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�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, ddÙ�l-�m.�Z. �e. G dÚ„ dÛ«      «       �Z/yÜ)Ýz8Compatibility interface between dense and sparse polys. é    )Úannotations)ÚTYPE_CHECKING)ÚExpr)ÚDomain)ÚMonomialOrder©ÚPolyElement)Údup_add_term)Údmp_add_term)Údup_sub_term)Údmp_sub_term)Údup_mul_term)Údmp_mul_term)Údup_add_ground)Údmp_add_ground)Údup_sub_ground)Údmp_sub_ground)Údup_mul_ground)Údmp_mul_ground)Údup_quo_ground)Údmp_quo_ground)Údup_exquo_ground)Údmp_exquo_ground)Ú
dup_lshift)Ú
dup_rshift)Údup_abs)Údmp_abs)Údup_neg)Údmp_neg)Údup_add)Údmp_add)Údup_sub)Údmp_sub)Údup_add_mul)Údmp_add_mul)Údup_sub_mul)Údmp_sub_mul)Údup_mul)Údmp_mul)Údup_sqr)Údmp_sqr)Údup_pow)Údmp_pow)Údup_pdiv)Údup_prem)Údup_pquo)Ú
dup_pexquo)Údmp_pdiv)Údmp_prem)Údmp_pquo)Ú
dmp_pexquo)Ú
dup_rr_div)Ú
dmp_rr_div)Ú
dup_ff_div)Ú
dmp_ff_div)Údup_div)Údup_rem)Údup_quo)Ú	dup_exquo)Údmp_div)Údmp_rem)Údmp_quo)Ú	dmp_exquo)Údup_max_norm)Údmp_max_norm)Údup_l1_norm)Údmp_l1_norm)Údup_l2_norm_squared)Údmp_l2_norm_squared)Ú
dup_expand)Ú
dmp_expand)Údup_LC)Údmp_LC)Údup_TC)Údmp_TC)Údmp_ground_LC)Údmp_ground_TC)Ú
dup_degree)Ú
dmp_degree)Údmp_degree_in)Údmp_to_dict)Údup_integrate)Údmp_integrate)Údmp_integrate_in)Údup_diff)Údmp_diff)Údmp_diff_in)Údup_eval)Údmp_eval)Údmp_eval_in)Údmp_eval_tail)Údmp_diff_eval_in)Ú	dup_trunc)Ú	dmp_trunc)Údmp_ground_trunc)Ú	dup_monic)Údmp_ground_monic)Údup_content)Údmp_ground_content)Údup_primitive)Údmp_ground_primitive)Údup_extract)Údmp_ground_extract)Údup_real_imag)Ú
dup_mirror)Ú	dup_scale)Ú	dup_shift)Ú	dmp_shift)Údup_transform)Údup_compose)Údmp_compose)Údup_decompose)Údmp_lift)Údup_sign_variations)Údup_clear_denoms)Údmp_clear_denoms)Ú
dup_revert)Údup_half_gcdex)Údmp_half_gcdex)Ú	dup_gcdex)Ú	dmp_gcdex)Ú
dup_invert)Ú
dmp_invert)Údup_euclidean_prs)Údmp_euclidean_prs)Údup_primitive_prs)Údmp_primitive_prs)Údup_inner_subresultants)Údup_subresultants)Údup_prs_resultant)Údup_resultant)Údmp_inner_subresultants)Údmp_subresultants)Údmp_prs_resultant)Údmp_zz_modular_resultant)Údmp_zz_collins_resultant)Údmp_qq_collins_resultant)Údmp_resultant)Údup_discriminant)Údmp_discriminant)Údup_rr_prs_gcd)Údup_ff_prs_gcd)Údmp_rr_prs_gcd)Údmp_ff_prs_gcd)Údup_zz_heu_gcd)Údmp_zz_heu_gcd)Údup_qq_heu_gcd)Údmp_qq_heu_gcd)Údup_inner_gcd)Údmp_inner_gcd)Údup_gcd)Údmp_gcd)Ú
dup_rr_lcm)Ú
dup_ff_lcm)Údup_lcm)Ú
dmp_rr_lcm)Ú
dmp_ff_lcm)Údmp_lcm)Údmp_content)Údmp_primitive)Ú
dup_cancel)Ú
dmp_cancel)Údup_trial_division)Údmp_trial_division)Údup_zz_mignotte_bound)Údmp_zz_mignotte_bound)Údup_zz_hensel_step)Údup_zz_hensel_lift)Údup_zz_zassenhaus)Údup_zz_irreducible_p)Údup_cyclotomic_p)Údup_zz_cyclotomic_poly)Údup_zz_cyclotomic_factor)Údup_zz_factor_sqf)Údup_zz_factor)Údmp_zz_wang_non_divisors)Údmp_zz_wang_lead_coeffs)Údup_zz_diophantine)Údmp_zz_diophantine)Údmp_zz_wang_hensel_lifting)Údmp_zz_wang)Údmp_zz_factor)Údup_qq_i_factor)Údup_zz_i_factor)Údmp_qq_i_factor)Údmp_zz_i_factor)Údup_ext_factor)Údmp_ext_factor)Údup_gf_factor)Údmp_gf_factor)Údup_factor_list)Údup_factor_list_include)Údmp_factor_list)Údmp_factor_list_include)Údup_irreducible_p)Údmp_irreducible_p)Ú	dup_sturm)Údup_root_upper_bound)Údup_root_lower_bound)Údup_step_refine_real_root)Údup_inner_refine_real_root)Údup_outer_refine_real_root)Údup_refine_real_root)Údup_inner_isolate_real_roots)Ú dup_inner_isolate_positive_roots)Ú dup_inner_isolate_negative_roots)Údup_isolate_real_roots_sqf)Údup_isolate_real_roots)Údup_isolate_real_roots_list)Údup_count_real_roots)Údup_count_complex_roots)Údup_isolate_complex_roots_sqf)Údup_isolate_all_roots_sqf)Údup_isolate_all_roots)Ú	dup_sqf_pÚ	dmp_sqf_pÚdmp_normÚdup_sqf_normÚdmp_sqf_normÚdup_gf_sqf_partÚdmp_gf_sqf_partÚdup_sqf_partÚdmp_sqf_partÚdup_gf_sqf_listÚdmp_gf_sqf_listÚdup_sqf_listÚdup_sqf_list_includeÚdmp_sqf_listÚdmp_sqf_list_includeÚdup_gff_listÚdmp_gff_list)8Ú	gf_degreeÚgf_LCÚgf_TCÚgf_stripÚgf_from_dictÚ
gf_to_dictÚgf_from_int_polyÚgf_to_int_polyÚgf_negÚgf_add_groundÚgf_sub_groundÚgf_mul_groundÚgf_quo_groundÚgf_addÚgf_subÚgf_mulÚgf_sqrÚ
gf_add_mulÚ
gf_sub_mulÚ	gf_expandÚgf_divÚgf_remÚgf_quoÚgf_exquoÚ	gf_lshiftÚ	gf_rshiftÚgf_powÚ
gf_pow_modÚgf_gcdÚgf_lcmÚgf_cofactorsÚgf_gcdexÚgf_monicÚgf_diffÚgf_evalÚgf_multi_evalÚ
gf_composeÚgf_compose_modÚgf_trace_mapÚ	gf_randomÚgf_irreducibleÚgf_irred_p_ben_orÚgf_irred_p_rabinÚgf_irreducible_pÚgf_sqf_pÚgf_sqf_partÚ
gf_QmatrixÚgf_berlekampÚgf_ddf_zassenhausÚgf_edf_zassenhausÚgf_ddf_shoupÚgf_edf_shoupÚgf_zassenhausÚgf_shoupÚgf_factor_sqfÚ	gf_factor)Úpublicc                  óp  — e Zd ZU ded<   ded<   ded<   ded<   d	ed
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�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„ �Z�d „ �Z�d!„ �Z�d"„ �Z�d#„ �Z�d$„ �Z�d%„ �Z�d&„ �Z�d'„ �Z�d(„ �Z �d5�d)„�Z!�d*„ �Z"�d+„ �Z#�d,„ �Z$�d-„ �Z%�d.„ �Z&�d/„ �Z'�d0„ �Z(�d1„ �Z)�d<�d2„�Z*�d3„ �Z+y(=  ÚIPolysztuple[PolyElement, ...]Úgensztuple[Expr, ...]ÚsymbolsÚintÚngensr   Údomainr   Úorderc                 ó   — y ©N© )ÚselfÚgens     úW/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/polys/compatibility.pyÚdropzIPolys.dropù   ó   € Øó    Nc                 ó   — y r,  r-  )r.  r&  r)  r*  s       r0  ÚclonezIPolys.cloneü   r2  r3  c                 ó   — y r,  r-  )r.  s    r0  Ú	to_groundzIPolys.to_groundÿ   r2  r3  c                 ó   — y r,  r-  ©r.  Úelements     r0  Ú
ground_newzIPolys.ground_new  r2  r3  c                 ó   — y r,  r-  r9  s     r0  Ú
domain_newzIPolys.domain_new  r2  r3  c                 ó   — y r,  r-  )r.  Úds     r0  Ú	from_dictzIPolys.from_dict  r2  r3  c                ó€   — ddl m} t        ||«      r|j                  | k(  r|S t	        d«      ‚| j                  |«      S )Nr   r   zdomain conversions)Úsympy.polys.ringsr	   Ú
isinstanceÚringÚNotImplementedErrorr;  )r.  r:  r	   s      r0  ÚwrapzIPolys.wrap  s;   € Ý1Ü�g˜{Ô+Ø�|‰|˜tÒ#Ø�ä)Ð*>Ó?Ð?à—?‘? 7Ó+Ð+r3  c                ó@   — | j                  |«      j                  «       S r,  )rF  Úto_denser9  s     r0  rH  zIPolys.to_dense  s   € Ø�y‰y˜Ó!×*Ñ*Ó,Ð,r3  c                óh   — | j                  t        || j                  dz
  | j                  «      «      S ©Né   )r@  rS   r(  r)  r9  s     r0  Ú
from_densezIPolys.from_dense  s&   € Ø�~‰~œk¨'°4·:±:¸a±<ÀÇÁÓMÓNÐNr3  c                ón   — | j                  t        | j                  |«      ||| j                  «      «      S r,  )rL  r
   rH  r)  ©r.  ÚfÚcÚis       r0  r
   zIPolys.dup_add_term  ó)   € Ø�‰œ|¨D¯M©M¸!Ó,<¸aÀÀDÇKÁKÓPÓQÐQr3  c           	     óâ   — | j                  t        | j                  |«      | j                  |«      j	                  d«      j                  «       || j
                  dz
  | j                  «      «      S ©Nr   rK  )rL  r   rH  rF  r1  r(  r)  rN  s       r0  r   zIPolys.dmp_add_term  óY   € Ø�‰œ|¨D¯M©M¸!Ó,<¸d¿i¹iÈ»l×>OÑ>OÐPQÓ>R×>[Ñ>[Ó>]Ð_`Ðbf×blÑblÐmnÑbnÐpt×p{Ñp{Ó|Ó}Ð}r3  c                ón   — | j                  t        | j                  |«      ||| j                  «      «      S r,  )rL  r   rH  r)  rN  s       r0  r   zIPolys.dup_sub_term  rR  r3  c           	     óâ   — | j                  t        | j                  |«      | j                  |«      j	                  d«      j                  «       || j
                  dz
  | j                  «      «      S rT  )rL  r   rH  rF  r1  r(  r)  rN  s       r0  r   zIPolys.dmp_sub_term!  rU  r3  c                ón   — | j                  t        | j                  |«      ||| j                  «      «      S r,  )rL  r   rH  r)  rN  s       r0  r   zIPolys.dup_mul_term#  rR  r3  c           	     óâ   — | j                  t        | j                  |«      | j                  |«      j	                  d«      j                  «       || j
                  dz
  | j                  «      «      S rT  )rL  r   rH  rF  r1  r(  r)  rN  s       r0  r   zIPolys.dmp_mul_term%  rU  r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  r   rH  r)  ©r.  rO  rP  s      r0  r   zIPolys.dup_add_ground(  ó'   € Ø�‰œ~¨d¯m©m¸AÓ.>ÀÀ4Ç;Á;ÓOÓPÐPr3  c                óˆ   — | j                  t        | j                  |«      || j                  dz
  | j                  «      «      S rJ  )rL  r   rH  r(  r)  r[  s      r0  r   zIPolys.dmp_add_ground*  ó4   € Ø�‰œ~¨d¯m©m¸AÓ.>ÀÀ4Ç:Á:ÈaÁ<ÐQU×Q\ÑQ\Ó]Ó^Ð^r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  r   rH  r)  r[  s      r0  r   zIPolys.dup_sub_ground,  r\  r3  c                óˆ   — | j                  t        | j                  |«      || j                  dz
  | j                  «      «      S rJ  )rL  r   rH  r(  r)  r[  s      r0  r   zIPolys.dmp_sub_ground.  r^  r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  r   rH  r)  r[  s      r0  r   zIPolys.dup_mul_ground0  r\  r3  c                óˆ   — | j                  t        | j                  |«      || j                  dz
  | j                  «      «      S rJ  )rL  r   rH  r(  r)  r[  s      r0  r   zIPolys.dmp_mul_ground2  r^  r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  r   rH  r)  r[  s      r0  r   zIPolys.dup_quo_ground4  r\  r3  c                óˆ   — | j                  t        | j                  |«      || j                  dz
  | j                  «      «      S rJ  )rL  r   rH  r(  r)  r[  s      r0  r   zIPolys.dmp_quo_ground6  r^  r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  r   rH  r)  r[  s      r0  r   zIPolys.dup_exquo_ground8  s(   € Ø�‰Ô/°·±¸aÓ0@À!ÀTÇ[Á[ÓQÓRÐRr3  c                óˆ   — | j                  t        | j                  |«      || j                  dz
  | j                  «      «      S rJ  )rL  r   rH  r(  r)  r[  s      r0  r   zIPolys.dmp_exquo_ground:  ó6   € Ø�‰Ô/°·±¸aÓ0@À!ÀTÇZÁZÐPQÁ\ÐSW×S^ÑS^Ó_Ó`Ð`r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  r   rH  r)  ©r.  rO  Úns      r0  r   zIPolys.dup_lshift=  ó'   € Ø�‰œz¨$¯-©-¸Ó*:¸A¸t¿{¹{ÓKÓLÐLr3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  r   rH  r)  ri  s      r0  r   zIPolys.dup_rshift?  rk  r3  c                ój   — | j                  t        | j                  |«      | j                  «      «      S r,  )rL  r   rH  r)  ©r.  rO  s     r0  r   zIPolys.dup_absB  ó%   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÓEÓFÐFr3  c                ó†   — | j                  t        | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r   rH  r(  r)  rn  s     r0  r   zIPolys.dmp_absD  ó/   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÀA¹ÀtÇ{Á{ÓSÓTÐTr3  c                ój   — | j                  t        | j                  |«      | j                  «      «      S r,  )rL  r   rH  r)  rn  s     r0  r   zIPolys.dup_negG  ro  r3  c                ó†   — | j                  t        | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r   rH  r(  r)  rn  s     r0  r   zIPolys.dmp_negI  rq  r3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r    rH  r)  ©r.  rO  Úgs      r0  r    zIPolys.dup_addL  ó0   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï;É;ÓWÓXÐXr3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r!   rH  r(  r)  ru  s      r0  r!   zIPolys.dmp_addN  ó>   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï:É:ÐVWÉ<ÐY]×YdÑYdÓeÓfÐfr3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r"   rH  r)  ru  s      r0  r"   zIPolys.dup_subQ  rw  r3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r#   rH  r(  r)  ru  s      r0  r#   zIPolys.dmp_subS  ry  r3  c           	     óª   — | j                  t        | j                  |«      | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r$   rH  r)  ©r.  rO  rv  Úhs       r0  r$   zIPolys.dup_add_mulV  ó?   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏ}É}Ð]^ÓO_Ðae×alÑalÓmÓnÐnr3  c           	     óÆ   — | j                  t        | j                  |«      | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r%   rH  r(  r)  r}  s       r0  r%   zIPolys.dmp_add_mulX  óN   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏ}É}Ð]^ÓO_Ðae×akÑakÐlmÑamÐos×ozÑozÓ{Ó|Ð|r3  c           	     óª   — | j                  t        | j                  |«      | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r&   rH  r)  r}  s       r0  r&   zIPolys.dup_sub_mulZ  r  r3  c           	     óÆ   — | j                  t        | j                  |«      | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r'   rH  r(  r)  r}  s       r0  r'   zIPolys.dmp_sub_mul\  r�  r3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r(   rH  r)  ru  s      r0  r(   zIPolys.dup_mul_  rw  r3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r)   rH  r(  r)  ru  s      r0  r)   zIPolys.dmp_mula  ry  r3  c                ój   — | j                  t        | j                  |«      | j                  «      «      S r,  )rL  r*   rH  r)  rn  s     r0  r*   zIPolys.dup_sqrd  ro  r3  c                ó†   — | j                  t        | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r+   rH  r(  r)  rn  s     r0  r+   zIPolys.dmp_sqrf  rq  r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  r,   rH  r)  ri  s      r0  r,   zIPolys.dup_powh  s'   € Ø�‰œw t§}¡}°QÓ'7¸¸D¿K¹KÓHÓIÐIr3  c                óˆ   — | j                  t        | j                  |«      || j                  dz
  | j                  «      «      S rJ  )rL  r-   rH  r(  r)  ri  s      r0  r-   zIPolys.dmp_powj  s1   € Ø�‰œw t§}¡}°QÓ'7¸¸D¿J¹JÀq¹LÈ$Ï+É+ÓVÓWÐWr3  c                ó¶   — t        | j                  |«      | j                  |«      | j                  «      \  }}| j                  |«      | j                  |«      fS r,  )r.   rH  r)  rL  ©r.  rO  rv  ÚqÚrs        r0  r.   zIPolys.dup_pdivm  sG   € Ü˜Ÿ™ aÓ(¨$¯-©-¸Ó*:¸D¿K¹KÓH‰ˆˆ1Ø—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r/   rH  r)  ru  s      r0  r/   zIPolys.dup_premp  ó0   € Ø�‰œx¨¯©°aÓ(8¸$¿-¹-ÈÓ:JÈDÏKÉKÓXÓYÐYr3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r0   rH  r)  ru  s      r0  r0   zIPolys.dup_pquor  r�  r3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r1   rH  r)  ru  s      r0  r1   zIPolys.dup_pexquot  ó0   € Ø�‰œz¨$¯-©-¸Ó*:¸D¿M¹MÈ!Ó<LÈdÏkÉkÓZÓ[Ð[r3  c                óÒ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}| j	                  |«      | j	                  |«      fS rJ  )r2   rH  r(  r)  rL  r‹  s        r0  r2   zIPolys.dmp_pdivw  sQ   € Ü˜Ÿ™ aÓ(¨$¯-©-¸Ó*:¸D¿J¹JÀq¹LÈ$Ï+É+ÓV‰ˆˆ1Ø—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r3   rH  r(  r)  ru  s      r0  r3   zIPolys.dmp_premz  ó>   € Ø�‰œx¨¯©°aÓ(8¸$¿-¹-ÈÓ:JÈDÏJÉJÐWXÉLÐZ^×ZeÑZeÓfÓgÐgr3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r4   rH  r(  r)  ru  s      r0  r4   zIPolys.dmp_pquo|  r•  r3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r5   rH  r(  r)  ru  s      r0  r5   zIPolys.dmp_pexquo~  ó>   € Ø�‰œz¨$¯-©-¸Ó*:¸D¿M¹MÈ!Ó<LÈdÏjÉjÐYZÉlÐ\`×\gÑ\gÓhÓiÐir3  c                ó¶   — t        | j                  |«      | j                  |«      | j                  «      \  }}| j                  |«      | j                  |«      fS r,  )r6   rH  r)  rL  r‹  s        r0  r6   zIPolys.dup_rr_div�  óG   € Ü˜$Ÿ-™-¨Ó*¨D¯M©M¸!Ó,<¸d¿k¹kÓJ‰ˆˆ1Ø—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                óÒ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}| j	                  |«      | j	                  |«      fS rJ  )r7   rH  r(  r)  rL  r‹  s        r0  r7   zIPolys.dmp_rr_div„  óQ   € Ü˜$Ÿ-™-¨Ó*¨D¯M©M¸!Ó,<¸d¿j¹jÈ¹lÈDÏKÉKÓX‰ˆˆ1Ø—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                ó¶   — t        | j                  |«      | j                  |«      | j                  «      \  }}| j                  |«      | j                  |«      fS r,  )r8   rH  r)  rL  r‹  s        r0  r8   zIPolys.dup_ff_div‡  rš  r3  c                óÒ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}| j	                  |«      | j	                  |«      fS rJ  )r9   rH  r(  r)  rL  r‹  s        r0  r9   zIPolys.dmp_ff_divŠ  rœ  r3  c                ó¶   — t        | j                  |«      | j                  |«      | j                  «      \  }}| j                  |«      | j                  |«      fS r,  )r:   rH  r)  rL  r‹  s        r0  r:   zIPolys.dup_divŽ  sG   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿;¹;ÓG‰ˆˆ1Ø—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r;   rH  r)  ru  s      r0  r;   zIPolys.dup_rem‘  rw  r3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r<   rH  r)  ru  s      r0  r<   zIPolys.dup_quo“  rw  r3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r=   rH  r)  ru  s      r0  r=   zIPolys.dup_exquo•  s0   € Ø�‰œy¨¯©°qÓ)9¸4¿=¹=ÈÓ;KÈTÏ[É[ÓYÓZÐZr3  c                óÒ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}| j	                  |«      | j	                  |«      fS rJ  )r>   rH  r(  r)  rL  r‹  s        r0  r>   zIPolys.dmp_div˜  sQ   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿:¹:Àa¹<ÈÏÉÓU‰ˆˆ1Ø—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r?   rH  r(  r)  ru  s      r0  r?   zIPolys.dmp_rem›  ry  r3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r@   rH  r(  r)  ru  s      r0  r@   zIPolys.dmp_quo�  ry  r3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  rA   rH  r(  r)  ru  s      r0  rA   zIPolys.dmp_exquoŸ  s>   € Ø�‰œy¨¯©°qÓ)9¸4¿=¹=ÈÓ;KÈTÏZÉZÐXYÉ\Ð[_×[fÑ[fÓgÓhÐhr3  c                óL   — t        | j                  |«      | j                  «      S r,  )rB   rH  r)  rn  s     r0  rB   zIPolys.dup_max_norm¢  s   € Ü˜DŸM™M¨!Ó,¨d¯k©kÓ:Ð:r3  c                óh   — t        | j                  |«      | j                  dz
  | j                  «      S rJ  )rC   rH  r(  r)  rn  s     r0  rC   zIPolys.dmp_max_norm¤  s&   € Ü˜DŸM™M¨!Ó,¨d¯j©j¸©l¸D¿K¹KÓHÐHr3  c                óL   — t        | j                  |«      | j                  «      S r,  )rD   rH  r)  rn  s     r0  rD   zIPolys.dup_l1_norm§  s   € Ü˜4Ÿ=™=¨Ó+¨T¯[©[Ó9Ð9r3  c                óh   — t        | j                  |«      | j                  dz
  | j                  «      S rJ  )rE   rH  r(  r)  rn  s     r0  rE   zIPolys.dmp_l1_norm©  s&   € Ü˜4Ÿ=™=¨Ó+¨T¯Z©Z¸©\¸4¿;¹;ÓGÐGr3  c                óL   — t        | j                  |«      | j                  «      S r,  )rF   rH  r)  rn  s     r0  rF   zIPolys.dup_l2_norm_squared¬  ó   € Ü" 4§=¡=°Ó#3°T·[±[ÓAÐAr3  c                óh   — t        | j                  |«      | j                  dz
  | j                  «      S rJ  )rG   rH  r(  r)  rn  s     r0  rG   zIPolys.dmp_l2_norm_squared®  s&   € Ü" 4§=¡=°Ó#3°T·Z±ZÀ±\À4Ç;Á;ÓOÐOr3  c           
     ó†   — | j                  t        t        t        | j                  |«      «      | j
                  «      «      S r,  )rL  rH   ÚlistÚmaprH  r)  ©r.  Úpolyss     r0  rH   zIPolys.dup_expand±  s,   € Ø�‰œz¬$¬s°4·=±=À%Ó/HÓ*IÈ4Ï;É;ÓWÓXÐXr3  c           
     ó¢   — | j                  t        t        t        | j                  |«      «      | j
                  dz
  | j                  «      «      S rJ  )rL  rI   r¯  r°  rH  r(  r)  r±  s     r0  rI   zIPolys.dmp_expand³  s:   € Ø�‰œz¬$¬s°4·=±=À%Ó/HÓ*IÈ4Ï:É:ÐVWÉ<ÐY]×YdÑYdÓeÓfÐfr3  c                óL   — t        | j                  |«      | j                  «      S r,  )rJ   rH  r)  rn  s     r0  rJ   zIPolys.dup_LC¶  ó   € Ü�d—m‘m AÓ&¨¯©Ó4Ð4r3  c                ó˜   — t        | j                  |«      | j                  «      }t        |t        «      r| dd  j                  |«      S |S rJ  )rK   rH  r)  rC  r¯  rL  )r.  rO  ÚLCs      r0  rK   zIPolys.dmp_LC¸  óA   € Ü�D—M‘M !Ó$ d§k¡kÓ2ˆÜ�bœ$ÔØ˜˜�8×&Ñ& rÓ*Ð*àˆIr3  c                óL   — t        | j                  |«      | j                  «      S r,  )rL   rH  r)  rn  s     r0  rL   zIPolys.dup_TC¾  rµ  r3  c                ó˜   — t        | j                  |«      | j                  «      }t        |t        «      r| dd  j                  |«      S |S rJ  )rM   rH  r)  rC  r¯  rL  )r.  rO  ÚTCs      r0  rM   zIPolys.dmp_TCÀ  r¸  r3  c                óh   — t        | j                  |«      | j                  dz
  | j                  «      S rJ  )rN   rH  r(  r)  rn  s     r0  rN   zIPolys.dmp_ground_LCÇ  ó&   € Ü˜TŸ]™]¨1Ó-¨t¯z©z¸!©|¸T¿[¹[ÓIÐIr3  c                óh   — t        | j                  |«      | j                  dz
  | j                  «      S rJ  )rO   rH  r(  r)  rn  s     r0  rO   zIPolys.dmp_ground_TCÉ  r½  r3  c                ó6   — t        | j                  |«      «      S r,  )rP   rH  rn  s     r0  rP   zIPolys.dup_degreeÌ  s   € Ü˜$Ÿ-™-¨Ó*Ó+Ð+r3  c                óR   — t        | j                  |«      | j                  dz
  «      S rJ  )rQ   rH  r(  rn  s     r0  rQ   zIPolys.dmp_degreeÎ  s    € Ü˜$Ÿ-™-¨Ó*¨D¯J©J°q©LÓ9Ð9r3  c                óT   — t        | j                  |«      || j                  dz
  «      S rJ  )rR   rH  r(  )r.  rO  Újs      r0  rR   zIPolys.dmp_degree_inÐ  s"   € Ü˜TŸ]™]¨1Ó-¨q°$·*±*¸Q±,Ó?Ð?r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  rT   rH  r)  ©r.  rO  Úms      r0  rT   zIPolys.dup_integrateÒ  s'   € Ø�‰œ}¨T¯]©]¸1Ó-=¸qÀ$Ç+Á+ÓNÓOÐOr3  c                óˆ   — | j                  t        | j                  |«      || j                  dz
  | j                  «      «      S rJ  )rL  rU   rH  r(  r)  rÄ  s      r0  rU   zIPolys.dmp_integrateÔ  s4   € Ø�‰œ}¨T¯]©]¸1Ó-=¸qÀ$Ç*Á*ÈQÁ,ÐPT×P[ÑP[Ó\Ó]Ð]r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  rW   rH  r)  rÄ  s      r0  rW   zIPolys.dup_diff×  s'   € Ø�‰œx¨¯©°aÓ(8¸!¸T¿[¹[ÓIÓJÐJr3  c                óˆ   — | j                  t        | j                  |«      || j                  dz
  | j                  «      «      S rJ  )rL  rX   rH  r(  r)  rÄ  s      r0  rX   zIPolys.dmp_diffÙ  s1   € Ø�‰œx¨¯©°aÓ(8¸!¸T¿Z¹ZÈ¹\È4Ï;É;ÓWÓXÐXr3  c           	     óŠ   — | j                  t        | j                  |«      ||| j                  dz
  | j                  «      «      S rJ  )rL  rY   rH  r(  r)  ©r.  rO  rÅ  rÂ  s       r0  rY   zIPolys.dmp_diff_inÜ  s6   € Ø�‰œ{¨4¯=©=¸Ó+;¸QÀÀ4Ç:Á:ÈaÁ<ÐQU×Q\ÑQ\Ó]Ó^Ð^r3  c           	     óŠ   — | j                  t        | j                  |«      ||| j                  dz
  | j                  «      «      S rJ  )rL  rV   rH  r(  r)  rÊ  s       r0  rV   zIPolys.dmp_integrate_inÞ  s8   € Ø�‰Ô/°·±¸aÓ0@À!ÀQÈÏ
É
ÐSTÉÐVZ×VaÑVaÓbÓcÐcr3  c                óN   — t        | j                  |«      || j                  «      S r,  )rZ   rH  r)  ©r.  rO  Úas      r0  rZ   zIPolys.dup_evalá  s   € Ü˜Ÿ™ aÓ(¨!¨T¯[©[Ó9Ð9r3  c                ó’   — t        | j                  |«      || j                  dz
  | j                  «      }| dd  j	                  |«      S rJ  )r[   rH  r(  r)  rL  )r.  rO  rÎ  Úresults       r0  r[   zIPolys.dmp_evalã  s>   € Ü˜$Ÿ-™-¨Ó*¨A¨t¯z©z¸!©|¸T¿[¹[ÓIˆØ�A�Bˆx×"Ñ" 6Ó*Ð*r3  c                ó¬   — t        | j                  |«      ||| j                  dz
  | j                  «      }| j	                  |«      j                  |«      S rJ  )r\   rH  r(  r)  r1  rL  )r.  rO  rÎ  rÂ  rÐ  s        r0  r\   zIPolys.dmp_eval_inç  sB   € Ü˜TŸ]™]¨1Ó-¨q°!°T·Z±ZÀ±\À4Ç;Á;ÓOˆØ�y‰y˜‹|×&Ñ& vÓ.Ð.r3  c                ó®   — t        | j                  |«      |||| j                  dz
  | j                  «      }| j	                  |«      j                  |«      S rJ  )r^   rH  r(  r)  r1  rL  )r.  rO  rÅ  rÎ  rÂ  rÐ  s         r0  r^   zIPolys.dmp_diff_eval_inê  sD   € Ü! $§-¡-°Ó"2°A°q¸!¸T¿Z¹ZÈ¹\È4Ï;É;ÓWˆØ�y‰y˜‹|×&Ñ& vÓ.Ð.r3  c                óÊ   — t        | j                  |«      || j                  dz
  | j                  «      }t	        |t
        «      r| d t        |«        j                  |«      S |S rJ  )r]   rH  r(  r)  rC  r¯  ÚlenrL  )r.  rO  ÚArÐ  s       r0  r]   zIPolys.dmp_eval_tailî  sS   € Ü˜tŸ}™}¨QÓ/°°D·J±J¸q±LÀ$Ç+Á+ÓNˆÜ�fœdÔ#Ø˜œ#˜a›&˜�>×,Ñ,¨VÓ4Ð4àˆMr3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  r_   rH  r)  ©r.  rO  Úps      r0  r_   zIPolys.dup_truncõ  ó'   € Ø�‰œy¨¯©°qÓ)9¸1¸d¿k¹kÓJÓKÐKr3  c                ó¬   — | j                  t        | j                  |«      | dd  j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r`   rH  r(  r)  ru  s      r0  r`   zIPolys.dmp_trunc÷  sJ   € Ø�‰œy¨¯©°qÓ)9¸4ÀÀ¸8×;LÑ;LÈQÓ;OÐQU×Q[ÑQ[Ð\]ÑQ]Ð_c×_jÑ_jÓkÓlÐlr3  c                óˆ   — | j                  t        | j                  |«      || j                  dz
  | j                  «      «      S rJ  )rL  ra   rH  r(  r)  r×  s      r0  ra   zIPolys.dmp_ground_truncù  rg  r3  c                ój   — | j                  t        | j                  |«      | j                  «      «      S r,  )rL  rb   rH  r)  rn  s     r0  rb   zIPolys.dup_monicü  s%   € Ø�‰œy¨¯©°qÓ)9¸4¿;¹;ÓGÓHÐHr3  c                ó†   — | j                  t        | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  rc   rH  r(  r)  rn  s     r0  rc   zIPolys.dmp_ground_monicþ  s3   € Ø�‰Ô/°·±¸aÓ0@À$Ç*Á*ÈQÁ,ÐPT×P[ÑP[Ó\Ó]Ð]r3  c                óº   — t        | j                  |«      | j                  |«      | j                  «      \  }}}|| j                  |«      | j                  |«      fS r,  )rh   rH  r)  rL  ©r.  rO  rv  rP  ÚFÚGs         r0  rh   zIPolys.dup_extract  sK   € Ü˜dŸm™m¨AÓ.°·±¸aÓ0@À$Ç+Á+ÓN‰ˆˆ1ˆaØ�4—?‘? 1Ó% t§¡°qÓ'9Ð:Ð:r3  c                óÖ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}}|| j	                  |«      | j	                  |«      fS rJ  )ri   rH  r(  r)  rL  rß  s         r0  ri   zIPolys.dmp_ground_extract  sY   € Ü$ T§]¡]°1Ó%5°t·}±}ÀQÓ7GÈÏÉÐTUÉÐW[×WbÑWbÓc‰ˆˆ1ˆaØ�4—?‘? 1Ó% t§¡°qÓ'9Ð:Ð:r3  c                óÐ   — t        | j                  |«      j                  d«      j                  «       | j                  «      \  }}| j                  |«      | j                  |«      fS rJ  )rj   rF  r1  rH  r)  rL  ©r.  rO  rØ  rŒ  s       r0  rj   zIPolys.dup_real_imag  sO   € Ü˜TŸY™Y q›\×.Ñ.¨qÓ1×:Ñ:Ó<¸d¿k¹kÓJ‰ˆˆ1Ø—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                ój   — | j                  t        | j                  |«      | j                  «      «      S r,  )rL  rk   rH  r)  rn  s     r0  rk   zIPolys.dup_mirror  s%   € Ø�‰œz¨$¯-©-¸Ó*:¸D¿K¹KÓHÓIÐIr3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  rl   rH  r)  rÍ  s      r0  rl   zIPolys.dup_scale  rÙ  r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  rm   rH  r)  rÍ  s      r0  rm   zIPolys.dup_shift  rÙ  r3  c                óˆ   — | j                  t        | j                  |«      || j                  dz
  | j                  «      «      S rJ  )rL  rn   rH  r(  r)  rÍ  s      r0  rn   zIPolys.dmp_shift  s1   € Ø�‰œy¨¯©°qÓ)9¸1¸d¿j¹jÈ¹lÈDÏKÉKÓXÓYÐYr3  c           	     óª   — | j                  t        | j                  |«      | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  ro   rH  r)  rä  s       r0  ro   zIPolys.dup_transform  sB   € Ø�‰œ}¨T¯]©]¸1Ó-=¸t¿}¹}ÈQÓ?OÐQU×Q^ÑQ^Ð_`ÓQaÐcg×cnÑcnÓoÓpÐpr3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  rp   rH  r)  ru  s      r0  rp   zIPolys.dup_compose  s0   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏ{É{Ó[Ó\Ð\r3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  rq   rH  r(  r)  ru  s      r0  rq   zIPolys.dmp_compose  s>   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏzÉzÐZ[É|Ð]a×]hÑ]hÓiÓjÐjr3  c                óŠ   — t        | j                  |«      | j                  «      }t        t	        | j
                  |«      «      S r,  )rr   rH  r)  r¯  r°  rL  )r.  rO  Ú
componentss      r0  rr   zIPolys.dup_decompose  s1   € Ü" 4§=¡=°Ó#3°T·[±[ÓAˆ
Ü”C˜Ÿ™¨Ó4Ó5Ð5r3  c                ó¦   — t        | j                  |«      | j                  dz
  | j                  «      }| j	                  «       j                  |«      S rJ  )rs   rH  r(  r)  r7  rL  ©r.  rO  rÐ  s      r0  rs   zIPolys.dmp_lift   s=   € Ü˜$Ÿ-™-¨Ó*¨D¯J©J°q©L¸$¿+¹+ÓFˆØ�~‰~Ó×*Ñ*¨6Ó2Ð2r3  c                óL   — t        | j                  |«      | j                  «      S r,  )rt   rH  r)  rn  s     r0  rt   zIPolys.dup_sign_variations$  r¬  r3  c                óÚ   — t        | j                  |«      | j                  |¬«      \  }}|r+| j                  | j                  j	                  «       ¬«      }n| }||j                  |«      fS )N©Úconvert©r)  )ru   rH  r)  r5  Úget_ringrL  ©r.  rO  ró  rP  rà  rD  s         r0  ru   zIPolys.dup_clear_denoms'  sZ   € Ü §¡¨aÓ 0°$·+±+ÀwÔO‰ˆˆ1ÙØ—:‘: T§[¡[×%9Ñ%9Ó%;�:Ó<‰DàˆDØ�4—?‘? 1Ó%Ð&Ð&r3  c                óö   — t        | j                  |«      | j                  dz
  | j                  |¬«      \  }}|r+| j	                  | j                  j                  «       ¬«      }n| }||j                  |«      fS )NrK  rò  rô  )rv   rH  r(  r)  r5  rõ  rL  rö  s         r0  rv   zIPolys.dmp_clear_denoms.  se   € Ü §¡¨aÓ 0°$·*±*¸Q±,ÀÇÁÐU\Ô]‰ˆˆ1ÙØ—:‘: T§[¡[×%9Ñ%9Ó%;�:Ó<‰DàˆDØ�4—?‘? 1Ó%Ð&Ð&r3  c                ól   — | j                  t        | j                  |«      || j                  «      «      S r,  )rL  rw   rH  r)  ri  s      r0  rw   zIPolys.dup_revert6  rk  r3  c                ó¶   — t        | j                  |«      | j                  |«      | j                  «      \  }}| j                  |«      | j                  |«      fS r,  )rx   rH  r)  rL  ©r.  rO  rv  Úsr~  s        r0  rx   zIPolys.dup_half_gcdex9  sG   € Ü˜dŸm™m¨AÓ.°·±¸aÓ0@À$Ç+Á+ÓN‰ˆˆ1Ø—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                óÒ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}| j	                  |«      | j	                  |«      fS rJ  )ry   rH  r(  r)  rL  rú  s        r0  ry   zIPolys.dmp_half_gcdex<  sT   € Ü˜dŸm™m¨AÓ.°·±¸aÓ0@À$Ç*Á*ÈQÁ,ÐPT×P[ÑP[Ó\‰ˆˆ1Ø—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                óØ   — t        | j                  |«      | j                  |«      | j                  «      \  }}}| j                  |«      | j                  |«      | j                  |«      fS r,  )rz   rH  r)  rL  ©r.  rO  rv  rû  Útr~  s         r0  rz   zIPolys.dup_gcdex?  sT   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇÁÓL‰ˆˆ1ˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr3  c                óô   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}}| j	                  |«      | j	                  |«      | j	                  |«      fS rJ  )r{   rH  r(  r)  rL  rþ  s         r0  r{   zIPolys.dmp_gcdexB  s^   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇ
Á
È1ÁÈdÏkÉkÓZ‰ˆˆ1ˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr3  c                óŠ   — | j                  t        | j                  |«      | j                  |«      | j                  «      «      S r,  )rL  r|   rH  r)  ru  s      r0  r|   zIPolys.dup_invertF  r’  r3  c                ó¦   — | j                  t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  r}   rH  r(  r)  ru  s      r0  r}   zIPolys.dmp_invertH  r˜  r3  c                óª   — t        | j                  |«      | j                  |«      | j                  «      }t        t	        | j
                  |«      «      S r,  )r~   rH  r)  r¯  r°  rL  ©r.  rO  rv  Úprss       r0  r~   zIPolys.dup_euclidean_prsK  ó<   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇKÁKÓPˆÜ”C˜Ÿ™¨Ó-Ó.Ð.r3  c                óÆ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      }t	        t        | j                  |«      «      S rJ  )r   rH  r(  r)  r¯  r°  rL  r  s       r0  r   zIPolys.dmp_euclidean_prsN  óI   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇJÁJÈqÁLÐRV×R]ÑR]Ó^ˆÜ”C˜Ÿ™¨Ó-Ó.Ð.r3  c                óª   — t        | j                  |«      | j                  |«      | j                  «      }t        t	        | j
                  |«      «      S r,  )r€   rH  r)  r¯  r°  rL  r  s       r0  r€   zIPolys.dup_primitive_prsQ  r  r3  c                óÆ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      }t	        t        | j                  |«      «      S rJ  )r�   rH  r(  r)  r¯  r°  rL  r  s       r0  r�   zIPolys.dmp_primitive_prsT  r  r3  c                ó´   — t        | j                  |«      | j                  |«      | j                  «      \  }}t        t	        | j
                  |«      «      |fS r,  )r‚   rH  r)  r¯  r°  rL  ©r.  rO  rv  r  Úsress        r0  r‚   zIPolys.dup_inner_subresultantsX  sH   € Ü+¨D¯M©M¸!Ó,<¸d¿m¹mÈAÓ>NÐPT×P[ÑP[Ó\‰	ˆˆTÜ”S˜Ÿ™¨#Ó.Ó/°Ð6Ð6r3  c                óÐ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}t	        t        | j                  |«      «      |fS rJ  )r†   rH  r(  r)  r¯  r°  rL  r  s        r0  r†   zIPolys.dmp_inner_subresultants[  sW   € Ü,¨T¯]©]¸1Ó-=¸t¿}¹}ÈQÓ?OÐQU×Q[ÑQ[Ð\]ÑQ]Ð_c×_jÑ_jÓk‰	ˆˆTÜ”S˜Ÿ™¨#Ó.Ó/°Ð6Ð6r3  c                óª   — t        | j                  |«      | j                  |«      | j                  «      }t        t	        | j
                  |«      «      S r,  )rƒ   rH  r)  r¯  r°  rL  r  s       r0  rƒ   zIPolys.dup_subresultants_  r  r3  c                óÆ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      }t	        t        | j                  |«      «      S rJ  )r‡   rH  r(  r)  r¯  r°  rL  r  s       r0  r‡   zIPolys.dmp_subresultantsb  r  r3  c                ó´   — t        | j                  |«      | j                  |«      | j                  «      \  }}|t        t	        | j
                  |«      «      fS r,  )r„   rH  r)  r¯  r°  rL  ©r.  rO  rv  Úresr  s        r0  r„   zIPolys.dup_prs_resultantf  sE   € Ü$ T§]¡]°1Ó%5°t·}±}ÀQÓ7GÈÏÉÓU‰ˆˆSØ”Tœ#˜dŸo™o¨sÓ3Ó4Ð5Ð5r3  c                óô   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}| dd  j	                  |«      t        t        | j                  |«      «      fS rJ  )rˆ   rH  r(  r)  rL  r¯  r°  r  s        r0  rˆ   zIPolys.dmp_prs_resultanti  sd   € Ü$ T§]¡]°1Ó%5°t·}±}ÀQÓ7GÈÏÉÐTUÉÐW[×WbÑWbÓc‰ˆˆSØ�Q�R�×#Ñ# CÓ(¬$¬s°4·?±?ÀCÓ/HÓ*IÐJÐJr3  c                óÐ   — t        | j                  |«      | j                  |«      | j                  |«      | j                  dz
  | j                  «      }| dd  j                  |«      S rJ  )r‰   rH  r=  r(  r)  rL  )r.  rO  rv  rØ  r  s        r0  r‰   zIPolys.dmp_zz_modular_resultantm  s[   € Ü& t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï?É?Ð[\ÓK]Ð_c×_iÑ_iÐjkÑ_kÐmq×mxÑmxÓyˆØ�A�Bˆx×"Ñ" 3Ó'Ð'r3  c                ó°   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      }| dd  j	                  |«      S rJ  )rŠ   rH  r(  r)  rL  ©r.  rO  rv  r  s       r0  rŠ   zIPolys.dmp_zz_collins_resultantp  óK   € Ü& t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï:É:ÐVWÉ<ÐY]×YdÑYdÓeˆØ�A�Bˆx×"Ñ" 3Ó'Ð'r3  c                ó°   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      }| dd  j	                  |«      S rJ  )r‹   rH  r(  r)  rL  r  s       r0  r‹   zIPolys.dmp_qq_collins_resultants  r  r3  c                ól   — t        | j                  |«      | j                  |«      | j                  «      S r,  )r…   rH  r)  ru  s      r0  r…   zIPolys.dup_resultantw  s'   € Ü˜TŸ]™]¨1Ó-¨t¯}©}¸QÓ/?ÀÇÁÓMÐMr3  c                óÔ   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      }t	        |t
        «      r| dd  j                  |«      S |S rJ  )rŒ   rH  r(  r)  rC  r¯  rL  r  s       r0  rŒ   zIPolys.dmp_resultanty  sV   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇ
Á
È1ÁÈdÏkÉkÓZˆÜ�cœ4Ô Ø˜˜�8×&Ñ& sÓ+Ð+àˆJr3  c                óL   — t        | j                  |«      | j                  «      S r,  )r�   rH  r)  rn  s     r0  r�   zIPolys.dup_discriminant€  s   € Ü §¡¨aÓ 0°$·+±+Ó>Ð>r3  c                ó´   — t        | j                  |«      | j                  dz
  | j                  «      }t	        |t
        «      r| dd  j                  |«      S |S rJ  )rŽ   rH  r(  r)  rC  r¯  rL  )r.  rO  Údiscs      r0  rŽ   zIPolys.dmp_discriminant‚  sK   € Ü §¡¨aÓ 0°$·*±*¸Q±,ÀÇÁÓLˆÜ�dœDÔ!Ø˜˜�8×&Ñ& tÓ,Ð,àˆKr3  c                óØ   — t        | j                  |«      | j                  |«      | j                  «      \  }}}| j                  |«      | j                  |«      | j                  |«      fS r,  )r�   rH  r)  rL  ©r.  rO  rv  ÚHrà  rá  s         r0  r�   zIPolys.dup_rr_prs_gcd‰  óT   € Ü  §¡¨qÓ!1°4·=±=ÀÓ3CÀTÇ[Á[ÓQ‰ˆˆ1ˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr3  c                óØ   — t        | j                  |«      | j                  |«      | j                  «      \  }}}| j                  |«      | j                  |«      | j                  |«      fS r,  )r�   rH  r)  rL  r   s         r0  r�   zIPolys.dup_ff_prs_gcdŒ  r"  r3  c                óô   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}}| j	                  |«      | j	                  |«      | j	                  |«      fS rJ  )r‘   rH  r(  r)  rL  r   s         r0  r‘   zIPolys.dmp_rr_prs_gcd�  ób   € Ü  §¡¨qÓ!1°4·=±=ÀÓ3CÀTÇZÁZÐPQÁ\ÐSW×S^ÑS^Ó_‰ˆˆ1ˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr3  c                óô   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}}| j	                  |«      | j	                  |«      | j	                  |«      fS rJ  )r’   rH  r(  r)  rL  r   s         r0  r’   zIPolys.dmp_ff_prs_gcd’  r%  r3  c                óØ   — t        | j                  |«      | j                  |«      | j                  «      \  }}}| j                  |«      | j                  |«      | j                  |«      fS r,  )r“   rH  r)  rL  r   s         r0  r“   zIPolys.dup_zz_heu_gcd•  r"  r3  c                óô   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}}| j	                  |«      | j	                  |«      | j	                  |«      fS rJ  )r”   rH  r(  r)  rL  r   s         r0  r”   zIPolys.dmp_zz_heu_gcd˜  r%  r3  c                óØ   — t        | j                  |«      | j                  |«      | j                  «      \  }}}| j                  |«      | j                  |«      | j                  |«      fS r,  )r•   rH  r)  rL  r   s         r0  r•   zIPolys.dup_qq_heu_gcd›  r"  r3  c                óô   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}}| j	                  |«      | j	                  |«      | j	                  |«      fS rJ  )r–   rH  r(  r)  rL  r   s         r0  r–   zIPolys.dmp_qq_heu_gcdž  r%  r3  c                óØ   — t        | j                  |«      | j                  |«      | j                  «      \  }}}| j                  |«      | j                  |«      | j                  |«      fS r,  )r—   rH  r)  rL  r   s         r0  r—   zIPolys.dup_inner_gcd¡  sT   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇKÁKÓP‰ˆˆ1ˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr3  c                óô   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      \  }}}| j	                  |«      | j	                  |«      | j	                  |«      fS rJ  )r˜   rH  r(  r)  rL  r   s         r0  r˜   zIPolys.dmp_inner_gcd¤  sa   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇJÁJÈqÁLÐRV×R]ÑR]Ó^‰ˆˆ1ˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr3  c                óŽ   — t        | j                  |«      | j                  |«      | j                  «      }| j                  |«      S r,  )r™   rH  r)  rL  ©r.  rO  rv  r!  s       r0  r™   zIPolys.dup_gcd§  ó5   € Ü�D—M‘M !Ó$ d§m¡m°AÓ&6¸¿¹ÓDˆØ�‰˜qÓ!Ð!r3  c                óª   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      }| j	                  |«      S rJ  )rš   rH  r(  r)  rL  r.  s       r0  rš   zIPolys.dmp_gcdª  ó?   € Ü�D—M‘M !Ó$ d§m¡m°AÓ&6¸¿
¹
À1¹ÀdÇkÁkÓRˆØ�‰˜qÓ!Ð!r3  c                óŽ   — t        | j                  |«      | j                  |«      | j                  «      }| j                  |«      S r,  )r›   rH  r)  rL  r.  s       r0  r›   zIPolys.dup_rr_lcm­  ó5   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿;¹;ÓGˆØ�‰˜qÓ!Ð!r3  c                óŽ   — t        | j                  |«      | j                  |«      | j                  «      }| j                  |«      S r,  )rœ   rH  r)  rL  r.  s       r0  rœ   zIPolys.dup_ff_lcm°  r3  r3  c                óŽ   — t        | j                  |«      | j                  |«      | j                  «      }| j                  |«      S r,  )r�   rH  r)  rL  r.  s       r0  r�   zIPolys.dup_lcm³  r/  r3  c                óª   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      }| j	                  |«      S rJ  )rž   rH  r(  r)  rL  r.  s       r0  rž   zIPolys.dmp_rr_lcm¶  ó?   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿:¹:Àa¹<ÈÏÉÓUˆØ�‰˜qÓ!Ð!r3  c                óª   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      }| j	                  |«      S rJ  )rŸ   rH  r(  r)  rL  r.  s       r0  rŸ   zIPolys.dmp_ff_lcm¹  r7  r3  c                óª   — t        | j                  |«      | j                  |«      | j                  dz
  | j                  «      }| j	                  |«      S rJ  )r    rH  r(  r)  rL  r.  s       r0  r    zIPolys.dmp_lcm¼  r1  r3  c                óP   — t        | j                  |«      | j                  «      }|S r,  )rd   rH  r)  ©r.  rO  Úconts      r0  rd   zIPolys.dup_contentÀ  s    € Ü˜4Ÿ=™=¨Ó+¨T¯[©[Ó9ˆØˆr3  c                óx   — t        | j                  |«      | j                  «      \  }}|| j                  |«      fS r,  )rf   rH  r)  rL  ©r.  rO  r<  Úprims       r0  rf   zIPolys.dup_primitiveÃ  s3   € Ü" 4§=¡=°Ó#3°T·[±[ÓA‰
ˆˆdØ�T—_‘_ TÓ*Ð*Ð*r3  c                ó´   — t        | j                  |«      | j                  dz
  | j                  «      }t	        |t
        «      r| dd  j                  |«      S |S rJ  )r¡   rH  r(  r)  rC  r¯  rL  r;  s      r0  r¡   zIPolys.dmp_contentÇ  sK   € Ü˜4Ÿ=™=¨Ó+¨T¯Z©Z¸©\¸4¿;¹;ÓGˆÜ�dœDÔ!Ø˜˜�8×&Ñ& tÓ,Ð,àˆKr3  c                óþ   — t        | j                  |«      | j                  dz
  | j                  «      \  }}t	        |t
        «      r%| dd  j                  |«      | j                  |«      fS || j                  |«      fS rJ  )r¢   rH  r(  r)  rC  r¯  rL  r>  s       r0  r¢   zIPolys.dmp_primitiveÍ  sl   € Ü" 4§=¡=°Ó#3°T·Z±ZÀ±\À4Ç;Á;ÓO‰
ˆˆdÜ�dœDÔ!Ø˜˜�H×'Ñ'¨Ó-¨t¯©¸tÓ/DÐEÐEà˜$Ÿ/™/¨$Ó/Ð0Ð0r3  c                ól   — t        | j                  |«      | j                  dz
  | j                  «      }|S rJ  )re   rH  r(  r)  r;  s      r0  re   zIPolys.dmp_ground_contentÔ  s*   € Ü! $§-¡-°Ó"2°D·J±J¸q±LÀ$Ç+Á+ÓNˆØˆr3  c                ó”   — t        | j                  |«      | j                  dz
  | j                  «      \  }}|| j	                  |«      fS rJ  )rg   rH  r(  r)  rL  r>  s       r0  rg   zIPolys.dmp_ground_primitive×  s=   € Ü)¨$¯-©-¸Ó*:¸D¿J¹JÀq¹LÈ$Ï+É+ÓV‰
ˆˆdØ�d—o‘o dÓ+Ð,Ð,r3  c                ó  — t        | j                  |«      | j                  |«      | j                  |¬«      }|s+|\  }}}}||| j                  |«      | j                  |«      fS |\  }}| j                  |«      | j                  |«      fS )N©Úinclude)r£   rH  r)  rL  ©	r.  rO  rv  rF  rÐ  ÚcfÚcgrà  rá  s	            r0  r£   zIPolys.dup_cancelÛ  s€   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇÁÐU\Ô]ˆÙØ!‰LˆB��A�qØ˜˜DŸO™O¨AÓ.°·±ÀÓ0BÐCÐCà‰DˆAˆqØ—O‘O AÓ&¨¯©¸Ó(:Ð;Ð;r3  c                ó4  — t        | j                  |«      | j                  |«      | j                  dz
  | j                  |¬«      }|s+|\  }}}}||| j	                  |«      | j	                  |«      fS |\  }}| j	                  |«      | j	                  |«      fS )NrK  rE  )r¤   rH  r(  r)  rL  rG  s	            r0  r¤   zIPolys.dmp_cancelã  sŠ   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇ
Á
È1ÁÈdÏkÉkÐcjÔkˆÙØ!‰LˆB��A�qØ˜˜DŸO™O¨AÓ.°·±ÀÓ0BÐCÐCà‰DˆAˆqØ—O‘O AÓ&¨¯©¸Ó(:Ð;Ð;r3  c           	     óà   — t        | j                  |«      t        t        | j                  |«      «      | j                  «      }|D ��cg c]  \  }}| j                  |«      |f‘Œ c}}S c c}}w r,  )r¥   rH  r¯  r°  r)  rL  ©r.  rO  Úfactorsrv  Úks        r0  r¥   zIPolys.dup_trial_divisionì  sV   € Ü$ T§]¡]°1Ó%5´t¼CÀÇÁÈwÓ<WÓ7XÐZ^×ZeÑZeÓfˆØ5<×>©T¨Q°�$—/‘/ !Ó$ aÒ(Ó>Ð>ùÓ>s   Á	A*c           	     óü   — t        | j                  |«      t        t        | j                  |«      «      | j                  dz
  | j
                  «      }|D ��cg c]  \  }}| j                  |«      |f‘Œ c}}S c c}}w rJ  )r¦   rH  r¯  r°  r(  r)  rL  rL  s        r0  r¦   zIPolys.dmp_trial_divisionï  se   € Ü$ T§]¡]°1Ó%5´t¼CÀÇÁÈwÓ<WÓ7XÐZ^×ZdÑZdÐefÑZfÐhl×hsÑhsÓtˆØ5<×>©T¨Q°�$—/‘/ !Ó$ aÒ(Ó>Ð>ùÓ>s   ÁA8c                óL   — t        | j                  |«      | j                  «      S r,  )r§   rH  r)  rn  s     r0  r§   zIPolys.dup_zz_mignotte_boundó  s   € Ü$ T§]¡]°1Ó%5°t·{±{ÓCÐCr3  c                óh   — t        | j                  |«      | j                  dz
  | j                  «      S rJ  )r¨   rH  r(  r)  rn  s     r0  r¨   zIPolys.dmp_zz_mignotte_boundõ  s&   € Ü$ T§]¡]°1Ó%5°t·z±zÀ!±|ÀTÇ[Á[ÓQÐQr3  c           
     ó  — | j                   }t        | ||«       ||«       ||«       ||«       ||«      | j                  «      \  }}	}
}| j                  |«      | j                  |	«      | j                  |
«      | j                  |«      fS r,  )rH  r©   r)  rL  )r.  rÅ  rO  rv  r~  rû  rÿ  ÚDrá  r!  ÚSÚTs               r0  r©   zIPolys.dup_zz_hensel_stepø  su   € Ø�M‰MˆÜ'¨©1¨Q«4±°1³±q¸³t¹Q¸q»TÁ1ÀQÃ4ÈÏÉÓU‰
ˆˆ1ˆa�Ø—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÈDÏOÉOÐ\]ÓL^Ð_Ð_r3  c           
     ó¼   — | j                   }t        | ||«      t        t        ||«      «      || j                  «      }t        t        | j
                  |«      «      S r,  )rH  rª   r¯  r°  r)  rL  )r.  rØ  rO  Úf_listÚlrS  r²  s          r0  rª   zIPolys.dup_zz_hensel_liftü  sF   € Ø�M‰MˆÜ" 1¡a¨£d¬D´°Q¸³Ó,@À!ÀTÇ[Á[ÓQˆÜ”C˜Ÿ™¨Ó/Ó0Ð0r3  c                ó¤   — t        | j                  |«      | j                  «      }|D ��cg c]  \  }}| j                  |«      |f‘Œ c}}S c c}}w r,  )r«   rH  r)  rL  rL  s        r0  r«   zIPolys.dup_zz_zassenhaus  sA   € Ü# D§M¡M°!Ó$4°d·k±kÓBˆØ5<×>©T¨Q°�$—/‘/ !Ó$ aÒ(Ó>Ð>ùÓ>ó   «Ac                óL   — t        | j                  |«      | j                  «      S r,  )r¬   rH  r)  rn  s     r0  r¬   zIPolys.dup_zz_irreducible_p  ó   € Ü# D§M¡M°!Ó$4°d·k±kÓBÐBr3  c                óP   — t        | j                  |«      | j                  |¬«      S )N)Úirreducible)r­   rH  r)  )r.  rO  r^  s      r0  r­   zIPolys.dup_cyclotomic_p  s   € Ü §¡¨aÓ 0°$·+±+È;ÔWÐWr3  c                óP   — t        || j                  «      }| j                  |«      S r,  )r®   r)  rL  )r.  rj  rà  s      r0  r®   zIPolys.dup_zz_cyclotomic_poly	  s!   € Ü" 1 d§k¡kÓ2ˆØ�‰˜qÓ!Ð!r3  c                ó’   — t        | j                  |«      | j                  «      }|€|S t        t	        | j
                  |«      «      S r,  )r¯   rH  r)  r¯  r°  rL  rï  s      r0  r¯   zIPolys.dup_zz_cyclotomic_factor  s;   € Ü)¨$¯-©-¸Ó*:¸D¿K¹KÓHˆØˆ>ØˆMäœ˜DŸO™O¨VÓ4Ó5Ð5r3  c                ó2   — t        |||| j                  «      S r,  )r²   r)  )r.  ÚEÚcsÚcts       r0  r²   zIPolys.dmp_zz_wang_non_divisors  s   € Ü'¨¨2¨r°4·;±;Ó?Ð?r3  c           
     ó¾  — | dd  }|D ��	cg c]  \  }}	|j                  |«      |	f‘Œ }}}	| d d }
t        t        |
j                   |«      «      }t        | j                  |«      |||||| j                  dz
  | j
                  «      \  }}}| j                  |«      t        t        |
j                  |«      «      t        t        |j                  |«      «      fS c c}	}w rJ  )rH  r¯  r°  r³   r(  r)  rL  )r.  rO  rU  rc  rb  r!  rÕ  Úmvrÿ  rN  ÚuvÚHHÚCCs                r0  r³   zIPolys.dmp_zz_wang_lead_coeffs  sÄ   € Ø�!�"ˆXˆØ./×1¡d a¨ˆr�{‰{˜1‹~˜qÒ!Ð1ˆÑ1Ø�"�1ˆXˆÜ”�R—[‘[ !Ó$Ó%ˆÜ+¨D¯M©M¸!Ó,<¸aÀÀQÈÈ1ÈdÏjÉjÐYZÉlÐ\`×\gÑ\gÓh‰	ˆˆ2ˆrØ�‰˜qÓ!¤4¬¨B¯M©M¸2Ó(>Ó#?ÄÄcÈ"Ï-É-ÐY[ÓF\ÓA]Ð]Ð]ùó	 2s   ‹Cc                óª   — t        t        t        | j                  |«      «      ||| j                  «      }t        t        | j
                  |«      «      S r,  )r´   r¯  r°  rH  r)  rL  )r.  rà  rÅ  rØ  rÐ  s        r0  r´   zIPolys.dup_zz_diophantine%  s<   € Ü#¤D¬¨T¯]©]¸AÓ)>Ó$?ÀÀAÀtÇ{Á{ÓSˆÜ”C˜Ÿ™¨Ó0Ó1Ð1r3  c           	     óè   — t        t        t        | j                  |«      «      | j                  |«      |||| j                  dz
  | j
                  «      }t        t        | j                  |«      «      S rJ  )rµ   r¯  r°  rH  r(  r)  rL  )r.  rà  rP  rÕ  r?  rØ  rÐ  s          r0  rµ   zIPolys.dmp_zz_diophantine*  s^   € Ü#¤D¬¨T¯]©]¸AÓ)>Ó$?ÀÇÁÈqÓAQÐSTÐVWÐYZÐ\`×\fÑ\fÐghÑ\hÐjn×juÑjuÓvˆÜ”C˜Ÿ™¨Ó0Ó1Ð1r3  c           	     ó>  — | d d }| dd  }t        t        |j                  |«      «      }t        t        |j                  |«      «      }t        | j                  |«      ||||| j                  dz
  | j
                  «      }t        t        | j                  |«      «      S rJ  )r¯  r°  rH  r¶   r(  r)  rL  )	r.  rO  r!  r·  rÕ  rØ  rg  rf  rÐ  s	            r0  r¶   z!IPolys.dmp_zz_wang_hensel_lifting/  s‡   € Ø�"�1ˆXˆØ�!�"ˆXˆÜ”�R—[‘[ !Ó$Ó%ˆÜ”#�b—k‘k 2Ó&Ó'ˆÜ+¨D¯M©M¸!Ó,<¸aÀÀQÈÈ4Ï:É:ÐVWÉ<ÐY]×YdÑYdÓeˆÜ”C˜Ÿ™¨Ó0Ó1Ð1r3  c                ó¶   — t        | j                  |«      | j                  dz
  | j                  ||¬«      }|D �cg c]  }| j	                  |«      ‘Œ c}S c c}w )NrK  )ÚmodÚseed)r·   rH  r(  r)  rL  )r.  rO  rn  ro  rM  rv  s         r0  r·   zIPolys.dmp_zz_wang7  sG   € Ü˜dŸm™m¨AÓ.°·
±
¸1±¸d¿k¹kÈsÐY]Ô^ˆØ-4Ö6¨�—‘ Õ#Ò6Ð6ùÒ6s   »Ac                óž   — t        | j                  |«      | j                  «      \  }}||D �cg c]  }| j                  |«      ‘Œ c}fS c c}w r,  )r°   rH  r)  rL  )r.  rO  ÚcoeffrM  rv  s        r0  r°   zIPolys.dup_zz_factor_sqf;  sA   € Ü*¨4¯=©=¸Ó+;¸T¿[¹[ÓI‰ˆˆwØ°WÖ>°˜Ÿ™¨Õ+Ò>Ð?Ð?ùÒ>s   ®A
c                ó®   — t        | j                  |«      | j                  «      \  }}||D ��cg c]  \  }}| j                  |«      |f‘Œ c}}fS c c}}w r,  )r±   rH  r)  rL  ©r.  rO  rq  rM  rv  rN  s         r0  r±   zIPolys.dup_zz_factor?  óJ   € Ü& t§}¡}°QÓ'7¸¿¹ÓE‰ˆˆwØ¸W×F±T°Q¸˜$Ÿ/™/¨!Ó,¨aÒ0ÓFÐGÐGùÓFó   ¯Ac                óÊ   — t        | j                  |«      | j                  dz
  | j                  «      \  }}||D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}fS c c}}w rJ  )r¸   rH  r(  r)  rL  rs  s         r0  r¸   zIPolys.dmp_zz_factorB  óT   € Ü& t§}¡}°QÓ'7¸¿¹ÀA¹ÀtÇ{Á{ÓS‰ˆˆwØ¸W×F±T°Q¸˜$Ÿ/™/¨!Ó,¨aÒ0ÓFÐGÐGùÓFó   ½Ac                ó®   — t        | j                  |«      | j                  «      \  }}||D ��cg c]  \  }}| j                  |«      |f‘Œ c}}fS c c}}w r,  )r¹   rH  r)  rL  rs  s         r0  r¹   zIPolys.dup_qq_i_factorF  óJ   € Ü(¨¯©°qÓ)9¸4¿;¹;ÓG‰ˆˆwØ¸W×F±T°Q¸˜$Ÿ/™/¨!Ó,¨aÒ0ÓFÐGÐGùÓFru  c                óÊ   — t        | j                  |«      | j                  dz
  | j                  «      \  }}||D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}fS c c}}w rJ  )r»   rH  r(  r)  rL  rs  s         r0  r»   zIPolys.dmp_qq_i_factorI  óT   € Ü(¨¯©°qÓ)9¸4¿:¹:Àa¹<ÈÏÉÓU‰ˆˆwØ¸W×F±T°Q¸˜$Ÿ/™/¨!Ó,¨aÒ0ÓFÐGÐGùÓFrx  c                ó®   — t        | j                  |«      | j                  «      \  }}||D ��cg c]  \  }}| j                  |«      |f‘Œ c}}fS c c}}w r,  )rº   rH  r)  rL  rs  s         r0  rº   zIPolys.dup_zz_i_factorM  rz  ru  c                óÊ   — t        | j                  |«      | j                  dz
  | j                  «      \  }}||D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}fS c c}}w rJ  )r¼   rH  r(  r)  rL  rs  s         r0  r¼   zIPolys.dmp_zz_i_factorP  r|  rx  c                ó®   — t        | j                  |«      | j                  «      \  }}||D ��cg c]  \  }}| j                  |«      |f‘Œ c}}fS c c}}w r,  )r½   rH  r)  rL  rs  s         r0  r½   zIPolys.dup_ext_factorT  sJ   € Ü'¨¯©°aÓ(8¸$¿+¹+ÓF‰ˆˆwØ¸W×F±T°Q¸˜$Ÿ/™/¨!Ó,¨aÒ0ÓFÐGÐGùÓFru  c                óÊ   — t        | j                  |«      | j                  dz
  | j                  «      \  }}||D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}fS c c}}w rJ  )r¾   rH  r(  r)  rL  rs  s         r0  r¾   zIPolys.dmp_ext_factorW  sT   € Ü'¨¯©°aÓ(8¸$¿*¹*ÀQ¹,ÈÏÉÓT‰ˆˆwØ¸W×F±T°Q¸˜$Ÿ/™/¨!Ó,¨aÒ0ÓFÐGÐGùÓFrx  c                ó®   — t        | j                  |«      | j                  «      \  }}||D ��cg c]  \  }}| j                  |«      |f‘Œ c}}fS c c}}w r,  )r¿   rH  r)  rL  rs  s         r0  r¿   zIPolys.dup_gf_factor[  rt  ru  c                óÊ   — t        | j                  |«      | j                  dz
  | j                  «      \  }}||D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}fS c c}}w rJ  )rÀ   rH  r(  r)  rL  rs  s         r0  rÀ   zIPolys.dmp_gf_factor^  rw  rx  c                ó®   — t        | j                  |«      | j                  «      \  }}||D ��cg c]  \  }}| j                  |«      |f‘Œ c}}fS c c}}w r,  )rÁ   rH  r)  rL  rs  s         r0  rÁ   zIPolys.dup_factor_listb  rz  ru  c                ó¤   — t        | j                  |«      | j                  «      }|D ��cg c]  \  }}| j                  |«      |f‘Œ c}}S c c}}w r,  )rÂ   rH  r)  rL  rL  s        r0  rÂ   zIPolys.dup_factor_list_includee  sA   € Ü)¨$¯-©-¸Ó*:¸D¿K¹KÓHˆØ5<×>©T¨Q°�$—/‘/ !Ó$ aÒ(Ó>Ð>ùÓ>rZ  c                óÊ   — t        | j                  |«      | j                  dz
  | j                  «      \  }}||D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}fS c c}}w rJ  )rÃ   rH  r(  r)  rL  rs  s         r0  rÃ   zIPolys.dmp_factor_listi  r|  rx  c                óÀ   — t        | j                  |«      | j                  dz
  | j                  «      }|D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}S c c}}w rJ  )rÄ   rH  r(  r)  rL  rL  s        r0  rÄ   zIPolys.dmp_factor_list_includel  sK   € Ü)¨$¯-©-¸Ó*:¸D¿J¹JÀq¹LÈ$Ï+É+ÓVˆØ5<×>©T¨Q°�$—/‘/ !Ó$ aÒ(Ó>Ð>ùÓ>ó   ¹Ac                óL   — t        | j                  |«      | j                  «      S r,  )rÅ   rH  r)  rn  s     r0  rÅ   zIPolys.dup_irreducible_pp  s   € Ü  §¡¨qÓ!1°4·;±;Ó?Ð?r3  c                óh   — t        | j                  |«      | j                  dz
  | j                  «      S rJ  )rÆ   rH  r(  r)  rn  s     r0  rÆ   zIPolys.dmp_irreducible_pr  s&   € Ü  §¡¨qÓ!1°4·:±:¸a±<ÀÇÁÓMÐMr3  c                óŠ   — t        | j                  |«      | j                  «      }t        t	        | j
                  |«      «      S r,  )rÇ   rH  r)  r¯  r°  rL  )r.  rO  Úseqs      r0  rÇ   zIPolys.dup_sturmu  s1   € Ü˜Ÿ™ aÓ(¨$¯+©+Ó6ˆÜ”C˜Ÿ™¨Ó-Ó.Ð.r3  c                óL   — t        | j                  |«      | j                  «      S r,  )rÙ   rH  r)  rn  s     r0  rÙ   zIPolys.dup_sqf_py  s   € Ü˜Ÿ™ qÓ)¨4¯;©;Ó7Ð7r3  c                óh   — t        | j                  |«      | j                  dz
  | j                  «      S rJ  )rÚ   rH  r(  r)  rn  s     r0  rÚ   zIPolys.dmp_sqf_p{  s&   € Ü˜Ÿ™ qÓ)¨4¯:©:°a©<¸¿¹ÓEÐEr3  c                ó¦   — t        | j                  |«      | j                  dz
  | j                  «      }| j	                  «       j                  |«      S rJ  )rÛ   rH  r(  r)  r7  rL  ri  s      r0  rÛ   zIPolys.dmp_norm~  s=   € Ü�T—]‘] 1Ó% t§z¡z°!¡|°T·[±[ÓAˆØ�~‰~Ó×*Ñ*¨1Ó-Ð-r3  c                ó¶   — t        | j                  |«      | j                  «      \  }}}|| j                  |«      | j	                  «       j                  |«      fS r,  )rÜ   rH  r)  rL  r7  ©r.  rO  rû  rà  ÚRs        r0  rÜ   zIPolys.dup_sqf_norm‚  sI   € Ü˜tŸ}™}¨QÓ/°·±Ó=‰ˆˆ1ˆaØ�4—?‘? 1Ó% t§~¡~Ó'7×'BÑ'BÀ1Ó'EÐFÐFr3  c                óÒ   — t        | j                  |«      | j                  dz
  | j                  «      \  }}}|| j	                  |«      | j                  «       j	                  |«      fS rJ  )rÝ   rH  r(  r)  rL  r7  r�  s        r0  rÝ   zIPolys.dmp_sqf_norm…  sS   € Ü˜tŸ}™}¨QÓ/°·±¸A±¸t¿{¹{ÓK‰ˆˆ1ˆaØ�4—?‘? 1Ó% t§~¡~Ó'7×'BÑ'BÀ1Ó'EÐFÐFr3  c                ój   — | j                  t        | j                  |«      | j                  «      «      S r,  )rL  rÞ   rH  r)  rn  s     r0  rÞ   zIPolys.dup_gf_sqf_part‰  ó%   € Ø�‰œ¨t¯}©}¸QÓ/?ÀÇÁÓMÓNÐNr3  c                ój   — | j                  t        | j                  |«      | j                  «      «      S r,  )rL  rß   rH  r)  rn  s     r0  rß   zIPolys.dmp_gf_sqf_part‹  r”  r3  c                ój   — | j                  t        | j                  |«      | j                  «      «      S r,  )rL  rà   rH  r)  rn  s     r0  rà   zIPolys.dup_sqf_part�  s%   € Ø�‰œ|¨D¯M©M¸!Ó,<¸d¿k¹kÓJÓKÐKr3  c                ó†   — | j                  t        | j                  |«      | j                  dz
  | j                  «      «      S rJ  )rL  rá   rH  r(  r)  rn  s     r0  rá   zIPolys.dmp_sqf_part�  s/   € Ø�‰œ|¨D¯M©M¸!Ó,<¸d¿j¹jÈ¹lÈDÏKÉKÓXÓYÐYr3  c                ó²   — t        | j                  |«      | j                  |¬«      \  }}||D ��cg c]  \  }}| j                  |«      |f‘Œ c}}fS c c}}w ©N©Úall)râ   rH  r)  rL  ©r.  rO  r›  rq  rM  rv  rN  s          r0  râ   zIPolys.dup_gf_sqf_list’  sL   € Ü(¨¯©°qÓ)9¸4¿;¹;ÈCÔP‰ˆˆwØ¸W×F±T°Q¸˜$Ÿ/™/¨!Ó,¨aÒ0ÓFÐGÐGùÓFó   ±Ac                óÎ   — t        | j                  |«      | j                  dz
  | j                  |¬«      \  }}||D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}fS c c}}w ©NrK  rš  )rã   rH  r(  r)  rL  rœ  s          r0  rã   zIPolys.dmp_gf_sqf_list•  sW   € Ü(¨¯©°qÓ)9¸4¿:¹:Àa¹<ÈÏÉÐZ]Ô^‰ˆˆwØ¸W×F±T°Q¸˜$Ÿ/™/¨!Ó,¨aÒ0ÓFÐGÐGùÓFó   ¿A!c                ó²   — t        | j                  |«      | j                  |¬«      \  }}||D ��cg c]  \  }}| j                  |«      |f‘Œ c}}fS c c}}w r™  )rä   rH  r)  rL  rœ  s          r0  rä   zIPolys.dup_sqf_list™  sL   € Ü% d§m¡m°AÓ&6¸¿¹ÈÔM‰ˆˆwØ¸W×F±T°Q¸˜$Ÿ/™/¨!Ó,¨aÒ0ÓFÐGÐGùÓFr�  c                ó¨   — t        | j                  |«      | j                  |¬«      }|D ��cg c]  \  }}| j                  |«      |f‘Œ c}}S c c}}w r™  )rå   rH  r)  rL  ©r.  rO  r›  rM  rv  rN  s         r0  rå   zIPolys.dup_sqf_list_includeœ  sC   € Ü& t§}¡}°QÓ'7¸¿¹È#ÔNˆØ5<×>©T¨Q°�$—/‘/ !Ó$ aÒ(Ó>Ð>ùÓ>s   ­Ac                óÎ   — t        | j                  |«      | j                  dz
  | j                  |¬«      \  }}||D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}fS c c}}w rŸ  )ræ   rH  r(  r)  rL  rœ  s          r0  ræ   zIPolys.dmp_sqf_listŸ  sW   € Ü% d§m¡m°AÓ&6¸¿
¹
À1¹ÀdÇkÁkÐWZÔ[‰ˆˆwØ¸W×F±T°Q¸˜$Ÿ/™/¨!Ó,¨aÒ0ÓFÐGÐGùÓFr   c                óÄ   — t        | j                  |«      | j                  dz
  | j                  |¬«      }|D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}S c c}}w rŸ  )rç   rH  r(  r)  rL  r£  s         r0  rç   zIPolys.dmp_sqf_list_include¢  sN   € Ü& t§}¡}°QÓ'7¸¿¹ÀA¹ÀtÇ{Á{ÐX[Ô\ˆØ5<×>©T¨Q°�$—/‘/ !Ó$ aÒ(Ó>Ð>ùÓ>s   »Ac                ó¤   — t        | j                  |«      | j                  «      }|D ��cg c]  \  }}| j                  |«      |f‘Œ c}}S c c}}w r,  )rè   rH  r)  rL  rL  s        r0  rè   zIPolys.dup_gff_list¦  sA   € Ü˜tŸ}™}¨QÓ/°·±Ó=ˆØ5<×>©T¨Q°�$—/‘/ !Ó$ aÒ(Ó>Ð>ùÓ>rZ  c                óÀ   — t        | j                  |«      | j                  dz
  | j                  «      }|D ��cg c]  \  }}| j	                  |«      |f‘Œ c}}S c c}}w rJ  )ré   rH  r(  r)  rL  rL  s        r0  ré   zIPolys.dmp_gff_list©  sK   € Ü˜tŸ}™}¨QÓ/°·±¸A±¸t¿{¹{ÓKˆØ5<×>©T¨Q°�$—/‘/ !Ó$ aÒ(Ó>Ð>ùÓ>r‡  c                óL   — t        | j                  |«      | j                  «      S r,  )rÈ   rH  r)  rn  s     r0  rÈ   zIPolys.dup_root_upper_bound­  r\  r3  c                óL   — t        | j                  |«      | j                  «      S r,  )rÉ   rH  r)  rn  s     r0  rÉ   zIPolys.dup_root_lower_bound¯  r\  r3  c                óR   — t        | j                  |«      || j                  |¬«      S )N)Úfast)rÊ   rH  r)  )r.  rO  ÚMr«  s       r0  rÊ   z IPolys.dup_step_refine_real_root²  s!   € Ü(¨¯©°qÓ)9¸1¸d¿k¹kÐPTÔUÐUr3  c           
     óZ   — t        | j                  |«      || j                  |||||¬«      S )N)ÚepsÚstepsÚdisjointr«  Úmobius)rË   rH  r)  )r.  rO  r¬  r®  r¯  r°  r«  r±  s           r0  rË   z!IPolys.dup_inner_refine_real_root´  s7   € Ü)¨$¯-©-¸Ó*:¸A¸t¿{¹{ÐPSÐ[`ÐksÐz~ð  HNô  Oð  	Or3  c           
     óZ   — t        | j                  |«      ||| j                  ||||¬«      S ©N)r®  r¯  r°  r«  )rÌ   rH  r)  ©r.  rO  rû  rÿ  r®  r¯  r°  r«  s           r0  rÌ   z!IPolys.dup_outer_refine_real_root¶  s6   € Ü)¨$¯-©-¸Ó*:¸A¸qÀ$Ç+Á+ÐSVÐ^cÐnvð  ~Bô  Cð  	Cr3  c           
     óZ   — t        | j                  |«      ||| j                  ||||¬«      S r³  )rÍ   rH  r)  r´  s           r0  rÍ   zIPolys.dup_refine_real_root¸  s+   € Ü# D§M¡M°!Ó$4°a¸¸D¿K¹KÈSÐX]ÐhpÐw{Ô|Ð|r3  c                óR   — t        | j                  |«      | j                  ||¬«      S )N)r®  r«  )rÎ   rH  r)  )r.  rO  r®  r«  s       r0  rÎ   z#IPolys.dup_inner_isolate_real_rootsº  s!   € Ü+¨D¯M©M¸!Ó,<¸d¿k¹kÈsÐY]Ô^Ð^r3  c           	     óX   — t        | j                  |«      | j                  |||||¬«      S )N)r®  ÚinfÚsupr«  r±  )rÏ   rH  r)  )r.  rO  r®  r¸  r¹  r«  r±  s          r0  rÏ   z'IPolys.dup_inner_isolate_positive_roots¼  ó5   € Ü/°·±¸aÓ0@À$Ç+Á+ÐSVÐ\_ÐehÐosð  }Cô  Dð  	Dr3  c           	     óX   — t        | j                  |«      | j                  |||||¬«      S )N)r¸  r¹  r®  r«  r±  )rÐ   rH  r)  )r.  rO  r¸  r¹  r®  r«  r±  s          r0  rÐ   z'IPolys.dup_inner_isolate_negative_roots¾  rº  r3  c           	     óX   — t        | j                  |«      | j                  |||||¬«      S ©N)r®  r¸  r¹  r«  Úblackbox)rÑ   rH  r)  ©r.  rO  r®  r¸  r¹  r«  r¾  s          r0  rÑ   z!IPolys.dup_isolate_real_roots_sqfÀ  s4   € Ü)¨$¯-©-¸Ó*:¸D¿K¹KÈSÐVYÐ_bÐimð  yAô  Bð  	Br3  c           	     óX   — t        | j                  |«      | j                  |||||¬«      S )N)r®  r¸  r¹  Úbasisr«  )rÒ   rH  r)  )r.  rO  r®  r¸  r¹  rÁ  r«  s          r0  rÒ   zIPolys.dup_isolate_real_rootsÂ  s*   € Ü% d§m¡m°AÓ&6¸¿¹ÈÐRUÐ[^ÐfkÐrvÔwÐwr3  c           
     óv   — t        t        t        | j                  |«      «      | j                  ||||||¬«      S )N)r®  r¸  r¹  ÚstrictrÁ  r«  )rÓ   r¯  r°  rH  r)  )r.  r²  r®  r¸  r¹  rÃ  rÁ  r«  s           r0  rÓ   z"IPolys.dup_isolate_real_roots_listÄ  sG   € Ü*¬4´°D·M±MÀ5Ó0IÓ+JÈDÏKÉKÐ]`ÐfiÐorð  |Bð  JOð  VZô  [ð  	[r3  c                óR   — t        | j                  |«      | j                  ||¬«      S )N)r¸  r¹  )rÔ   rH  r)  )r.  rO  r¸  r¹  s       r0  rÔ   zIPolys.dup_count_real_rootsÆ  s!   € Ü# D§M¡M°!Ó$4°d·k±kÀsÐPSÔTÐTr3  c                óT   — t        | j                  |«      | j                  |||¬«      S )N)r¸  r¹  Úexclude)rÕ   rH  r)  )r.  rO  r¸  r¹  rÆ  s        r0  rÕ   zIPolys.dup_count_complex_rootsÈ  s$   € Ü& t§}¡}°QÓ'7¸¿¹È#ÐSVÐ`gÔhÐhr3  c                óV   — t        | j                  |«      | j                  ||||¬«      S )N)r®  r¸  r¹  r¾  )rÖ   rH  r)  )r.  rO  r®  r¸  r¹  r¾  s         r0  rÖ   z$IPolys.dup_isolate_complex_roots_sqfÊ  s(   € Ü,¨T¯]©]¸1Ó-=¸t¿{¹{ÐPSÐY\ÐbeÐpxÔyÐyr3  c           	     óX   — t        | j                  |«      | j                  |||||¬«      S r½  )r×   rH  r)  r¿  s          r0  r×   z IPolys.dup_isolate_all_roots_sqfÌ  s0   € Ü(¨¯©°qÓ)9¸4¿;¹;ÈCÐUXÐ^aÐhlÐwô  Að  	Ar3  c                óV   — t        | j                  |«      | j                  ||||¬«      S )N)r®  r¸  r¹  r«  )rØ   rH  r)  )r.  rO  r®  r¸  r¹  r«  s         r0  rØ   zIPolys.dup_isolate_all_rootsÎ  s'   € Ü$ T§]¡]°1Ó%5°t·{±{ÈÐQTÐZ]ÐdhÔiÐir3  c           	     óˆ   — ddl m} t        t        | j                   || j
                  dz
  | j                  «      «      «      S )Nr   )Údmp_fateman_poly_F_1rK  )Úsympy.polys.specialpolysrË  Útupler°  rL  r(  r)  )r.  rË  s     r0  Úfateman_poly_F_1zIPolys.fateman_poly_F_1Ñ  ó/   € ÝAÜ”S˜Ÿ™Ñ*>¸t¿z¹zÈ!¹|ÈTÏ[É[Ó*YÓZÓ[Ð[r3  c           	     óˆ   — ddl m} t        t        | j                   || j
                  dz
  | j                  «      «      «      S )Nr   )Údmp_fateman_poly_F_2rK  )rÌ  rÑ  rÍ  r°  rL  r(  r)  )r.  rÑ  s     r0  Úfateman_poly_F_2zIPolys.fateman_poly_F_2Ô  rÏ  r3  c           	     óˆ   — ddl m} t        t        | j                   || j
                  dz
  | j                  «      «      «      S )Nr   )Údmp_fateman_poly_F_3rK  )rÌ  rÔ  rÍ  r°  rL  r(  r)  )r.  rÔ  s     r0  Úfateman_poly_F_3zIPolys.fateman_poly_F_3×  rÏ  r3  c           	     óÔ   — t        | j                  |«      j                  «       D �cg c]2  }| j                  j                  j                  || j                  «      ‘Œ4 c}«      S c c}w r,  )rí   rF  rH  r)  Údomró  )r.  r:  rP  s      r0  Úto_gf_densezIPolys.to_gf_denseÛ  sG   € ÜÈ4Ï9É9ÐU\ÓK]×KfÑKfÓKhÖjÀa˜$Ÿ+™+Ÿ/™/×1Ñ1°!°T·[±[ÕAÒjÓkÐkùÒjs   §7A%c                ó|   — | j                  t        || j                  dz
  | j                  j                  «      «      S rJ  )r@  rS   r(  r)  r×  r9  s     r0  Úfrom_gf_densezIPolys.from_gf_denseÞ  s*   € Ø�~‰~œk¨'°4·:±:¸a±<ÀÇÁÇÁÓQÓRÐRr3  c                ó6   — t        | j                  |«      «      S r,  )rê   rØ  rn  s     r0  rê   zIPolys.gf_degreeá  s   € Ü˜×)Ñ)¨!Ó,Ó-Ð-r3  c                ó`   — t        | j                  |«      | j                  j                  «      S r,  )rë   rØ  r)  r×  rn  s     r0  rë   zIPolys.gf_LCä  ó"   € Ü�T×%Ñ% aÓ(¨$¯+©+¯/©/Ó:Ð:r3  c                ó`   — t        | j                  |«      | j                  j                  «      S r,  )rì   rØ  r)  r×  rn  s     r0  rì   zIPolys.gf_TCæ  rÝ  r3  c                óT   — | j                  t        | j                  |«      «      «      S r,  )rÚ  rí   rØ  rn  s     r0  rí   zIPolys.gf_stripé  s#   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>Ó"?Ó@Ð@r3  c                ó~   — | j                  t        | j                  |«      | j                  j                  «      «      S r,  )rÚ  rí   rØ  r)  rn  rn  s     r0  Úgf_trunczIPolys.gf_truncë  s-   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>ÀÇÁÇÁÓ"PÓQÐQr3  c                ó¨   — | j                  t        | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  rí   rØ  r)  rn  r×  rn  s     r0  Ú	gf_normalzIPolys.gf_normalí  ó<   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>ÀÇÁÇÁÐQU×Q\ÑQ\×Q`ÑQ`Ó"aÓbÐbr3  c                óŠ   — | j                  t        || j                  j                  | j                  j                  «      «      S r,  )rÚ  rî   r)  rn  r×  rn  s     r0  rî   zIPolys.gf_from_dictð  s,   € Ø×!Ñ!¤,¨q°$·+±+·/±/À4Ç;Á;Ç?Á?Ó"SÓTÐTr3  c                ód   — t        | j                  |«      | j                  j                  |¬«      S ©N)Ú	symmetric)rï   rØ  r)  rn  ©r.  rO  rè  s      r0  rï   zIPolys.gf_to_dictò  s$   € Ü˜$×*Ñ*¨1Ó-¨t¯{©{¯©È)ÔTÐTr3  c                ó`   — | j                  t        || j                  j                  «      «      S r,  )rÚ  rð   r)  rn  rn  s     r0  rð   zIPolys.gf_from_int_polyõ  s#   € Ø×!Ñ!Ô"2°1°d·k±k·o±oÓ"FÓGÐGr3  c                ód   — t        | j                  |«      | j                  j                  |¬«      S rç  )rñ   rØ  r)  rn  ré  s      r0  rñ   zIPolys.gf_to_int_poly÷  s$   € Ü˜d×.Ñ.¨qÓ1°4·;±;·?±?ÈiÔXÐXr3  c                ó¨   — | j                  t        | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  rò   rØ  r)  rn  r×  rn  s     r0  rò   zIPolys.gf_negú  ó7   € Ø×!Ñ!¤&¨×)9Ñ)9¸!Ó)<¸d¿k¹k¿o¹oÈtÏ{É{ÏÉÓ"_Ó`Ð`r3  c                óª   — | j                  t        | j                  |«      || j                  j                  | j                  j
                  «      «      S r,  )rÚ  ró   rØ  r)  rn  r×  rÍ  s      r0  ró   zIPolys.gf_add_groundý  ó>   € Ø×!Ñ!¤-°×0@Ñ0@ÀÓ0CÀQÈÏÉÏÉÐY]×YdÑYd×YhÑYhÓ"iÓjÐjr3  c                óª   — | j                  t        | j                  |«      || j                  j                  | j                  j
                  «      «      S r,  )rÚ  rô   rØ  r)  rn  r×  rÍ  s      r0  rô   zIPolys.gf_sub_groundÿ  rï  r3  c                óª   — | j                  t        | j                  |«      || j                  j                  | j                  j
                  «      «      S r,  )rÚ  rõ   rØ  r)  rn  r×  rÍ  s      r0  rõ   zIPolys.gf_mul_ground  rï  r3  c                óª   — | j                  t        | j                  |«      || j                  j                  | j                  j
                  «      «      S r,  )rÚ  rö   rØ  r)  rn  r×  rÍ  s      r0  rö   zIPolys.gf_quo_ground  rï  r3  c                óÈ   — | j                  t        | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r÷   rØ  r)  rn  r×  ru  s      r0  r÷   zIPolys.gf_add  óN   € Ø×!Ñ!¤&¨×)9Ñ)9¸!Ó)<¸d×>NÑ>NÈqÓ>QÐSW×S^ÑS^×SbÑSbÐdh×doÑdo×dsÑdsÓ"tÓuÐur3  c                óÈ   — | j                  t        | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  rø   rØ  r)  rn  r×  ru  s      r0  rø   zIPolys.gf_sub  rô  r3  c                óÈ   — | j                  t        | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  rù   rØ  r)  rn  r×  ru  s      r0  rù   zIPolys.gf_mul
  rô  r3  c                ó¨   — | j                  t        | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  rú   rØ  r)  rn  r×  rn  s     r0  rú   zIPolys.gf_sqr  rí  r3  c           	     óè   — | j                  t        | j                  |«      | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  rû   rØ  r)  rn  r×  r}  s       r0  rû   zIPolys.gf_add_mul  ó{   € Ø×!Ñ!¤*¨T×-=Ñ-=¸aÓ-@À$×BRÑBRÐSTÓBUÐW[×WgÑWgÐhiÓWjÐlp×lwÑlw×l{Ñl{ð  ~B÷  ~Iñ  ~I÷  ~Mñ  ~Mó  #Nó  Oð  	Or3  c           	     óè   — | j                  t        | j                  |«      | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  rü   rØ  r)  rn  r×  r}  s       r0  rü   zIPolys.gf_sub_mul  rù  r3  c           
     óÄ   — | j                  t        t        t        | j                  |«      «      | j
                  j                  | j
                  j                  «      «      S r,  )rÚ  rý   r¯  r°  rØ  r)  rn  r×  )r.  rà  s     r0  rý   zIPolys.gf_expand  sC   € Ø×!Ñ!¤)¬D´°T×5EÑ5EÀqÓ1IÓ,JÈDÏKÉKÏOÉOÐ]a×]hÑ]h×]lÑ]lÓ"mÓnÐnr3  c                óô   — t        | j                  |«      | j                  |«      | j                  j                  | j                  j                  «      \  }}| j                  |«      | j                  |«      fS r,  )rþ   rØ  r)  rn  r×  rÚ  r‹  s        r0  rþ   zIPolys.gf_div  sb   € Ü�d×&Ñ& qÓ)¨4×+;Ñ+;¸AÓ+>ÀÇÁÇÁÐQU×Q\ÑQ\×Q`ÑQ`Óa‰ˆˆ1Ø×!Ñ! !Ó$ d×&8Ñ&8¸Ó&;Ð;Ð;r3  c                óÈ   — | j                  t        | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  rÿ   rØ  r)  rn  r×  ru  s      r0  rÿ   zIPolys.gf_rem  rô  r3  c                óÈ   — | j                  t        | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r   rØ  r)  rn  r×  ru  s      r0  r   zIPolys.gf_quo  rô  r3  c                óÈ   — | j                  t        | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r  rØ  r)  rn  r×  ru  s      r0  r  zIPolys.gf_exquo  óO   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>À×@PÑ@PÐQRÓ@SÐUY×U`ÑU`×UdÑUdÐfj×fqÑfq×fuÑfuÓ"vÓwÐwr3  c                ó€   — | j                  t        | j                  |«      || j                  j                  «      «      S r,  )rÚ  r  rØ  r)  r×  ri  s      r0  r  zIPolys.gf_lshift!  ó/   € Ø×!Ñ!¤)¨D×,<Ñ,<¸QÓ,?ÀÀDÇKÁKÇOÁOÓ"TÓUÐUr3  c                ó€   — | j                  t        | j                  |«      || j                  j                  «      «      S r,  )rÚ  r  rØ  r)  r×  ri  s      r0  r  zIPolys.gf_rshift#  r  r3  c                óª   — | j                  t        | j                  |«      || j                  j                  | j                  j
                  «      «      S r,  )rÚ  r  rØ  r)  rn  r×  ri  s      r0  r  zIPolys.gf_pow&  s>   € Ø×!Ñ!¤&¨×)9Ñ)9¸!Ó)<¸aÀÇÁÇÁÐRV×R]ÑR]×RaÑRaÓ"bÓcÐcr3  c           	     óÊ   — | j                  t        | j                  |«      || j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r  rØ  r)  rn  r×  )r.  rO  rj  rv  s       r0  r  zIPolys.gf_pow_mod(  sQ   € Ø×!Ñ!¤*¨T×-=Ñ-=¸aÓ-@À!ÀT×EUÑEUÐVWÓEXÐZ^×ZeÑZe×ZiÑZiÐko×kvÑkv×kzÑkzÓ"{Ó|Ð|r3  c                ó  — t        | j                  |«      | j                  |«      | j                  j                  | j                  j                  «      \  }}}| j                  |«      | j                  |«      | j                  |«      fS r,  )r  rØ  r)  rn  r×  rÚ  )r.  rO  rv  r~  ÚcffÚcfgs         r0  r  zIPolys.gf_cofactors+  sr   € Ü" 4×#3Ñ#3°AÓ#6¸×8HÑ8HÈÓ8KÈTÏ[É[Ï_É_Ð^b×^iÑ^i×^mÑ^mÓn‰ˆˆ3�Ø×!Ñ! !Ó$ d×&8Ñ&8¸Ó&=¸t×?QÑ?QÐRUÓ?VÐVÐVr3  c                óÈ   — | j                  t        | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r  rØ  r)  rn  r×  ru  s      r0  r  zIPolys.gf_gcd.  rô  r3  c                óÈ   — | j                  t        | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r  rØ  r)  rn  r×  ru  s      r0  r  zIPolys.gf_lcm0  rô  r3  c                óÈ   — | j                  t        | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r	  rØ  r)  rn  r×  ru  s      r0  r	  zIPolys.gf_gcdex2  r   r3  c                ó¨   — | j                  t        | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r
  rØ  r)  rn  r×  rn  s     r0  r
  zIPolys.gf_monic5  rä  r3  c                ó¨   — | j                  t        | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r  rØ  r)  rn  r×  rn  s     r0  r  zIPolys.gf_diff7  s<   € Ø×!Ñ!¤'¨$×*:Ñ*:¸1Ó*=¸t¿{¹{¿¹ÐPT×P[ÑP[×P_ÑP_Ó"`ÓaÐar3  c                óŒ   — t        | j                  |«      || j                  j                  | j                  j                  «      S r,  )r  rØ  r)  rn  r×  rÍ  s      r0  r  zIPolys.gf_eval:  s.   € Ü�t×'Ñ'¨Ó*¨A¨t¯{©{¯©ÀÇÁÇÁÓPÐPr3  c                óŒ   — t        | j                  |«      || j                  j                  | j                  j                  «      S r,  )r  rØ  r)  rn  r×  )r.  rO  rÕ  s      r0  r  zIPolys.gf_multi_eval<  s.   € Ü˜T×-Ñ-¨aÓ0°!°T·[±[·_±_ÀdÇkÁkÇoÁoÓVÐVr3  c                óÈ   — | j                  t        | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r  rØ  r)  rn  r×  ru  s      r0  r  zIPolys.gf_compose?  sO   € Ø×!Ñ!¤*¨T×-=Ñ-=¸aÓ-@À$×BRÑBRÐSTÓBUÐW[×WbÑWb×WfÑWfÐhl×hsÑhs×hwÑhwÓ"xÓyÐyr3  c           	     óè   — | j                  t        | j                  |«      | j                  |«      | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r  rØ  r)  rn  r×  )r.  rv  r~  rO  s       r0  r  zIPolys.gf_compose_modA  s{   € Ø×!Ñ!¤.°×1AÑ1AÀ!Ó1DÀd×FVÑFVÐWXÓFYÐ[_×[kÑ[kÐlmÓ[nÐpt×p{Ñp{×pÑpð  BF÷  BMñ  BM÷  BQñ  BQó  #Ró  Sð  	Sr3  c           	     óF  — | j                  |«      }| j                  |«      }| j                  |«      }| j                  |«      }t        |||||| j                  j                  | j                  j                  «      \  }}| j                  |«      | j                  |«      fS r,  )rØ  r  r)  rn  r×  rÚ  )r.  rÎ  ÚbrP  rj  rO  ÚUÚVs           r0  r  zIPolys.gf_trace_mapD  s�   € Ø×Ñ˜QÓˆØ×Ñ˜QÓˆØ×Ñ˜QÓˆØ×Ñ˜QÓˆÜ˜A˜q ! Q¨¨4¯;©;¯?©?¸D¿K¹K¿O¹OÓL‰ˆˆ1Ø×!Ñ! !Ó$ d×&8Ñ&8¸Ó&;Ð;Ð;r3  c                óŠ   — | j                  t        || j                  j                  | j                  j                  «      «      S r,  )rÚ  r  r)  rn  r×  ©r.  rj  s     r0  r  zIPolys.gf_randomL  s,   € Ø×!Ñ!¤)¨A¨t¯{©{¯©ÀÇÁÇÁÓ"PÓQÐQr3  c                óŠ   — | j                  t        || j                  j                  | j                  j                  «      «      S r,  )rÚ  r  r)  rn  r×  r  s     r0  r  zIPolys.gf_irreducibleN  s,   € Ø×!Ñ!¤.°°D·K±K·O±OÀTÇ[Á[Ç_Á_Ó"UÓVÐVr3  c                óŠ   — t        | j                  |«      | j                  j                  | j                  j                  «      S r,  )r  rØ  r)  rn  r×  rn  s     r0  r  zIPolys.gf_irred_p_ben_orQ  s,   € Ü  ×!1Ñ!1°!Ó!4°d·k±k·o±oÀtÇ{Á{ÇÁÓWÐWr3  c                óŠ   — t        | j                  |«      | j                  j                  | j                  j                  «      S r,  )r  rØ  r)  rn  r×  rn  s     r0  r  zIPolys.gf_irred_p_rabinS  ó,   € Ü × 0Ñ 0°Ó 3°T·[±[·_±_ÀdÇkÁkÇoÁoÓVÐVr3  c                óŠ   — t        | j                  |«      | j                  j                  | j                  j                  «      S r,  )r  rØ  r)  rn  r×  rn  s     r0  r  zIPolys.gf_irreducible_pU  r  r3  c                óŠ   — t        | j                  |«      | j                  j                  | j                  j                  «      S r,  )r  rØ  r)  rn  r×  rn  s     r0  r  zIPolys.gf_sqf_pW  s,   € Ü˜×(Ñ(¨Ó+¨T¯[©[¯_©_¸d¿k¹k¿o¹oÓNÐNr3  c                ó¨   — | j                  t        | j                  |«      | j                  j                  | j                  j
                  «      «      S r,  )rÚ  r  rØ  r)  rn  r×  rn  s     r0  r  zIPolys.gf_sqf_partZ  s<   € Ø×!Ñ!¤+¨d×.>Ñ.>¸qÓ.AÀ4Ç;Á;Ç?Á?ÐTX×T_ÑT_×TcÑTcÓ"dÓeÐer3  c                óì   — t        | j                  |«      | j                  j                  | j                  j                  «      \  }}||D ��cg c]  \  }}| j                  |«      |f‘Œ c}}fS c c}}w r,  )r  rØ  r)  rn  r×  rÚ  rœ  s          r0  Úgf_sqf_listzIPolys.gf_sqf_list\  s\   € Ü$ T×%5Ñ%5°aÓ%8¸$¿+¹+¿/¹/È4Ï;É;Ï?É?Ó[‰ˆˆwØ¸w×H±t°q¸!˜×+Ñ+¨AÓ.°Ò2ÓHÐHÐHùÓHó   ÁA0c                óŠ   — t        | j                  |«      | j                  j                  | j                  j                  «      S r,  )r  rØ  r)  rn  r×  rn  s     r0  r  zIPolys.gf_Qmatrix`  s,   € Ü˜$×*Ñ*¨1Ó-¨t¯{©{¯©ÀÇÁÇÁÓPÐPr3  c                óÒ   — t        | j                  |«      | j                  j                  | j                  j                  «      }|D �cg c]  }| j                  |«      ‘Œ c}S c c}w r,  )r  rØ  r)  rn  r×  rÚ  ©r.  rO  rM  rv  s       r0  r  zIPolys.gf_berlekampb  óJ   € Ü˜t×/Ñ/°Ó2°D·K±K·O±OÀTÇ[Á[Ç_Á_ÓUˆØ07Ö9¨1�×#Ñ# AÕ&Ò9Ð9ùÒ9ó   Á	A$c                óâ   — t        | j                  |«      | j                  j                  | j                  j                  «      }|D ��cg c]  \  }}| j                  |«      |f‘Œ c}}S c c}}w r,  )r  rØ  r)  rn  r×  rÚ  rL  s        r0  r  zIPolys.gf_ddf_zassenhausf  sS   € Ü# D×$4Ñ$4°QÓ$7¸¿¹¿¹È$Ï+É+Ï/É/ÓZˆØ8?×A±°°1�$×$Ñ$ QÓ'¨Ò+ÓAÐAùÓAó   Á
A+c                óÒ   — t        | j                  |«      | j                  j                  | j                  j                  «      }|D �cg c]  }| j                  |«      ‘Œ c}S c c}w r,  )r  rØ  r)  rn  r×  rÚ  ©r.  rO  rj  rM  rv  s        r0  r  zIPolys.gf_edf_zassenhausi  sJ   € Ü# D×$4Ñ$4°QÓ$7¸¿¹¿¹È$Ï+É+Ï/É/ÓZˆØ07Ö9¨1�×#Ñ# AÕ&Ò9Ð9ùÒ9r&  c                óâ   — t        | j                  |«      | j                  j                  | j                  j                  «      }|D ��cg c]  \  }}| j                  |«      |f‘Œ c}}S c c}}w r,  )r  rØ  r)  rn  r×  rÚ  rL  s        r0  r  zIPolys.gf_ddf_shoupm  sS   € Ü˜t×/Ñ/°Ó2°D·K±K·O±OÀTÇ[Á[Ç_Á_ÓUˆØ8?×A±°°1�$×$Ñ$ QÓ'¨Ò+ÓAÐAùÓAr(  c                óÒ   — t        | j                  |«      | j                  j                  | j                  j                  «      }|D �cg c]  }| j                  |«      ‘Œ c}S c c}w r,  )r  rØ  r)  rn  r×  rÚ  r*  s        r0  r  zIPolys.gf_edf_shoupp  r%  r&  c                óÒ   — t        | j                  |«      | j                  j                  | j                  j                  «      }|D �cg c]  }| j                  |«      ‘Œ c}S c c}w r,  )r  rØ  r)  rn  r×  rÚ  r$  s       r0  r  zIPolys.gf_zassenhaust  sJ   € Ü × 0Ñ 0°Ó 3°T·[±[·_±_ÀdÇkÁkÇoÁoÓVˆØ07Ö9¨1�×#Ñ# AÕ&Ò9Ð9ùÒ9r&  c                óÒ   — t        | j                  |«      | j                  j                  | j                  j                  «      }|D �cg c]  }| j                  |«      ‘Œ c}S c c}w r,  )r  rØ  r)  rn  r×  rÚ  r$  s       r0  r  zIPolys.gf_shoupw  sJ   € Ü˜4×+Ñ+¨AÓ.°·±·±ÀÇÁÇÁÓQˆØ07Ö9¨1�×#Ñ# AÕ&Ò9Ð9ùÒ9r&  c                óà   — t        | j                  |«      | j                  j                  | j                  j                  |¬«      \  }}||D �cg c]  }| j                  |«      ‘Œ c}fS c c}w )N)Úmethod)r   rØ  r)  rn  r×  rÚ  )r.  rO  r0  rq  rM  rv  s         r0  r   zIPolys.gf_factor_sqf{  sV   € Ü& t×'7Ñ'7¸Ó':¸D¿K¹K¿O¹OÈTÏ[É[Ï_É_ÐekÔl‰ˆˆwØ°wÖ@°!˜×*Ñ*¨1Õ-Ò@Ð@Ð@ùÒ@s   ÁA+c                óì   — t        | j                  |«      | j                  j                  | j                  j                  «      \  }}||D ��cg c]  \  }}| j                  |«      |f‘Œ c}}fS c c}}w r,  )r!  rØ  r)  rn  r×  rÚ  rs  s         r0  r!  zIPolys.gf_factor~  s\   € Ü" 4×#3Ñ#3°AÓ#6¸¿¹¿¹ÈÏÉÏÉÓY‰ˆˆwØ¸w×H±t°q¸!˜×+Ñ+¨AÓ.°Ò2ÓHÐHÐHùÓHr!  )NNN)F)T)NN)NNNFF)NNNF)NF)NNNFFFr,  (,  Ú__name__Ú
__module__Ú__qualname__Ú__annotations__r1  r5  r7  r;  r=  r@  rF  rH  rL  r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rT   rU   rW   rX   rY   rV   rZ   r[   r\   r^   r]   r_   r`   ra   rb   rc   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r€   r�   r‚   r†   rƒ   r‡   r„   rˆ   r‰   rŠ   r‹   r…   rŒ   r�   rŽ   r�   r�   r‘   r’   r“   r”   r•   r–   r—   r˜   r™   rš   r›   rœ   r�   rž   rŸ   r    rd   rf   r¡   r¢   re   rg   r£   r¤   r¥   r¦   r§   r¨   r©   rª   r«   r¬   r­   r®   r¯   r²   r³   r´   rµ   r¶   r·   r°   r±   r¸   r¹   r»   rº   r¼   r½   r¾   r¿   rÀ   rÁ   rÂ   rÃ   rÄ   rÅ   rÆ   rÇ   rÙ   rÚ   rÛ   rÜ   rÝ   rÞ   rß   rà   rá   râ   rã   rä   rå   ræ   rç   rè   ré   rÈ   rÉ   rÊ   rË   rÌ   rÍ   rÎ   rÏ   rÐ   rÑ   rÒ   rÓ   rÔ   rÕ   rÖ   r×   rØ   rÎ  rÒ  rÕ  rØ  rÚ  rê   rë   rì   rí   rá  rã  rî   rï   rð   rñ   rò   ró   rô   rõ   rö   r÷   rø   rù   rú   rû   rü   rý   rþ   rÿ   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r   r!  r-  r3  r0  r$  r$  ð   s®  … ð "Ó!ØÓØƒJØƒNØÓòôòòòòò,ò-òOòRò~òRò~òRò~òQò_òQò_òQò_òQò_òSòaòMòMòGòUòGòUòYògòYògòoò}òoò}òYògòGòUòJòXò8òZòZò\ò8òhòhòjò8ò8ò8ò8ò8òYòYò[ò8ògògòiò;òIò:òHòBòPòYògò5òò5òòJòJò,ò:ò@òPò^òKòYò_òdò:ò+ò/ò/òòLòmòaòIò^ò;ò;ò8òJòLòLòZòqò]òkò6ò3òBô'ô'òMò8ò8òLòLò\òjò/ò/ò/ò/ò7ò7ò/ò/ò6òKò(ò(ò(òNòò?òòLòLòLòLòLòLòLòLòLòLò"ò"ò"ò"ò"ò"ò"ò"òò+òò1òò-ô<ô<ò?ò?òDòRò`ò1ò
?òCôXò"ò6ò@ò^ò2ò
2ò
2ô7ò@òHòHòHòHòHòHòHòHòHòHòHò?òHò?ò@òNò/ò8òFò.òGòGòOòOòLòZôHôHôHô?ôHô?ò?ò?òCòCôVôOôCô}ô_ôDôDôBôxô[ôUôiôzôAôjò\ò\ò\òlòSò.ò;ò;òAòRòcòUõUóHõYóaókókókókôvôvôvôaôOôOôoô<ôvôvôxôVôVôdô}ôWôvôvôxôcôbôQôWôzôSô<ôRôWôXôWôWôOôföIôQô:ôBô:ôBô:ô:ô:öAõIr3  r$  N(0  Ú__doc__Ú
__future__r   Útypingr   Úsympy.core.exprr   Úsympy.polys.domains.domainr   Úsympy.polys.orderingsr   rB  r	   Ú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$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   Úsympy.polys.densebasicrJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   Úsympy.polys.densetoolsrT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   Úsympy.polys.euclidtoolsrx   ry   rz   r{   r|   r}   r~   r   r€   r�   r‚   rƒ   r„   r…   r†   r‡   rˆ   r‰   rŠ   r‹   rŒ   r�   rŽ   r�   r�   r‘   r’   r“   r”   r•   r–   r—   r˜   r™   rš   r›   rœ   r�   rž   rŸ   r    r¡   r¢   r£   r¤   Úsympy.polys.factortoolsr¥   r¦   r§   r¨   r©   rª   r«   r¬   r­   r®   r¯   r°   r±   r²   r³   r´   rµ   r¶   r·   r¸   r¹   rº   r»   r¼   r½   r¾   r¿   rÀ   rÁ   rÂ   rÃ   rÄ   rÅ   rÆ   Úsympy.polys.rootisolationrÇ   rÈ   rÉ   rÊ   rË   rÌ   rÍ   rÎ   rÏ   rÐ   rÑ   rÒ   rÓ   rÔ   rÕ   rÖ   r×   rØ   Úsympy.polys.sqfreetoolsrÙ   rÚ   rÛ   rÜ   rÝ   rÞ   rß   rà   rá   râ   rã   rä   rå   ræ   rç   rè   ré   Úsympy.polys.galoistoolsrê   rë   rì   rí   rî   rï   rð   rñ   rò   ró   rô   rõ   rö   r÷   rø   rù   rú   rû   rü   rý   rþ   rÿ   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  Úsympy.utilitiesr"  r$  r-  r3  r0  ú<module>rE     sO  ðÙ >å "å  áÝ$Ý1Ý3Ý-å /Ý /Ý /Ý /Ý /Ý /Ý 1Ý 1Ý 1Ý 1Ý 1Ý 1Ý 1Ý 1Ý 3Ý 3Ý -Ý -Ý *Ý *Ý *Ý *Ý *Ý *Ý *Ý *Ý .Ý .Ý .Ý .Ý *Ý *Ý *Ý *Ý *Ý *Ý +Ý +Ý +Ý -Ý +Ý +Ý +Ý -Ý -Ý -Ý -Ý -Ý *Ý *Ý *Ý ,Ý *Ý *Ý *Ý ,Ý /Ý /Ý .Ý .Ý 6Ý 6Ý -Ý -Ý )Ý )Ý )Ý )Ý 0Ý 0Ý -Ý -Ý 0Ý .Ý 0Ý 0Ý 3Ý +Ý +Ý .Ý +Ý +Ý .Ý 0Ý 3Ý ,Ý ,Ý 3Ý ,Ý 3Ý .Ý 5Ý 0Ý 7Ý .Ý 5Ý 0Ý -Ý ,Ý ,Ý ,Ý 0Ý .Ý .Ý 0Ý +Ý 6Ý 3Ý 3Ý -Ý 2Ý 2Ý -Ý -Ý .Ý .Ý 5Ý 5Ý 5Ý 5Ý ;Ý 5Ý 5Ý 1Ý ;Ý 5Ý 5Ý <Ý <Ý <Ý 1Ý 4Ý 4Ý 2Ý 2Ý 2Ý 2Ý 2Ý 2Ý 2Ý 2Ý 1Ý 1Ý +Ý +Ý .Ý .Ý +Ý .Ý .Ý +Ý /Ý 1Ý .Ý .Ý 6Ý 6Ý 9Ý 9Ý 6Ý 6Ý 5Ý 8Ý 4Ý :Ý <Ý 5Ý 1Ý <Ý ;Ý 6Ý 6Ý >Ý /Ý 1Ý 3Ý 3Ý 3Ý 3Ý 2Ý 2Ý 1Ý 1Ý 3Ý ;Ý 3Ý ;Ý 5Ý 5Ý /Ý :Ý :Ý ?Ý @Ý @Ý :Ý BÝ FÝ FÝ @Ý <Ý AÝ :Ý =Ý CÝ ?Ý ;÷D÷ D÷ D÷ Dõ D÷	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7÷ 	7õ 	7÷ #Ð "á÷OIð OIó òOIr3  