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GJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJGrGJ Gr GJ!Gr!GJ"Gr"GJ#Gr#GJ$Gr$GJ%Gr%GJ&Gr&GJ'Gr'GJ(Gr(GJ)Gr)GJ*Gr*GJ+Gr+GJ,Gr,  SSÙGK-GJ.Gr.  G\. " SÚ SÛ5      5       Gr/gÜ)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                  óÀ  • \ rS rSr% S\S'   S\S'   S\S'   S\S	'   S
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S rS rS rS rS rS rS rS rS rS rS rS rS rS  rS! rS" rS# rS$ rS% rS& rS' rS( r S) r!S* r"S+ r#S, r$S- r%S. r&S/ r'S0 r(S1 r)S2 r*S3 r+S4 r,S5 r-S6 r.S7 r/S8 r0S9 r1S: r2S; r3S< r4S= r5S> r6S? r7S@ r8SA r9SB r:SC r;SD r<SE r=SF r>SG r?SH r@SI rASJ rBSK rCSL rDSM rESN rFSO rGSP rHSQ rISR rJSS rKST rLSU rMSV rNSW rOSX rPSY rQSZ rRS[ rSS\ rTS] rUS^ rVS_ rWS` rXSa rYSb rZSc r[Sd r\Se r]Sf r^Sg r_Sh r`Si raSj rbSk rcSl rdSm reSn rfSo rgSp rhSq riSr rjSs rkSt rlSu rmSv rnSw roSx rpSy rqSz rrS{ rsGS7S| jrtGS7S} jruS~ rvS rwS€ rxS� ryS‚ rzSƒ r{S„ r|S… r}S† r~S‡ rSˆ r€S‰ r�SŠ r‚S‹ rƒSŒ r„S� r…SŽ r†S� r‡S� rˆS‘ r‰S’ rŠS“ r‹S” rŒS• r�S– rŽS— r�S˜ r�S™ r‘Sš r’S› r“Sœ r”S� r•Sž r–SŸ r—S  r˜S¡ r™S¢ ršS£ r›S¤ rœS¥ r�S¦ ržS§ rŸS¨ r S© r¡Sª r¢S« r£S¬ r¤S­ r¥GS8S® jr¦GS8S¯ jr§S° r¨S± r©S² rªS³ r«S´ r¬Sµ r­S¶ r®S· r¯GS7S¸ jr°S¹ r±Sº r²S» r³S¼ r´S½ rµS¾ r¶S¿ r·GS9SÀ jr¸SÁ r¹SÂ rºSÃ r»SÄ r¼SÅ r½SÆ r¾SÇ r¿SÈ rÀSÉ rÁSÊ rÂSË rÃSÌ rÄSÍ rÅSÎ rÆSÏ rÇSÐ rÈSÑ rÉSÒ rÊSÓ rËSÔ rÌSÕ rÍSÖ rÎS× rÏSØ rÐSÙ rÑSÚ rÒSÛ rÓGS7SÜ jrÔGS7SÝ jrÕGS7SÞ jrÖGS7Sß jr×GS7Sà jrØGS7Sá jrÙSâ rÚSã rÛSä rÜSå rÝGS7Sæ jrÞGS:Sç jrßGS;Sè jràGS;Sé jráGS<Sê jrâGS:Së jrãGS:Sì jräGS:Sí jråGS:Sî jræGS=Sï jrçGS9Sð jrèGS6Sñ jréGS;Sò jrêGS:Só jrëGS;Sô jrìSõ ríSö rîS÷ rïSø rðSù rñSú ròSû róSü rôSý rõSþ röSÿ r÷GS  røGS8GS jrùGS rúGS8GS jrûGS rüGS rýGS rþGS rÿGS Gr GS	 GrGS
 GrGS GrGS GrGS GrGS GrGS GrGS GrGS Gr	GS Gr
GS GrGS GrGS GrGS GrGS GrGS GrGS GrGS GrGS GrGS GrGS GrGS GrGS GrGS  GrGS! GrGS" GrGS# GrGS$ GrGS% GrGS& GrGS' GrGS( Gr GS) Gr!GS7GS* jGr"GS+ Gr#GS, Gr$GS- Gr%GS. Gr&GS/ Gr'GS0 Gr(GS1 Gr)GS2 Gr*GS>GS3 jGr+GS4 Gr,GS5Gr-g(?  ÚIPolyséð   ztuple[PolyElement, ...]Úgensztuple[Expr, ...]ÚsymbolsÚintÚngensr   Údomainr   Úorderc                ó   • g ©N© )ÚselfÚgens     ÚV/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/polys/compatibility.pyÚdropÚIPolys.dropù   ó   € Øó    Nc                ó   • g r-  r.  )r/  r'  r*  r+  s       r1  ÚcloneÚIPolys.cloneü   r4  r5  c                ó   • g r-  r.  )r/  s    r1  Ú	to_groundÚIPolys.to_groundÿ   r4  r5  c                ó   • g r-  r.  ©r/  Úelements     r1  Ú
ground_newÚIPolys.ground_new  r4  r5  c                ó   • g r-  r.  r=  s     r1  Ú
domain_newÚIPolys.domain_new  r4  r5  c                ó   • g r-  r.  )r/  Úds     r1  Ú	from_dictÚIPolys.from_dict  r4  r5  c                óŠ   • SSK Jn  [        X5      (       a  UR                  U :X  a  U$ [	        S5      eU R                  U5      $ )Nr   r   zdomain conversions)Úsympy.polys.ringsr	   Ú
isinstanceÚringÚNotImplementedErrorr?  )r/  r>  r	   s      r1  ÚwrapÚIPolys.wrap  s<   € Ý1Ü�g×+Ñ+Ø�|‰|˜tÓ#Ø�ä)Ð*>Ó?Ð?à—?‘? 7Ó+Ð+r5  c                ó@   • U R                  U5      R                  5       $ r-  )rM  Úto_denser=  s     r1  rP  ÚIPolys.to_dense  s   € Ø�y‰y˜Ó!×*Ñ*Ó,Ð,r5  c                óf   • U R                  [        XR                  S-
  U R                  5      5      $ ©Né   )rF  rS   r)  r*  r=  s     r1  Ú
from_denseÚIPolys.from_dense  s$   € Ø�~‰~œk¨'·:±:¸a±<ÀÇÁÓMÓNÐNr5  c                ól   • U R                  [        U R                  U5      X#U R                  5      5      $ r-  )rU  r
   rP  r*  ©r/  ÚfÚcÚis       r1  r
   ÚIPolys.dup_add_term  ó'   € Ø�‰œ|¨D¯M©M¸!Ó,<¸aÀDÇKÁKÓPÓQÐQr5  c           	     óà   • U R                  [        U R                  U5      U R                  U5      R	                  S5      R                  5       X0R
                  S-
  U R                  5      5      $ ©Nr   rT  )rU  r   rP  rM  r2  r)  r*  rX  s       r1  r   ÚIPolys.dmp_add_term  óV   € Ø�‰œ|¨D¯M©M¸!Ó,<¸d¿i¹iÈ»l×>OÑ>OÐPQÓ>R×>[Ñ>[Ó>]Ð_`×blÑblÐmnÑbnÐpt×p{Ñp{Ó|Ó}Ð}r5  c                ól   • U R                  [        U R                  U5      X#U R                  5      5      $ r-  )rU  r   rP  r*  rX  s       r1  r   ÚIPolys.dup_sub_term  r]  r5  c           	     óà   • U R                  [        U R                  U5      U R                  U5      R	                  S5      R                  5       X0R
                  S-
  U R                  5      5      $ r_  )rU  r   rP  rM  r2  r)  r*  rX  s       r1  r   ÚIPolys.dmp_sub_term!  ra  r5  c                ól   • U R                  [        U R                  U5      X#U R                  5      5      $ r-  )rU  r   rP  r*  rX  s       r1  r   ÚIPolys.dup_mul_term#  r]  r5  c           	     óà   • U R                  [        U R                  U5      U R                  U5      R	                  S5      R                  5       X0R
                  S-
  U R                  5      5      $ r_  )rU  r   rP  rM  r2  r)  r*  rX  s       r1  r   ÚIPolys.dmp_mul_term%  ra  r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  r   rP  r*  ©r/  rY  rZ  s      r1  r   ÚIPolys.dup_add_ground(  ó%   € Ø�‰œ~¨d¯m©m¸AÓ.>ÀÇ;Á;ÓOÓPÐPr5  c                ó†   • U R                  [        U R                  U5      X R                  S-
  U R                  5      5      $ rS  )rU  r   rP  r)  r*  rk  s      r1  r   ÚIPolys.dmp_add_ground*  ó2   € Ø�‰œ~¨d¯m©m¸AÓ.>ÀÇ:Á:ÈaÁ<ÐQU×Q\ÑQ\Ó]Ó^Ð^r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  r   rP  r*  rk  s      r1  r   ÚIPolys.dup_sub_ground,  rm  r5  c                ó†   • U R                  [        U R                  U5      X R                  S-
  U R                  5      5      $ rS  )rU  r   rP  r)  r*  rk  s      r1  r   ÚIPolys.dmp_sub_ground.  rp  r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  r   rP  r*  rk  s      r1  r   ÚIPolys.dup_mul_ground0  rm  r5  c                ó†   • U R                  [        U R                  U5      X R                  S-
  U R                  5      5      $ rS  )rU  r   rP  r)  r*  rk  s      r1  r   ÚIPolys.dmp_mul_ground2  rp  r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  r   rP  r*  rk  s      r1  r   ÚIPolys.dup_quo_ground4  rm  r5  c                ó†   • U R                  [        U R                  U5      X R                  S-
  U R                  5      5      $ rS  )rU  r   rP  r)  r*  rk  s      r1  r   ÚIPolys.dmp_quo_ground6  rp  r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  r   rP  r*  rk  s      r1  r   ÚIPolys.dup_exquo_ground8  s&   € Ø�‰Ô/°·±¸aÓ0@À!Ç[Á[ÓQÓRÐRr5  c                ó†   • U R                  [        U R                  U5      X R                  S-
  U R                  5      5      $ rS  )rU  r   rP  r)  r*  rk  s      r1  r   ÚIPolys.dmp_exquo_ground:  ó4   € Ø�‰Ô/°·±¸aÓ0@À!ÇZÁZÐPQÁ\ÐSW×S^ÑS^Ó_Ó`Ð`r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  r   rP  r*  ©r/  rY  Úns      r1  r   ÚIPolys.dup_lshift=  ó%   € Ø�‰œz¨$¯-©-¸Ó*:¸A¿{¹{ÓKÓLÐLr5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  r   rP  r*  rƒ  s      r1  r   ÚIPolys.dup_rshift?  r†  r5  c                ój   • U R                  [        U R                  U5      U R                  5      5      $ r-  )rU  r   rP  r*  ©r/  rY  s     r1  r   ÚIPolys.dup_absB  ó%   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÓEÓFÐFr5  c                ó†   • U R                  [        U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r   rP  r)  r*  rŠ  s     r1  r   ÚIPolys.dmp_absD  ó/   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÀA¹ÀtÇ{Á{ÓSÓTÐTr5  c                ój   • U R                  [        U R                  U5      U R                  5      5      $ r-  )rU  r   rP  r*  rŠ  s     r1  r   ÚIPolys.dup_negG  rŒ  r5  c                ó†   • U R                  [        U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r   rP  r)  r*  rŠ  s     r1  r   ÚIPolys.dmp_negI  r�  r5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r    rP  r*  ©r/  rY  Úgs      r1  r    ÚIPolys.dup_addL  ó0   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï;É;ÓWÓXÐXr5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r!   rP  r)  r*  r•  s      r1  r!   ÚIPolys.dmp_addN  ó>   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï:É:ÐVWÉ<ÐY]×YdÑYdÓeÓfÐfr5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r"   rP  r*  r•  s      r1  r"   ÚIPolys.dup_subQ  r˜  r5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r#   rP  r)  r*  r•  s      r1  r#   ÚIPolys.dmp_subS  r›  r5  c           	     óª   • U R                  [        U R                  U5      U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r$   rP  r*  ©r/  rY  r–  Úhs       r1  r$   ÚIPolys.dup_add_mulV  ó?   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏ}É}Ð]^ÓO_Ðae×alÑalÓmÓnÐnr5  c           	     óÆ   • U R                  [        U R                  U5      U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r%   rP  r)  r*  r¡  s       r1  r%   ÚIPolys.dmp_add_mulX  óN   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏ}É}Ð]^ÓO_Ðae×akÑakÐlmÑamÐos×ozÑozÓ{Ó|Ð|r5  c           	     óª   • U R                  [        U R                  U5      U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r&   rP  r*  r¡  s       r1  r&   ÚIPolys.dup_sub_mulZ  r¤  r5  c           	     óÆ   • U R                  [        U R                  U5      U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r'   rP  r)  r*  r¡  s       r1  r'   ÚIPolys.dmp_sub_mul\  r§  r5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r(   rP  r*  r•  s      r1  r(   ÚIPolys.dup_mul_  r˜  r5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r)   rP  r)  r*  r•  s      r1  r)   ÚIPolys.dmp_mula  r›  r5  c                ój   • U R                  [        U R                  U5      U R                  5      5      $ r-  )rU  r*   rP  r*  rŠ  s     r1  r*   ÚIPolys.dup_sqrd  rŒ  r5  c                ó†   • U R                  [        U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r+   rP  r)  r*  rŠ  s     r1  r+   ÚIPolys.dmp_sqrf  r�  r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  r,   rP  r*  rƒ  s      r1  r,   ÚIPolys.dup_powh  s%   € Ø�‰œw t§}¡}°QÓ'7¸¿K¹KÓHÓIÐIr5  c                ó†   • U R                  [        U R                  U5      X R                  S-
  U R                  5      5      $ rS  )rU  r-   rP  r)  r*  rƒ  s      r1  r-   ÚIPolys.dmp_powj  s/   € Ø�‰œw t§}¡}°QÓ'7¸¿J¹JÀq¹LÈ$Ï+É+ÓVÓWÐWr5  c                ó´   • [        U R                  U5      U R                  U5      U R                  5      u  p4U R                  U5      U R                  U5      4$ r-  )r.   rP  r*  rU  ©r/  rY  r–  ÚqÚrs        r1  r.   ÚIPolys.dup_pdivm  sE   € Ü˜Ÿ™ aÓ(¨$¯-©-¸Ó*:¸D¿K¹KÓH‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r/   rP  r*  r•  s      r1  r/   ÚIPolys.dup_premp  ó0   € Ø�‰œx¨¯©°aÓ(8¸$¿-¹-ÈÓ:JÈDÏKÉKÓXÓYÐYr5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r0   rP  r*  r•  s      r1  r0   ÚIPolys.dup_pquor  r¿  r5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r1   rP  r*  r•  s      r1  r1   ÚIPolys.dup_pexquot  ó0   € Ø�‰œz¨$¯-©-¸Ó*:¸D¿M¹MÈ!Ó<LÈdÏkÉkÓZÓ[Ð[r5  c                óÐ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4U R	                  U5      U R	                  U5      4$ rS  )r2   rP  r)  r*  rU  r¹  s        r1  r2   ÚIPolys.dmp_pdivw  sO   € Ü˜Ÿ™ aÓ(¨$¯-©-¸Ó*:¸D¿J¹JÀq¹LÈ$Ï+É+ÓV‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r3   rP  r)  r*  r•  s      r1  r3   ÚIPolys.dmp_premz  ó>   € Ø�‰œx¨¯©°aÓ(8¸$¿-¹-ÈÓ:JÈDÏJÉJÐWXÉLÐZ^×ZeÑZeÓfÓgÐgr5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r4   rP  r)  r*  r•  s      r1  r4   ÚIPolys.dmp_pquo|  rÉ  r5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r5   rP  r)  r*  r•  s      r1  r5   ÚIPolys.dmp_pexquo~  ó>   € Ø�‰œz¨$¯-©-¸Ó*:¸D¿M¹MÈ!Ó<LÈdÏjÉjÐYZÉlÐ\`×\gÑ\gÓhÓiÐir5  c                ó´   • [        U R                  U5      U R                  U5      U R                  5      u  p4U R                  U5      U R                  U5      4$ r-  )r6   rP  r*  rU  r¹  s        r1  r6   ÚIPolys.dup_rr_div�  óE   € Ü˜$Ÿ-™-¨Ó*¨D¯M©M¸!Ó,<¸d¿k¹kÓJ‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r5  c                óÐ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4U R	                  U5      U R	                  U5      4$ rS  )r7   rP  r)  r*  rU  r¹  s        r1  r7   ÚIPolys.dmp_rr_div„  óO   € Ü˜$Ÿ-™-¨Ó*¨D¯M©M¸!Ó,<¸d¿j¹jÈ¹lÈDÏKÉKÓX‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r5  c                ó´   • [        U R                  U5      U R                  U5      U R                  5      u  p4U R                  U5      U R                  U5      4$ r-  )r8   rP  r*  rU  r¹  s        r1  r8   ÚIPolys.dup_ff_div‡  rÑ  r5  c                óÐ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4U R	                  U5      U R	                  U5      4$ rS  )r9   rP  r)  r*  rU  r¹  s        r1  r9   ÚIPolys.dmp_ff_divŠ  rÔ  r5  c                ó´   • [        U R                  U5      U R                  U5      U R                  5      u  p4U R                  U5      U R                  U5      4$ r-  )r:   rP  r*  rU  r¹  s        r1  r:   ÚIPolys.dup_divŽ  sE   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿;¹;ÓG‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r;   rP  r*  r•  s      r1  r;   ÚIPolys.dup_rem‘  r˜  r5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r<   rP  r*  r•  s      r1  r<   ÚIPolys.dup_quo“  r˜  r5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r=   rP  r*  r•  s      r1  r=   ÚIPolys.dup_exquo•  s0   € Ø�‰œy¨¯©°qÓ)9¸4¿=¹=ÈÓ;KÈTÏ[É[ÓYÓZÐZr5  c                óÐ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4U R	                  U5      U R	                  U5      4$ rS  )r>   rP  r)  r*  rU  r¹  s        r1  r>   ÚIPolys.dmp_div˜  sO   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿:¹:Àa¹<ÈÏÉÓU‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r?   rP  r)  r*  r•  s      r1  r?   ÚIPolys.dmp_rem›  r›  r5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r@   rP  r)  r*  r•  s      r1  r@   ÚIPolys.dmp_quo�  r›  r5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  rA   rP  r)  r*  r•  s      r1  rA   ÚIPolys.dmp_exquoŸ  s>   € Ø�‰œy¨¯©°qÓ)9¸4¿=¹=ÈÓ;KÈTÏZÉZÐXYÉ\Ð[_×[fÑ[fÓgÓhÐhr5  c                óL   • [        U R                  U5      U R                  5      $ r-  )rB   rP  r*  rŠ  s     r1  rB   ÚIPolys.dup_max_norm¢  s   € Ü˜DŸM™M¨!Ó,¨d¯k©kÓ:Ð:r5  c                óh   • [        U R                  U5      U R                  S-
  U R                  5      $ rS  )rC   rP  r)  r*  rŠ  s     r1  rC   ÚIPolys.dmp_max_norm¤  s&   € Ü˜DŸM™M¨!Ó,¨d¯j©j¸©l¸D¿K¹KÓHÐHr5  c                óL   • [        U R                  U5      U R                  5      $ r-  )rD   rP  r*  rŠ  s     r1  rD   ÚIPolys.dup_l1_norm§  s   € Ü˜4Ÿ=™=¨Ó+¨T¯[©[Ó9Ð9r5  c                óh   • [        U R                  U5      U R                  S-
  U R                  5      $ rS  )rE   rP  r)  r*  rŠ  s     r1  rE   ÚIPolys.dmp_l1_norm©  s&   € Ü˜4Ÿ=™=¨Ó+¨T¯Z©Z¸©\¸4¿;¹;ÓGÐGr5  c                óL   • [        U R                  U5      U R                  5      $ r-  )rF   rP  r*  rŠ  s     r1  rF   ÚIPolys.dup_l2_norm_squared¬  ó   € Ü" 4§=¡=°Ó#3°T·[±[ÓAÐAr5  c                óh   • [        U R                  U5      U R                  S-
  U R                  5      $ rS  )rG   rP  r)  r*  rŠ  s     r1  rG   ÚIPolys.dmp_l2_norm_squared®  s&   € Ü" 4§=¡=°Ó#3°T·Z±ZÀ±\À4Ç;Á;ÓOÐOr5  c           
     ó†   • U R                  [        [        [        U R                  U5      5      U R
                  5      5      $ r-  )rU  rH   ÚlistÚmaprP  r*  ©r/  Úpolyss     r1  rH   ÚIPolys.dup_expand±  s,   € Ø�‰œz¬$¬s°4·=±=À%Ó/HÓ*IÈ4Ï;É;ÓWÓXÐXr5  c           
     ó¢   • U R                  [        [        [        U R                  U5      5      U R
                  S-
  U R                  5      5      $ rS  )rU  rI   r÷  rø  rP  r)  r*  rù  s     r1  rI   ÚIPolys.dmp_expand³  s:   € Ø�‰œz¬$¬s°4·=±=À%Ó/HÓ*IÈ4Ï:É:ÐVWÉ<ÐY]×YdÑYdÓeÓfÐfr5  c                óL   • [        U R                  U5      U R                  5      $ r-  )rJ   rP  r*  rŠ  s     r1  rJ   ÚIPolys.dup_LC¶  ó   € Ü�d—m‘m AÓ&¨¯©Ó4Ð4r5  c                ó¢   • [        U R                  U5      U R                  5      n[        U[        5      (       a  U SS  R                  U5      $ U$ rS  )rK   rP  r*  rJ  r÷  rU  )r/  rY  ÚLCs      r1  rK   ÚIPolys.dmp_LC¸  óD   € Ü�D—M‘M !Ó$ d§k¡kÓ2ˆÜ�bœ$×ÑØ˜˜�8×&Ñ& rÓ*Ð*àˆIr5  c                óL   • [        U R                  U5      U R                  5      $ r-  )rL   rP  r*  rŠ  s     r1  rL   ÚIPolys.dup_TC¾  r   r5  c                ó¢   • [        U R                  U5      U R                  5      n[        U[        5      (       a  U SS  R                  U5      $ U$ rS  )rM   rP  r*  rJ  r÷  rU  )r/  rY  ÚTCs      r1  rM   ÚIPolys.dmp_TCÀ  r  r5  c                óh   • [        U R                  U5      U R                  S-
  U R                  5      $ rS  )rN   rP  r)  r*  rŠ  s     r1  rN   ÚIPolys.dmp_ground_LCÇ  ó&   € Ü˜TŸ]™]¨1Ó-¨t¯z©z¸!©|¸T¿[¹[ÓIÐIr5  c                óh   • [        U R                  U5      U R                  S-
  U R                  5      $ rS  )rO   rP  r)  r*  rŠ  s     r1  rO   ÚIPolys.dmp_ground_TCÉ  r  r5  c                ó6   • [        U R                  U5      5      $ r-  )rP   rP  rŠ  s     r1  rP   ÚIPolys.dup_degreeÌ  s   € Ü˜$Ÿ-™-¨Ó*Ó+Ð+r5  c                óR   • [        U R                  U5      U R                  S-
  5      $ rS  )rQ   rP  r)  rŠ  s     r1  rQ   ÚIPolys.dmp_degreeÎ  s    € Ü˜$Ÿ-™-¨Ó*¨D¯J©J°q©LÓ9Ð9r5  c                óR   • [        U R                  U5      X R                  S-
  5      $ rS  )rR   rP  r)  )r/  rY  Újs      r1  rR   ÚIPolys.dmp_degree_inÐ  s    € Ü˜TŸ]™]¨1Ó-¨q·*±*¸Q±,Ó?Ð?r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  rT   rP  r*  ©r/  rY  Úms      r1  rT   ÚIPolys.dup_integrateÒ  s%   € Ø�‰œ}¨T¯]©]¸1Ó-=¸qÇ+Á+ÓNÓOÐOr5  c                ó†   • U R                  [        U R                  U5      X R                  S-
  U R                  5      5      $ rS  )rU  rU   rP  r)  r*  r  s      r1  rU   ÚIPolys.dmp_integrateÔ  s2   € Ø�‰œ}¨T¯]©]¸1Ó-=¸qÇ*Á*ÈQÁ,ÐPT×P[ÑP[Ó\Ó]Ð]r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  rW   rP  r*  r  s      r1  rW   ÚIPolys.dup_diff×  s%   € Ø�‰œx¨¯©°aÓ(8¸!¿[¹[ÓIÓJÐJr5  c                ó†   • U R                  [        U R                  U5      X R                  S-
  U R                  5      5      $ rS  )rU  rX   rP  r)  r*  r  s      r1  rX   ÚIPolys.dmp_diffÙ  s/   € Ø�‰œx¨¯©°aÓ(8¸!¿Z¹ZÈ¹\È4Ï;É;ÓWÓXÐXr5  c           	     óˆ   • U R                  [        U R                  U5      X#U R                  S-
  U R                  5      5      $ rS  )rU  rY   rP  r)  r*  ©r/  rY  r  r  s       r1  rY   ÚIPolys.dmp_diff_inÜ  s4   € Ø�‰œ{¨4¯=©=¸Ó+;¸QÀ4Ç:Á:ÈaÁ<ÐQU×Q\ÑQ\Ó]Ó^Ð^r5  c           	     óˆ   • U R                  [        U R                  U5      X#U R                  S-
  U R                  5      5      $ rS  )rU  rV   rP  r)  r*  r!  s       r1  rV   ÚIPolys.dmp_integrate_inÞ  s6   € Ø�‰Ô/°·±¸aÓ0@À!ÈÏ
É
ÐSTÉÐVZ×VaÑVaÓbÓcÐcr5  c                óL   • [        U R                  U5      X R                  5      $ r-  )rZ   rP  r*  ©r/  rY  Úas      r1  rZ   ÚIPolys.dup_evalá  s   € Ü˜Ÿ™ aÓ(¨!¯[©[Ó9Ð9r5  c                ó�   • [        U R                  U5      X R                  S-
  U R                  5      nU SS  R	                  U5      $ rS  )r[   rP  r)  r*  rU  )r/  rY  r'  Úresults       r1  r[   ÚIPolys.dmp_evalã  s<   € Ü˜$Ÿ-™-¨Ó*¨A¯z©z¸!©|¸T¿[¹[ÓIˆØ�A�Bˆx×"Ñ" 6Ó*Ð*r5  c                óª   • [        U R                  U5      X#U R                  S-
  U R                  5      nU R	                  U5      R                  U5      $ rS  )r\   rP  r)  r*  r2  rU  )r/  rY  r'  r  r*  s        r1  r\   ÚIPolys.dmp_eval_inç  s@   € Ü˜TŸ]™]¨1Ó-¨q°T·Z±ZÀ±\À4Ç;Á;ÓOˆØ�y‰y˜‹|×&Ñ& vÓ.Ð.r5  c                óª   • [        U R                  U5      X#X@R                  S-
  U R                  5      nU R	                  U5      R                  U5      $ rS  )r^   rP  r)  r*  r2  rU  )r/  rY  r  r'  r  r*  s         r1  r^   ÚIPolys.dmp_diff_eval_inê  s@   € Ü! $§-¡-°Ó"2°A¸!¿Z¹ZÈ¹\È4Ï;É;ÓWˆØ�y‰y˜‹|×&Ñ& vÓ.Ð.r5  c                óÒ   • [        U R                  U5      X R                  S-
  U R                  5      n[	        U[
        5      (       a  U S [        U5      *  R                  U5      $ U$ rS  )r]   rP  r)  r*  rJ  r÷  ÚlenrU  )r/  rY  ÚAr*  s       r1  r]   ÚIPolys.dmp_eval_tailî  sT   € Ü˜tŸ}™}¨QÓ/°·J±J¸q±LÀ$Ç+Á+ÓNˆÜ�fœd×#Ñ#Ø˜œ#˜a›&˜�>×,Ñ,¨VÓ4Ð4àˆMr5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  r_   rP  r*  ©r/  rY  Úps      r1  r_   ÚIPolys.dup_truncõ  ó%   € Ø�‰œy¨¯©°qÓ)9¸1¿k¹kÓJÓKÐKr5  c                ó¬   • U R                  [        U R                  U5      U SS  R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r`   rP  r)  r*  r•  s      r1  r`   ÚIPolys.dmp_trunc÷  sJ   € Ø�‰œy¨¯©°qÓ)9¸4ÀÀ¸8×;LÑ;LÈQÓ;OÐQU×Q[ÑQ[Ð\]ÑQ]Ð_c×_jÑ_jÓkÓlÐlr5  c                ó†   • U R                  [        U R                  U5      X R                  S-
  U R                  5      5      $ rS  )rU  ra   rP  r)  r*  r5  s      r1  ra   ÚIPolys.dmp_ground_truncù  r�  r5  c                ój   • U R                  [        U R                  U5      U R                  5      5      $ r-  )rU  rb   rP  r*  rŠ  s     r1  rb   ÚIPolys.dup_monicü  s%   € Ø�‰œy¨¯©°qÓ)9¸4¿;¹;ÓGÓHÐHr5  c                ó†   • U R                  [        U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  rc   rP  r)  r*  rŠ  s     r1  rc   ÚIPolys.dmp_ground_monicþ  s3   € Ø�‰Ô/°·±¸aÓ0@À$Ç*Á*ÈQÁ,ÐPT×P[ÑP[Ó\Ó]Ð]r5  c                ó¶   • [        U R                  U5      U R                  U5      U R                  5      u  p4nX0R                  U5      U R                  U5      4$ r-  )rh   rP  r*  rU  ©r/  rY  r–  rZ  ÚFÚGs         r1  rh   ÚIPolys.dup_extract  sG   € Ü˜dŸm™m¨AÓ.°·±¸aÓ0@À$Ç+Á+ÓN‰ˆˆaØ—?‘? 1Ó% t§¡°qÓ'9Ð:Ð:r5  c                óÒ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4nX0R	                  U5      U R	                  U5      4$ rS  )ri   rP  r)  r*  rU  rB  s         r1  ri   ÚIPolys.dmp_ground_extract  sU   € Ü$ T§]¡]°1Ó%5°t·}±}ÀQÓ7GÈÏÉÐTUÉÐW[×WbÑWbÓc‰ˆˆaØ—?‘? 1Ó% t§¡°qÓ'9Ð:Ð:r5  c                óÎ   • [        U R                  U5      R                  S5      R                  5       U R                  5      u  p#U R                  U5      U R                  U5      4$ rS  )rj   rM  r2  rP  r*  rU  ©r/  rY  r6  rº  s       r1  rj   ÚIPolys.dup_real_imag  sM   € Ü˜TŸY™Y q›\×.Ñ.¨qÓ1×:Ñ:Ó<¸d¿k¹kÓJ‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r5  c                ój   • U R                  [        U R                  U5      U R                  5      5      $ r-  )rU  rk   rP  r*  rŠ  s     r1  rk   ÚIPolys.dup_mirror  s%   € Ø�‰œz¨$¯-©-¸Ó*:¸D¿K¹KÓHÓIÐIr5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  rl   rP  r*  r&  s      r1  rl   ÚIPolys.dup_scale  r8  r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  rm   rP  r*  r&  s      r1  rm   ÚIPolys.dup_shift  r8  r5  c                ó†   • U R                  [        U R                  U5      X R                  S-
  U R                  5      5      $ rS  )rU  rn   rP  r)  r*  r&  s      r1  rn   ÚIPolys.dmp_shift  s/   € Ø�‰œy¨¯©°qÓ)9¸1¿j¹jÈ¹lÈDÏKÉKÓXÓYÐYr5  c           	     óª   • U R                  [        U R                  U5      U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  ro   rP  r*  rI  s       r1  ro   ÚIPolys.dup_transform  sB   € Ø�‰œ}¨T¯]©]¸1Ó-=¸t¿}¹}ÈQÓ?OÐQU×Q^ÑQ^Ð_`ÓQaÐcg×cnÑcnÓoÓpÐpr5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  rp   rP  r*  r•  s      r1  rp   ÚIPolys.dup_compose  s0   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏ{É{Ó[Ó\Ð\r5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  rq   rP  r)  r*  r•  s      r1  rq   ÚIPolys.dmp_compose  s>   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏzÉzÐZ[É|Ð]a×]hÑ]hÓiÓjÐjr5  c                óŠ   • [        U R                  U5      U R                  5      n[        [	        U R
                  U5      5      $ r-  )rr   rP  r*  r÷  rø  rU  )r/  rY  Ú
componentss      r1  rr   ÚIPolys.dup_decompose  s1   € Ü" 4§=¡=°Ó#3°T·[±[ÓAˆ
Ü”C˜Ÿ™¨Ó4Ó5Ð5r5  c                ó¦   • [        U R                  U5      U R                  S-
  U R                  5      nU R	                  5       R                  U5      $ rS  )rs   rP  r)  r*  r:  rU  ©r/  rY  r*  s      r1  rs   ÚIPolys.dmp_lift   s=   € Ü˜$Ÿ-™-¨Ó*¨D¯J©J°q©L¸$¿+¹+ÓFˆØ�~‰~Ó×*Ñ*¨6Ó2Ð2r5  c                óL   • [        U R                  U5      U R                  5      $ r-  )rt   rP  r*  rŠ  s     r1  rt   ÚIPolys.dup_sign_variations$  ró  r5  c                óÔ   • [        U R                  U5      U R                  US9u  p4U(       a(  U R                  U R                  R	                  5       S9nOU nX5R                  U5      4$ )N©Úconvert©r*  )ru   rP  r*  r7  Úget_ringrU  ©r/  rY  rc  rZ  rC  rK  s         r1  ru   ÚIPolys.dup_clear_denoms'  sV   € Ü §¡¨aÓ 0°$·+±+ÀwÑO‰ˆÞØ—:‘: T§[¡[×%9Ñ%9Ó%;�:Ð<‰DàˆDØ—?‘? 1Ó%Ð&Ð&r5  c                óð   • [        U R                  U5      U R                  S-
  U R                  US9u  p4U(       a(  U R	                  U R                  R                  5       S9nOU nX5R                  U5      4$ )NrT  rb  rd  )rv   rP  r)  r*  r7  re  rU  rf  s         r1  rv   ÚIPolys.dmp_clear_denoms.  sa   € Ü §¡¨aÓ 0°$·*±*¸Q±,ÀÇÁÐU\Ñ]‰ˆÞØ—:‘: T§[¡[×%9Ñ%9Ó%;�:Ð<‰DàˆDØ—?‘? 1Ó%Ð&Ð&r5  c                ój   • U R                  [        U R                  U5      X R                  5      5      $ r-  )rU  rw   rP  r*  rƒ  s      r1  rw   ÚIPolys.dup_revert6  r†  r5  c                ó´   • [        U R                  U5      U R                  U5      U R                  5      u  p4U R                  U5      U R                  U5      4$ r-  )rx   rP  r*  rU  ©r/  rY  r–  Úsr¢  s        r1  rx   ÚIPolys.dup_half_gcdex9  sE   € Ü˜dŸm™m¨AÓ.°·±¸aÓ0@À$Ç+Á+ÓN‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r5  c                óÐ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4U R	                  U5      U R	                  U5      4$ rS  )ry   rP  r)  r*  rU  rm  s        r1  ry   ÚIPolys.dmp_half_gcdex<  sR   € Ü˜dŸm™m¨AÓ.°·±¸aÓ0@À$Ç*Á*ÈQÁ,ÐPT×P[ÑP[Ó\‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r5  c                óÖ   • [        U R                  U5      U R                  U5      U R                  5      u  p4nU R                  U5      U R                  U5      U R                  U5      4$ r-  )rz   rP  r*  rU  ©r/  rY  r–  rn  Útr¢  s         r1  rz   ÚIPolys.dup_gcdex?  sR   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇÁÓL‰ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr5  c                óò   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4nU R	                  U5      U R	                  U5      U R	                  U5      4$ rS  )r{   rP  r)  r*  rU  rs  s         r1  r{   ÚIPolys.dmp_gcdexB  s\   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇ
Á
È1ÁÈdÏkÉkÓZ‰ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr5  c                óŠ   • U R                  [        U R                  U5      U R                  U5      U R                  5      5      $ r-  )rU  r|   rP  r*  r•  s      r1  r|   ÚIPolys.dup_invertF  rÄ  r5  c                ó¦   • U R                  [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  r}   rP  r)  r*  r•  s      r1  r}   ÚIPolys.dmp_invertH  rÎ  r5  c                óª   • [        U R                  U5      U R                  U5      U R                  5      n[        [	        U R
                  U5      5      $ r-  )r~   rP  r*  r÷  rø  rU  ©r/  rY  r–  Úprss       r1  r~   ÚIPolys.dup_euclidean_prsK  ó<   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇKÁKÓPˆÜ”C˜Ÿ™¨Ó-Ó.Ð.r5  c                óÆ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      n[	        [        U R                  U5      5      $ rS  )r   rP  r)  r*  r÷  rø  rU  r}  s       r1  r   ÚIPolys.dmp_euclidean_prsN  óI   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇJÁJÈqÁLÐRV×R]ÑR]Ó^ˆÜ”C˜Ÿ™¨Ó-Ó.Ð.r5  c                óª   • [        U R                  U5      U R                  U5      U R                  5      n[        [	        U R
                  U5      5      $ r-  )r€   rP  r*  r÷  rø  rU  r}  s       r1  r€   ÚIPolys.dup_primitive_prsQ  r€  r5  c                óÆ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      n[	        [        U R                  U5      5      $ rS  )r�   rP  r)  r*  r÷  rø  rU  r}  s       r1  r�   ÚIPolys.dmp_primitive_prsT  rƒ  r5  c                ó²   • [        U R                  U5      U R                  U5      U R                  5      u  p4[        [	        U R
                  U5      5      U4$ r-  )r‚   rP  r*  r÷  rø  rU  ©r/  rY  r–  r~  Úsress        r1  r‚   ÚIPolys.dup_inner_subresultantsX  sF   € Ü+¨D¯M©M¸!Ó,<¸d¿m¹mÈAÓ>NÐPT×P[ÑP[Ó\‰	ˆÜ”S˜Ÿ™¨#Ó.Ó/°Ð6Ð6r5  c                óÎ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4[	        [        U R                  U5      5      U4$ rS  )r†   rP  r)  r*  r÷  rø  rU  r‰  s        r1  r†   ÚIPolys.dmp_inner_subresultants[  sU   € Ü,¨T¯]©]¸1Ó-=¸t¿}¹}ÈQÓ?OÐQU×Q[ÑQ[Ð\]ÑQ]Ð_c×_jÑ_jÓk‰	ˆÜ”S˜Ÿ™¨#Ó.Ó/°Ð6Ð6r5  c                óª   • [        U R                  U5      U R                  U5      U R                  5      n[        [	        U R
                  U5      5      $ r-  )rƒ   rP  r*  r÷  rø  rU  r}  s       r1  rƒ   ÚIPolys.dup_subresultants_  r€  r5  c                óÆ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      n[	        [        U R                  U5      5      $ rS  )r‡   rP  r)  r*  r÷  rø  rU  r}  s       r1  r‡   ÚIPolys.dmp_subresultantsb  rƒ  r5  c                ó²   • [        U R                  U5      U R                  U5      U R                  5      u  p4U[        [	        U R
                  U5      5      4$ r-  )r„   rP  r*  r÷  rø  rU  ©r/  rY  r–  Úresr~  s        r1  r„   ÚIPolys.dup_prs_resultantf  sC   € Ü$ T§]¡]°1Ó%5°t·}±}ÀQÓ7GÈÏÉÓU‰ˆØ”Tœ#˜dŸo™o¨sÓ3Ó4Ð5Ð5r5  c                óò   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4U SS  R	                  U5      [        [        U R                  U5      5      4$ rS  )rˆ   rP  r)  r*  rU  r÷  rø  r“  s        r1  rˆ   ÚIPolys.dmp_prs_resultanti  sb   € Ü$ T§]¡]°1Ó%5°t·}±}ÀQÓ7GÈÏÉÐTUÉÐW[×WbÑWbÓc‰ˆØ�Q�R�×#Ñ# CÓ(¬$¬s°4·?±?ÀCÓ/HÓ*IÐJÐJr5  c                óÐ   • [        U R                  U5      U R                  U5      U R                  U5      U R                  S-
  U R                  5      nU SS  R                  U5      $ rS  )r‰   rP  rB  r)  r*  rU  )r/  rY  r–  r6  r”  s        r1  r‰   Ú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'r5  c                ó°   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      nU SS  R	                  U5      $ rS  )rŠ   rP  r)  r*  rU  ©r/  rY  r–  r”  s       r1  rŠ   ÚIPolys.dmp_zz_collins_resultantp  óK   € Ü& t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï:É:ÐVWÉ<ÐY]×YdÑYdÓeˆØ�A�Bˆx×"Ñ" 3Ó'Ð'r5  c                ó°   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      nU SS  R	                  U5      $ rS  )r‹   rP  r)  r*  rU  r›  s       r1  r‹   ÚIPolys.dmp_qq_collins_resultants  r�  r5  c                ól   • [        U R                  U5      U R                  U5      U R                  5      $ r-  )r…   rP  r*  r•  s      r1  r…   ÚIPolys.dup_resultantw  s'   € Ü˜TŸ]™]¨1Ó-¨t¯}©}¸QÓ/?ÀÇÁÓMÐMr5  c                óÞ   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      n[	        U[
        5      (       a  U SS  R                  U5      $ U$ rS  )rŒ   rP  r)  r*  rJ  r÷  rU  r›  s       r1  rŒ   ÚIPolys.dmp_resultanty  sY   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇ
Á
È1ÁÈdÏkÉkÓZˆÜ�cœ4× Ñ Ø˜˜�8×&Ñ& sÓ+Ð+àˆJr5  c                óL   • [        U R                  U5      U R                  5      $ r-  )r�   rP  r*  rŠ  s     r1  r�   ÚIPolys.dup_discriminant€  s   € Ü §¡¨aÓ 0°$·+±+Ó>Ð>r5  c                ó¾   • [        U R                  U5      U R                  S-
  U R                  5      n[	        U[
        5      (       a  U SS  R                  U5      $ U$ rS  )rŽ   rP  r)  r*  rJ  r÷  rU  )r/  rY  Údiscs      r1  rŽ   ÚIPolys.dmp_discriminant‚  sN   € Ü §¡¨aÓ 0°$·*±*¸Q±,ÀÇÁÓLˆÜ�dœD×!Ñ!Ø˜˜�8×&Ñ& tÓ,Ð,àˆKr5  c                óÖ   • [        U R                  U5      U R                  U5      U R                  5      u  p4nU R                  U5      U R                  U5      U R                  U5      4$ r-  )r�   rP  r*  rU  ©r/  rY  r–  ÚHrC  rD  s         r1  r�   ÚIPolys.dup_rr_prs_gcd‰  óR   € Ü  §¡¨qÓ!1°4·=±=ÀÓ3CÀTÇ[Á[ÓQ‰ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr5  c                óÖ   • [        U R                  U5      U R                  U5      U R                  5      u  p4nU R                  U5      U R                  U5      U R                  U5      4$ r-  )r�   rP  r*  rU  rª  s         r1  r�   ÚIPolys.dup_ff_prs_gcdŒ  r­  r5  c                óò   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4nU R	                  U5      U R	                  U5      U R	                  U5      4$ rS  )r‘   rP  r)  r*  rU  rª  s         r1  r‘   ÚIPolys.dmp_rr_prs_gcd�  ó`   € Ü  §¡¨qÓ!1°4·=±=ÀÓ3CÀTÇZÁZÐPQÁ\ÐSW×S^ÑS^Ó_‰ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr5  c                óò   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4nU R	                  U5      U R	                  U5      U R	                  U5      4$ rS  )r’   rP  r)  r*  rU  rª  s         r1  r’   ÚIPolys.dmp_ff_prs_gcd’  r²  r5  c                óÖ   • [        U R                  U5      U R                  U5      U R                  5      u  p4nU R                  U5      U R                  U5      U R                  U5      4$ r-  )r“   rP  r*  rU  rª  s         r1  r“   ÚIPolys.dup_zz_heu_gcd•  r­  r5  c                óò   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4nU R	                  U5      U R	                  U5      U R	                  U5      4$ rS  )r”   rP  r)  r*  rU  rª  s         r1  r”   ÚIPolys.dmp_zz_heu_gcd˜  r²  r5  c                óÖ   • [        U R                  U5      U R                  U5      U R                  5      u  p4nU R                  U5      U R                  U5      U R                  U5      4$ r-  )r•   rP  r*  rU  rª  s         r1  r•   ÚIPolys.dup_qq_heu_gcd›  r­  r5  c                óò   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4nU R	                  U5      U R	                  U5      U R	                  U5      4$ rS  )r–   rP  r)  r*  rU  rª  s         r1  r–   ÚIPolys.dmp_qq_heu_gcdž  r²  r5  c                óÖ   • [        U R                  U5      U R                  U5      U R                  5      u  p4nU R                  U5      U R                  U5      U R                  U5      4$ r-  )r—   rP  r*  rU  rª  s         r1  r—   ÚIPolys.dup_inner_gcd¡  sR   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇKÁKÓP‰ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr5  c                óò   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      u  p4nU R	                  U5      U R	                  U5      U R	                  U5      4$ rS  )r˜   rP  r)  r*  rU  rª  s         r1  r˜   ÚIPolys.dmp_inner_gcd¤  s_   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇJÁJÈqÁLÐRV×R]ÑR]Ó^‰ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr5  c                óŽ   • [        U R                  U5      U R                  U5      U R                  5      nU R                  U5      $ r-  )r™   rP  r*  rU  ©r/  rY  r–  r«  s       r1  r™   ÚIPolys.dup_gcd§  ó5   € Ü�D—M‘M !Ó$ d§m¡m°AÓ&6¸¿¹ÓDˆØ�‰˜qÓ!Ð!r5  c                óª   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      nU R	                  U5      $ rS  )rš   rP  r)  r*  rU  rÂ  s       r1  rš   ÚIPolys.dmp_gcdª  ó?   € Ü�D—M‘M !Ó$ d§m¡m°AÓ&6¸¿
¹
À1¹ÀdÇkÁkÓRˆØ�‰˜qÓ!Ð!r5  c                óŽ   • [        U R                  U5      U R                  U5      U R                  5      nU R                  U5      $ r-  )r›   rP  r*  rU  rÂ  s       r1  r›   ÚIPolys.dup_rr_lcm­  ó5   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿;¹;ÓGˆØ�‰˜qÓ!Ð!r5  c                óŽ   • [        U R                  U5      U R                  U5      U R                  5      nU R                  U5      $ r-  )rœ   rP  r*  rU  rÂ  s       r1  rœ   ÚIPolys.dup_ff_lcm°  rÊ  r5  c                óŽ   • [        U R                  U5      U R                  U5      U R                  5      nU R                  U5      $ r-  )r�   rP  r*  rU  rÂ  s       r1  r�   ÚIPolys.dup_lcm³  rÄ  r5  c                óª   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      nU R	                  U5      $ rS  )rž   rP  r)  r*  rU  rÂ  s       r1  rž   ÚIPolys.dmp_rr_lcm¶  ó?   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿:¹:Àa¹<ÈÏÉÓUˆØ�‰˜qÓ!Ð!r5  c                óª   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      nU R	                  U5      $ rS  )rŸ   rP  r)  r*  rU  rÂ  s       r1  rŸ   ÚIPolys.dmp_ff_lcm¹  rÑ  r5  c                óª   • [        U R                  U5      U R                  U5      U R                  S-
  U R                  5      nU R	                  U5      $ rS  )r    rP  r)  r*  rU  rÂ  s       r1  r    ÚIPolys.dmp_lcm¼  rÇ  r5  c                óP   • [        U R                  U5      U R                  5      nU$ r-  )rd   rP  r*  ©r/  rY  Úconts      r1  rd   ÚIPolys.dup_contentÀ  s    € Ü˜4Ÿ=™=¨Ó+¨T¯[©[Ó9ˆØˆr5  c                ót   • [        U R                  U5      U R                  5      u  p#X R                  U5      4$ r-  )rf   rP  r*  rU  ©r/  rY  rØ  Úprims       r1  rf   ÚIPolys.dup_primitiveÃ  s/   € Ü" 4§=¡=°Ó#3°T·[±[ÓA‰
ˆØ—_‘_ TÓ*Ð*Ð*r5  c                ó¾   • [        U R                  U5      U R                  S-
  U R                  5      n[	        U[
        5      (       a  U SS  R                  U5      $ U$ rS  )r¡   rP  r)  r*  rJ  r÷  rU  r×  s      r1  r¡   ÚIPolys.dmp_contentÇ  sN   € Ü˜4Ÿ=™=¨Ó+¨T¯Z©Z¸©\¸4¿;¹;ÓGˆÜ�dœD×!Ñ!Ø˜˜�8×&Ñ& tÓ,Ð,àˆKr5  c                ó  • [        U R                  U5      U R                  S-
  U R                  5      u  p#[	        U[
        5      (       a%  U SS  R                  U5      U R                  U5      4$ X R                  U5      4$ rS  )r¢   rP  r)  r*  rJ  r÷  rU  rÛ  s       r1  r¢   ÚIPolys.dmp_primitiveÍ  sk   € Ü" 4§=¡=°Ó#3°T·Z±ZÀ±\À4Ç;Á;ÓO‰
ˆÜ�dœD×!Ñ!Ø˜˜�H×'Ñ'¨Ó-¨t¯©¸tÓ/DÐEÐEàŸ/™/¨$Ó/Ð0Ð0r5  c                ól   • [        U R                  U5      U R                  S-
  U R                  5      nU$ rS  )re   rP  r)  r*  r×  s      r1  re   ÚIPolys.dmp_ground_contentÔ  s*   € Ü! $§-¡-°Ó"2°D·J±J¸q±LÀ$Ç+Á+ÓNˆØˆr5  c                ó�   • [        U R                  U5      U R                  S-
  U R                  5      u  p#X R	                  U5      4$ rS  )rg   rP  r)  r*  rU  rÛ  s       r1  rg   ÚIPolys.dmp_ground_primitive×  s9   € Ü)¨$¯-©-¸Ó*:¸D¿J¹JÀq¹LÈ$Ï+É+ÓV‰
ˆØ—o‘o dÓ+Ð,Ð,r5  c                ó  • [        U R                  U5      U R                  U5      U R                  US9nU(       d(  Uu  pVpxXVU R                  U5      U R                  U5      4$ Uu  pxU R                  U5      U R                  U5      4$ )N©Úinclude)r£   rP  r*  rU  ©	r/  rY  r–  rè  r*  ÚcfÚcgrC  rD  s	            r1  r£   ÚIPolys.dup_cancelÛ  sx   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇÁÐU\Ñ]ˆÞØ!‰LˆB�AØ˜DŸO™O¨AÓ.°·±ÀÓ0BÐCÐCà‰DˆAØ—O‘O AÓ&¨¯©¸Ó(:Ð;Ð;r5  c                ó0  • [        U R                  U5      U R                  U5      U R                  S-
  U R                  US9nU(       d(  Uu  pVpxXVU R	                  U5      U R	                  U5      4$ Uu  pxU R	                  U5      U R	                  U5      4$ )NrT  rç  )r¤   rP  r)  r*  rU  ré  s	            r1  r¤   ÚIPolys.dmp_cancelã  s‚   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇ
Á
È1ÁÈdÏkÉkÐcjÑkˆÞØ!‰LˆB�AØ˜DŸO™O¨AÓ.°·±ÀÓ0BÐCÐCà‰DˆAØ—O‘O AÓ&¨¯©¸Ó(:Ð;Ð;r5  c           	     óä   • [        U R                  U5      [        [        U R                  U5      5      U R                  5      nU VVs/ s H  u  p4U R                  U5      U4PM     snn$ s  snnf r-  )r¥   rP  r÷  rø  r*  rU  ©r/  rY  Úfactorsr–  Úks        r1  r¥   ÚIPolys.dup_trial_divisionì  sX   € Ü$ T§]¡]°1Ó%5´t¼CÀÇÁÈwÓ<WÓ7XÐZ^×ZeÑZeÓfˆÙ5<Ô>²W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>s   Á	A,c           	     ó   • [        U R                  U5      [        [        U R                  U5      5      U R                  S-
  U R
                  5      nU VVs/ s H  u  p4U R                  U5      U4PM     snn$ s  snnf rS  )r¦   rP  r÷  rø  r)  r*  rU  rð  s        r1  r¦   ÚIPolys.dmp_trial_divisionï  sg   € Ü$ T§]¡]°1Ó%5´t¼CÀÇÁÈwÓ<WÓ7XÐZ^×ZdÑZdÐefÑZfÐhl×hsÑhsÓtˆÙ5<Ô>²W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>s   ÁA:c                óL   • [        U R                  U5      U R                  5      $ r-  )r§   rP  r*  rŠ  s     r1  r§   ÚIPolys.dup_zz_mignotte_boundó  s   € Ü$ T§]¡]°1Ó%5°t·{±{ÓCÐCr5  c                óh   • [        U R                  U5      U R                  S-
  U R                  5      $ rS  )r¨   rP  r)  r*  rŠ  s     r1  r¨   ÚIPolys.dmp_zz_mignotte_boundõ  s&   € Ü$ T§]¡]°1Ó%5°t·z±zÀ!±|ÀTÇ[Á[ÓQÐQr5  c           
     ó  • U R                   n[        X" U5      U" U5      U" U5      U" U5      U" U5      U R                  5      u  p‰p«U R                  U5      U R                  U	5      U R                  U
5      U R                  U5      4$ r-  )rP  r©   r*  rU  )r/  r  rY  r–  r¢  rn  rt  ÚDrD  r«  ÚSÚTs               r1  r©   ÚIPolys.dup_zz_hensel_stepø  sq   € Ø�M‰MˆÜ'¨¨1¨Q«4±°1³±q¸³t¹Q¸q»TÁ1ÀQÃ4ÈÏÉÓU‰
ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÈDÏOÉOÐ\]ÓL^Ð_Ð_r5  c           
     ó¶   • U R                   n[        X" U5      [        [        XS5      5      X@R                  5      n[        [        U R
                  U5      5      $ r-  )rP  rª   r÷  rø  r*  rU  )r/  r6  rY  Úf_listÚlrû  rú  s          r1  rª   ÚIPolys.dup_zz_hensel_liftü  sB   € Ø�M‰MˆÜ" 1 a¨£d¬D´°Q³Ó,@À!Ç[Á[ÓQˆÜ”C˜Ÿ™¨Ó/Ó0Ð0r5  c                ó¨   • [        U R                  U5      U R                  5      nU VVs/ s H  u  p4U R                  U5      U4PM     snn$ s  snnf r-  )r«   rP  r*  rU  rð  s        r1  r«   ÚIPolys.dup_zz_zassenhaus  sC   € Ü# D§M¡M°!Ó$4°d·k±kÓBˆÙ5<Ô>²W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>ó   «Ac                óL   • [        U R                  U5      U R                  5      $ r-  )r¬   rP  r*  rŠ  s     r1  r¬   ÚIPolys.dup_zz_irreducible_p  ó   € Ü# D§M¡M°!Ó$4°d·k±kÓBÐBr5  c                óJ   • [        U R                  U5      U R                  US9$ )N)Úirreducible)r­   rP  r*  )r/  rY  r
  s      r1  r­   ÚIPolys.dup_cyclotomic_p  s   € Ü §¡¨aÓ 0°$·+±+È;ÑWÐWr5  c                óN   • [        XR                  5      nU R                  U5      $ r-  )r®   r*  rU  )r/  r„  rC  s      r1  r®   ÚIPolys.dup_zz_cyclotomic_poly	  s   € Ü" 1§k¡kÓ2ˆØ�‰˜qÓ!Ð!r5  c                ó”   • [        U R                  U5      U R                  5      nUc  U$ [        [	        U R
                  U5      5      $ r-  )r¯   rP  r*  r÷  rø  rU  r]  s      r1  r¯   ÚIPolys.dup_zz_cyclotomic_factor  s;   € Ü)¨$¯-©-¸Ó*:¸D¿K¹KÓHˆØ‰>ØˆMäœ˜DŸO™O¨VÓ4Ó5Ð5r5  c                ó.   • [        XX0R                  5      $ r-  )r²   r*  )r/  ÚEÚcsÚcts       r1  r²   ÚIPolys.dmp_zz_wang_non_divisors  s   € Ü'¨¨r·;±;Ó?Ð?r5  c           
     óº  • U SS  nU VV	s/ s H  u  p‰UR                  U5      U	4PM     nnn	U S S n
[        [        U
R                   U5      5      n[        U R                  U5      X#XEX`R                  S-
  U R
                  5      u  pnU R                  U5      [        [        U
R                  U5      5      [        [        UR                  U5      5      4$ s  sn	nf rS  )rP  r÷  rø  r³   r)  r*  rU  )r/  rY  rý  r  r  r«  r2  Úmvrt  rò  ÚuvÚHHÚCCs                r1  r³   ÚIPolys.dmp_zz_wang_lead_coeffs  s»   € Ø�!�"ˆXˆÙ./Ô1ªa¡d aˆr�{‰{˜1‹~˜qÓ!©aˆÑ1Ø�"�1ˆXˆÜ”�R—[‘[ !Ó$Ó%ˆÜ+¨D¯M©M¸!Ó,<¸aÀQÈ1ÏjÉjÐYZÉlÐ\`×\gÑ\gÓh‰	ˆˆrØ�‰˜qÓ!¤4¬¨B¯M©M¸2Ó(>Ó#?ÄÄcÈ"Ï-É-ÐY[ÓF\ÓA]Ð]Ð]ùó	 2s   ‹Cc                ó¨   • [        [        [        U R                  U5      5      X#U R                  5      n[        [        U R
                  U5      5      $ r-  )r´   r÷  rø  rP  r*  rU  )r/  rC  r  r6  r*  s        r1  r´   ÚIPolys.dup_zz_diophantine%  s:   € Ü#¤D¬¨T¯]©]¸AÓ)>Ó$?ÀÀtÇ{Á{ÓSˆÜ”C˜Ÿ™¨Ó0Ó1Ð1r5  c           	     óä   • [        [        [        U R                  U5      5      U R                  U5      X4XPR                  S-
  U R
                  5      n[        [        U R                  U5      5      $ rS  )rµ   r÷  rø  rP  r)  r*  rU  )r/  rC  rZ  r2  rE  r6  r*  s          r1  rµ   ÚIPolys.dmp_zz_diophantine*  sX   € Ü#¤D¬¨T¯]©]¸AÓ)>Ó$?ÀÇÁÈqÓAQÐSTÐYZ×\fÑ\fÐghÑ\hÐjn×juÑjuÓvˆÜ”C˜Ÿ™¨Ó0Ó1Ð1r5  c           	     ó:  • U S S nU SS  n[        [        UR                  U5      5      n[        [        UR                  U5      5      n[        U R                  U5      X#XEU R                  S-
  U R
                  5      n[        [        U R                  U5      5      $ rS  )r÷  rø  rP  r¶   r)  r*  rU  )	r/  rY  r«  r  r2  r6  r  r  r*  s	            r1  r¶   Ú!IPolys.dmp_zz_wang_hensel_lifting/  sƒ   € Ø�"�1ˆXˆØ�!�"ˆXˆÜ”�R—[‘[ !Ó$Ó%ˆÜ”#�b—k‘k 2Ó&Ó'ˆÜ+¨D¯M©M¸!Ó,<¸aÀQÈ4Ï:É:ÐVWÉ<ÐY]×YdÑYdÓeˆÜ”C˜Ÿ™¨Ó0Ó1Ð1r5  c                ó²   • [        U R                  U5      U R                  S-
  U R                  X#S9nU Vs/ s H  oPR	                  U5      PM     sn$ s  snf )NrT  )ÚmodÚseed)r·   rP  r)  r*  rU  )r/  rY  r"  r#  rñ  r–  s         r1  r·   ÚIPolys.dmp_zz_wang7  sF   € Ü˜dŸm™m¨AÓ.°·
±
¸1±¸d¿k¹kÈsÑ^ˆÙ-4Ó6ªW¨—‘ Ö#©WÑ6Ð6ùÒ6s   ·Ac                óž   • [        U R                  U5      U R                  5      u  p#X# Vs/ s H  o@R                  U5      PM     sn4$ s  snf r-  )r°   rP  r*  rU  )r/  rY  Úcoeffrñ  r–  s        r1  r°   ÚIPolys.dup_zz_factor_sqf;  sA   € Ü*¨4¯=©=¸Ó+;¸T¿[¹[ÓI‰ˆØ°WÓ>²W°Ÿ™¨Ö+±WÑ>Ð?Ð?ùÒ>s   ¬A
c                ó®   • [        U R                  U5      U R                  5      u  p#X# VVs/ s H  u  pEU R                  U5      U4PM     snn4$ s  snnf r-  )r±   rP  r*  rU  ©r/  rY  r&  rñ  r–  rò  s         r1  r±   ÚIPolys.dup_zz_factor?  óJ   € Ü& t§}¡}°QÓ'7¸¿¹ÓE‰ˆØ¸WÔFºW±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFó   ­Ac                óÊ   • [        U R                  U5      U R                  S-
  U R                  5      u  p#X# VVs/ s H  u  pEU R	                  U5      U4PM     snn4$ s  snnf rS  )r¸   rP  r)  r*  rU  r)  s         r1  r¸   ÚIPolys.dmp_zz_factorB  óT   € Ü& t§}¡}°QÓ'7¸¿¹ÀA¹ÀtÇ{Á{ÓS‰ˆØ¸WÔFºW±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFó   »Ac                ó®   • [        U R                  U5      U R                  5      u  p#X# VVs/ s H  u  pEU R                  U5      U4PM     snn4$ s  snnf r-  )r¹   rP  r*  rU  r)  s         r1  r¹   ÚIPolys.dup_qq_i_factorF  óJ   € Ü(¨¯©°qÓ)9¸4¿;¹;ÓG‰ˆØ¸WÔFºW±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFr,  c                óÊ   • [        U R                  U5      U R                  S-
  U R                  5      u  p#X# VVs/ s H  u  pEU R	                  U5      U4PM     snn4$ s  snnf rS  )r»   rP  r)  r*  rU  r)  s         r1  r»   ÚIPolys.dmp_qq_i_factorI  óT   € Ü(¨¯©°qÓ)9¸4¿:¹:Àa¹<ÈÏÉÓU‰ˆØ¸WÔFºW±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFr0  c                ó®   • [        U R                  U5      U R                  5      u  p#X# VVs/ s H  u  pEU R                  U5      U4PM     snn4$ s  snnf r-  )rº   rP  r*  rU  r)  s         r1  rº   ÚIPolys.dup_zz_i_factorM  r3  r,  c                óÊ   • [        U R                  U5      U R                  S-
  U R                  5      u  p#X# VVs/ s H  u  pEU R	                  U5      U4PM     snn4$ s  snnf rS  )r¼   rP  r)  r*  rU  r)  s         r1  r¼   ÚIPolys.dmp_zz_i_factorP  r6  r0  c                ó®   • [        U R                  U5      U R                  5      u  p#X# VVs/ s H  u  pEU R                  U5      U4PM     snn4$ s  snnf r-  )r½   rP  r*  rU  r)  s         r1  r½   ÚIPolys.dup_ext_factorT  sJ   € Ü'¨¯©°aÓ(8¸$¿+¹+ÓF‰ˆØ¸WÔFºW±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFr,  c                óÊ   • [        U R                  U5      U R                  S-
  U R                  5      u  p#X# VVs/ s H  u  pEU R	                  U5      U4PM     snn4$ s  snnf rS  )r¾   rP  r)  r*  rU  r)  s         r1  r¾   ÚIPolys.dmp_ext_factorW  sT   € Ü'¨¯©°aÓ(8¸$¿*¹*ÀQ¹,ÈÏÉÓT‰ˆØ¸WÔFºW±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFr0  c                ó®   • [        U R                  U5      U R                  5      u  p#X# VVs/ s H  u  pEU R                  U5      U4PM     snn4$ s  snnf r-  )r¿   rP  r*  rU  r)  s         r1  r¿   ÚIPolys.dup_gf_factor[  r+  r,  c                óÊ   • [        U R                  U5      U R                  S-
  U R                  5      u  p#X# VVs/ s H  u  pEU R	                  U5      U4PM     snn4$ s  snnf rS  )rÀ   rP  r)  r*  rU  r)  s         r1  rÀ   ÚIPolys.dmp_gf_factor^  r/  r0  c                ó®   • [        U R                  U5      U R                  5      u  p#X# VVs/ s H  u  pEU R                  U5      U4PM     snn4$ s  snnf r-  )rÁ   rP  r*  rU  r)  s         r1  rÁ   ÚIPolys.dup_factor_listb  r3  r,  c                ó¨   • [        U R                  U5      U R                  5      nU VVs/ s H  u  p4U R                  U5      U4PM     snn$ s  snnf r-  )rÂ   rP  r*  rU  rð  s        r1  rÂ   ÚIPolys.dup_factor_list_includee  sC   € Ü)¨$¯-©-¸Ó*:¸D¿K¹KÓHˆÙ5<Ô>²W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>r  c                óÊ   • [        U R                  U5      U R                  S-
  U R                  5      u  p#X# VVs/ s H  u  pEU R	                  U5      U4PM     snn4$ s  snnf rS  )rÃ   rP  r)  r*  rU  r)  s         r1  rÃ   ÚIPolys.dmp_factor_listi  r6  r0  c                óÄ   • [        U R                  U5      U R                  S-
  U R                  5      nU VVs/ s H  u  p4U R	                  U5      U4PM     snn$ s  snnf rS  )rÄ   rP  r)  r*  rU  rð  s        r1  rÄ   ÚIPolys.dmp_factor_list_includel  sM   € Ü)¨$¯-©-¸Ó*:¸D¿J¹JÀq¹LÈ$Ï+É+ÓVˆÙ5<Ô>²W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>ó   ¹Ac                óL   • [        U R                  U5      U R                  5      $ r-  )rÅ   rP  r*  rŠ  s     r1  rÅ   ÚIPolys.dup_irreducible_pp  s   € Ü  §¡¨qÓ!1°4·;±;Ó?Ð?r5  c                óh   • [        U R                  U5      U R                  S-
  U R                  5      $ rS  )rÆ   rP  r)  r*  rŠ  s     r1  rÆ   ÚIPolys.dmp_irreducible_pr  s&   € Ü  §¡¨qÓ!1°4·:±:¸a±<ÀÇÁÓMÐMr5  c                óŠ   • [        U R                  U5      U R                  5      n[        [	        U R
                  U5      5      $ r-  )rÇ   rP  r*  r÷  rø  rU  )r/  rY  Úseqs      r1  rÇ   ÚIPolys.dup_sturmu  s1   € Ü˜Ÿ™ aÓ(¨$¯+©+Ó6ˆÜ”C˜Ÿ™¨Ó-Ó.Ð.r5  c                óL   • [        U R                  U5      U R                  5      $ r-  )rÙ   rP  r*  rŠ  s     r1  rÙ   ÚIPolys.dup_sqf_py  s   € Ü˜Ÿ™ qÓ)¨4¯;©;Ó7Ð7r5  c                óh   • [        U R                  U5      U R                  S-
  U R                  5      $ rS  )rÚ   rP  r)  r*  rŠ  s     r1  rÚ   ÚIPolys.dmp_sqf_p{  s&   € Ü˜Ÿ™ qÓ)¨4¯:©:°a©<¸¿¹ÓEÐEr5  c                ó¦   • [        U R                  U5      U R                  S-
  U R                  5      nU R	                  5       R                  U5      $ rS  )rÛ   rP  r)  r*  r:  rU  rƒ  s      r1  rÛ   ÚIPolys.dmp_norm~  s=   € Ü�T—]‘] 1Ó% t§z¡z°!¡|°T·[±[ÓAˆØ�~‰~Ó×*Ñ*¨1Ó-Ð-r5  c                ó²   • [        U R                  U5      U R                  5      u  p#nX R                  U5      U R	                  5       R                  U5      4$ r-  )rÜ   rP  r*  rU  r:  ©r/  rY  rn  rC  ÚRs        r1  rÜ   ÚIPolys.dup_sqf_norm‚  sE   € Ü˜tŸ}™}¨QÓ/°·±Ó=‰ˆˆaØ—?‘? 1Ó% t§~¡~Ó'7×'BÑ'BÀ1Ó'EÐFÐFr5  c                óÎ   • [        U R                  U5      U R                  S-
  U R                  5      u  p#nX R	                  U5      U R                  5       R	                  U5      4$ rS  )rÝ   rP  r)  r*  rU  r:  rZ  s        r1  rÝ   ÚIPolys.dmp_sqf_norm…  sO   € Ü˜tŸ}™}¨QÓ/°·±¸A±¸t¿{¹{ÓK‰ˆˆaØ—?‘? 1Ó% t§~¡~Ó'7×'BÑ'BÀ1Ó'EÐFÐFr5  c                ój   • U R                  [        U R                  U5      U R                  5      5      $ r-  )rU  rÞ   rP  r*  rŠ  s     r1  rÞ   ÚIPolys.dup_gf_sqf_part‰  ó%   € Ø�‰œ¨t¯}©}¸QÓ/?ÀÇÁÓMÓNÐNr5  c                ój   • U R                  [        U R                  U5      U R                  5      5      $ r-  )rU  rß   rP  r*  rŠ  s     r1  rß   ÚIPolys.dmp_gf_sqf_part‹  ra  r5  c                ój   • U R                  [        U R                  U5      U R                  5      5      $ r-  )rU  rà   rP  r*  rŠ  s     r1  rà   ÚIPolys.dup_sqf_part�  s%   € Ø�‰œ|¨D¯M©M¸!Ó,<¸d¿k¹kÓJÓKÐKr5  c                ó†   • U R                  [        U R                  U5      U R                  S-
  U R                  5      5      $ rS  )rU  rá   rP  r)  r*  rŠ  s     r1  rá   ÚIPolys.dmp_sqf_part�  s/   € Ø�‰œ|¨D¯M©M¸!Ó,<¸d¿j¹jÈ¹lÈDÏKÉKÓXÓYÐYr5  c                ó¬   • [        U R                  U5      U R                  US9u  p4X4 VVs/ s H  u  pVU R                  U5      U4PM     snn4$ s  snnf ©N©Úall)râ   rP  r*  rU  ©r/  rY  rk  r&  rñ  r–  rò  s          r1  râ   ÚIPolys.dup_gf_sqf_list’  sL   € Ü(¨¯©°qÓ)9¸4¿;¹;ÈCÑP‰ˆØ¸WÔFºW±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFó   ¬Ac                óÈ   • [        U R                  U5      U R                  S-
  U R                  US9u  p4X4 VVs/ s H  u  pVU R	                  U5      U4PM     snn4$ s  snnf ©NrT  rj  )rã   rP  r)  r*  rU  rl  s          r1  rã   ÚIPolys.dmp_gf_sqf_list•  sW   € Ü(¨¯©°qÓ)9¸4¿:¹:Àa¹<ÈÏÉÐZ]Ñ^‰ˆØ¸WÔFºW±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFó   ºAc                ó¬   • [        U R                  U5      U R                  US9u  p4X4 VVs/ s H  u  pVU R                  U5      U4PM     snn4$ s  snnf ri  )rä   rP  r*  rU  rl  s          r1  rä   ÚIPolys.dup_sqf_list™  sL   € Ü% d§m¡m°AÓ&6¸¿¹ÈÑM‰ˆØ¸WÔFºW±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFrn  c                ó¦   • [        U R                  U5      U R                  US9nU VVs/ s H  u  pEU R                  U5      U4PM     snn$ s  snnf ri  )rå   rP  r*  rU  ©r/  rY  rk  rñ  r–  rò  s         r1  rå   ÚIPolys.dup_sqf_list_includeœ  sE   € Ü& t§}¡}°QÓ'7¸¿¹È#ÑNˆÙ5<Ô>²W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>s   ªAc                óÈ   • [        U R                  U5      U R                  S-
  U R                  US9u  p4X4 VVs/ s H  u  pVU R	                  U5      U4PM     snn4$ s  snnf rp  )ræ   rP  r)  r*  rU  rl  s          r1  ræ   ÚIPolys.dmp_sqf_listŸ  sW   € Ü% d§m¡m°AÓ&6¸¿
¹
À1¹ÀdÇkÁkÐWZÑ[‰ˆØ¸WÔFºW±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFrr  c                óÂ   • [        U R                  U5      U R                  S-
  U R                  US9nU VVs/ s H  u  pEU R	                  U5      U4PM     snn$ s  snnf rp  )rç   rP  r)  r*  rU  rv  s         r1  rç   ÚIPolys.dmp_sqf_list_include¢  sP   € Ü& t§}¡}°QÓ'7¸¿¹ÀA¹ÀtÇ{Á{ÐX[Ñ\ˆÙ5<Ô>²W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>s   ¸Ac                ó¨   • [        U R                  U5      U R                  5      nU VVs/ s H  u  p4U R                  U5      U4PM     snn$ s  snnf r-  )rè   rP  r*  rU  rð  s        r1  rè   ÚIPolys.dup_gff_list¦  sC   € Ü˜tŸ}™}¨QÓ/°·±Ó=ˆÙ5<Ô>²W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>r  c                óÄ   • [        U R                  U5      U R                  S-
  U R                  5      nU VVs/ s H  u  p4U R	                  U5      U4PM     snn$ s  snnf rS  )ré   rP  r)  r*  rU  rð  s        r1  ré   ÚIPolys.dmp_gff_list©  sM   € Ü˜tŸ}™}¨QÓ/°·±¸A±¸t¿{¹{ÓKˆÙ5<Ô>²W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>rK  c                óL   • [        U R                  U5      U R                  5      $ r-  )rÈ   rP  r*  rŠ  s     r1  rÈ   ÚIPolys.dup_root_upper_bound­  r  r5  c                óL   • [        U R                  U5      U R                  5      $ r-  )rÉ   rP  r*  rŠ  s     r1  rÉ   ÚIPolys.dup_root_lower_bound¯  r  r5  c                óJ   • [        U R                  U5      X R                  US9$ )N)Úfast)rÊ   rP  r*  )r/  rY  ÚMr…  s       r1  rÊ   Ú IPolys.dup_step_refine_real_root²  s   € Ü(¨¯©°qÓ)9¸1¿k¹kÐPTÑUÐUr5  c                óN   • [        U R                  U5      X R                  X4XVUS9$ )N)ÚepsÚstepsÚdisjointr…  Úmobius)rË   rP  r*  )r/  rY  r†  r‰  rŠ  r‹  r…  rŒ  s           r1  rË   Ú!IPolys.dup_inner_refine_real_root´  s/   € Ü)¨$¯-©-¸Ó*:¸A¿{¹{ÐPSÐksð  HNñ  Oð  	Or5  c                óN   • [        U R                  U5      X#U R                  XEXgS9$ ©N)r‰  rŠ  r‹  r…  )rÌ   rP  r*  ©r/  rY  rn  rt  r‰  rŠ  r‹  r…  s           r1  rÌ   Ú!IPolys.dup_outer_refine_real_root¶  s*   € Ü)¨$¯-©-¸Ó*:¸AÀ$Ç+Á+ÐSVÐnvñ  Cð  	Cr5  c                óN   • [        U R                  U5      X#U R                  XEXgS9$ r�  )rÍ   rP  r*  r�  s           r1  rÍ   ÚIPolys.dup_refine_real_root¸  s#   € Ü# D§M¡M°!Ó$4°a¸D¿K¹KÈSÐhpÑ|Ð|r5  c                óJ   • [        U R                  U5      U R                  X#S9$ )N)r‰  r…  )rÎ   rP  r*  )r/  rY  r‰  r…  s       r1  rÎ   Ú#IPolys.dup_inner_isolate_real_rootsº  s   € Ü+¨D¯M©M¸!Ó,<¸d¿k¹kÈsÑ^Ð^r5  c           
     óN   • [        U R                  U5      U R                  X#XEUS9$ )N)r‰  ÚinfÚsupr…  rŒ  )rÏ   rP  r*  )r/  rY  r‰  r—  r˜  r…  rŒ  s          r1  rÏ   Ú'IPolys.dup_inner_isolate_positive_roots¼  ó/   € Ü/°·±¸aÓ0@À$Ç+Á+ÐSVÐehð  }Cñ  Dð  	Dr5  c           
     óN   • [        U R                  U5      U R                  X#XEUS9$ )N)r—  r˜  r‰  r…  rŒ  )rÐ   rP  r*  )r/  rY  r—  r˜  r‰  r…  rŒ  s          r1  rÐ   Ú'IPolys.dup_inner_isolate_negative_roots¾  rš  r5  c           
     óN   • [        U R                  U5      U R                  X#XEUS9$ ©N)r‰  r—  r˜  r…  Úblackbox)rÑ   rP  r*  ©r/  rY  r‰  r—  r˜  r…  rŸ  s          r1  rÑ   Ú!IPolys.dup_isolate_real_roots_sqfÀ  s.   € Ü)¨$¯-©-¸Ó*:¸D¿K¹KÈSÐ_bð  yAñ  Bð  	Br5  c           
     óN   • [        U R                  U5      U R                  X#XEUS9$ )N)r‰  r—  r˜  Úbasisr…  )rÒ   rP  r*  )r/  rY  r‰  r—  r˜  r£  r…  s          r1  rÒ   ÚIPolys.dup_isolate_real_rootsÂ  s$   € Ü% d§m¡m°AÓ&6¸¿¹ÈÐ[^ÐrvÑwÐwr5  c                ój   • [        [        [        U R                  U5      5      U R                  X#XEXgS9$ )N)r‰  r—  r˜  Ústrictr£  r…  )rÓ   r÷  rø  rP  r*  )r/  rú  r‰  r—  r˜  r¦  r£  r…  s           r1  rÓ   Ú"IPolys.dup_isolate_real_roots_listÄ  s6   € Ü*¬4´°D·M±MÀ5Ó0IÓ+JÈDÏKÉKÐ]`Ðorð  JOñ  [ð  	[r5  c                óJ   • [        U R                  U5      U R                  X#S9$ )N)r—  r˜  )rÔ   rP  r*  )r/  rY  r—  r˜  s       r1  rÔ   ÚIPolys.dup_count_real_rootsÆ  s   € Ü# D§M¡M°!Ó$4°d·k±kÀsÑTÐTr5  c                óL   • [        U R                  U5      U R                  X#US9$ )N)r—  r˜  Úexclude)rÕ   rP  r*  )r/  rY  r—  r˜  r«  s        r1  rÕ   ÚIPolys.dup_count_complex_rootsÈ  s!   € Ü& t§}¡}°QÓ'7¸¿¹È#Ð`gÑhÐhr5  c           	     óL   • [        U R                  U5      U R                  X#XES9$ )N)r‰  r—  r˜  rŸ  )rÖ   rP  r*  )r/  rY  r‰  r—  r˜  rŸ  s         r1  rÖ   Ú$IPolys.dup_isolate_complex_roots_sqfÊ  s"   € Ü,¨T¯]©]¸1Ó-=¸t¿{¹{ÐPSÐbeÑyÐyr5  c           
     óN   • [        U R                  U5      U R                  X#XEUS9$ rž  )r×   rP  r*  r   s          r1  r×   Ú IPolys.dup_isolate_all_roots_sqfÌ  s*   € Ü(¨¯©°qÓ)9¸4¿;¹;ÈCÐ^aÐwñ  Að  	Ar5  c           	     óL   • [        U R                  U5      U R                  X#XES9$ )N)r‰  r—  r˜  r…  )rØ   rP  r*  )r/  rY  r‰  r—  r˜  r…  s         r1  rØ   ÚIPolys.dup_isolate_all_rootsÎ  s!   € Ü$ T§]¡]°1Ó%5°t·{±{ÈÐZ]ÑiÐir5  c           	     óˆ   • SSK Jn  [        [        U R                  U" U R
                  S-
  U R                  5      5      5      $ )Nr   )Údmp_fateman_poly_F_1rT  )Úsympy.polys.specialpolysr´  Útuplerø  rU  r)  r*  )r/  r´  s     r1  Úfateman_poly_F_1ÚIPolys.fateman_poly_F_1Ñ  ó/   € ÝAÜ”S˜Ÿ™Ñ*>¸t¿z¹zÈ!¹|ÈTÏ[É[Ó*YÓZÓ[Ð[r5  c           	     óˆ   • SSK Jn  [        [        U R                  U" U R
                  S-
  U R                  5      5      5      $ )Nr   )Údmp_fateman_poly_F_2rT  )rµ  r»  r¶  rø  rU  r)  r*  )r/  r»  s     r1  Úfateman_poly_F_2ÚIPolys.fateman_poly_F_2Ô  r¹  r5  c           	     óˆ   • SSK Jn  [        [        U R                  U" U R
                  S-
  U R                  5      5      5      $ )Nr   )Údmp_fateman_poly_F_3rT  )rµ  r¿  r¶  rø  rU  r)  r*  )r/  r¿  s     r1  Úfateman_poly_F_3ÚIPolys.fateman_poly_F_3×  r¹  r5  c           	     óÖ   • [        U R                  U5      R                  5        Vs/ s H1  o R                  R                  R                  X R                  5      PM3     sn5      $ s  snf r-  )rí   rM  rP  r*  Údomrc  )r/  r>  rZ  s      r1  Úto_gf_denseÚIPolys.to_gf_denseÛ  sI   € ÜÈ4Ï9É9ÐU\ÓK]×KfÑKfÔKhÓjÒKhÀaŸ+™+Ÿ/™/×1Ñ1°!·[±[ÖAÑKhÑjÓkÐkùÒjs   §8A&c                óz   • U R                  [        XR                  S-
  U R                  R                  5      5      $ rS  )rF  rS   r)  r*  rÃ  r=  s     r1  Úfrom_gf_denseÚIPolys.from_gf_denseÞ  s(   € Ø�~‰~œk¨'·:±:¸a±<ÀÇÁÇÁÓQÓRÐRr5  c                ó6   • [        U R                  U5      5      $ r-  )rê   rÄ  rŠ  s     r1  rê   ÚIPolys.gf_degreeá  s   € Ü˜×)Ñ)¨!Ó,Ó-Ð-r5  c                ó`   • [        U R                  U5      U R                  R                  5      $ r-  )rë   rÄ  r*  rÃ  rŠ  s     r1  rë   ÚIPolys.gf_LCä  ó"   € Ü�T×%Ñ% aÓ(¨$¯+©+¯/©/Ó:Ð:r5  c                ó`   • [        U R                  U5      U R                  R                  5      $ r-  )rì   rÄ  r*  rÃ  rŠ  s     r1  rì   ÚIPolys.gf_TCæ  rÍ  r5  c                óT   • U R                  [        U R                  U5      5      5      $ r-  )rÇ  rí   rÄ  rŠ  s     r1  rí   ÚIPolys.gf_stripé  s#   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>Ó"?Ó@Ð@r5  c                ó~   • U R                  [        U R                  U5      U R                  R                  5      5      $ r-  )rÇ  rí   rÄ  r*  r"  rŠ  s     r1  Úgf_truncÚIPolys.gf_truncë  s-   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>ÀÇÁÇÁÓ"PÓQÐQr5  c                ó¨   • U R                  [        U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rí   rÄ  r*  r"  rÃ  rŠ  s     r1  Ú	gf_normalÚIPolys.gf_normalí  ó<   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>ÀÇÁÇÁÐQU×Q\ÑQ\×Q`ÑQ`Ó"aÓbÐbr5  c                óˆ   • U R                  [        XR                  R                  U R                  R                  5      5      $ r-  )rÇ  rî   r*  r"  rÃ  rŠ  s     r1  rî   ÚIPolys.gf_from_dictð  s*   € Ø×!Ñ!¤,¨q·+±+·/±/À4Ç;Á;Ç?Á?Ó"SÓTÐTr5  c                ó^   • [        U R                  U5      U R                  R                  US9$ ©N)Ú	symmetric)rï   rÄ  r*  r"  ©r/  rY  rÝ  s      r1  rï   ÚIPolys.gf_to_dictò  s$   € Ü˜$×*Ñ*¨1Ó-¨t¯{©{¯©È)ÑTÐTr5  c                ó^   • U R                  [        XR                  R                  5      5      $ r-  )rÇ  rð   r*  r"  rŠ  s     r1  rð   ÚIPolys.gf_from_int_polyõ  s!   € Ø×!Ñ!Ô"2°1·k±k·o±oÓ"FÓGÐGr5  c                ó^   • [        U R                  U5      U R                  R                  US9$ rÜ  )rñ   rÄ  r*  r"  rÞ  s      r1  rñ   ÚIPolys.gf_to_int_poly÷  s$   € Ü˜d×.Ñ.¨qÓ1°4·;±;·?±?ÈiÑXÐXr5  c                ó¨   • U R                  [        U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rò   rÄ  r*  r"  rÃ  rŠ  s     r1  rò   ÚIPolys.gf_negú  ó7   € Ø×!Ñ!¤&¨×)9Ñ)9¸!Ó)<¸d¿k¹k¿o¹oÈtÏ{É{ÏÉÓ"_Ó`Ð`r5  c                ó¨   • U R                  [        U R                  U5      X R                  R                  U R                  R
                  5      5      $ r-  )rÇ  ró   rÄ  r*  r"  rÃ  r&  s      r1  ró   ÚIPolys.gf_add_groundý  ó<   € Ø×!Ñ!¤-°×0@Ñ0@ÀÓ0CÀQÏÉÏÉÐY]×YdÑYd×YhÑYhÓ"iÓjÐjr5  c                ó¨   • U R                  [        U R                  U5      X R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rô   rÄ  r*  r"  rÃ  r&  s      r1  rô   ÚIPolys.gf_sub_groundÿ  ré  r5  c                ó¨   • U R                  [        U R                  U5      X R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rõ   rÄ  r*  r"  rÃ  r&  s      r1  rõ   ÚIPolys.gf_mul_ground  ré  r5  c                ó¨   • U R                  [        U R                  U5      X R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rö   rÄ  r*  r"  rÃ  r&  s      r1  rö   ÚIPolys.gf_quo_ground  ré  r5  c                óÈ   • U R                  [        U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r÷   rÄ  r*  r"  rÃ  r•  s      r1  r÷   ÚIPolys.gf_add  óN   € Ø×!Ñ!¤&¨×)9Ñ)9¸!Ó)<¸d×>NÑ>NÈqÓ>QÐSW×S^ÑS^×SbÑSbÐdh×doÑdo×dsÑdsÓ"tÓuÐur5  c                óÈ   • U R                  [        U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rø   rÄ  r*  r"  rÃ  r•  s      r1  rø   ÚIPolys.gf_sub  rò  r5  c                óÈ   • U R                  [        U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rù   rÄ  r*  r"  rÃ  r•  s      r1  rù   ÚIPolys.gf_mul
  rò  r5  c                ó¨   • U R                  [        U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rú   rÄ  r*  r"  rÃ  rŠ  s     r1  rú   ÚIPolys.gf_sqr  ræ  r5  c           	     óè   • U R                  [        U R                  U5      U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rû   rÄ  r*  r"  rÃ  r¡  s       r1  rû   ÚIPolys.gf_add_mul  ó{   € Ø×!Ñ!¤*¨T×-=Ñ-=¸aÓ-@À$×BRÑBRÐSTÓBUÐW[×WgÑWgÐhiÓWjÐlp×lwÑlw×l{Ñl{ð  ~B÷  ~Iñ  ~I÷  ~Mñ  ~Mó  #Nó  Oð  	Or5  c           	     óè   • U R                  [        U R                  U5      U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rü   rÄ  r*  r"  rÃ  r¡  s       r1  rü   ÚIPolys.gf_sub_mul  rû  r5  c           
     óÄ   • U R                  [        [        [        U R                  U5      5      U R
                  R                  U R
                  R                  5      5      $ r-  )rÇ  rý   r÷  rø  rÄ  r*  r"  rÃ  )r/  rC  s     r1  rý   ÚIPolys.gf_expand  sC   € Ø×!Ñ!¤)¬D´°T×5EÑ5EÀqÓ1IÓ,JÈDÏKÉKÏOÉOÐ]a×]hÑ]h×]lÑ]lÓ"mÓnÐnr5  c                óò   • [        U R                  U5      U R                  U5      U R                  R                  U R                  R                  5      u  p4U R                  U5      U R                  U5      4$ r-  )rþ   rÄ  r*  r"  rÃ  rÇ  r¹  s        r1  rþ   ÚIPolys.gf_div  s`   € Ü�d×&Ñ& qÓ)¨4×+;Ñ+;¸AÓ+>ÀÇÁÇÁÐQU×Q\ÑQ\×Q`ÑQ`Óa‰ˆØ×!Ñ! !Ó$ d×&8Ñ&8¸Ó&;Ð;Ð;r5  c                óÈ   • U R                  [        U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  rÿ   rÄ  r*  r"  rÃ  r•  s      r1  rÿ   ÚIPolys.gf_rem  rò  r5  c                óÈ   • U R                  [        U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r   rÄ  r*  r"  rÃ  r•  s      r1  r   ÚIPolys.gf_quo  rò  r5  c                óÈ   • U R                  [        U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r  rÄ  r*  r"  rÃ  r•  s      r1  r  ÚIPolys.gf_exquo  óO   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>À×@PÑ@PÐQRÓ@SÐUY×U`ÑU`×UdÑUdÐfj×fqÑfq×fuÑfuÓ"vÓwÐwr5  c                ó~   • U R                  [        U R                  U5      X R                  R                  5      5      $ r-  )rÇ  r  rÄ  r*  rÃ  rƒ  s      r1  r  ÚIPolys.gf_lshift!  ó-   € Ø×!Ñ!¤)¨D×,<Ñ,<¸QÓ,?ÀÇKÁKÇOÁOÓ"TÓUÐUr5  c                ó~   • U R                  [        U R                  U5      X R                  R                  5      5      $ r-  )rÇ  r  rÄ  r*  rÃ  rƒ  s      r1  r  ÚIPolys.gf_rshift#  r  r5  c                ó¨   • U R                  [        U R                  U5      X R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r  rÄ  r*  r"  rÃ  rƒ  s      r1  r  ÚIPolys.gf_pow&  s<   € Ø×!Ñ!¤&¨×)9Ñ)9¸!Ó)<¸aÇÁÇÁÐRV×R]ÑR]×RaÑRaÓ"bÓcÐcr5  c           	     óÈ   • U R                  [        U R                  U5      X R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r  rÄ  r*  r"  rÃ  )r/  rY  r„  r–  s       r1  r  ÚIPolys.gf_pow_mod(  sO   € Ø×!Ñ!¤*¨T×-=Ñ-=¸aÓ-@À!×EUÑEUÐVWÓEXÐZ^×ZeÑZe×ZiÑZiÐko×kvÑkv×kzÑkzÓ"{Ó|Ð|r5  c                ó  • [        U R                  U5      U R                  U5      U R                  R                  U R                  R                  5      u  p4nU R                  U5      U R                  U5      U R                  U5      4$ r-  )r  rÄ  r*  r"  rÃ  rÇ  )r/  rY  r–  r¢  ÚcffÚcfgs         r1  r  ÚIPolys.gf_cofactors+  sp   € Ü" 4×#3Ñ#3°AÓ#6¸×8HÑ8HÈÓ8KÈTÏ[É[Ï_É_Ð^b×^iÑ^i×^mÑ^mÓn‰ˆ�Ø×!Ñ! !Ó$ d×&8Ñ&8¸Ó&=¸t×?QÑ?QÐRUÓ?VÐVÐVr5  c                óÈ   • U R                  [        U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r  rÄ  r*  r"  rÃ  r•  s      r1  r  ÚIPolys.gf_gcd.  rò  r5  c                óÈ   • U R                  [        U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r  rÄ  r*  r"  rÃ  r•  s      r1  r  ÚIPolys.gf_lcm0  rò  r5  c                óÈ   • U R                  [        U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r	  rÄ  r*  r"  rÃ  r•  s      r1  r	  ÚIPolys.gf_gcdex2  r  r5  c                ó¨   • U R                  [        U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r
  rÄ  r*  r"  rÃ  rŠ  s     r1  r
  ÚIPolys.gf_monic5  rØ  r5  c                ó¨   • U R                  [        U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r  rÄ  r*  r"  rÃ  rŠ  s     r1  r  ÚIPolys.gf_diff7  s<   € Ø×!Ñ!¤'¨$×*:Ñ*:¸1Ó*=¸t¿{¹{¿¹ÐPT×P[ÑP[×P_ÑP_Ó"`ÓaÐar5  c                óŠ   • [        U R                  U5      X R                  R                  U R                  R                  5      $ r-  )r  rÄ  r*  r"  rÃ  r&  s      r1  r  ÚIPolys.gf_eval:  s,   € Ü�t×'Ñ'¨Ó*¨A¯{©{¯©ÀÇÁÇÁÓPÐPr5  c                óŠ   • [        U R                  U5      X R                  R                  U R                  R                  5      $ r-  )r  rÄ  r*  r"  rÃ  )r/  rY  r2  s      r1  r  ÚIPolys.gf_multi_eval<  s,   € Ü˜T×-Ñ-¨aÓ0°!·[±[·_±_ÀdÇkÁkÇoÁoÓVÐVr5  c                óÈ   • U R                  [        U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r  rÄ  r*  r"  rÃ  r•  s      r1  r  ÚIPolys.gf_compose?  sO   € Ø×!Ñ!¤*¨T×-=Ñ-=¸aÓ-@À$×BRÑBRÐSTÓBUÐW[×WbÑWb×WfÑWfÐhl×hsÑhs×hwÑhwÓ"xÓyÐyr5  c           	     óè   • U R                  [        U R                  U5      U R                  U5      U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r  rÄ  r*  r"  rÃ  )r/  r–  r¢  rY  s       r1  r  ÚIPolys.gf_compose_modA  s{   € Ø×!Ñ!¤.°×1AÑ1AÀ!Ó1DÀd×FVÑFVÐWXÓFYÐ[_×[kÑ[kÐlmÓ[nÐpt×p{Ñp{×pÑpð  BF÷  BMñ  BM÷  BQñ  BQó  #Ró  Sð  	Sr5  c           	     ó>  • U R                  U5      nU R                  U5      nU R                  U5      nU R                  U5      n[        XX4XPR                  R                  U R                  R                  5      u  pgU R                  U5      U R                  U5      4$ r-  )rÄ  r  r*  r"  rÃ  rÇ  )r/  r'  ÚbrZ  r„  rY  ÚUÚVs           r1  r  ÚIPolys.gf_trace_mapD  s…   € Ø×Ñ˜QÓˆØ×Ñ˜QÓˆØ×Ñ˜QÓˆØ×Ñ˜QÓˆÜ˜A !¨¯;©;¯?©?¸D¿K¹K¿O¹OÓL‰ˆØ×!Ñ! !Ó$ d×&8Ñ&8¸Ó&;Ð;Ð;r5  c                óˆ   • U R                  [        XR                  R                  U R                  R                  5      5      $ r-  )rÇ  r  r*  r"  rÃ  ©r/  r„  s     r1  r  ÚIPolys.gf_randomL  s*   € Ø×!Ñ!¤)¨A¯{©{¯©ÀÇÁÇÁÓ"PÓQÐQr5  c                óˆ   • U R                  [        XR                  R                  U R                  R                  5      5      $ r-  )rÇ  r  r*  r"  rÃ  r.  s     r1  r  ÚIPolys.gf_irreducibleN  s*   € Ø×!Ñ!¤.°·K±K·O±OÀTÇ[Á[Ç_Á_Ó"UÓVÐVr5  c                óŠ   • [        U R                  U5      U R                  R                  U R                  R                  5      $ r-  )r  rÄ  r*  r"  rÃ  rŠ  s     r1  r  ÚIPolys.gf_irred_p_ben_orQ  s,   € Ü  ×!1Ñ!1°!Ó!4°d·k±k·o±oÀtÇ{Á{ÇÁÓWÐWr5  c                óŠ   • [        U R                  U5      U R                  R                  U R                  R                  5      $ r-  )r  rÄ  r*  r"  rÃ  rŠ  s     r1  r  ÚIPolys.gf_irred_p_rabinS  ó,   € Ü × 0Ñ 0°Ó 3°T·[±[·_±_ÀdÇkÁkÇoÁoÓVÐVr5  c                óŠ   • [        U R                  U5      U R                  R                  U R                  R                  5      $ r-  )r  rÄ  r*  r"  rÃ  rŠ  s     r1  r  ÚIPolys.gf_irreducible_pU  r6  r5  c                óŠ   • [        U R                  U5      U R                  R                  U R                  R                  5      $ r-  )r  rÄ  r*  r"  rÃ  rŠ  s     r1  r  ÚIPolys.gf_sqf_pW  s,   € Ü˜×(Ñ(¨Ó+¨T¯[©[¯_©_¸d¿k¹k¿o¹oÓNÐNr5  c                ó¨   • U R                  [        U R                  U5      U R                  R                  U R                  R
                  5      5      $ r-  )rÇ  r  rÄ  r*  r"  rÃ  rŠ  s     r1  r  ÚIPolys.gf_sqf_partZ  s<   € Ø×!Ñ!¤+¨d×.>Ñ.>¸qÓ.AÀ4Ç;Á;Ç?Á?ÐTX×T_ÑT_×TcÑTcÓ"dÓeÐer5  c                óì   • [        U R                  U5      U R                  R                  U R                  R                  5      u  p4X4 VVs/ s H  u  pVU R                  U5      U4PM     snn4$ s  snnf r-  )r  rÄ  r*  r"  rÃ  rÇ  rl  s          r1  Úgf_sqf_listÚIPolys.gf_sqf_list\  s\   € Ü$ T×%5Ñ%5°aÓ%8¸$¿+¹+¿/¹/È4Ï;É;Ï?É?Ó[‰ˆØ¸wÔHºw±t°q˜×+Ñ+¨AÓ.°Ó2¹wÒHÐHÐHùÓHó   ÁA0c                óŠ   • [        U R                  U5      U R                  R                  U R                  R                  5      $ r-  )r  rÄ  r*  r"  rÃ  rŠ  s     r1  r  ÚIPolys.gf_Qmatrix`  s,   € Ü˜$×*Ñ*¨1Ó-¨t¯{©{¯©ÀÇÁÇÁÓPÐPr5  c                óÖ   • [        U R                  U5      U R                  R                  U R                  R                  5      nU Vs/ s H  o0R                  U5      PM     sn$ s  snf r-  )r  rÄ  r*  r"  rÃ  rÇ  ©r/  rY  rñ  r–  s       r1  r  ÚIPolys.gf_berlekampb  óL   € Ü˜t×/Ñ/°Ó2°D·K±K·O±OÀTÇ[Á[Ç_Á_ÓUˆÙ07Ó9²¨1×#Ñ# AÖ&±Ñ9Ð9ùÒ9ó   Á	A&c                óæ   • [        U R                  U5      U R                  R                  U R                  R                  5      nU VVs/ s H  u  p4U R                  U5      U4PM     snn$ s  snnf r-  )r  rÄ  r*  r"  rÃ  rÇ  rð  s        r1  r  ÚIPolys.gf_ddf_zassenhausf  sU   € Ü# D×$4Ñ$4°QÓ$7¸¿¹¿¹È$Ï+É+Ï/É/ÓZˆÙ8?ÔAº±°�$×$Ñ$ QÓ'¨Ó+¹ÒAÐAùÓAó   Á
A-c                óÖ   • [        U R                  U5      U R                  R                  U R                  R                  5      nU Vs/ s H  o@R                  U5      PM     sn$ s  snf r-  )r  rÄ  r*  r"  rÃ  rÇ  ©r/  rY  r„  rñ  r–  s        r1  r  ÚIPolys.gf_edf_zassenhausi  sL   € Ü# D×$4Ñ$4°QÓ$7¸¿¹¿¹È$Ï+É+Ï/É/ÓZˆÙ07Ó9²¨1×#Ñ# AÖ&±Ñ9Ð9ùÒ9rG  c                óæ   • [        U R                  U5      U R                  R                  U R                  R                  5      nU VVs/ s H  u  p4U R                  U5      U4PM     snn$ s  snnf r-  )r  rÄ  r*  r"  rÃ  rÇ  rð  s        r1  r  ÚIPolys.gf_ddf_shoupm  sU   € Ü˜t×/Ñ/°Ó2°D·K±K·O±OÀTÇ[Á[Ç_Á_ÓUˆÙ8?ÔAº±°�$×$Ñ$ QÓ'¨Ó+¹ÒAÐAùÓArJ  c                óÖ   • [        U R                  U5      U R                  R                  U R                  R                  5      nU Vs/ s H  o@R                  U5      PM     sn$ s  snf r-  )r  rÄ  r*  r"  rÃ  rÇ  rL  s        r1  r  ÚIPolys.gf_edf_shoupp  rF  rG  c                óÖ   • [        U R                  U5      U R                  R                  U R                  R                  5      nU Vs/ s H  o0R                  U5      PM     sn$ s  snf r-  )r  rÄ  r*  r"  rÃ  rÇ  rD  s       r1  r  ÚIPolys.gf_zassenhaust  sL   € Ü × 0Ñ 0°Ó 3°T·[±[·_±_ÀdÇkÁkÇoÁoÓVˆÙ07Ó9²¨1×#Ñ# AÖ&±Ñ9Ð9ùÒ9rG  c                óÖ   • [        U R                  U5      U R                  R                  U R                  R                  5      nU Vs/ s H  o0R                  U5      PM     sn$ s  snf r-  )r  rÄ  r*  r"  rÃ  rÇ  rD  s       r1  r  ÚIPolys.gf_shoupw  sL   € Ü˜4×+Ñ+¨AÓ.°·±·±ÀÇÁÇÁÓQˆÙ07Ó9²¨1×#Ñ# AÖ&±Ñ9Ð9ùÒ9rG  c                óÚ   • [        U R                  U5      U R                  R                  U R                  R                  US9u  p4X4 Vs/ s H  oPR                  U5      PM     sn4$ s  snf )N)Úmethod)r   rÄ  r*  r"  rÃ  rÇ  )r/  rY  rW  r&  rñ  r–  s         r1  r   ÚIPolys.gf_factor_sqf{  sV   € Ü& t×'7Ñ'7¸Ó':¸D¿K¹K¿O¹OÈTÏ[É[Ï_É_ÐekÑl‰ˆØ°wÓ@²w°!×*Ñ*¨1Ö-±wÑ@Ð@Ð@ùÒ@s   Á
A(c                óì   • [        U R                  U5      U R                  R                  U R                  R                  5      u  p#X# VVs/ s H  u  pEU R                  U5      U4PM     snn4$ s  snnf r-  )r!  rÄ  r*  r"  rÃ  rÇ  r)  s         r1  r!  ÚIPolys.gf_factor~  s\   € Ü" 4×#3Ñ#3°AÓ#6¸¿¹¿¹ÈÏÉÏÉÓY‰ˆØ¸wÔHºw±t°q˜×+Ñ+¨AÓ.°Ó2¹wÒHÐHÐHùÓHr@  r.  )NNN)F)T)NN)NNNFF)NNNF)NF)NNNFFFr-  (.  Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__Ú__annotations__r2  r7  r:  r?  rB  rF  rM  rP  rU  r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   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   r·  r¼  rÀ  rÄ  rÇ  rê   rë   rì   rí   rÓ  rÖ  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!  Ú__static_attributes__r.  r5  r1  r$  r$  ð   s´  ‡ ð "Ó!ØÓØƒJØƒNØÓòõ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õ'õ'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-õ<õ<ò?ò?òDòRò`ò1ò
?òCõXò"ò6ò@ò^ò2ò
2ò
2õ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õHõHõHõ?õHõ?ò?ò?òCòCõVõOõCõ}õ_õDõDõBõxõ[õUõiõzõAõjò\ò\ò\òlòSò.ò;ò;òAòRòcóUöUóHöYóaókókókô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÷IôQô:ôBô:ôBô:ô:ô:÷A÷Iñ Ir5  r$  N(0  Ú__doc__Ú
__future__r   Útypingr   Úsympy.core.exprr   Úsympy.polys.domains.domainr   Úsympy.polys.orderingsr   rI  r	   Úsympy.polys.densearithr
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   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$  r.  r5  r1  Ú<module>rp     sO  ðÙ >å "å  æÝ$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r5  