o
    3Ih{                     @   sR  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lImJZJmKZKmLZL ddlMmNZNmOZOmPZPmQZQ ddlRmSZS eKd	ZTd
d eJ D \ZUZVZWZXZYZZZ[eeeUdePePdddePZ\dd Z]dd Z^dd Z_dd Z`dd Zadd Zbdd Zcdd Zddd  Zed!d" Zfd#d$ Zgd%d& Zhd'd( Zid)d* Zjd+d, Zkd-d. Zld/d0 Zmd1d2 Znd3d4 Zod5d6 Zpd7d8 Zqd9d: Zrd;d< Zsd=d> Ztd?d@ ZudAdB ZvdCdD ZwdEdF ZxdGdH ZydIdJ ZzdKdL Z{dMdN Z|dOdP Z}dQdR Z~dSdT ZdUdV ZdWdX ZdYdZ Zd[d\ Zd]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr Zdsdt Zdudv ZdwS )xz4Tests 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SymbolPoly)FFZZQQCC)raisesxc                 C   s   g | ]}|  qS  )to_dense).0frO   rO   a/home/air/sanwanet/gpt-api/venv/lib/python3.10/site-packages/sympy/polys/tests/test_densearith.py
<listcomp>3   s    rT            c                  C   s  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s8J t| tddtt g dtksJJ t g dt} t| tddtt g dtkscJ t| tddtt g dtksuJ t| tddtt g dtksJ t| tdd	tt g d
tksJ t| tddtt g dtksJ t| tddtt g dtksJ t| tddtt g dtksJ t| tddtt ddgtksJ d S )Nr   rV   rU   rV   r   r   rV   rV   rV   )rV   rV   rU   )rV   rU   rV   )rU   rV   rV      )rV   rV   rV   rV      )rV   r   rV   rV   rV      )rV   r   r   rV   rV   rV      )rV   r   r   r   rV   rV   rV   )r   rJ   r   rR   rO   rO   rS   test_dup_add_term6   $   
 "$$$$$$$$(r`   c                   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 tg gddttks4J t tg gddttksAJ d S NrV   rU   r   rZ   )r   rJ   r   f_0F_0rK   rO   rO   rO   rS   test_dmp_add_termN   
   $"rf   c                  C   s  t g t} t| tddtt g tksJ t| tddtt dgtks&J t| tddtt ddgtks8J t| tddtt g dtksJJ t g dt} t| tddtt g dtkscJ t| tddtt g dtksuJ t| tddtt g d	tksJ t| tdd
tt g dtksJ t| tddtt g dtksJ t| tddtt g dtksJ t| tddtt g dtksJ t| tddtt ddgtksJ d S )Nr   rV   r^   rU   )r^   r   r   rY   )rV   rV   r^   )rV   r^   rV   )r^   rV   rV   rZ   )r^   rV   rV   rV   r[   )r^   r   rV   rV   rV   r\   )r^   r   r   rV   rV   rV   r]   )r^   r   r   r   rV   rV   rV   )r   rJ   r   r_   rO   rO   rS   test_dup_sub_termU   ra   rh   c                   C   rb   rc   )r   rJ   r   rd   re   rK   rO   rO   rO   rS   test_dmp_sub_termm   rg   ri   c                  C   s   t g t} t| tddtt g tksJ t ddgt} t| tddtt g tks,J t g dt} t| tddtt g dtksEJ t| tddtt g dtksWJ t| tddtt g dtksiJ t| tddtt g d	tks{J d S )
NrU   rZ   rV   r   rV   rU   rZ   rU   r[   r]   )rU   r[   r]   r   )rU   r[   r]   r   r   )rU   r[   r]   r   r   r   )r   rJ   r	   r_   rO   rO   rS   test_dup_mul_termt   s   
  $$$(rl   c                   C   s  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s8J t tdggg ddtg gksIJ 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spJ t g gtddgddtg gksJ t tddggg ddtg gksJ 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sJ d S )	NrV   rU   rZ   r   r[   r]   r\      )r
   rJ   r	   rK   rO   rO   rO   rS   test_dmp_mul_term   s   $"""*$$2"rn   c                  C   8   t g d} t g d}t| t dt |ksJ d S )NrV   rU   rZ   r[   )rV   rU   rZ      r[   )rJ   mapr   rR   grO   rO   rS   test_dup_add_ground      ru   c                  C   sR   t dgdgdgdgg} t dgdgdgdgg}t| t ddt |ks'J d S )NrV   rU   rZ   r[   rq   )rJ   rr   r   rs   rO   rO   rS   test_dmp_add_ground   s   rw   c                  C   ro   )Nrp   )rV   rU   rZ   r   r[   )rJ   rr   r   rs   rO   rO   rS   test_dup_sub_ground   rv   rx   c                  C   sP   t dgdgdgdgg} t dgdgdgg g}t| t ddt |ks&J d S )NrV   rU   rZ   r[   )rJ   rr   r   rs   rO   rO   rS   test_dmp_sub_ground   s   ry   c                  C   sz   t g t} t| tdtt g tksJ t g dt} t| tdtt g tks*J t| tdtt g dtks;J d S )NrU   rj   r   rk   )r   rJ   r   r_   rO   rO   rS   test_dup_mul_ground   s
   
&rz   c                	   C   s  t ttddttdtdtdgtdggtdggtdtdtdgtdtdtdgtdgggks:J t ttdddttddtddtd	dgtddggtd	dggtddtd
dtddgtddtddtddgtddgggksJ d S )NrU   r[   r]   rq   
      rV      rZ   r\   )r   rd   rJ   re   rK   rO   rO   rO   rS   test_dmp_mul_ground   s   
2
&*
r~   c                  C   s$  t td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sPJ tg dt} t| tdt| kscJ t| tdttdtdtd	gksxJ t| td
ttdd
tdd
tdd
gksJ d S )Nc                   S      t tg dttdtS Nrj   r   )r   r   rJ   rO   rO   rO   rS   <lambda>   
   
 z%test_dup_quo_ground.<locals>.<lambda>rZ   r]   rU   rq   rV   rU   rZ   rV   r[   )rU   r   rU   r[   rW   r]   rq   )rM   ZeroDivisionErrorr   rJ   r   rK   r_   rO   rO   rS   test_dup_quo_ground   s   
""*4r   c                  C   s  t tdd  t tdd  tg t} t| tdttg tks"J tg dt} t| tdt| ks5J t| tdttg dtksFJ tg dt} t| tdt| ksYJ t| tdttdtdtd	gksnJ t| td
ttdd
tdd
tdd
gksJ d S )Nc                   S   r   r   r   r   rJ   rO   rO   rO   rS   r      r   z'test_dup_exquo_ground.<locals>.<lambda>c                   S   r   )Nrj   rZ   r   rO   rO   rO   rS   r      r   rZ   r   rV   rU   r   r[   rW   r]   rq   )rM   r   rE   r   rJ   r   rK   r_   rO   rO   rS   test_dup_exquo_ground   s   
"*4r   c                  C   s   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s0J t t| tddtdtt dgg dggdtksJJ d S Nr]   rU   rq   rV   rZ   r[   )r   rJ   r   r_   rO   rO   rS   test_dmp_quo_ground   s   r   c                  C   sd   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s0J d S r   )r   rJ   r   r_   rO   rO   rS   test_dmp_exquo_ground  s   r   c                   C   s2   t g dtg ks
J t dgdtg dksJ d S )NrZ   rV   rV   r   r   r   )r   rJ   rO   rO   rO   rS   test_dup_lshift     r   c                   C   s2   t g dtg ks
J t g ddtdgksJ d S )NrZ   r   rV   )r   rJ   rO   rO   rO   rS   test_dup_rshift  r   r   c                   C   s   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sBJ t g tg ksKJ t tddgttddgks\J t tddgttddgksmJ t tddtddtddgttddtddtddgksJ d S )NrV   rW   r^   rU   rZ   )r   rJ   rK   rO   rO   rO   rS   test_dup_abs  s   6""r   c                   C   s(  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s0J t tdgggdttdgggksDJ t tdgggdttdgggksXJ t g ggdtg ggksfJ 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sJ d S Nr^   r   rV   rU   r   rW   	   )r   rJ   rK   rO   rO   rO   rS   test_dmp_abs"      $((,0r   c                   C   s   t g tg ks	J t tdgttdgksJ t tdgttdgks'J t tdtdtdgttdtdtdgksBJ t g tg ksKJ t tddgttddgks\J t tdd	gttdd	gksmJ t tddtddtddgttddtddtddgksJ d S )
NrV   r^   r   rW   rU   rZ   r   )r   rJ   rK   rO   rO   rO   rS   test_dup_neg/  s    6""r   c                   C   s(  t tdgdttdgksJ t tddgdttddgks"J t g ggdtg ggks0J t tdgggdttdgggksDJ t tdgggdttdgggksXJ t g ggdtg ggksfJ t tddgggdttddgggks|J t tddgggdttddgggksJ d S r   )r   rJ   rK   rO   rO   rO   rS   test_dmp_neg<  r   r   c                   C   s  t g g tg ks
J t tdgg ttdgksJ t g tdgttdgks*J t tdgtdgttdgks=J t tdgtdgttdgksPJ t tdtdgtdgttdtdgksiJ t tdgtdtdgttdtdgksJ t tdtdtdgtdtdtdgttdtdtdgksJ t g g tg ksJ t tddgg ttddgksJ t g tddgttddgksJ t tdd	gtdd	gttddgksJ t tdd	gtddgttdd	gksJ t tddtddgtdgttddtd
dgks J t tdgtddtddgttddtd
dgks>J t tddtddtddgtddtddtddgttddtddtddgksmJ d S )NrV   rU   rZ   rq   r   r{         r[   r\   rW   )r   rJ   rK   rO   rO   rO   rS   test_dup_addI  s@     &&22
$$,.<<r   c                   C   st  t tdtdgtdgdtttdtdgtdgtks!J t tddtddgtdgdtttddtddgtdgtksFJ t g ggg ggdtg ggksWJ t tdgggg ggdttdgggksnJ t g ggtdgggdttdgggksJ t tdgggtdgggdttdgggksJ t tdgggtdgggdttdgggksJ t g ggg ggdtg ggksJ t tddgggg ggdttddgggksJ t g ggtddgggdttddgggksJ t tddgggtddgggdttddgggksJ t tddgggtddgggdttddgggks8J d S )NrV   rU   r   rZ   rW   )r   rJ   r   rK   rO   rO   rO   rS   test_dmp_addc      " "..44"22<@r   c                   C   s  t g g tg ks
J t tdgg ttdgksJ t g tdgttdgks*J t tdgtdgtg ks:J t tdgtdgttdgksMJ t tdtdgtdgttdtdgksfJ t tdgtdtdgttdtdgksJ t tdtdtdgtdtdtdgttdtd	td
gksJ t g g tg ksJ t tddgg ttddgksJ t g tddgttddgksJ t tddgtddgtg ksJ t tddgtddgttddgksJ t tddtddgtdgttddtddgksJ t tdgtddtddgttddtddgks6J t tddtddtddgtddtddtddgttddtd	dtd
dgkseJ d S )NrV   r^   rU   rZ   rq   r   r{   r   rW   r\   )r   rJ   rK   rO   rO   rO   rS   test_dup_subv  s@      &22
$$$,<<r   c                   C   st  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sFJ t g ggg ggdtg ggksWJ t tdgggg ggdttdgggksnJ t g ggtdgggdttdgggksJ t tdgggtdgggdttdgggksJ t tdgggtdgggdttdgggksJ t g ggg ggdtg ggksJ t tddgggg ggdttddgggksJ t g ggtddgggdttddgggksJ 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s8J d S )NrV   rU   r   rZ   r^   rW   )r   rJ   r   rK   rO   rO   rO   rS   test_dmp_sub  r   r   c                   C   s   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skJ d S )NrV   rU   rZ   r   rW   r\   r[   )r%   rJ   r&   rO   rO   rO   rS   test_dup_add_mul     *2&r   c                   C   s   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skJ d S )	NrV   rU   rZ   r   r   r^   r   )r'   rJ   r(   rO   rO   rO   rS   test_dup_sub_mul  r   r   c                  C   s~  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s7J t tdgtdgttdgksJJ t g g tg ksTJ t g tddgtg ksbJ t tddgg tg kspJ t tddgtddgttddgksJ t tddgtddgttdd	gksJ tg d
t} tg dt}tg dt}t | |t|ksJ t || t|ksJ tg dt} tg dt}t | | t|ksJ td}t |d|dg|d|dg||d|dgksJ 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 d S )NrV   r\   rW   #   rU   r[   rZ   rm   1   )rZ   r   r   r]   rV   rU   )r[   r   rV   r   )	r|   r   rZ      r[   r}   rV   rU   r   rU   r   r   rV   rW   	r[   r   r   r[      r   rV   r}   r   r]   )O   r^   N   r       r   rU      I   *   U   M   S   r   _   %   r   r   C      L   rU   F   r   A   9   r   r   a   Y   !   r   Q   r   <   +      ,      r   r   r   rZ   5      r   B   rV   r   b   r   r]   rq   r   r|      r      r   7   r   D   r   T   ^   -   r   \   r   r   r   rq   K   r   [   r   "   r}   r   r   r   r   r]   r      r   :   r      r   r   rW   r   r   r  r   r   r   r   r\   3   r   r  r   r   r   r   R   r   r   r   r   r   r  r   r   r  ?   r   r   r]   r   r   rZ   rZ   .   r  >   X   r   r  r^   r   H   r}   r	  r  r   r   r   r   r  r   r   r   r   d   r  r   r   r   r#  4   V   r   r   r  r   r   r  r   r   r  (\  r   r   rV   Z   r   r   r      r   r   2   r   r      rV   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   r"  r  r   r   r   r#  r   r  r   r   r  r	  r   r   r  r\   r(  r   r   r  r  r   r   r   r   0   r   r   r   r   r{   r   r  r   =   r   r  r   r2  r   r   r   rU   r]   r   r  r   r:  r   r  r<  r^   r6  `   r   r   r   8   r  r   r  r@  r*  r  r   r   r   r   r  r   r   r   r2  (   r   r   r   r#  r  r   r  '   r  r   r}   W   @   r   r  r   rm   r  r   r   r   r   6   rA  r   r]   r'  r  r<  r   rG  r   r   r   r   r   r   r   r   r6  r   $   r   r\   r*  r  r2  r%  r)  r   ir   r   r   r  r[   rC  rH  r   r   r   r   r   r   r6  r$  r   r   r  r  rJ  r   r   r8  r   r   r   r3  r  r  r   r-  r   r!  r  r   r   r(  r  r  r'  r   r   rC  r   &   r   rL  r#  r   r   rG  r  r  r      r   r   r   r   r&  r   r   r|   r|   r   r.  rJ  r9  r  r-  r-  r(  r  r   r  rJ  r  r   r   r   r   r   r   r   rV   r   r   rq   rq   r?  r   r   r   r9  r   r   r  r   r   r1  r1  r\   r   r   r  rD  r   r\   r   rH  r   r0  r  rJ  r   r   r5  r   r   r.  r   r   r   r  rF  r   r  r   r  r  r   r   r%  r   r(  r   r   r   rN  r   r   r  r  r   r   r   rM  r   r|   r
  r   r  r   r   r   r#  rq   r  r   r   r   (C  i  ii`  ii  i-  iA  iigiiY  ii_  iOi.  iin%  i0$  io  i[  i	J  i5'  i\ii*  ii?i  i*  iizi?  iDz  i`  i|  i  i  ii  i=  is  i  i|  i  ivki}i%  rP  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$iZi  iQ  i9i%}  5ig  ivF  i;if|  ii4ii0  ib  i&Mi^  i'iHi>iiTiߟir4  iuii'  ixiciL  iilg  iiU  i  ip  iXi  i  i0  i5i,  i iCi7  i  ibi/ i_  iYir  i  iM6  iiS  ii|d i  iY ii ii  iPi#i<  iii  i+  ii  i  iiii9i0|iiibiE  itiy  ii:  id  i ii iii  iwi% iW i  iiiiHxii*Fi[iiuUi+iieiy;  izi+  ii<i  i  i/8  iiihihsi  ii, iPi  i#  ibcii3  i*  iI6i&  i6/  iij ioiiѶiI  i?  i)  iii)  iii  iN  ii i߷  i  iϱ  ii<D  i!i1 iiwiix  isw i!  i]  ii}  i[  i  iiyai  io  i1zi'aidaimiVi  iiԔ i iiiIviJ
  i/  i iVK  ixii&i$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rQ  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%iWrT  iU  ild  i   i  ii  iQ  iN  iX  i-  i3  i	  ii7iEii8i  iiiirii  i	  i  ii|)r   r5  r   r6  r|   r   r   r   r   r   rD  r.  r   r   r   r   r   r[   r   r]   r   r   r   r   i/   r  r  r%  r   r   r   r,  r2  r6  rE  r   r   r  r)  r^   rB  r   r   r   r   r   r  r2  r   r   r   r   r4  r  r|   r   r   ir   r  r>  r5  r*  rV   G   r[   r|   r9  r[   r  r(  r   r\   r9  r  r  r   r   r   r  r   r9  r5  r   rV  r   r   rD  r   r  r   r  r   r   r  rN  r   r)  r  r   r@  r  r   rB  r?  r  r8  r   r   r  r   r  rN  r   r   r   r-  r   r   rZ   rJ  r9  r   r6  r   r   r   r   r   r4  r  r&  r}   r8  r   r"  r   r  rF  r&  r   r   r  r   r  r   r|   r   ;   r   c   r   r   r   r  r   r   rV   r  r  r/  r   r(  r   r   r   rE  r  r   r   r{   r   rA  rK  r3  rD  r   r   r  r   r  r   r   r   r>  rF  rX  r   r   r   r5  r   r   r   r5  r[   r   r   r?  r  r   r   r   r   r   r}   r"  r   r   r8  r   r   r   r#  r'  r   r@  r   rZ   rA  r   r   r  r   r   r   r0  rC  r  r   r   r  r  r>  r   r   r9  r   r9  r   r   r   (+  r$  r  r   r   r   r  r  r   r   r4  r   r@  rM  r   r   r   r   r   r   r  r   r   r*  r   r.  r   r  r[   rV  r   r   r   rX  r.  r  rY  r  r4  rE  r   r  r   rE  rX  r   r8  r   r   rC  r  r[   r   r  r   r   r>  r   rZ      r@  rI  r   r   r   r]   r   r   rB  r   r"  rH  r   rX  r   r   rG  r   rJ  r1  r   r*  r   r   r   r   r   r   r   r   rW  r   r  r=  r@  r  rq   r^   r@  r   r   r   r   rJ  rW  r   r   r   r!  rY  r$  rK  r\   rG  r   r8  r:  r   r  r#  r  r  r&  rD  r   r   rV   r   rO  r$  r   r  rZ   r|   r   r   r  r7  r   r   r   r   r   r   r\   r   r   ]   r   r  r*  r.  r   r]  rY  r'  r   r  r   r   r  r?  r   r   r   r]  r   r   r   r[  r   r   r  r   r   rL  r1  r   r%  r   r*  r   r   rV  r  r  r   r!  r   r'  r  r  r   r   r   r]   r   r   r   rm   r   r]  r   r  r  r"  r*  r   r)  rX  rE  r   r   r[  r   r   r7  r;  r<  r+  r   r\   r   rZ  r   r   r  r   r   r   r   r   r  rM  r   r"  r'  r-  rV   r   r   r  r   r9  r)  r  r   r   rI  rM  r   r?  r   r   r-  r   r*  r   r   r   r  r<  r  rZ   r   r   rU   r:  r   r   r   r  r   r   r   r'  r   r[   r&  r   r)  r$  r  rN  r   r-  rX  r   rY  r  r   r\  r7  r   r   r   rJ  rO  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&iieiirU  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{rS  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  iPrR  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   rJ   rK   r   rI   )rR   rt   hKp1p2resrO   rO   rS   test_dup_mul  sP   &&,,8=?8:re  c                  C   s  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sKJ 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ssJ t tdgggtdgggdttdgggksJ t tdgggtdgggdttdgggksJ t g ggg ggdtg ggksJ t tddgggg ggdtg ggksJ t g ggtddgggdtg ggksJ t tddgggtddgggdttddgggksJ 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sEJ d S )
Nr\   rW   r   rZ   rU   rV   r   r]   r[   )r    rJ   r   rK   rI   ra  rO   rO   rS   test_dmp_mul  s,   "((44"**:<(rg  c                  C   s.  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s0J t g tg ks9J t tddgttddgksJJ t tddtddgttddtddtddgksgJ tg dt} t | ttg dtks|J td}t |d|dg||d|d	gksJ d S )
NrU   r[   rV   rZ   r   r   r   r]   rW   )r!   rJ   rK   r   rI   )rR   ra  rO   rO   rS   test_dup_sqr  s   0":.rh  c                  C   s   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sIJ 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 d S )	NrV   rU   r   r[   rZ   r   r]   rW   )r"   rJ   r!   rK   rI   rf  rO   rO   rS   test_dmp_sqr  s   (,8ri  c                  C   s  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$J t g dtg ks.J t tdgdttdgks>J t tdgdttdgksNJ t tdgdttdgks^J t tdgdttdgksnJ t tdgdttdgks~J t tdgdttdgksJ t tddgdttddgksJ t tddgdttddgksJ t tddgdttddgksJ t tddgdttddgksJ t tddgdttddgksJ t tddgdttddgksJ tg dt} t | dttdgtksJ t | dttg dtks J t | dttg d	tks0J t | dttg d
tks@J d S )Nr   rV   rW   rZ      r   rU   r   )rq   r   r   r|   r   r   r]   r   i&  rV   r      iW  )r#   rJ   rK   r   r_   rO   rO   rS   test_dup_pow  s.         $$$$$$  rm  c                  C   s  t g gddttdggksJ t g gddttdggks J t g gddtg gks-J t g gddtg gks:J t tdggddttdggksMJ t tdggddttdggks`J t tdggddttdggkssJ t tddggddttddggksJ t tddggddttddggksJ t tddggddttddggksJ tg dt} t | ddtt| dtksJ d S )	Nr   rV   rW   rZ   rj  rk  r   rU   )r$   rJ   rK   r   r#   r_   rO   rO   rS   test_dmp_pow  s     &&&***"rn  c                     s  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s2J t t|ks<J tt fdd t g dt t g dtt ddgt} t ddgt}t t| |fksnJ t t| ksxJ t t|ksJ tt fd	d d S )
NrZ   rV   rV   r\   r\   r   rV   rm   r}   r$  o   c                         t  tS N)r,   rJ   rO   rs   rO   rS   r         ztest_dup_pdiv.<locals>.<lambda>c                      rr  rs  )r,   rK   rO   rs   rO   rS   r     rt  )r   rJ   r)   r+   r*   rM   rE   rK   qrrO   rs   rS   test_dup_pdiv  s    rx  c                     sd  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s8J t dt| ksCJ t dt|ksNJ tt fd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sJ t dt| ksJ t dt|ksJ tt fdd d S )NrV   rX   r^   r   rU   r   r   c                         t  dtS NrV   r0   rJ   rO   rs   rO   rS   r   &      ztest_dmp_pdiv.<locals>.<lambda>rU   r   )rq   r   r   c                      rz  r{  r|  rO   rs   rO   rS   r   2  r}  )r   rJ   r-   r/   r.   rM   rE   ru  rO   rs   rS   test_dmp_pdiv  s    r~  c                  C   sP   t tdd  tg dt} tg dt}g | }}t| |t||fks&J d S )Nc                   S      t g dg tS Nrj   )r1   rJ   rO   rO   rO   rS   r   6      z!test_dup_rr_div.<locals>.<lambda>ro  rp  )rM   r   r   rJ   r1   rR   rt   rv  rw  rO   rO   rS   test_dup_rr_div5  s
   
r  c                  C   sF  t td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swJ 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sJ d S )
Nc                   S      t ddgdggg gdtS NrV   rU   rZ   )r2   rJ   rO   rO   rO   rS   r   A      z!test_dmp_rr_div.<locals>.<lambda>rV   rX   r^   r   ry  rU   r   )rM   r   r   rJ   r2   r  rO   rO   rS   test_dmp_rr_div@  s   r  c                  C   sn   t td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s5J d S )Nc                   S   r  r  )r3   rK   rO   rO   rO   rS   r   \  r  z!test_dup_ff_div.<locals>.<lambda>ro  rp  rZ   r\   r}   r*  r$  rq  )rM   r   r   rK   r3   r  rO   rO   rS   test_dup_ff_div[  s   r  c                  C   s   t dkrd S 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swJ d S )Ngmpy2r   )mpq)GMPYRationalFieldrV   rZ   rU   r]   r[   r\   r^   r   rW   r|   r   r   )r   r  r  sympy.polys.domainsr  r4   )r  r  ra  rR   rt   rO   rO   rS   test_dup_ff_div_gmpy2f  s   *$>r  c                  C   s  t tdd  tdgg g dgdt} tdgddggdt}tddgtddtddgg}tddtddtddgg}t| |dt||fksJJ tdgg g dgdt} tdgddggdt}tddgtddtddgg}tddtddtddgg}t| |dt||fksJ tdgg g dgdt} tdgddggdt}tddgtddtddgg}tddtddtddgg}t| |dt||fksJ d S )	Nc                   S   r  r  )r4   rK   rO   rO   rO   rS   r   w  r  z!test_dmp_ff_div.<locals>.<lambda>rV   rX   r^   r   rU   r   )rM   r   r   rK   r4   r  rO   rO   rS   test_dmp_ff_divv  s       r  c                     s   g dg dg dddgf\ } }t  t| |fksJ t t| ks(J t t|ks2J tt fdd g dg d	d
dgg df\ } }t  t| |fksZJ t t| ksdJ t t|ksnJ tt fdd d S )Nr\   r[   rZ   rU   rV   rj   r\   r  r   r
  rV   c                      rr  rs  r8   rJ   rO   rs   rO   rS   r     rt  ztest_dup_div.<locals>.<lambda>)r\   r[   rZ   rU   rV   r   )rV   rU   r   r   r   r\   r  )rm   rU   r   rI  c                      rr  rs  r  rO   rs   rO   rS   r     rt  )r5   rJ   r7   r6   rM   rE   ru  rO   rs   rS   test_dup_div  s   $$r  c                     s
  g dg dg dddgf\ } }t  dt| |fksJ t dt| ks*J t dt|ks5J tt fdd dgggd	ggdggg ggdgggf\ } }t  d	t| |fkscJ t d	t| ksnJ t d	t|ksyJ tt fd
d d S )Nr  rj   r  r
  rV   r   c                      rz  )Nr   r<   rJ   rO   rs   rO   rS   r     r}  ztest_dmp_div.<locals>.<lambda>rU   c                      rz  )NrU   r  rO   rs   rO   rS   r     r}  )r9   rJ   r;   r:   rM   rE   ru  rO   rs   rS   test_dmp_div  s   $.r  c                   C   @   t g tdks	J t dgtdksJ t g dtdksJ d S )Nr   rV   rV   r[   rU   rZ   r[   )r=   rJ   rO   rO   rO   rS   test_dup_max_norm  s   r  c                   C   J   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 d S )NrU   r   rV   r]   )r>   rJ   rd   rO   rO   rO   rS   test_dmp_max_norm     r  c                   C   r  )Nr   rV   r  r{   )r?   rJ   rO   rO   rO   rS   test_dup_l1_norm     r  c                   C   r  )NrU   r   rV   r-  )r@   rJ   rd   rO   rO   rO   rS   test_dmp_l1_norm  r  r  c                   C   r  )Nr   rV   r  r   )rA   rJ   rO   rO   rO   rS   test_dup_l2_norm_squared  r  r  c                   C   r  )NrU   r   rV   rq  )rB   rJ   rd   rO   rO   rO   rS   test_dmp_l2_norm_squared  s   r  c                   C   sX   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 d S )NrO   rV   rj   rU   )rW   r\   r[   rZ   )rC   rJ   r   rO   rO   rO   rS   test_dup_expand  s   r  c                	   C   s   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sGJ d S )NrO   rV   rU   rZ   rW   r\   r[   )rD   rJ   r    rO   rO   rO   rS   test_dmp_expand  s   4$r  c                  C   s   t dtd  dtd   tdd} t dtd  dtd   tdd}| t |ks*J | tt |tks8J | tt |tksFJ d S )	Ng     B   ge$]`Fr  RR)domain   r   )rH   rN   
set_domainrK   rL   )ppxrO   rO   rS   test_dup_mul_poly  s
   "" 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.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   sympy.polys.polyerrorsrE   sympy.polys.specialpolysrF   rG   rH   r  rI   rJ   rK   rL   sympy.testing.pytestrM   rN   rd   f_1f_2f_3f_4f_5f_6re   r`   rf   rh   ri   rl   rn   ru   rw   rx   ry   rz   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   re  rg  rh  ri  rm  rn  rx  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rO   rO   rO   rS   <module>   s    
  d 