r  r   r   rF  r0  r8  r   rJ  r  r4  r   r1  rX  r8  r  r   r0  r   r  r   r   r   ;   r   c   r   r   r  r.  r   r   rM   r!  r  rA  r   r:  r   r   r   rW  r'  r   r   r   r  rS  r]  rE  rV  r   r   r+  r   r  r  r   r  rP  rX  rj  r2  r   r   rG  r   r   r  rG  rS   r   r   rQ  r+  r   r   r	  r  r  r   r4  r  r  rJ  r  r   r   r5  r9  r  rR  r   rR   rS  r   r   r-  r   r   r   rB  rU  r  r   r   r%  r%  rP  r   r   rK  r   rK  r   r  r   (+  r6  r0  r   r   r   r1  r+  r   r  rF  r   rR  r_  r   r   r   r  r   r  r(  r   r   r<  r   r@  r  r   rS   rh  r   r   r   rj  r@  r/  rk  r   rF  rW  r   r.  r   rW  rj  r   rJ  r  r   rU  r  rS   r  r1  r  r   rP  r   rR      rR  r[  r   r  r   rU   r   r   rT  r   r4  rZ  r   rj  r   r   rY  r   r\  rC  r   r<  r   r  r   r   r   r   r   r   ri  r   r(  rO  rR  r  rp   rV   rR  r   r  r  r   r\  ri  r   r   r   r3  rk  r6  r]  rT   rY  r   rJ  rL  r   r  r5  r  r  r8  rV  r  r   rM   r   ra  r6  r   r  rR   r   r2  r   r)  rI  r   r   r
  r   r   r   rT   r   r   ]   r   r  r<  r@  r   ro  rk  r9  r  r(  r   r   r  rQ  r  r   r  ro  r   r   r   rm  r   r   r,  r  r   r^  rC  r   r7  r  r<  r   r   rh  r  r*  r   r3  r   r9  r  r  r   r   r   rU   r  r   r   rl   r   ro  r   r!  r$  r4  r<  r   r;  rj  rW  r   r   rm  r   r	  rI  rM  rN  r=  r   rT   r   rl  r   r   r+  r  r   r   r  r
  r'  r_  r   r4  r9  r?  rM   r  r   r#  r   rK  r;  r/  r   r   r[  r_  r   rQ  r   r   r?  r   r<  r  r   r   r"  rN  r!  rR   r   r  rL   rL  r   r   r   r  r  r   r   r9  r   rS   r8  r   r;  r6  r!  r`  r   r?  rj  r   rk  r(  r  rn  rI  r   r   r   r\  ra  r   r   (  i  i$  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&iieiirg  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{re  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  r9  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  iPrd  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_mulrw    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<$A126A1a!!!1a!!!?B'A126A1a!!!
1AAaD!A$<!A$!q1adAaD\AAA	 ; =?
@B 
 I* KM+
NB,  =z {=C~ 2r2#%%%	 8 :<
=B  
 A$ CE%
FB&  8/p 13q84Ct 2r2#%%%r[   c                  t   t        t        d      gt        d      gdt              t        t        d      gt        d      gt              k(  sJ t        t        dd      gt        dd      gdt              t        t        dd      gt        dd      gt              k(  sJ t        g ggg ggdt              g ggk(  sJ t        t        d      gggg ggdt              g ggk(  sJ t        g ggt        d      gggdt              g ggk(  sJ t        t        d      gggt        d      gggdt              t        d      gggk(  sJ t        t        d      gggt        d      gggdt              t        d      gggk(  sJ t        g ggg ggdt              g ggk(  sJ t        t        dd      gggg ggdt              g ggk(  sJ t        g ggt        dd      gggdt              g ggk(  sJ t        t        dd      gggt        dd      gggdt              t        dd      gggk(  sJ t        t        dd      gggt        dd      gggdt              t        dd      gggk(  sJ t	        d      } t         | d      g | d      gg | d      g | d	      ggd|        | d      g | d	      ggk(  sJ y )
NrT   rN   r   rR   rL   rM   r   rU   rS   )r!   rI   r    rJ   rH   rs  s    rY   test_dmp_mulrz    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                     t        g t              g k(  sJ t        t        d      gt              t        d      gk(  sJ t        t        d      t        d      gt              t        d      t        d      t        d      gk(  sJ t        g t              g k(  sJ t        t        dd      gt              t        dd      gk(  sJ t        t        dd      t        dd      gt              t        dd      t        dd      t        dd      gk(  sJ t        g dt              } t        | t              t        g dt              k(  sJ t	        d      }t         |d       |d      g|       |d       |d	      gk(  sJ y )
NrL   rS   rM   rR   r   r   r   rU   rN   )r"   rI   rJ   r   rH   )rX   rs  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                  :   t        t        d      t        d      gdt              t        t        d      t        d      gt              k(  sJ t        g ggdt              g ggk(  sJ t        t        d      gggdt              t        d      gggk(  sJ t        g ggdt              g ggk(  sJ t        t        dd      gggdt              t        dd      gggk(  sJ t	        d      } t         | d      g | d      ggd|        | d      g | d      ggk(  sJ y )	NrM   rL   r   rS   rR   r   rU   rN   )r#   rI   r"   rJ   rH   ry  s    rY   test_dmp_sqrr~    s   BqE2a5>1b)A1#$ $ $ RD61b!rdV+++beWI;2&RUG9+555RD61b!rdV+++bAhZL>1b)1azl^;;;
1AQqTFQqTF#Q*!v!v.>>>>r[   c                  6   t        g dt              t        d      gk(  sJ t        g dt              t        d      gk(  sJ t        g dt              g k(  sJ t        g dt              g k(  sJ t        t        d      gdt              t        d      gk(  sJ t        t        d      gdt              t        d      gk(  sJ t        t        d      gdt              t        d      gk(  sJ t        t        d      gdt              t        d      gk(  sJ t        t        d      gdt              t        d      gk(  sJ t        t        d      gdt              t        d      gk(  sJ t        t        dd      gdt              t        dd      gk(  sJ t        t        dd      gdt              t        dd      gk(  sJ t        t        dd      gdt              t        dd      gk(  sJ t        t        dd      gdt              t        dd      gk(  sJ t        t        dd      gdt              t        dd      gk(  sJ t        t        dd      gdt              t        dd      gk(  sJ t        g dt              } t        | dt              t        dgt              k(  sJ t        | dt              t        g dt              k(  sJ t        | dt              t        g d	t              k(  sJ t        | dt              t        g d
t              k(  sJ y )Nr   rM   rN   rR      r   rL   r   )rp   r   r   r   r  r   rU   r  i&  rM   r      iW  )r$   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$xj000Bq!H:q"%"Q(333Bq!H:q"%"Q(333Bq!H:q"%"Q(333Bq!H:q"%"Q(333Bq!H:q"%"Q(333Bq!H:q"%"T6*:);;;;?B'A1a
A3 33331a
?B ????1a
+I2 NNNN1a
92!? ? ? ?r[   c                     t        g gddt              t        d      ggk(  sJ t        g gddt              t        d      ggk(  sJ t        g gddt              g gk(  sJ t        g gddt              g gk(  sJ t        t        d      ggddt              t        d      ggk(  sJ t        t        d      ggddt              t        d      ggk(  sJ t        t        d      ggddt              t        d      ggk(  sJ t        t        dd      ggddt              t        dd      ggk(  sJ t        t        dd      ggddt              t        dd      ggk(  sJ t        t        dd      ggddt              t        dd      ggk(  sJ t        g dt              } t        | ddt              t	        | dt              k(  sJ y )	Nr   rM   rN   rR   r  r  r   rL   )r%   rI   rJ   r   r$   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                     t        g dt              t        g dt              t        ddgt              } t        ddgt              }t        t              | |fk(  sJ t        t              | k(  sJ t	        t              |k(  sJ t        t        fd       t        g dt              t        g dt              t        ddgt              } t        ddgt              }t        t              | |fk(  sJ t        t              | k(  sJ t	        t              |k(  sJ t        t        fd       y )	NrR   rM   rM   rT   rT   r   rM   rl   r   r6  o   c                  &    t         t              S N)r-   rI   rr   s   rY   r   ztest_dup_pdiv.<locals>.<lambda>
      
1a(< r[   c                  &    t         t              S r  )r-   rJ   rr   s   rY   r   ztest_dup_pdiv.<locals>.<lambda>  r  r[   )r   rI   r*   r,   r+   rK   rF   rJ   qrrX   rs   s     @@rY   test_dup_pdivr    s   <$A:r"AB8R AB9b!AAq"!Q'''Aq""""Aq""""
 <=<$A:r"AB8R AB9b!AAq"!Q'''Aq""""Aq""""
 <=r[   c                     t        dgg g dgdt              t        dgddggdt              t        dgddggdt              } t        g dgdt              }t        dt              | |fk(  sJ t        dt              | k(  sJ t	        dt              |k(  sJ t        t        fd       t        dgg g dgdt              t        dgddggdt              t        dgddggdt              } t        g d	gdt              }t        dt              | |fk(  sJ t        dt              | k(  sJ t	        dt              |k(  sJ t        t        fd
       y )NrM   rP   rV   r   rL   r   r   c                  (    t         dt              S NrM   r1   rI   rr   s   rY   r   ztest_dmp_pdiv.<locals>.<lambda>$      
1aB(? r[   rL   r   )rp   r   r   c                  (    t         dt              S r  r  rr   s   rY   r   ztest_dmp_pdiv.<locals>.<lambda>0  r  r[   )r   rI   r.   r0   r/   rK   rF   r  s     @@rY   test_dmp_pdivr    sg   QCY'B/AQC"a>1b)AQC!Q=!R(AI;2&AAq!R QF***Aq!R A%%%Aq!R A%%%
 ?@QCY'B/AQC"a>1b)AQC!Q=!R(AI;2&AAq!R QF***Aq!R A%%%Aq!R A%%%
 ?@r[   c                      t        t        d        t        g dt              } t        g dt              }g | }}t	        | |t              ||fk(  sJ y )Nc                  (    t        g dg t              S Nrh   )r2   rI   r`   r[   rY   r   z!test_dup_rr_div.<locals>.<lambda>4      jB&C r[   r  r  )rK   r   r   rI   r2   rX   rs   r  r  s       rY   test_dup_rr_divr  3  sJ    
CD<$A:r"AqqAaBAq6)))r[   c                  |   t        t        d        t        dgg g dgdt              } t        dgddggdt              }t        dgddggdt              }t        g dgdt              }t	        | |dt              ||fk(  sJ t        dgg g dgdt              } t        dgddggdt              }t        dgddggdt              }t        g dgdt              }t	        | |dt              ||fk(  sJ t        dgg g dgdt              } t        dgddggdt              }g g| }}t	        | |dt              ||fk(  sJ y )	Nc                  2    t        ddgdggg gdt              S NrM   rL   rR   )r3   rI   r`   r[   rY   r   z!test_dmp_rr_div.<locals>.<lambda>?      j1a&1#a&L r[   rM   rP   rV   r   r  rL   r   )rK   r   r   rI   r3   r  s       rY   test_dmp_rr_divr  >  sM   
LMQCY'B/AQC"a>1b)AQC!Q=!R(AI;2&AaAr"q!f,,,QCY'B/ARD1a&>1b)ARD2q'?Ar*AI;2&AaAr"q!f,,,QCY'B/AQC"a>1b)A4qAaAr"q!f,,,r[   c                      t        t        d        t        g dt              } t        g dt              }t        dd      t        dd      g}t        dd      t        d	d      g}t	        | |t              ||fk(  sJ y )
Nc                  (    t        g dg t              S r  )r4   rJ   r`   r[   rY   r   z!test_dup_ff_div.<locals>.<lambda>Z  r  r[   r  r  rR   rT   r   r<  r6  r  )rK   r   r   rJ   r4   r  s       rY   test_dup_ff_divr  Y  sm    
CD<$A:r"A	Aq2b":A	BRR[!AaBAq6)))r[   c                     t         dk7  ry ddlm}  ddlm}  |       } | dd       | dd      g} | dd      g}t        ||d|       | dd       | dd	      gg fk(  sJ  | dd       | dd       | dd	       | dd
      g} | dd       | dd       | dd      g}t        ||d|       | dd       | dd      g | dd       | dd      gfk(  sJ y )Ngmpy2r   )mpq)GMPYRationalFieldrM   rR   rL   rU   rS   rT   rV   r   rN   r   r   r   )r   r  r  sympy.polys.domainsr  r5   )r  r  rs  rX   rs   s        rY   test_dup_ff_div_gmpy2r  d  s    w5A	Qq3q8A	Qq
AaAq!s1QxQq&:B%????	Qq3q8S1Xs1Qx0A	RC!Hc"Qi(AaAq!s2ay#b)&<s1Ry#cRT+>V%WWWWr[   c                     t        t        d        t        dgg g dgdt              } t        dgddggdt              }t        dd      gt        dd      t        dd      gg}t        dd      t        dd      t        dd      gg}t	        | |dt              ||fk(  sJ t        dgg g dgdt              } t        dgddggdt              }t        dd      gt        dd      t        dd      gg}t        dd      t        dd      t        dd      gg}t	        | |dt              ||fk(  sJ t        dgg g dgdt              } t        dgddggdt              }t        dd      gt        dd      t        dd      gg}t        dd      t        dd      t        dd      gg}t	        | |dt              ||fk(  sJ y )Nc                  2    t        ddgdggg gdt              S r  )r5   rJ   r`   r[   rY   r   z!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aAr"q!f,,,QCY'B/ARD1a&>1b)A
R)r"ay"Q(+,A
Q(Bq!HbAh	'(AaAr"q!f,,,QCY'B/AQC"a>1b)A
Q(bAh1a)*A
Q(Bq!HbAh	'(AaAr"q!f,,,r[   c                     g dg dg dddgf\  } }t        t              | |fk(  sJ t        t              | k(  sJ t        t              |k(  sJ t	        t
        fd       g dg dd	d
gg df\  } }t        t              | |fk(  sJ t        t              | k(  sJ t        t              |k(  sJ t	        t
        fd       y )NrT   rS   rR   rL   rM   rh   rT   r   r   r  rM   c                  &    t         t              S r  r9   rI   rr   s   rY   r   z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              S r  r  rr   s   rY   r   ztest_dup_div.<locals>.<lambda>  r  r[   )r6   rI   r8   r7   rK   rF   r  s     @@rY   test_dup_divr    s     )Z"a@JAq!Q1aA&&&1a!!!1a!!!
 ;<#_q"g?OOJAq!Q1aA&&&1a!!!1a!!!
 ;<r[   c                     g dg dg dddgf\  } }t        dt              | |fk(  sJ t        dt              | k(  sJ t        dt              |k(  sJ t	        t
        fd       dgggdggdggg ggdgggf\  } }t        dt              | |fk(  sJ t        dt              | k(  sJ t        dt              |k(  sJ t	        t
        fd	       y )
Nr  rh   r  r  rM   r   c                  (    t         dt              S )Nr   r=   rI   rr   s   rY   r   ztest_dmp_div.<locals>.<lambda>      	!Q2(> r[   rL   c                  (    t         dt              S )NrL   r  rr   s   rY   r   ztest_dmp_div.<locals>.<lambda>  r  r[   )r:   rI   r<   r;   rK   rF   r  s     @@rY   test_dmp_divr    s    )Z"a@JAq!Q1aBAq6)))1aB1$$$1aB1$$$
 >?3%QC51#,"1#7JAq!Q1aBAq6)))1aB1$$$1aB1$$$
 >?r[   c                      t        g t              dk(  sJ t        dgt              dk(  sJ t        g dt              dk(  sJ y )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                      t        g ggdt              dk(  sJ t        dgggdt              dk(  sJ t        t        dt              dk(  sJ y )NrL   r   rM   rU   )r?   rI   r^   r`   r[   rY   test_dmp_max_normr    sQ    "2&!+++1#B'1,,,Q#q(((r[   c                      t        g t              dk(  sJ t        dgt              dk(  sJ t        g dt              dk(  sJ y )Nr   rM   r  r   )r@   rI   r`   r[   rY   test_dup_l1_normr    sC    r2!###sB1$$$|R(B...r[   c                      t        g ggdt              dk(  sJ t        dgggdt              dk(  sJ t        t        dt              dk(  sJ y )NrL   r   rM   r?  )rA   rI   r^   r`   r[   rY   test_dmp_l1_normr    sQ    vq"%***!w2&!+++sAr"b(((r[   c                      t        g t              dk(  sJ t        dgt              dk(  sJ t        g dt              dk(  sJ y )Nr   rM   r  r   )rB   rI   r`   r[   rY   test_dup_l2_norm_squaredr    sC    r2&!+++sB'1,,,|R0B666r[   c                      t        g ggdt              dk(  sJ t        dgggdt              dk(  sJ t        t        dt              dk(  sJ y )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            	          t        dt              dgk(  sJ t        g dddgg dft              t        g dt        ddgg dt              t              k(  sJ y )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                      t        ddt              dggk(  sJ t        dgdgdggdgdggdgdgdgdggfdt              t        dgdgdggt        dgdggdgdgdgdggdt              dt              k(  sJ y )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$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   sympy.polys.polyerrorsrF   sympy.polys.specialpolysrG   r  rH   rI   rJ   sympy.testing.pytestrK   to_denser^   f_1f_2f_3f_4f_5f_6r_   rZ   ra   rd   rf   rj   rm   rt   rw   ry   r{   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rw  rz  r|  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rW   s   0rY   <module>r     s   : ,                > - * * '<CI$Gqajjl$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