
    Qi3                     <   d dl mZ d dlmZmZmZmZ d dl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# d Z$d Z%d Z&d Z'd	 Z(d
 Z)d Z*d Z+d Z,d Z-d Z.d Z/d Z0d Z1d Z2d Z3d Z4d Z5d Z6d Z7d Z8d Z9d Z:d Z;d Z<dS )    )Symbol)pquopremsturmsubresultants)Matrix)	sylvesterresres_qres_zbezoutsubresultants_sylvmodified_subresultants_sylvsubresultants_bezoutmodified_subresultants_bezoutbackward_eyesturm_pgsturm_q	sturm_amv	euclid_pgeuclid_q
euclid_amvmodified_subresultants_pgsubresultants_pgsubresultants_amv_qquo_zrem_zsubresultants_amvmodified_subresultants_amvsubresultants_remsubresultants_vvsubresultants_vv_2c            
         t          d          } t          | dz  dz
  d|           t          | dz  dz
  d| d          cxk    rt          dgg          k    sn J t          d| dz  dz
  |           t          d| dz  dz
  | d          cxk    rt          dgg          k    sn J t          | dz  dz
  d| d          t          dgg          k    sJ t          d| dz  dz
  | d          t          dgg          k    sJ t          | dz  dz
  d|                                           t          | dz  dz
  d| d                                          cxk    rdk    sn J t          d| dz  dz
  |                                           t          d| dz  dz
  | d                                          cxk    rdk    sn J t          | dz  dz
  d| d                                          dk    sJ t          d| dz  dz
  | d                                          dk    sJ t          dd|                                           t          dd| d                                          cxk    r/t          dd| d                                          cxk    rdk    sn J t          dd|                                           t          dd| d                                          cxk    r/t          dd| d                                          cxk    rdk    sn J t          | dz
  | d	z
  |           t          | dz
  | d	z
  | d          cxk    r6t          | dz
  | d	z
  | d          cxk    rt          dd
gddgg          k    sn J t          | dz  d| z  z
  dz   d| dz  z  dz
  |           t          | dz  d| z  z
  dz   d| dz  z  dz
  | d          cxk    r"t          g dg dg dg dg dg          k    sn J t          | dz  d| z  z
  dz   d| dz  z  dz
  | d          t          g dg dg dg dg dg dg          k    sJ d S )Nx      r         iW  i   i)r'   r   r&   r   )r   r'   r   r+   r&   )r%   r   r+   r   r   )r   r%   r   r+   r   )r   r   r%   r   r+   )r'   r   r+   r&   r   r   )r   r%   r   r+   r   r   )r   r'   r   r+   r&   r   )r   r   r%   r   r+   r   )r   r   r'   r   r+   r&   )r   r   r   r%   r   r+   )r   r	   r   detr$   s    /var/www/development/aibuddy-work/election-extract/venv/lib/python3.11/site-packages/sympy/polys/tests/test_subresultants_qq_zz.pytest_sylvesterr/      s   sAQT1Wa##yAq!Q'B'BSSSSfqcUmmSSSSSSQ1a##yAqD!GQ'B'BSSSSfqcUmmSSSSSSQT1WaA&&&1#--7777Q1aA&&&1#--7777QT1Wa##''))Yq!tQw1a-H-H-L-L-N-NUUUURUUUUUUUQ1a##''))Yq!Q$'1a-H-H-L-L-N-NUUUURUUUUUUUQT1WaA&&**,,4444Q1aA&&**,,3333Q1!!##yAq!'<'<'@'@'B'BffffiPQSTVWYZF[F[F_F_FaFaffffefffffffQ1!!##yAq!'<'<'@'@'B'BffffiPQSTVWYZF[F[F_F_FaFaffffefffffffQUAE1%%1q5!a%A)F)F  F  F  F  F)TUXYTY[\_`[`bcefJgJg  F  F  F  Fkqtuwysz}~  AC  }D  sE  lF  lF  F  F  F  F  F  FQTAaCZ!^Qq!tVaZ33yA!aQRSTVWSWQWZ[Q[]^`a7b7b  S  S  S  Sfl  oA  oA  oA  CU  CU  CU  Wi  Wi  Wi  k}  k}  k}  Q  Q  Q  nR  gS  gS  S  S  S  S  S  SQTAaCZ!^Qq!tVaZA66&   ...0F0F0FH^H^H^`v`v`v  yO  yO  yOBP ;Q ;Q Q Q Q Q Q Q    c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          |||           t          |||           k    sJ t          |||           d
         t          |||           k    sJ t          |||           t	          |||           k    sJ g d}t          |||           d t          |t          |||                     D             k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t	          |||           k    sJ d S )Nr$   r)      r%      r(      	      r'   r'   r7   r'   r7   r'   c                     g | ]
\  }}||z  S  r:   .0ijs      r.   
<listcomp>z+test_subresultants_sylv.<locals>.<listcomp>0        *q*q*q41a1Q3*q*q*qr0   r&   )r   r   r   r
   r   zipr   r$   pqamv_factorss       r.   test_subresultants_sylvrF   '   s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AaA&&-1a*@*@@@@@aA&&r*c!Qll::::aA&&*Q1*=*=====&&&KaA&&*q*q3{LfghjkmnLoLo;p;p*q*q*qqqqq	1qs
QA	!Q$
AaA&&*Q1*=*=======r0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }g d
}t          |||           d t          |t          |||                     D             k    sJ t          |||           d         t	          || dz  z   ||           k    sJ t          |||           t          |||           k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ t          | ||           t          | ||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z4test_modified_subresultants_sylv.<locals>.<listcomp><   s     3q3q3qDAqAaC3q3q3qr0   r7   r&   )r   r   rA   r   r   r   rB   s       r.    test_modified_subresultants_sylvrI   6   s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+A&&&K&q!Q//3q3qCUfghjkmnUoUoDpDp3q3q3qqqqq&q!Q//3uQAXq!7L7LLLLL&q!Q//9Q13E3EEEEE	1qs
QA	!Q$
A&q!Q//9Q13E3EEEEE&r1a00Iqb!Q4G4GGGGGGGr0   c                  R    t          d          } t          dd|           dk    sJ d S Nr$   r%   r4   r'   )r   r
   r-   s    r.   test_resrL   E   s.    sAq!Q<<1r0   c                  R    t          d          } t          dd|           dk    sJ d S rK   )r   r   r-   s    r.   
test_res_qrN   J   s.    sAAq>>Qr0   c                      t          d          } t          dd|           dk    sJ t          dd|           t          dd|           cxk    rt          dd|           k    sn J d S rK   )r   r   r
   r   r-   s    r.   
test_res_zrP   O   sq    sAAq>>Qq!Q<<5Aq>>;;;;U1a^^;;;;;;;;r0   c                  ^   t          d          } d| dz  z  d| dz  z  z   d| dz  z  z   d| z  z
  dz   }d	| d
z  z  d| dz  z  z   d| z  z   dz
  }t          ||| d                                          t          ||| d                                          k    sJ t          ||| d                                          t          ||| d                                          k    sJ t          ||| d          t	          d          t          ||| d          z  t	          d          z  k    sJ d S )Nr$   r4   r&   r%   r5   r(   r'   ir3   r6      bzprs)r   r   r,   r	   r   r$   rC   rD   s      r.   test_bezoutrW   U   s=   sA
1a4!Q$qAvac!!#AAqDAqDAaA!Q4  $$&&)Aq!Q*?*?*C*C*E*EEEEE!Q4  $$&&)Aq!Q*?*?*C*C*E*EEEEE!Q5!!\!__vaAt7L7L%L|\]%^^^^^^^r0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          |||           t          |||           k    sJ t          |||           d
         t          |||                                           k    sJ t          |||           t          |||           k    sJ g d}t          |||           d t          |t          |||                     D             k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r7   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z-test_subresultants_bezout.<locals>.<listcomp>g   s     ,s,s,sTQQqS,s,s,sr0   r&   )r   r   r   r	   r,   r   rA   r   rB   s       r.   test_subresultants_bezoutrZ   ^   s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+A1a((M!Q,B,BBBBB1a((,	!Q0B0B0F0F0H0HHHHH1a((Jq!Q,?,?????&&&K1a((,s,sSNhijlmopNqNq=r=r,s,s,sssss	1qs
QA	!Q$
A1a((Jq!Q,?,???????r0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }g d
}t          |||           d t          |t          |||                     D             k    sJ t          |||           d         t	          || dz  z   ||                                           k    sJ t          |||           t          |||           k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ t          | ||           t          | ||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z6test_modified_subresultants_bezout.<locals>.<listcomp>s   s     5s5s5sdaac5s5s5sr0   r7   r&   )r   r   rA   r   r	   r,   r   rB   s       r.   "test_modified_subresultants_bezoutr]   m   s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+A&&&K(Aq115s5sc+WhijlmopWqWqFrFr5s5s5sssss(Aq11"51q!t8QPQ9R9R9V9V9X9XXXXX(Aq11Yq!Q5G5GGGGG	1qs
QA	!Q$
A(Aq11Yq!Q5G5GGGGG(!Q22iAq6I6IIIIIIIr0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          |||           d
         t          ||| d                                          k    sJ g d}t          |||           d t	          |t          |||                     D             k    sJ d| dz  z  d| dz  z  z
  dz
  }d| dz  z  d| dz  z  z
  }t          ||| d          d
         t          ||| d                                          k    sJ t          |||           d
         t          ||| d                                          k    sJ t          | ||           d
         t          | || d                                          k    sJ t          | ||           t          | ||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r7   r'   r'   r7   r7   r'   r'   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z!test_sturm_pg.<locals>.<listcomp>   s      U U U11 U U Ur0      r'   )r   r   r	   r,   rA   r   r   r$   rC   rD   sam_factorss       r.   test_sturm_pgrf   |   s8   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AAq!R IaAq$9$9$=$=$?$?????&&&KAq! U UK1aQRASAS0T0T U U UUUUU
1a4!AqD&1AAqD2ad7AAq!Q#yAq!'<'<'@'@'B'BBBBBAq!R IaAq$9$9$=$=$?$?????QB1b!Yr1a%;%;%?%?%A%AAAAAQB1!:A2q!!D!DDDDDDDr0   c                      t          d          } | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |          k    sJ t          | | |           t          |           k    sJ d S )Nr$   r%   r&   r(   )r   r   r   rV   s      r.   test_sturm_qrh      s    sA	1qs
QA	!Q$
A1auQxx''''A2r1r******r0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          |||           d
         t          ||| d                                          k    sJ g d}t          |||           d t	          |t          |||                     D             k    sJ d| dz  z  d| dz  z  z
  dz
  }d| dz  z  d| dz  z  z
  }t          ||| d          d
         t          ||| d                                          k    sJ t          |||           d
         t          ||| d                                          k    sJ t          | ||           d
         t          | || d                                          k    sJ t          | ||           t          | ||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r7   r_   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z"test_sturm_amv.<locals>.<listcomp>   s     !W!W!W#!A!A#!W!W!Wr0   ra   rb   rc   r'   )r   r   r	   r,   rA   r   r   r   rd   s       r.   test_sturm_amvrk      s9   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AQ1b!Yq!Q%:%:%>%>%@%@@@@@&&&KQ1!W!W[*QPQSTBUBU1V1V!W!W!WWWWW
1a4!AqD&1AAqD2ad7AQ1a  $	!Q1(=(=(A(A(C(CCCCCQ1b!Yq!Q%:%:%>%>%@%@@@@@aRAr"iAq!&<&<&@&@&B&BBBBBQB1!:A2q!!D!DDDDDDDr0   c            
      0   t          d          } | dz  | dz  z   | dz  z
  | dz  z
  | dz  z   | z
  dz   }d| dz  z  d| dz  z  z   d| dz  z  z
  d| dz  z  z
  d| z  z   dz
  }t          |||           d         t          |||                                           k    sJ t          |||           t	          |||           k    sJ | d	z  | dz  z   d| dz  z  z
  d| dz  z  z
  d	| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d
| z  z
  dz   }t          |||           d         t          ||| d                                          k    sJ g d}t          |||           d t          |t          |||                     D             k    sJ d S )Nr$   r2   r4   r3   r%   r(   r'   r7   r)   r5   r6   r_   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z"test_euclid_pg.<locals>.<listcomp>   s     !U!U!U#!A!A#!U!U!Ur0   )r   r   r	   r,   r   rA   r   rd   s       r.   test_euclid_pgrn      s   sA	1QT	!Q$q!tAqD "1$A	!Q$qAva1fQq!tV#AaC')AQ1b!Yq!Q%7%7%;%;%=%=====Q1!1!Q!:!:::::	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AQ1b!Yq!Q%:%:%>%>%@%@@@@@&&&KQ1!U!U[(1aQRBSBS1T1T!U!U!UUUUUUUr0   c                      t          d          } | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           d         t          |          d          k    sJ d S )Nr$   r%   r&   r(   r7   )r   r   r   rV   s      r.   test_euclid_qrp      sg    sA	1qs
QA	!Q$
AAq!R U1XXb\M111111r0   c            
         t          d          } | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           d         t          |||                                           k    sJ t          |||           t	          |||           k    sJ | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   d	z
  }d| dz  z  d	| dz  z  z   d| dz  z  z
  d
| z  z
  dz   }t          |||           d         t          ||| d                                          k    sJ g d}t          |||           d t          |t          |||                     D             k    sJ d S )Nr$   r%   r&   r(   r7   r)   r2   r3   r4   r5   r6   r_   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z#test_euclid_amv.<locals>.<listcomp>   s     "W"W"W31Q1Q3"W"W"Wr0   )r   r   r	   r,   r   rA   r   rd   s       r.   test_euclid_amvrs      s   sA	1qs
QA	!Q$
AaAr"i1a&8&8&<&<&>&>>>>>aA"3Aq!"<"<<<<<	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AaAr"i1a&;&;&?&?&A&AAAAA&&&KaA"W"W#k9QPQSTCUCU2V2V"W"W"WWWWWWWr0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }g d
}t          |||           d t          |t          |||                     D             k    sJ t          |||           d         t	          || dz  z   ||                                           k    sJ t          |||           t          |||           k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ t          | ||           t          | ||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z2test_modified_subresultants_pg.<locals>.<listcomp>   s     1n1n1n$!Q!A#1n1n1nr0   r7   r&   )r   r   rA   r   r	   r,   r   rB   s       r.   test_modified_subresultants_pgrv      s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+A&&&K$Q1--1n1n#kScdeghjkSlSlBmBm1n1n1nnnnn$Q1--b1Yq1a4xA5N5N5R5R5T5TTTTT$Q1--!Q1B1BBBBB	1qs
QA	!Q$
A$Q1--!Q1B1BBBBB$aRA..(A2q!2D2DDDDDDDr0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          |||           t          |||           k    sJ t          |||           d
         t          |||                                           k    sJ t          |||           t          |||           k    sJ g d}t          |||           d t          |t          |||                     D             k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r7   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z)test_subresultants_pg.<locals>.<listcomp>        (o(o(oA1(o(o(or0   r&   )r   r   r   r	   r,   r   rA   r   rB   s       r.   test_subresultants_pgrz      s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AAq!$$aA(>(>>>>>Aq!$$R(IaA,>,>,B,B,D,DDDDDAq!$$	!Q(:(:::::&&&KAq!$$(o(o[JdefhiklJmJm9n9n(o(o(ooooo	1qs
QA	!Q$
AAq!$$	!Q(:(:::::::r0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          |||           t          |||           k    sJ t          |||           d
         t          |||                                           k    sJ t          |||           t          |||           k    sJ g d}t          |||           d t          |t          |||                     D             k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r7   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z,test_subresultants_amv_q.<locals>.<listcomp>   s     +r+r+rDAqAaC+r+r+rr0   r&   )	r   r   r   r	   r,   r   rA   r   r   rB   s       r.   test_subresultants_amv_qr}      s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+Aq!Q''=Aq+A+AAAAAq!Q''+yAq/A/A/E/E/G/GGGGGq!Q'':aA+>+>>>>>&&&Kq!Q''+r+rCMghiklnoMpMp<q<q+r+r+rrrrr	1qs
QA	!Q$
AQ1%%Aq!)<)<<<<<<<r0   c                     t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          || |           t          || |           k    sJ d S )
Nr$   r)   r2   r%   r3   r(   r4   r5   r6   )r   r   r   rV   s      r.   
test_rem_zr      s    sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AQB??d1qb!nn,,,,,,r0   c                     t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          || |           t          || |           k    sJ t          d
          }d| dz  z  d|dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          || |           t          || |           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   y)r   r   r   )r$   rC   rD   r   s       r.   
test_quo_zr     s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AQB??d1qb!nn,,,,sA	!Q$1a4!AqD& 1Q3&+AQB??d1qb!nn,,,,,,r0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          |||           t          |||           k    sJ t          |||           d
         t          |||                                           k    sJ t          |||           t          |||           k    sJ g d}t          |||           d t          |t          |||                     D             k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r7   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z*test_subresultants_amv.<locals>.<listcomp>       )p)p)p$!Q!A#)p)p)pr0   r&   )r   r   r   r	   r,   r   rA   r   rB   s       r.   test_subresultants_amvr        sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AQ1%%q!Q)?)?????Q1%%b)Yq!Q-?-?-C-C-E-EEEEEQ1%%Aq!)<)<<<<<&&&KQ1%%)p)p#kKefgijlmKnKn:o:o)p)p)ppppp	1qs
QA	!Q$
AQ1%%Aq!)<)<<<<<<<r0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }g d
}t          |||           d t          |t          |||                     D             k    sJ t          |||           d         t	          || dz  z   ||                                           k    sJ t          |||           t          |||           k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ t          | ||           t          | ||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z3test_modified_subresultants_amv.<locals>.<listcomp>$  s     2p2p2p41a1Q32p2p2pr0   r7   r&   )r   r   rA   r   r	   r,   r   rB   s       r.   test_modified_subresultants_amvr     s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+A&&&K%aA..2p2p3{TefgijlmTnTnCoCo2p2p2ppppp%aA..r2iAqD!Q6O6O6S6S6U6UUUUU%aA..)Aq!2D2DDDDD	1qs
QA	!Q$
A%aA..)Aq!2D2DDDDD%qb!Q//9aRA3F3FFFFFFFr0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          |||           t          |||           k    sJ t          |||           d
         t          |||                                           k    sJ t          |||           t          |||           k    sJ g d}t          |||           d t          |t          |||                     D             k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r7   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z*test_subresultants_rem.<locals>.<listcomp>7  r   r0   r&   )r   r    r   r	   r,   r   rA   r   rB   s       r.   test_subresultants_remr   .  r   r0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          |||           t          |||           k    sJ t          |||           d
         t          |||                                           k    sJ t          |||           t          |||           k    sJ g d}t          |||           d t          |t          |||                     D             k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r7   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z)test_subresultants_vv.<locals>.<listcomp>G  ry   r0   r&   )r   r!   r   r	   r,   r   rA   r   rB   s       r.   test_subresultants_vvr   >  s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AAq!$$aA(>(>>>>>Aq!$$R(IaA,>,>,B,B,D,DDDDDAq!$$
1a(;(;;;;;&&&KAq!$$(o(o[JdefhiklJmJm9n9n(o(o(ooooo	1qs
QA	!Q$
AAq!$$
1a(;(;;;;;;;r0   c            
         t          d          } | dz  | dz  z   d| dz  z  z
  d| dz  z  z
  d| dz  z  z   d| z  z   dz
  }d| dz  z  d| dz  z  z   d| dz  z  z
  d| z  z
  d	z   }t          |||           t          |||           k    sJ t          |||           d
         t          |||                                           k    sJ t          |||           t          |||           k    sJ g d}t          |||           d t          |t          |||                     D             k    sJ | dz  d| z  z
  dz   }d| dz  z  dz
  }t          |||           t          |||           k    sJ d S )Nr$   r)   r2   r%   r3   r(   r4   r5   r6   r7   r8   c                     g | ]
\  }}||z  S r:   r:   r;   s      r.   r?   z+test_subresultants_vv_2.<locals>.<listcomp>W  r@   r0   r&   )r   r"   r   r	   r,   r   rA   r   rB   s       r.   test_subresultants_vv_2r   N  s   sA	1q!ta1fqAv%!Q$.14q8A	!Q$1a4!AqD& 1Q3&+AaA&&-1a*@*@@@@@aA&&r*i1a.@.@.D.D.F.FFFFFaA&&*Q1*=*=====&&&KaA&&*q*q3{LfghjkmnLoLo;p;p*q*q*qqqqq	1qs
QA	!Q$
AaA&&*Q1*=*=======r0   N)=sympy.core.symbolr   sympy.polys.polytoolsr   r   r   r   sympy.matricesr   sympy.polys.subresultants_qq_zzr	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r/   rF   rI   rL   rN   rP   rW   rZ   r]   rf   rh   rk   rn   rp   rs   rv   rz   r}   r   r   r   r   r   r   r   r:   r0   r.   <module>r      s   $ $ $ $ $ $ D D D D D D D D D D D D ! ! ! ! ! !* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *Q Q Q0> > >H H H  
  
< < <_ _ _@ @ @J J JE E E + + +E E E"V V V2 2 2X X XE E E ; ; ; = = = - - -	- 	- 	-= = = G G G = = = < < < > > > > >r0   