o
    *ήc                     @   s*  d 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-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZD ddlEmFZF ddlGmHZH ddlImJZJmKZKmLZL ddlMmNZN dd	 eH D \ZOZPZQZRZSZTZUeeeOd
eLeLddd
eLZVdd ZWdd ZXdd ZYdd ZZdd Z[dd 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/d0 Zhd1d2 Zid3d4 Zjd5d6 Zkd7d8 Zld9d: Zmd;d< Znd=d> Zod?d@ ZpdAdB ZqdCdD ZrdEdF ZsdGdH ZtdIdJ ZudKdL ZvdMdN ZwdOdP ZxdQdR ZydSdT ZzdUdV Z{dWdX Z|dYdZ Z}d[d\ Z~d]d^ Zd_d` Zdadb Zdcdd Zdedf Zdgdh Zdidj Zdkdl Zdmdn Zdodp Zdqdr ZdsS )tz4Tests for dense recursive polynomials' arithmetics.     )
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)raisesc                 C   s   g | ]}|  qS  )to_dense).0frJ   rJ   H/tmp/pip-target-vg8gfxp4/lib/python/sympy/polys/tests/test_densearith.py
<listcomp>/   s    rO            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   rQ   rP   rQ   r   r   rQ   rQ   rQ   )rQ   rQ   rP   )rQ   rP   rQ   )rP   rQ   rQ      )rQ   rQ   rQ   rQ      )rQ   r   rQ   rQ   rQ      )rQ   r   r   rQ   rQ   rQ      )rQ   r   r   r   rQ   rQ   rQ   )r   rG   r   rM   rJ   rJ   rN   test_dup_add_term2   $   
 "$$$$$$$$(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 NrQ   rP   r   rU   )r   rG   r   f_0F_0rH   rJ   rJ   rJ   rN   test_dmp_add_termJ   
   $"ra   c                  C   s  t g t} t| tddtt g tksJ t| tddtt dgtks&J t| tddtt ddgtks8J t| tddtt g dtksJJ t g dt} t| tddtt g dtkscJ t| tddtt g dtksuJ t| tddtt g d	tksJ t| tdd
tt g dtksJ t| tddtt g dtksJ t| tddtt g dtksJ t| tddtt g dtksJ t| tddtt ddgtksJ d S )Nr   rQ   rY   rP   )rY   r   r   rT   )rQ   rQ   rY   )rQ   rY   rQ   )rY   rQ   rQ   rU   )rY   rQ   rQ   rQ   rV   )rY   r   rQ   rQ   rQ   rW   )rY   r   r   rQ   rQ   rQ   rX   )rY   r   r   r   rQ   rQ   rQ   )r   rG   r   rZ   rJ   rJ   rN   test_dup_sub_termQ   r\   rc   c                   C   r]   r^   )r   rG   r   r_   r`   rH   rJ   rJ   rJ   rN   test_dmp_sub_termi   rb   rd   c                  C   s   t g t} t| tddtt g tksJ t ddgt} t| tddtt g tks,J t g dt} t| tddtt g dtksEJ t| tddtt g dtksWJ t| tddtt g dtksiJ t| tddtt g d	tks{J d S )
NrP   rU   rQ   r   rQ   rP   rU   rP   rV   rX   )rP   rV   rX   r   )rP   rV   rX   r   r   )rP   rV   rX   r   r   r   )r   rG   r   rZ   rJ   rJ   rN   test_dup_mul_termp   s   
  $$$(rg   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 )	NrQ   rP   rU   r   rV   rX   rW      )r	   rG   r   rH   rJ   rJ   rJ   rN   test_dmp_mul_term   s   $"""*$$2"ri   c                  C   8   t g d} t g d}t| t dt |ksJ d S )NrQ   rP   rU   rV   )rQ   rP   rU      rV   )rG   mapr
   rM   grJ   rJ   rN   test_dup_add_ground      rp   c                  C   sR   t dgdgdgdgg} t dgdgdgdgg}t| t ddt |ks'J d S )NrQ   rP   rU   rV   rl   )rG   rm   r   rn   rJ   rJ   rN   test_dmp_add_ground   s   rr   c                  C   rj   )Nrk   )rQ   rP   rU   r   rV   )rG   rm   r   rn   rJ   rJ   rN   test_dup_sub_ground   rq   rs   c                  C   sP   t dgdgdgdgg} t dgdgdgg g}t| t ddt |ks&J d S )NrQ   rP   rU   rV   )rG   rm   r   rn   rJ   rJ   rN   test_dmp_sub_ground   s   rt   c                  C   sz   t g t} t| tdtt g tksJ t g dt} t| tdtt g tks*J t| tdtt g dtks;J d S )NrP   re   r   rf   )r   rG   r   rZ   rJ   rJ   rN   test_dup_mul_ground   s
   
&ru   c                	   C   s  t ttddttdtdtdgtdggtdggtdtdtdgtdtdtdgtdgggks:J t ttdddttddtddtd	dgtddggtd	dggtddtd
dtddgtddtddtddgtddgggksJ d S )NrP   rV   rX   rl   
      rQ      rU   rW   )r   r_   rG   r`   rH   rJ   rJ   rJ   rN   test_dmp_mul_ground   s   
2
&*
ry   c                  C   s$  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 Nre   r   )r   r   rG   rJ   rJ   rJ   rN   <lambda>   
   
 z%test_dup_quo_ground.<locals>.<lambda>rU   rX   rP   rl   rQ   rP   rU   rQ   rV   )rP   r   rP   rV   rR   rX   rl   )rI   ZeroDivisionErrorr   rG   r   rH   rZ   rJ   rJ   rN   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   rz   r{   r   r   rG   rJ   rJ   rJ   rN   r|      r}   z'test_dup_exquo_ground.<locals>.<lambda>c                   S   rz   )Nre   rU   r   rJ   rJ   rJ   rN   r|      r}   rU   r~   rQ   rP   r   rV   rR   rX   rl   )rI   r   rD   r   rG   r   rH   rZ   rJ   rJ   rN   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 NrX   rP   rl   rQ   rU   rV   )r   rG   r   rZ   rJ   rJ   rN   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   rG   r   rZ   rJ   rJ   rN   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 )NrU   rQ   rQ   r   r   r   )r   rG   rJ   rJ   rJ   rN   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 )NrU   r   rQ   )r   rG   rJ   rJ   rJ   rN   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 )NrQ   rR   rY   rP   rU   )r   rG   rH   rJ   rJ   rJ   rN   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 NrY   r   rQ   rP   r   rR   	   )r   rG   rH   rJ   rJ   rJ   rN   test_dmp_abs      $((,0r   c                   C   s   t g tg ks	J t tdgttdgksJ t tdgttdgks'J t tdtdtdgttdtdtdgksBJ t g tg ksKJ t tddgttddgks\J t tdd	gttdd	gksmJ t tddtddtddgttddtddtddgksJ d S )
NrQ   rY   r   rR   rP   rU   r   )r   rG   rH   rJ   rJ   rJ   rN   test_dup_neg+  s    6""r   c                   C   s(  t tdgdttdgksJ t tddgdttddgks"J t g ggdtg ggks0J t tdgggdttdgggksDJ t tdgggdttdgggksXJ t g ggdtg ggksfJ t tddgggdttddgggks|J t tddgggdttddgggksJ d S r   )r   rG   rH   rJ   rJ   rJ   rN   test_dmp_neg8  r   r   c                   C   s  t g g tg ks
J t tdgg ttdgksJ t g tdgttdgks*J t tdgtdgttdgks=J t tdgtdgttdgksPJ t tdtdgtdgttdtdgksiJ t tdgtdtdgttdtdgksJ t tdtdtdgtdtdtdgttdtdtdgksJ t g g tg ksJ t tddgg ttddgksJ t g tddgttddgksJ t tdd	gtdd	gttddgksJ t tdd	gtddgttdd	gksJ t tddtddgtdgttddtd
dgks J t tdgtddtddgttddtd
dgks>J t tddtddtddgtddtddtddgttddtddtddgksmJ d S )NrQ   rP   rU   rl   r   rv         rV   rW   rR   )r   rG   rH   rJ   rJ   rJ   rN   test_dup_addE  s@     &&22
$$,.<<r   c                   C   st  t tdtdgtdgdtttdtdgtdgtks!J t tddtddgtdgdtttddtddgtdgtksFJ t g ggg ggdtg ggksWJ t tdgggg ggdttdgggksnJ t g ggtdgggdttdgggksJ t tdgggtdgggdttdgggksJ t tdgggtdgggdttdgggksJ t g ggg ggdtg ggksJ t tddgggg ggdttddgggksJ t g ggtddgggdttddgggksJ t tddgggtddgggdttddgggksJ t tddgggtddgggdttddgggks8J d S )NrQ   rP   r   rU   rR   )r   rG   r   rH   rJ   rJ   rJ   rN   test_dmp_add_      " "..44"22<@r   c                   C   s  t g g tg ks
J t tdgg ttdgksJ t g tdgttdgks*J t tdgtdgtg ks:J t tdgtdgttdgksMJ t tdtdgtdgttdtdgksfJ t tdgtdtdgttdtdgksJ t tdtdtdgtdtdtdgttdtd	td
gksJ t g g tg ksJ t tddgg ttddgksJ t g tddgttddgksJ t tddgtddgtg ksJ t tddgtddgttddgksJ t tddtddgtdgttddtddgksJ t tdgtddtddgttddtddgks6J t tddtddtddgtddtddtddgttddtd	dtd
dgkseJ d S )NrQ   rY   rP   rU   rl   r   rv   r   rR   rW   )r   rG   rH   rJ   rJ   rJ   rN   test_dup_subr  s@      &22
$$$,<<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 )NrQ   rP   r   rU   rY   rR   )r   rG   r   rH   rJ   rJ   rJ   rN   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 )NrQ   rP   rU   r   rR   rW   rV   )r$   rG   r%   rJ   rJ   rJ   rN   test_dup_add_mul     *2&r   c                   C   s   t tdtdtdgtdtdtdgtdtdgttdtdtdtdgks/J ttdtdgtdggtdgtdtdggtdgtdggdttdgtdtdgtdtdggkskJ d S )	NrQ   rP   rU   r   r   rY   r   )r&   rG   r'   rJ   rJ   rJ   rN   test_dup_sub_mul  r   r   c                  C   s~  t g g tg ks
J t g tdgtg ksJ t tdgg tg ks$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 )NrQ   rW   rR   #   rP   rV   rU   rh   1   )rU   r   r   rX   rQ   rP   )rV   r   rQ   r   )	rw   r   rU      rV   rx   rQ   rP   r   rP   r   r   rQ   rR   	rV   r   r   rV      r   rQ   rx   r   rX   )O   rY   N   r       r   rP      I   *   U   M   S   r   _   %   r   r   C      L   rP   F   r   A   9   r   r   a   Y   !   r   Q   r   <   +      ,      r   r   r   rU   5      r   B   rQ   r   b   r   rX   rl   r   rw      r      r   7   r   D   r   T   ^   -   r   \   r   r   r   rl   K   r   [   r   "   rx   r   r   r   r   rX   r      r   :   r      r   r   rR   r   r   r   r   r   r   r   rW   3   r   r  r   r   r   r   R   r   r   r   r   r   r  r   r   r  ?   r   r   rX   r   r   rU   rU   .   r   >   X   r   r  rY   r   H   rx   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   rQ   Z   r   r   r      r   r   2   r   r      rQ   r   r   r   J   P   r   r   r   )   r      r  r   r   E   r   r   r   rx   r   r   r   r   r   r   r   r  r   r  r  r   r   r   r  r   r  r   r   r  r  r   r   r  rW   r#  r   r   r  r  r   r   r   r   0   r   r   r   r   rv   r   r  r   =   r   r  r   r-  r   r   r   rP   rX   r   r	  r   r5  r   r   r7  rY   r1  `   r   r   r   8   r  r  r  r;  r%  r  r   r   r   r   r   r   r   r   r-  (   r   r   r   r  r  r   r  '   r  r   rx   W   @   r   r   r   rh   r  r   r   r   r   6   r<  r   rX   r"  r  r7  r   rB  r   r   r   r   r   r   r   r   r1  r   $   r   rW   r%  r  r-  r   r$  r   ir   r   r   r   rV   r>  rC  r   r   r   r   r   r   r1  r  r   r   r  r  rE  r   r   r3  r   r   r   r.  r
  r  r  r(  r   r  r  r   r   r#  r	  r  r"  r   r   r>  r   &   r   rG  r  r   r   rB  r  r  r      r   r   r   r   r!  r   r   rw   rw   r   r)  rE  r4  r  r(  r(  r#  r  r   r  rE  r  r   r   r   r   r   r   r   rQ   r   r   rl   rl   r:  r   r   r   r4  r   r   r  r   r   r,  r,  rW   r   r   r  r?  r   rW   r   rC  r   r+  r
  rE  r   r   r0  r   r   r)  r   r   r   r  rA  r   r	  r   r  r  r   r   r   r   r#  r   r   r   rI  r   r   r  r  r   r   r   rH  r   rw   r  r   r  r   r   r   r  rl   r  r   r   r   (C  i  ii`  ii  i-  iA  iigiiY  ii_  iOi.  iin%  i0$  io  i[  i	J  i5'  i\ii*  ii?i  i*  iizi?  iDz  i`  i|  i  i  ii  i=  is  i  i|  i  ivki}i%  rK  iQi  i`iHii4  iw  i%  i3Uii,  ii  ii  iY  i}i|idi"li޷iiti\ioiiiNb  iiM  i2  iMiiKl  i#iiiiwN  i$iZi  iQ  i9i%}  5ig  ivF  i;if|  ii4ii0  ib  i&Mi^  i'iHi>iiTiߟir/  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$c  iy`i"i4i  iOij  ii  i}i3  i4i\i i i  iri^ialiH
ii  ii i]  i.  iv  i  i  ii  i!ii  i^N iii
igi!  ivrL  iZ  i'  i  iZiini2 i~  i  iRiorili  iiia  i  iii71  i\ih  i  iiƺ  ii0  ii(ioifi  ii+i i3i" i+G  i8 ii_ iD  i%}ii  imi i9  i=Ri0*  ii2i  iYV  it  ii5  i  i  i.!  i$  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%iWrO  iU  ild  i   i  ii  iQ  iN  iX  i-  i3  i	  ii7iEii8i  iiiirii  i	  i  ii|)r   r0  r   r1  rw   r   r   r   r   r   r?  r)  r   r   r   r   r   rV   r   rX   r   r   r   r   i/   r  r  r   r   r   r   r'  r-  r1  r@  r   r   r   r$  rY   r=  r   r   r   r   r   r  r-  r   r   r   r   r/  r  rw   r   r   ir   r  r9  r0  r%  rQ   G   rV   rw   r4  rV   r   r#  r   rW   r4  r  r  r   r   r   r  r   r4  r0  r   rQ  r   r   r?  r   r	  r   r  r   r   r  rI  r   r$  r  r  r;  r  r   r=  r:  r  r3  r   r   r  r   r  rI  r   r   r   r(  r   r   rU   rE  r4  r   r1  r   r   r   r   r   r/  r  r!  rx   r3  r   r  r   r  rA  r!  r   r   r  r   r  r   rw   r   ;   r   c   r   r   r   r  r   r   rQ   r
  r  r*  r   r#  r   r   r   r@  r  r   r   rv   r   r<  rF  r.  r?  r   r   r  r   r  r   r   r   r9  rA  rS  r  r   r   r0  r   r   r   r0  rV   r   r   r:  r  r   r   r   r   r   rx   r  r   r   r3  r   r   r   r  r"  r   r;  r   rU   r<  r   r   r  r   r   r   r+  r>  r  r   r   r  r  r9  r   r   r4  r   r4  r   r   r   (+  r  r  r   r   r   r  r  r   r   r/  r   r;  rH  r   r   r   r   r   r   r  r   r   r%  r   r)  r   r	  rV   rQ  r   r   r   rS  r)  r  rT  r	  r/  r@  r   r  r   r@  rS  r   r3  r   r   r>  r  rV   r   r  r   r   r9  r   rU      r;  rD  r   r   r   rX   r   r   r=  r   r  rC  r   rS  r   r   rB  r   rE  r,  r   r%  r   r   r   r   r   r   r   r   rR  r   r  r8  r;  r  rl   rY   r;  r   r   r   r   rE  rR  r   r   r   r  rT  r  rF  rW   rB  r   r3  r5  r   r   r  r   r  r!  r?  r   r   rQ   r   rJ  r  r   r  rU   rw   r  r   r  r2  r   r   r   r   r   r   rW   r   r   ]   r   r   r%  r)  r   rX  rT  r"  r   r  r   r   r   r:  r   r   r   rX  r   r   r   rV  r   r   r  r   r   rG  r,  r   r   r   r%  r   r   rQ  r   r  r   r  r   r"  r  r   r   r   r   rX   r   r   r   rh   r   rX  r   r
  r  r  r%  r   r$  rS  r@  r   r   rV  r   r   r2  r6  r7  r&  r   rW   r   rU  r   r   r  r   r   r   r   r   r  rH  r   r  r"  r(  rQ   r   r   r  r   r4  r$  r  r   r   rD  rH  r   r:  r   r   r(  r   r%  r   r   r   r  r7  r
  rU   r   r   rP   r5  r   r   r   r  r   r   r   r"  r   rV   r!  r   r$  r  r
  rI  r   r(  rS  r   rT  r  r   rW  r2  r   r   r   rE  rJ  r   r   (  i  i$  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&iieiirP  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{rN  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  iPrM  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   rG   rH   r   rF   )rM   ro   hKp1p2resrJ   rJ   rN   test_dup_mul  sP   &&,,8=?8:r`  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 )
NrW   rR   r   rU   rP   rQ   r   rX   rV   )r   rG   r   rH   rF   r\  rJ   rJ   rN   test_dmp_mul  s,   "((44"**:<(rb  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 )
NrP   rV   rQ   rU   r   r   r   rX   rR   )r    rG   rH   r   rF   )rM   r\  rJ   rJ   rN   test_dup_sqr  s   0":.rc  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 )	NrQ   rP   r   rV   rU   r   rX   rR   )r!   rG   r    rH   rF   ra  rJ   rJ   rN   test_dmp_sqr  s   (,8rd  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   rQ   rR   rU      r   rP   r   )rl   r   r   rw   r   r   rX   r   i&  rQ   r      iW  )r"   rG   rH   r   rZ   rJ   rJ   rN   test_dup_pow  s.         $$$$$$  rh  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   rQ   rR   rU   re  rf  r   rP   )r#   rG   rH   r   r"   rZ   rJ   rJ   rN   test_dmp_pow  s     &&&***"ri  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rU   rQ   rQ   rW   rW   r   rQ   rh   rx   r  o   c                         t  tS N)r+   rG   rJ   rn   rJ   rN   r|         ztest_dup_pdiv.<locals>.<lambda>c                      rm  rn  )r+   rH   rJ   rn   rJ   rN   r|     ro  )r   rG   r(   r*   r)   rI   rD   rH   qrrJ   rn   rN   test_dup_pdiv  s    rs  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 )NrQ   rS   rY   r   rP   r   r   c                         t  dtS NrQ   r/   rG   rJ   rn   rJ   rN   r|   "      ztest_dmp_pdiv.<locals>.<lambda>rP   r   )rl   r   r   c                      ru  rv  rw  rJ   rn   rJ   rN   r|   .  rx  )r   rG   r,   r.   r-   rI   rD   rp  rJ   rn   rN   test_dmp_pdiv  s    ry  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 Nre   )r0   rG   rJ   rJ   rJ   rN   r|   2      z!test_dup_rr_div.<locals>.<lambda>rj  rk  )rI   r   r   rG   r0   rM   ro   rq  rr  rJ   rJ   rN   test_dup_rr_div1  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 NrQ   rP   rU   )r1   rG   rJ   rJ   rJ   rN   r|   =      z!test_dmp_rr_div.<locals>.<lambda>rQ   rS   rY   r   rt  rP   r   )rI   r   r   rG   r1   r}  rJ   rJ   rN   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   rz  r{  )r2   rH   rJ   rJ   rJ   rN   r|   X  r|  z!test_dup_ff_div.<locals>.<lambda>rj  rk  rU   rW   rx   r%  r  rl  )rI   r   r   rH   r2   r}  rJ   rJ   rN   test_dup_ff_divW  s   r  c                  C   s   zddl m}  W n
 ty   Y d S w ddlm} | }| dd| ddg}| ddg}t||d|| dd| ddgg fksAJ | 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 d S )Nr   )mpq)GMPYRationalFieldrQ   rU   rP   rX   rV   rW   rY   r   rR   rw   r   r   )gmpy2r  ImportErrorsympy.polys.domainsr  r3   )r  r  r\  rM   ro   rJ   rJ   rN   test_dup_ff_div_gmpy2b  s   *$>r  c                  C   s  t tdd  tdgg g dgdt} tdgddggdt}tddgtddtddgg}tddtddtddgg}t| |dt||fksJJ tdgg g dgdt} tdgddggdt}tddgtddtddgg}tddtddtddgg}t| |dt||fksJ tdgg g dgdt} tdgddggdt}tddgtddtddgg}tddtddtddgg}t| |dt||fksJ d S )	Nc                   S   r  r  )r3   rH   rJ   rJ   rJ   rN   r|   t  r  z!test_dmp_ff_div.<locals>.<lambda>rQ   rS   rY   r   rP   r   )rI   r   r   rH   r3   r}  rJ   rJ   rN   test_dmp_ff_divs  s       r  c                     s   g dg dg dddgf\ } }t  t| |fksJ t t| ks(J t t|ks2J tt fdd g dg d	d
dgg df\ } }t  t| |fksZJ t t| ksdJ t t|ksnJ tt fdd d S )NrW   rV   rU   rP   rQ   re   rW   r	  r   r  rQ   c                      rm  rn  r7   rG   rJ   rn   rJ   rN   r|     ro  ztest_dup_div.<locals>.<lambda>)rW   rV   rU   rP   rQ   r   )rQ   rP   r   r   r   rW   r	  )rh   rP   r   rD  c                      rm  rn  r  rJ   rn   rJ   rN   r|     ro  )r4   rG   r6   r5   rI   rD   rp  rJ   rn   rN   test_dup_div  s   $$r  c                     s
  g dg dg dddgf\ } }t  dt| |fksJ t dt| ks*J t dt|ks5J tt fdd dgggd	ggdggg ggdgggf\ } }t  d	t| |fkscJ t d	t| ksnJ t d	t|ksyJ tt fd
d d S )Nr  re   r  r  rQ   r   c                      ru  )Nr   r;   rG   rJ   rn   rJ   rN   r|     rx  ztest_dmp_div.<locals>.<lambda>rP   c                      ru  )NrP   r  rJ   rn   rJ   rN   r|     rx  )r8   rG   r:   r9   rI   rD   rp  rJ   rn   rN   test_dmp_div  s   $.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   rQ   rQ   rV   rP   rU   rV   )r<   rG   rJ   rJ   rJ   rN   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 )NrP   r   rQ   rX   )r=   rG   r_   rJ   rJ   rJ   rN   test_dmp_max_norm     r  c                   C   r  )Nr   rQ   r  rv   )r>   rG   rJ   rJ   rJ   rN   test_dup_l1_norm     r  c                   C   r  )NrP   r   rQ   r(  )r?   rG   r_   rJ   rJ   rJ   rN   test_dmp_l1_norm  r  r  c                   C   r  )Nr   rQ   r  r   )r@   rG   rJ   rJ   rJ   rN   test_dup_l2_norm_squared  r  r  c                   C   r  )NrP   r   rQ   rl  )rA   rG   r_   rJ   rJ   rJ   rN   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 )NrJ   rQ   re   rP   )rR   rW   rV   rU   )rB   rG   r   rJ   rJ   rJ   rN   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 )NrJ   rQ   rP   rU   rR   rW   rV   )rC   rG   r   rJ   rJ   rJ   rN   test_dmp_expand  s   4$r  N)__doc__sympy.polys.densebasicr   r   sympy.polys.densearithr   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   sympy.polys.polyerrorsrD   sympy.polys.specialpolysrE   r  rF   rG   rH   sympy.testing.pytestrI   r_   f_1f_2f_3f_4f_5f_6r`   r[   ra   rc   rd   rg   ri   rp   rr   rs   rt   ru   ry   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r`  rb  rc  rd  rh  ri  rs  ry  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rJ   rJ   rJ   rN   <module>   s|    
  d 