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EHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEHEtEH Et EH!Et!EH"Et"EH#Et#EH$Et$EH%Et%EH&Et&EH'Et'EH(Et(EH)Et)EH*Et*EH+Et+EH,Et, ^ RØEI-EH.Et. E]. ! RÙ RÚ4      4       Et/RÛ# )Üz8Compatibility interface between dense and sparse polys. )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  € ] tR t^ðt$ R]R&   R]R&   R]R&   R]R&   R	]R
&   R tER5R ltR tR tR t	R t
R tR tR tR tR tR tR tR tR tR tR tR tR tR tR  tR! tR" tR# tR$ tR% tR& tR' t R( t!R) t"R* t#R+ t$R, t%R- t&R. t'R/ t(R0 t)R1 t*R2 t+R3 t,R4 t-R5 t.R6 t/R7 t0R8 t1R9 t2R: t3R; t4R< t5R= t6R> t7R? t8R@ t9RA t:RB t;RC t<RD t=RE t>RF t?RG t@RH tARI tBRJ tCRK tDRL tERM tFRN tGRO tHRP tIRQ tJRR tKRS tLRT tMRU tNRV tORW tPRX tQRY tRRZ tSR[ tTR\ tUR] tVR^ tWR_ tXR` tYRa tZRb t[Rc t\Rd t]Re t^Rf t_Rg t`Rh taRi tbRj tcRk tdRl teRm tfRn tgRo thRp tiRq tjRr tkRs tlRt tmRu tnRv toRw tpRx tqRy trRz tsER6R{ lttER6R| ltuR} tvR~ twR txR€ tyR� tzR‚ t{Rƒ t|R„ t}R… t~R† tR‡ t€Rˆ t�R‰ t‚RŠ tƒR‹ t„RŒ t…R� t†RŽ t‡R� tˆR� t‰R‘ tŠR’ t‹R“ tŒR” t�R• tŽR– t�R— t�R˜ t‘R™ t’Rš t“R› t”Rœ t•R� t–Rž t—RŸ t˜R  t™R¡ tšR¢ t›R£ tœR¤ t�R¥ tžR¦ tŸR§ t R¨ t¡R© t¢Rª t£R« t¤R¬ t¥ER7R­ lt¦ER7R® lt§R¯ t¨R° t©R± tªR² t«R³ t¬R´ t­Rµ t®R¶ t¯ER6R· lt°R¸ t±R¹ t²Rº t³R» t´R¼ tµR½ t¶R¾ t·ER8R¿ lt¸RÀ t¹RÁ tºRÂ t»RÃ t¼RÄ t½RÅ t¾RÆ t¿RÇ tÀRÈ tÁRÉ tÂRÊ tÃRË tÄRÌ tÅRÍ tÆRÎ tÇRÏ tÈRÐ tÉRÑ tÊRÒ tËRÓ tÌRÔ tÍRÕ tÎRÖ tÏR× tÐRØ tÑRÙ tÒRÚ tÓER6RÛ ltÔER6RÜ ltÕER6RÝ ltÖER6RÞ lt×ER6Rß ltØER6Rà ltÙRá tÚRâ tÛRã tÜRä tÝER6Rå ltÞER9Ræ ltßER:Rç ltàER:Rè ltáER;Ré ltâER9Rê ltãER9Rë ltäER9Rì ltåER9Rí ltæER<Rî ltçER8Rï ltèER5Rð ltéER:Rñ ltêER9Rò ltëER:Ró ltìRô tíRõ tîRö tïR÷ tðRø tñRù tòRú tóRû tôRü tõRý töRþ t÷Rÿ tøER7ER  ltùER túER7ER ltûER tüER týER tþER tÿER Et ER EtER	 EtER
 EtER EtER EtER EtER EtER EtER Et	ER Et
ER EtER EtER EtER EtER EtER EtER EtER EtER EtER EtER EtER EtER EtER EtER  EtER! EtER" EtER# EtER$ EtER% EtER& EtER' Et ER( Et!ER6ER) lEt"ER* Et#ER+ Et$ER, Et%ER- Et&ER. Et'ER/ Et(ER0 Et)ER1 Et*ER=ER2 lEt+ER3 Et,ER4Et-R# (>  ÚIPolysztuple[PolyElement, ...]Úgensztuple[Expr, ...]ÚsymbolsÚintÚngensr   Údomainr   Úorderc                	ó   € R # ©N© )ÚselfÚgens   &&ÚZ/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/polys/compatibility.pyÚdropÚIPolys.dropù   ó   € Ùó    Nc                	ó   € R # r+  r,  )r-  r%  r(  r)  s   &&&&r/  ÚcloneÚIPolys.cloneü   r2  r3  c                	ó   € R # r+  r,  )r-  s   &r/  Ú	to_groundÚIPolys.to_groundÿ   r2  r3  c                	ó   € R # r+  r,  ©r-  Úelements   &&r/  Ú
ground_newÚIPolys.ground_new  r2  r3  c                	ó   € R # r+  r,  r;  s   &&r/  Ú
domain_newÚIPolys.domain_new  r2  r3  c                	ó   € R # r+  r,  )r-  Úds   &&r/  Ú	from_dictÚIPolys.from_dict  r2  r3  c                	óŽ   € ^ RI Hp \        W4      '       d   VP                  V 8X  d   V# \	        R4      hV P                  V4      # )é    r   zdomain conversions)Úsympy.polys.ringsr   Ú
isinstanceÚringÚNotImplementedErrorr=  )r-  r<  r   s   && r/  ÚwrapÚIPolys.wrap  s<   € Ý1Ü�g×+Ò+Ø�|‰|˜tÔ#Ø�ä)Ð*>Ó?Ð?à—?‘? 7Ó+Ð+r3  c                	ó@   € V P                  V4      P                  4       # r+  )rL  Úto_denser;  s   &&r/  rO  ÚIPolys.to_dense  s   € Ø�y‰y˜Ó!×*Ñ*Ó,Ð,r3  c                	ón   € V P                  \        WP                  ^,
          V P                  4      4      # ©é   )rD  rR   r'  r(  r;  s   &&r/  Ú
from_denseÚIPolys.from_dense  s$   € Ø�~‰~œk¨'·:±:¸aµ<ÀÇÁÓMÓNÐNr3  c                	ól   € V P                  \        V P                  V4      W#V P                  4      4      # r+  )rT  r	   rO  r(  ©r-  ÚfÚcÚis   &&&&r/  r	   ÚIPolys.dup_add_term  ó'   € Ø�‰œ|¨D¯M©M¸!Ó,<¸aÀDÇKÁKÓPÓQÐQr3  c           	     	óè   € V P                  \        V P                  V4      V P                  V4      P	                  ^ 4      P                  4       W0P
                  ^,
          V P                  4      4      # ©rG  )rT  r
   rO  rL  r0  r'  r(  rW  s   &&&&r/  r
   ÚIPolys.dmp_add_term  óV   € Ø�‰œ|¨D¯M©M¸!Ó,<¸d¿i¹iÈ»l×>OÑ>OÐPQÓ>R×>[Ñ>[Ó>]Ð_`×blÑblÐmnÕbnÐpt×p{Ñp{Ó|Ó}Ð}r3  c                	ól   € V P                  \        V P                  V4      W#V P                  4      4      # r+  )rT  r   rO  r(  rW  s   &&&&r/  r   ÚIPolys.dup_sub_term  r\  r3  c           	     	óè   € V P                  \        V P                  V4      V P                  V4      P	                  ^ 4      P                  4       W0P
                  ^,
          V P                  4      4      # r^  )rT  r   rO  rL  r0  r'  r(  rW  s   &&&&r/  r   ÚIPolys.dmp_sub_term!  r`  r3  c                	ól   € V P                  \        V P                  V4      W#V P                  4      4      # r+  )rT  r   rO  r(  rW  s   &&&&r/  r   ÚIPolys.dup_mul_term#  r\  r3  c           	     	óè   € V P                  \        V P                  V4      V P                  V4      P	                  ^ 4      P                  4       W0P
                  ^,
          V P                  4      4      # r^  )rT  r   rO  rL  r0  r'  r(  rW  s   &&&&r/  r   ÚIPolys.dmp_mul_term%  r`  r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  r   rO  r(  ©r-  rX  rY  s   &&&r/  r   ÚIPolys.dup_add_ground(  ó%   € Ø�‰œ~¨d¯m©m¸AÓ.>ÀÇ;Á;ÓOÓPÐPr3  c                	óŽ   € V P                  \        V P                  V4      W P                  ^,
          V P                  4      4      # rR  )rT  r   rO  r'  r(  rj  s   &&&r/  r   ÚIPolys.dmp_add_ground*  ó2   € Ø�‰œ~¨d¯m©m¸AÓ.>ÀÇ:Á:ÈaÅ<ÐQU×Q\ÑQ\Ó]Ó^Ð^r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  r   rO  r(  rj  s   &&&r/  r   ÚIPolys.dup_sub_ground,  rl  r3  c                	óŽ   € V P                  \        V P                  V4      W P                  ^,
          V P                  4      4      # rR  )rT  r   rO  r'  r(  rj  s   &&&r/  r   ÚIPolys.dmp_sub_ground.  ro  r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  r   rO  r(  rj  s   &&&r/  r   ÚIPolys.dup_mul_ground0  rl  r3  c                	óŽ   € V P                  \        V P                  V4      W P                  ^,
          V P                  4      4      # rR  )rT  r   rO  r'  r(  rj  s   &&&r/  r   ÚIPolys.dmp_mul_ground2  ro  r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  r   rO  r(  rj  s   &&&r/  r   ÚIPolys.dup_quo_ground4  rl  r3  c                	óŽ   € V P                  \        V P                  V4      W P                  ^,
          V P                  4      4      # rR  )rT  r   rO  r'  r(  rj  s   &&&r/  r   ÚIPolys.dmp_quo_ground6  ro  r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  r   rO  r(  rj  s   &&&r/  r   ÚIPolys.dup_exquo_ground8  s&   € Ø�‰Ô/°·±¸aÓ0@À!Ç[Á[ÓQÓRÐRr3  c                	óŽ   € V P                  \        V P                  V4      W P                  ^,
          V P                  4      4      # rR  )rT  r   rO  r'  r(  rj  s   &&&r/  r   ÚIPolys.dmp_exquo_ground:  ó4   € Ø�‰Ô/°·±¸aÓ0@À!ÇZÁZÐPQÅ\ÐSW×S^ÑS^Ó_Ó`Ð`r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  r   rO  r(  ©r-  rX  Úns   &&&r/  r   ÚIPolys.dup_lshift=  ó%   € Ø�‰œz¨$¯-©-¸Ó*:¸A¿{¹{ÓKÓLÐLr3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  r   rO  r(  r‚  s   &&&r/  r   ÚIPolys.dup_rshift?  r…  r3  c                	ój   € V P                  \        V P                  V4      V P                  4      4      # r+  )rT  r   rO  r(  ©r-  rX  s   &&r/  r   ÚIPolys.dup_absB  ó%   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÓEÓFÐFr3  c                	óŽ   € V P                  \        V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r   rO  r'  r(  r‰  s   &&r/  r   ÚIPolys.dmp_absD  ó/   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÀA½ÀtÇ{Á{ÓSÓTÐTr3  c                	ój   € V P                  \        V P                  V4      V P                  4      4      # r+  )rT  r   rO  r(  r‰  s   &&r/  r   ÚIPolys.dup_negG  r‹  r3  c                	óŽ   € V P                  \        V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r   rO  r'  r(  r‰  s   &&r/  r   ÚIPolys.dmp_negI  rŽ  r3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r   rO  r(  ©r-  rX  Úgs   &&&r/  r   ÚIPolys.dup_addL  ó0   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï;É;ÓWÓXÐXr3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r    rO  r'  r(  r”  s   &&&r/  r    ÚIPolys.dmp_addN  ó>   € Ø�‰œw t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï:É:ÐVWÍ<ÐY]×YdÑYdÓeÓfÐfr3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r!   rO  r(  r”  s   &&&r/  r!   ÚIPolys.dup_subQ  r—  r3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r"   rO  r'  r(  r”  s   &&&r/  r"   ÚIPolys.dmp_subS  rš  r3  c           	     	óª   € V P                  \        V P                  V4      V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r#   rO  r(  ©r-  rX  r•  Úhs   &&&&r/  r#   ÚIPolys.dup_add_mulV  ó?   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏ}É}Ð]^ÓO_Ðae×alÑalÓmÓnÐnr3  c           	     	óÎ   € V P                  \        V P                  V4      V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r$   rO  r'  r(  r   s   &&&&r/  r$   ÚIPolys.dmp_add_mulX  óN   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏ}É}Ð]^ÓO_Ðae×akÑakÐlmÕamÐos×ozÑozÓ{Ó|Ð|r3  c           	     	óª   € V P                  \        V P                  V4      V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r%   rO  r(  r   s   &&&&r/  r%   ÚIPolys.dup_sub_mulZ  r£  r3  c           	     	óÎ   € V P                  \        V P                  V4      V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r&   rO  r'  r(  r   s   &&&&r/  r&   ÚIPolys.dmp_sub_mul\  r¦  r3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r'   rO  r(  r”  s   &&&r/  r'   ÚIPolys.dup_mul_  r—  r3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r(   rO  r'  r(  r”  s   &&&r/  r(   ÚIPolys.dmp_mula  rš  r3  c                	ój   € V P                  \        V P                  V4      V P                  4      4      # r+  )rT  r)   rO  r(  r‰  s   &&r/  r)   ÚIPolys.dup_sqrd  r‹  r3  c                	óŽ   € V P                  \        V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r*   rO  r'  r(  r‰  s   &&r/  r*   ÚIPolys.dmp_sqrf  rŽ  r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  r+   rO  r(  r‚  s   &&&r/  r+   ÚIPolys.dup_powh  s%   € Ø�‰œw t§}¡}°QÓ'7¸¿K¹KÓHÓIÐIr3  c                	óŽ   € V P                  \        V P                  V4      W P                  ^,
          V P                  4      4      # rR  )rT  r,   rO  r'  r(  r‚  s   &&&r/  r,   ÚIPolys.dmp_powj  s/   € Ø�‰œw t§}¡}°QÓ'7¸¿J¹JÀq½LÈ$Ï+É+ÓVÓWÐWr3  c                	ó´   € \        V P                  V4      V P                  V4      V P                  4      w  r4V P                  V4      V P                  V4      3# r+  )r-   rO  r(  rT  ©r-  rX  r•  ÚqÚrs   &&&  r/  r-   ÚIPolys.dup_pdivm  sE   € Ü˜Ÿ™ aÓ(¨$¯-©-¸Ó*:¸D¿K¹KÓH‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r.   rO  r(  r”  s   &&&r/  r.   ÚIPolys.dup_premp  ó0   € Ø�‰œx¨¯©°aÓ(8¸$¿-¹-ÈÓ:JÈDÏKÉKÓXÓYÐYr3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r/   rO  r(  r”  s   &&&r/  r/   ÚIPolys.dup_pquor  r¾  r3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r0   rO  r(  r”  s   &&&r/  r0   ÚIPolys.dup_pexquot  ó0   € Ø�‰œz¨$¯-©-¸Ó*:¸D¿M¹MÈ!Ó<LÈdÏkÉkÓZÓ[Ð[r3  c                	óØ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4V P	                  V4      V P	                  V4      3# rR  )r1   rO  r'  r(  rT  r¸  s   &&&  r/  r1   ÚIPolys.dmp_pdivw  sO   € Ü˜Ÿ™ aÓ(¨$¯-©-¸Ó*:¸D¿J¹JÀq½LÈ$Ï+É+ÓV‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r2   rO  r'  r(  r”  s   &&&r/  r2   ÚIPolys.dmp_premz  ó>   € Ø�‰œx¨¯©°aÓ(8¸$¿-¹-ÈÓ:JÈDÏJÉJÐWXÍLÐZ^×ZeÑZeÓfÓgÐgr3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r3   rO  r'  r(  r”  s   &&&r/  r3   ÚIPolys.dmp_pquo|  rÈ  r3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r4   rO  r'  r(  r”  s   &&&r/  r4   ÚIPolys.dmp_pexquo~  ó>   € Ø�‰œz¨$¯-©-¸Ó*:¸D¿M¹MÈ!Ó<LÈdÏjÉjÐYZÍlÐ\`×\gÑ\gÓhÓiÐir3  c                	ó´   € \        V P                  V4      V P                  V4      V P                  4      w  r4V P                  V4      V P                  V4      3# r+  )r5   rO  r(  rT  r¸  s   &&&  r/  r5   ÚIPolys.dup_rr_div�  óE   € Ü˜$Ÿ-™-¨Ó*¨D¯M©M¸!Ó,<¸d¿k¹kÓJ‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                	óØ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4V P	                  V4      V P	                  V4      3# rR  )r6   rO  r'  r(  rT  r¸  s   &&&  r/  r6   ÚIPolys.dmp_rr_div„  óO   € Ü˜$Ÿ-™-¨Ó*¨D¯M©M¸!Ó,<¸d¿j¹jÈ½lÈDÏKÉKÓX‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                	ó´   € \        V P                  V4      V P                  V4      V P                  4      w  r4V P                  V4      V P                  V4      3# r+  )r7   rO  r(  rT  r¸  s   &&&  r/  r7   ÚIPolys.dup_ff_div‡  rÐ  r3  c                	óØ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4V P	                  V4      V P	                  V4      3# rR  )r8   rO  r'  r(  rT  r¸  s   &&&  r/  r8   ÚIPolys.dmp_ff_divŠ  rÓ  r3  c                	ó´   € \        V P                  V4      V P                  V4      V P                  4      w  r4V P                  V4      V P                  V4      3# r+  )r9   rO  r(  rT  r¸  s   &&&  r/  r9   ÚIPolys.dup_divŽ  sE   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿;¹;ÓG‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r:   rO  r(  r”  s   &&&r/  r:   ÚIPolys.dup_rem‘  r—  r3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r;   rO  r(  r”  s   &&&r/  r;   ÚIPolys.dup_quo“  r—  r3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r<   rO  r(  r”  s   &&&r/  r<   ÚIPolys.dup_exquo•  s0   € Ø�‰œy¨¯©°qÓ)9¸4¿=¹=ÈÓ;KÈTÏ[É[ÓYÓZÐZr3  c                	óØ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4V P	                  V4      V P	                  V4      3# rR  )r=   rO  r'  r(  rT  r¸  s   &&&  r/  r=   ÚIPolys.dmp_div˜  sO   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿:¹:Àa½<ÈÏÉÓU‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r>   rO  r'  r(  r”  s   &&&r/  r>   ÚIPolys.dmp_rem›  rš  r3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r?   rO  r'  r(  r”  s   &&&r/  r?   ÚIPolys.dmp_quo�  rš  r3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r@   rO  r'  r(  r”  s   &&&r/  r@   ÚIPolys.dmp_exquoŸ  s>   € Ø�‰œy¨¯©°qÓ)9¸4¿=¹=ÈÓ;KÈTÏZÉZÐXYÍ\Ð[_×[fÑ[fÓgÓhÐhr3  c                	óL   € \        V P                  V4      V P                  4      # r+  )rA   rO  r(  r‰  s   &&r/  rA   ÚIPolys.dup_max_norm¢  s   € Ü˜DŸM™M¨!Ó,¨d¯k©kÓ:Ð:r3  c                	óp   € \        V P                  V4      V P                  ^,
          V P                  4      # rR  )rB   rO  r'  r(  r‰  s   &&r/  rB   ÚIPolys.dmp_max_norm¤  s&   € Ü˜DŸM™M¨!Ó,¨d¯j©j¸­l¸D¿K¹KÓHÐHr3  c                	óL   € \        V P                  V4      V P                  4      # r+  )rC   rO  r(  r‰  s   &&r/  rC   ÚIPolys.dup_l1_norm§  s   € Ü˜4Ÿ=™=¨Ó+¨T¯[©[Ó9Ð9r3  c                	óp   € \        V P                  V4      V P                  ^,
          V P                  4      # rR  )rD   rO  r'  r(  r‰  s   &&r/  rD   ÚIPolys.dmp_l1_norm©  s&   € Ü˜4Ÿ=™=¨Ó+¨T¯Z©Z¸­\¸4¿;¹;ÓGÐGr3  c                	óL   € \        V P                  V4      V P                  4      # r+  )rE   rO  r(  r‰  s   &&r/  rE   ÚIPolys.dup_l2_norm_squared¬  ó   € Ü" 4§=¡=°Ó#3°T·[±[ÓAÐAr3  c                	óp   € \        V P                  V4      V P                  ^,
          V P                  4      # rR  )rF   rO  r'  r(  r‰  s   &&r/  rF   ÚIPolys.dmp_l2_norm_squared®  s&   € Ü" 4§=¡=°Ó#3°T·Z±ZÀµ\À4Ç;Á;ÓOÐOr3  c           
     	ó†   € V P                  \        \        \        V P                  V4      4      V P
                  4      4      # r+  )rT  rG   ÚlistÚmaprO  r(  ©r-  Úpolyss   &&r/  rG   ÚIPolys.dup_expand±  s,   € Ø�‰œz¬$¬s°4·=±=À%Ó/HÓ*IÈ4Ï;É;ÓWÓXÐXr3  c           
     	óª   € V P                  \        \        \        V P                  V4      4      V P
                  ^,
          V P                  4      4      # rR  )rT  rH   rö  r÷  rO  r'  r(  rø  s   &&r/  rH   ÚIPolys.dmp_expand³  s:   € Ø�‰œz¬$¬s°4·=±=À%Ó/HÓ*IÈ4Ï:É:ÐVWÍ<ÐY]×YdÑYdÓeÓfÐfr3  c                	óL   € \        V P                  V4      V P                  4      # r+  )rI   rO  r(  r‰  s   &&r/  rI   ÚIPolys.dup_LC¶  ó   € Ü�d—m‘m AÓ&¨¯©Ó4Ð4r3  c                	ó¬   € \        V P                  V4      V P                  4      p\        V\        4      '       d   V R ,          P                  V4      # V# ©ºrS  NN)rJ   rO  r(  rI  rö  rT  )r-  rX  ÚLCs   && r/  rJ   ÚIPolys.dmp_LC¸  óB   € Ü�D—M‘M !Ó$ d§k¡kÓ2ˆÜ�bœ$×ÒØ˜•8×&Ñ& rÓ*Ð*àˆIr3  c                	óL   € \        V P                  V4      V P                  4      # r+  )rK   rO  r(  r‰  s   &&r/  rK   ÚIPolys.dup_TC¾  rÿ  r3  c                	ó¬   € \        V P                  V4      V P                  4      p\        V\        4      '       d   V R ,          P                  V4      # V# r  )rL   rO  r(  rI  rö  rT  )r-  rX  ÚTCs   && r/  rL   ÚIPolys.dmp_TCÀ  r  r3  c                	óp   € \        V P                  V4      V P                  ^,
          V P                  4      # rR  )rM   rO  r'  r(  r‰  s   &&r/  rM   ÚIPolys.dmp_ground_LCÇ  ó&   € Ü˜TŸ]™]¨1Ó-¨t¯z©z¸!­|¸T¿[¹[ÓIÐIr3  c                	óp   € \        V P                  V4      V P                  ^,
          V P                  4      # rR  )rN   rO  r'  r(  r‰  s   &&r/  rN   ÚIPolys.dmp_ground_TCÉ  r  r3  c                	ó6   € \        V P                  V4      4      # r+  )rO   rO  r‰  s   &&r/  rO   ÚIPolys.dup_degreeÌ  s   € Ü˜$Ÿ-™-¨Ó*Ó+Ð+r3  c                	óZ   € \        V P                  V4      V P                  ^,
          4      # rR  )rP   rO  r'  r‰  s   &&r/  rP   ÚIPolys.dmp_degreeÎ  s    € Ü˜$Ÿ-™-¨Ó*¨D¯J©J°q­LÓ9Ð9r3  c                	óZ   € \        V P                  V4      W P                  ^,
          4      # rR  )rQ   rO  r'  )r-  rX  Újs   &&&r/  rQ   ÚIPolys.dmp_degree_inÐ  s    € Ü˜TŸ]™]¨1Ó-¨q·*±*¸Qµ,Ó?Ð?r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  rS   rO  r(  ©r-  rX  Úms   &&&r/  rS   ÚIPolys.dup_integrateÒ  s%   € Ø�‰œ}¨T¯]©]¸1Ó-=¸qÇ+Á+ÓNÓOÐOr3  c                	óŽ   € V P                  \        V P                  V4      W P                  ^,
          V P                  4      4      # rR  )rT  rT   rO  r'  r(  r  s   &&&r/  rT   ÚIPolys.dmp_integrateÔ  s2   € Ø�‰œ}¨T¯]©]¸1Ó-=¸qÇ*Á*ÈQÅ,ÐPT×P[ÑP[Ó\Ó]Ð]r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  rV   rO  r(  r  s   &&&r/  rV   ÚIPolys.dup_diff×  s%   € Ø�‰œx¨¯©°aÓ(8¸!¿[¹[ÓIÓJÐJr3  c                	óŽ   € V P                  \        V P                  V4      W P                  ^,
          V P                  4      4      # rR  )rT  rW   rO  r'  r(  r  s   &&&r/  rW   ÚIPolys.dmp_diffÙ  s/   € Ø�‰œx¨¯©°aÓ(8¸!¿Z¹ZÈ½\È4Ï;É;ÓWÓXÐXr3  c           	     	ó�   € V P                  \        V P                  V4      W#V P                  ^,
          V P                  4      4      # rR  )rT  rX   rO  r'  r(  ©r-  rX  r  r  s   &&&&r/  rX   ÚIPolys.dmp_diff_inÜ  s4   € Ø�‰œ{¨4¯=©=¸Ó+;¸QÀ4Ç:Á:ÈaÅ<ÐQU×Q\ÑQ\Ó]Ó^Ð^r3  c           	     	ó�   € V P                  \        V P                  V4      W#V P                  ^,
          V P                  4      4      # rR  )rT  rU   rO  r'  r(  r"  s   &&&&r/  rU   ÚIPolys.dmp_integrate_inÞ  s6   € Ø�‰Ô/°·±¸aÓ0@À!ÈÏ
É
ÐSTÍÐVZ×VaÑVaÓbÓcÐcr3  c                	óL   € \        V P                  V4      W P                  4      # r+  )rY   rO  r(  ©r-  rX  Úas   &&&r/  rY   ÚIPolys.dup_evalá  s   € Ü˜Ÿ™ aÓ(¨!¯[©[Ó9Ð9r3  c                	ó    € \        V P                  V4      W P                  ^,
          V P                  4      pV R,          P	                  V4      # ©rS  r  )rZ   rO  r'  r(  rT  )r-  rX  r(  Úresults   &&& r/  rZ   ÚIPolys.dmp_evalã  s:   € Ü˜$Ÿ-™-¨Ó*¨A¯z©z¸!­|¸T¿[¹[ÓIˆØ�B�x×"Ñ" 6Ó*Ð*r3  c                	ó²   € \        V P                  V4      W#V P                  ^,
          V P                  4      pV P	                  V4      P                  V4      # rR  )r[   rO  r'  r(  r0  rT  )r-  rX  r(  r  r,  s   &&&& r/  r[   ÚIPolys.dmp_eval_inç  s@   € Ü˜TŸ]™]¨1Ó-¨q°T·Z±ZÀµ\À4Ç;Á;ÓOˆØ�y‰y˜‹|×&Ñ& vÓ.Ð.r3  c                	ó²   € \        V P                  V4      W#W@P                  ^,
          V P                  4      pV P	                  V4      P                  V4      # rR  )r]   rO  r'  r(  r0  rT  )r-  rX  r  r(  r  r,  s   &&&&& r/  r]   ÚIPolys.dmp_diff_eval_inê  s@   € Ü! $§-¡-°Ó"2°A¸!¿Z¹ZÈ½\È4Ï;É;ÓWˆØ�y‰y˜‹|×&Ñ& vÓ.Ð.r3  c                	óÜ   € \        V P                  V4      W P                  ^,
          V P                  4      p\	        V\
        4      '       d   V R\        V4      )  P                  V4      # V# )rS  N)r\   rO  r'  r(  rI  rö  ÚlenrT  )r-  rX  ÚAr,  s   &&& r/  r\   ÚIPolys.dmp_eval_tailî  sT   € Ü˜tŸ}™}¨QÓ/°·J±J¸qµLÀ$Ç+Á+ÓNˆÜ�fœd×#Ò#Ø˜œ#˜a›&˜�>×,Ñ,¨VÓ4Ð4àˆMr3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  r^   rO  r(  ©r-  rX  Úps   &&&r/  r^   ÚIPolys.dup_truncõ  ó%   € Ø�‰œy¨¯©°qÓ)9¸1¿k¹kÓJÓKÐKr3  c                	ó¼   € V P                  \        V P                  V4      V R ,          P                  V4      V P                  ^,
          V P                  4      4      # r  )rT  r_   rO  r'  r(  r”  s   &&&r/  r_   ÚIPolys.dmp_trunc÷  sH   € Ø�‰œy¨¯©°qÓ)9¸4À½8×;LÑ;LÈQÓ;OÐQU×Q[ÑQ[Ð\]ÕQ]Ð_c×_jÑ_jÓkÓlÐlr3  c                	óŽ   € V P                  \        V P                  V4      W P                  ^,
          V P                  4      4      # rR  )rT  r`   rO  r'  r(  r7  s   &&&r/  r`   ÚIPolys.dmp_ground_truncù  r€  r3  c                	ój   € V P                  \        V P                  V4      V P                  4      4      # r+  )rT  ra   rO  r(  r‰  s   &&r/  ra   ÚIPolys.dup_monicü  s%   € Ø�‰œy¨¯©°qÓ)9¸4¿;¹;ÓGÓHÐHr3  c                	óŽ   € V P                  \        V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  rb   rO  r'  r(  r‰  s   &&r/  rb   ÚIPolys.dmp_ground_monicþ  s3   € Ø�‰Ô/°·±¸aÓ0@À$Ç*Á*ÈQÅ,ÐPT×P[ÑP[Ó\Ó]Ð]r3  c                	ó¶   € \        V P                  V4      V P                  V4      V P                  4      w  r4pW0P                  V4      V P                  V4      3# r+  )rg   rO  r(  rT  ©r-  rX  r•  rY  ÚFÚGs   &&&   r/  rg   ÚIPolys.dup_extract  sG   € Ü˜dŸm™m¨AÓ.°·±¸aÓ0@À$Ç+Á+ÓN‰ˆˆaØ—?‘? 1Ó% t§¡°qÓ'9Ð:Ð:r3  c                	óÚ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4pW0P	                  V4      V P	                  V4      3# rR  )rh   rO  r'  r(  rT  rD  s   &&&   r/  rh   ÚIPolys.dmp_ground_extract  sU   € Ü$ T§]¡]°1Ó%5°t·}±}ÀQÓ7GÈÏÉÐTUÍÐW[×WbÑWbÓc‰ˆˆaØ—?‘? 1Ó% t§¡°qÓ'9Ð:Ð:r3  c                	óÎ   € \        V P                  V4      P                  ^4      P                  4       V P                  4      w  r#V P                  V4      V P                  V4      3# rR  )ri   rL  r0  rO  r(  rT  ©r-  rX  r8  r¹  s   &&  r/  ri   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$6Ð7Ð7r3  c                	ój   € V P                  \        V P                  V4      V P                  4      4      # r+  )rT  rj   rO  r(  r‰  s   &&r/  rj   ÚIPolys.dup_mirror  s%   € Ø�‰œz¨$¯-©-¸Ó*:¸D¿K¹KÓHÓIÐIr3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  rk   rO  r(  r'  s   &&&r/  rk   ÚIPolys.dup_scale  r:  r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  rl   rO  r(  r'  s   &&&r/  rl   ÚIPolys.dup_shift  r:  r3  c                	óŽ   € V P                  \        V P                  V4      W P                  ^,
          V P                  4      4      # rR  )rT  rm   rO  r'  r(  r'  s   &&&r/  rm   ÚIPolys.dmp_shift  s/   € Ø�‰œy¨¯©°qÓ)9¸1¿j¹jÈ½lÈDÏKÉKÓXÓYÐYr3  c           	     	óª   € V P                  \        V P                  V4      V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  rn   rO  r(  rK  s   &&&&r/  rn   ÚIPolys.dup_transform  sB   € Ø�‰œ}¨T¯]©]¸1Ó-=¸t¿}¹}ÈQÓ?OÐQU×Q^ÑQ^Ð_`ÓQaÐcg×cnÑcnÓoÓpÐpr3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  ro   rO  r(  r”  s   &&&r/  ro   ÚIPolys.dup_compose  s0   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏ{É{Ó[Ó\Ð\r3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  rp   rO  r'  r(  r”  s   &&&r/  rp   ÚIPolys.dmp_compose  s>   € Ø�‰œ{¨4¯=©=¸Ó+;¸T¿]¹]È1Ó=MÈtÏzÉzÐZ[Í|Ð]a×]hÑ]hÓiÓjÐjr3  c                	óŠ   € \        V P                  V4      V P                  4      p\        \	        V P
                  V4      4      # r+  )rq   rO  r(  rö  r÷  rT  )r-  rX  Ú
componentss   && r/  rq   ÚIPolys.dup_decompose  s1   € Ü" 4§=¡=°Ó#3°T·[±[ÓAˆ
Ü”C˜Ÿ™¨Ó4Ó5Ð5r3  c                	ó®   € \        V P                  V4      V P                  ^,
          V P                  4      pV P	                  4       P                  V4      # rR  )rr   rO  r'  r(  r8  rT  ©r-  rX  r,  s   && r/  rr   ÚIPolys.dmp_lift   s=   € Ü˜$Ÿ-™-¨Ó*¨D¯J©J°q­L¸$¿+¹+ÓFˆØ�~‰~Ó×*Ñ*¨6Ó2Ð2r3  c                	óL   € \        V P                  V4      V P                  4      # r+  )rs   rO  r(  r‰  s   &&r/  rs   ÚIPolys.dup_sign_variations$  rò  r3  c                	óâ   € \        V P                  V4      V P                  VR 7      w  r4V'       d,   V P                  V P                  P	                  4       R7      pMT pW5P                  V4      3# )©Úconvert©r(  )rt   rO  r(  r5  Úget_ringrT  ©r-  rX  re  rY  rE  rJ  s   &&&   r/  rt   ÚIPolys.dup_clear_denoms'  sV   € Ü §¡¨aÓ 0°$·+±+ÀwÔO‰ˆßØ—:‘: T§[¡[×%9Ñ%9Ó%;�:Ó<‰DàˆDØ—?‘? 1Ó%Ð&Ð&r3  c                	ó  € \        V P                  V4      V P                  ^,
          V P                  VR7      w  r4V'       d,   V P	                  V P                  P                  4       R7      pMT pW5P                  V4      3# )rS  rd  rf  )ru   rO  r'  r(  r5  rg  rT  rh  s   &&&   r/  ru   ÚIPolys.dmp_clear_denoms.  sa   € Ü §¡¨aÓ 0°$·*±*¸Qµ,ÀÇÁÐU\Ô]‰ˆßØ—:‘: T§[¡[×%9Ñ%9Ó%;�:Ó<‰DàˆDØ—?‘? 1Ó%Ð&Ð&r3  c                	ój   € V P                  \        V P                  V4      W P                  4      4      # r+  )rT  rv   rO  r(  r‚  s   &&&r/  rv   ÚIPolys.dup_revert6  r…  r3  c                	ó´   € \        V P                  V4      V P                  V4      V P                  4      w  r4V P                  V4      V P                  V4      3# r+  )rw   rO  r(  rT  ©r-  rX  r•  Úsr¡  s   &&&  r/  rw   ÚIPolys.dup_half_gcdex9  sE   € Ü˜dŸm™m¨AÓ.°·±¸aÓ0@À$Ç+Á+ÓN‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                	óØ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4V P	                  V4      V P	                  V4      3# rR  )rx   rO  r'  r(  rT  ro  s   &&&  r/  rx   ÚIPolys.dmp_half_gcdex<  sR   € Ü˜dŸm™m¨AÓ.°·±¸aÓ0@À$Ç*Á*ÈQÅ,ÐPT×P[ÑP[Ó\‰ˆØ—‘ Ó" D§O¡O°AÓ$6Ð7Ð7r3  c                	óÖ   € \        V P                  V4      V P                  V4      V P                  4      w  r4pV P                  V4      V P                  V4      V P                  V4      3# r+  )ry   rO  r(  rT  ©r-  rX  r•  rp  Útr¡  s   &&&   r/  ry   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Kr3  c                	óú   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4pV P	                  V4      V P	                  V4      V P	                  V4      3# rR  )rz   rO  r'  r(  rT  ru  s   &&&   r/  rz   ÚIPolys.dmp_gcdexB  s\   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇ
Á
È1ÅÈdÏkÉkÓZ‰ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr3  c                	óŠ   € V P                  \        V P                  V4      V P                  V4      V P                  4      4      # r+  )rT  r{   rO  r(  r”  s   &&&r/  r{   ÚIPolys.dup_invertF  rÃ  r3  c                	ó®   € V P                  \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  r|   rO  r'  r(  r”  s   &&&r/  r|   ÚIPolys.dmp_invertH  rÍ  r3  c                	óª   € \        V P                  V4      V P                  V4      V P                  4      p\        \	        V P
                  V4      4      # r+  )r}   rO  r(  rö  r÷  rT  ©r-  rX  r•  Úprss   &&& r/  r}   ÚIPolys.dup_euclidean_prsK  ó<   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇKÁKÓPˆÜ”C˜Ÿ™¨Ó-Ó.Ð.r3  c                	óÎ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      p\	        \        V P                  V4      4      # rR  )r~   rO  r'  r(  rö  r÷  rT  r  s   &&& r/  r~   ÚIPolys.dmp_euclidean_prsN  óI   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇJÁJÈqÅLÐRV×R]ÑR]Ó^ˆÜ”C˜Ÿ™¨Ó-Ó.Ð.r3  c                	óª   € \        V P                  V4      V P                  V4      V P                  4      p\        \	        V P
                  V4      4      # r+  )r   rO  r(  rö  r÷  rT  r  s   &&& r/  r   ÚIPolys.dup_primitive_prsQ  r‚  r3  c                	óÎ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      p\	        \        V P                  V4      4      # rR  )r€   rO  r'  r(  rö  r÷  rT  r  s   &&& r/  r€   ÚIPolys.dmp_primitive_prsT  r…  r3  c                	ó²   € \        V P                  V4      V P                  V4      V P                  4      w  r4\        \	        V P
                  V4      4      V3# r+  )r�   rO  r(  rö  r÷  rT  ©r-  rX  r•  r€  Úsress   &&&  r/  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6r3  c                	óÖ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4\	        \        V P                  V4      4      V3# rR  )r…   rO  r'  r(  rö  r÷  rT  r‹  s   &&&  r/  r…   ÚIPolys.dmp_inner_subresultants[  sU   € Ü,¨T¯]©]¸1Ó-=¸t¿}¹}ÈQÓ?OÐQU×Q[ÑQ[Ð\]ÕQ]Ð_c×_jÑ_jÓk‰	ˆÜ”S˜Ÿ™¨#Ó.Ó/°Ð6Ð6r3  c                	óª   € \        V P                  V4      V P                  V4      V P                  4      p\        \	        V P
                  V4      4      # r+  )r‚   rO  r(  rö  r÷  rT  r  s   &&& r/  r‚   ÚIPolys.dup_subresultants_  r‚  r3  c                	óÎ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      p\	        \        V P                  V4      4      # rR  )r†   rO  r'  r(  rö  r÷  rT  r  s   &&& r/  r†   ÚIPolys.dmp_subresultantsb  r…  r3  c                	ó²   € \        V P                  V4      V P                  V4      V P                  4      w  r4V\        \	        V P
                  V4      4      3# r+  )rƒ   rO  r(  rö  r÷  rT  ©r-  rX  r•  Úresr€  s   &&&  r/  rƒ   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5r3  c                	ó  € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4V R,          P	                  V4      \        \        V P                  V4      4      3# r+  )r‡   rO  r'  r(  rT  rö  r÷  r•  s   &&&  r/  r‡   ÚIPolys.dmp_prs_resultanti  s`   € Ü$ T§]¡]°1Ó%5°t·}±}ÀQÓ7GÈÏÉÐTUÍÐW[×WbÑWbÓc‰ˆØ�R•×#Ñ# CÓ(¬$¬s°4·?±?ÀCÓ/HÓ*IÐJÐJr3  c                	óà   € \        V P                  V4      V P                  V4      V P                  V4      V P                  ^,
          V P                  4      pV R,          P                  V4      # r+  )rˆ   rO  r@  r'  r(  rT  )r-  rX  r•  r8  r–  s   &&&& r/  rˆ   ÚIPolys.dmp_zz_modular_resultantm  sY   € Ü& t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï?É?Ð[\ÓK]Ð_c×_iÑ_iÐjkÕ_kÐmq×mxÑmxÓyˆØ�B�x×"Ñ" 3Ó'Ð'r3  c                	óÀ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      pV R,          P	                  V4      # r+  )r‰   rO  r'  r(  rT  ©r-  rX  r•  r–  s   &&& r/  r‰   ÚIPolys.dmp_zz_collins_resultantp  óI   € Ü& t§}¡}°QÓ'7¸¿¹ÀqÓ9IÈ4Ï:É:ÐVWÍ<ÐY]×YdÑYdÓeˆØ�B�x×"Ñ" 3Ó'Ð'r3  c                	óÀ   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      pV R,          P	                  V4      # r+  )rŠ   rO  r'  r(  rT  r�  s   &&& r/  rŠ   ÚIPolys.dmp_qq_collins_resultants  rŸ  r3  c                	ól   € \        V P                  V4      V P                  V4      V P                  4      # r+  )r„   rO  r(  r”  s   &&&r/  r„   ÚIPolys.dup_resultantw  s'   € Ü˜TŸ]™]¨1Ó-¨t¯}©}¸QÓ/?ÀÇÁÓMÐMr3  c                	óð   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      p\	        V\
        4      '       d   V R,          P                  V4      # V# r+  )r‹   rO  r'  r(  rI  rö  rT  r�  s   &&& r/  r‹   ÚIPolys.dmp_resultanty  sW   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇ
Á
È1ÅÈdÏkÉkÓZˆÜ�cœ4× Ò Ø˜•8×&Ñ& sÓ+Ð+àˆJr3  c                	óL   € \        V P                  V4      V P                  4      # r+  )rŒ   rO  r(  r‰  s   &&r/  rŒ   ÚIPolys.dup_discriminant€  s   € Ü §¡¨aÓ 0°$·+±+Ó>Ð>r3  c                	óÐ   € \        V P                  V4      V P                  ^,
          V P                  4      p\	        V\
        4      '       d   V R,          P                  V4      # V# r+  )r�   rO  r'  r(  rI  rö  rT  )r-  rX  Údiscs   && r/  r�   ÚIPolys.dmp_discriminant‚  sL   € Ü §¡¨aÓ 0°$·*±*¸Qµ,ÀÇÁÓLˆÜ�dœD×!Ò!Ø˜•8×&Ñ& tÓ,Ð,àˆKr3  c                	óÖ   € \        V P                  V4      V P                  V4      V P                  4      w  r4pV P                  V4      V P                  V4      V P                  V4      3# r+  )rŽ   rO  r(  rT  ©r-  rX  r•  ÚHrE  rF  s   &&&   r/  rŽ   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Kr3  c                	óÖ   € \        V P                  V4      V P                  V4      V P                  4      w  r4pV P                  V4      V P                  V4      V P                  V4      3# r+  )r�   rO  r(  rT  r¬  s   &&&   r/  r�   ÚIPolys.dup_ff_prs_gcdŒ  r¯  r3  c                	óú   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4pV P	                  V4      V P	                  V4      V P	                  V4      3# rR  )r�   rO  r'  r(  rT  r¬  s   &&&   r/  r�   ÚIPolys.dmp_rr_prs_gcd�  ó`   € Ü  §¡¨qÓ!1°4·=±=ÀÓ3CÀTÇZÁZÐPQÅ\ÐSW×S^ÑS^Ó_‰ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr3  c                	óú   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4pV P	                  V4      V P	                  V4      V P	                  V4      3# rR  )r‘   rO  r'  r(  rT  r¬  s   &&&   r/  r‘   ÚIPolys.dmp_ff_prs_gcd’  r´  r3  c                	óÖ   € \        V P                  V4      V P                  V4      V P                  4      w  r4pV P                  V4      V P                  V4      V P                  V4      3# r+  )r’   rO  r(  rT  r¬  s   &&&   r/  r’   ÚIPolys.dup_zz_heu_gcd•  r¯  r3  c                	óú   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4pV P	                  V4      V P	                  V4      V P	                  V4      3# rR  )r“   rO  r'  r(  rT  r¬  s   &&&   r/  r“   ÚIPolys.dmp_zz_heu_gcd˜  r´  r3  c                	óÖ   € \        V P                  V4      V P                  V4      V P                  4      w  r4pV P                  V4      V P                  V4      V P                  V4      3# r+  )r”   rO  r(  rT  r¬  s   &&&   r/  r”   ÚIPolys.dup_qq_heu_gcd›  r¯  r3  c                	óú   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4pV P	                  V4      V P	                  V4      V P	                  V4      3# rR  )r•   rO  r'  r(  rT  r¬  s   &&&   r/  r•   ÚIPolys.dmp_qq_heu_gcdž  r´  r3  c                	óÖ   € \        V P                  V4      V P                  V4      V P                  4      w  r4pV P                  V4      V P                  V4      V P                  V4      3# r+  )r–   rO  r(  rT  r¬  s   &&&   r/  r–   ÚIPolys.dup_inner_gcd¡  sR   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇKÁKÓP‰ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr3  c                	óú   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      w  r4pV P	                  V4      V P	                  V4      V P	                  V4      3# rR  )r—   rO  r'  r(  rT  r¬  s   &&&   r/  r—   ÚIPolys.dmp_inner_gcd¤  s_   € Ü §¡¨aÓ 0°$·-±-ÀÓ2BÀDÇJÁJÈqÅLÐRV×R]ÑR]Ó^‰ˆˆaØ—‘ Ó" D§O¡O°AÓ$6¸¿¹ÈÓ8JÐKÐKr3  c                	óŽ   € \        V P                  V4      V P                  V4      V P                  4      pV P                  V4      # r+  )r˜   rO  r(  rT  ©r-  rX  r•  r­  s   &&& r/  r˜   ÚIPolys.dup_gcd§  ó5   € Ü�D—M‘M !Ó$ d§m¡m°AÓ&6¸¿¹ÓDˆØ�‰˜qÓ!Ð!r3  c                	ó²   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      pV P	                  V4      # rR  )r™   rO  r'  r(  rT  rÄ  s   &&& r/  r™   ÚIPolys.dmp_gcdª  ó?   € Ü�D—M‘M !Ó$ d§m¡m°AÓ&6¸¿
¹
À1½ÀdÇkÁkÓRˆØ�‰˜qÓ!Ð!r3  c                	óŽ   € \        V P                  V4      V P                  V4      V P                  4      pV P                  V4      # r+  )rš   rO  r(  rT  rÄ  s   &&& r/  rš   ÚIPolys.dup_rr_lcm­  ó5   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿;¹;ÓGˆØ�‰˜qÓ!Ð!r3  c                	óŽ   € \        V P                  V4      V P                  V4      V P                  4      pV P                  V4      # r+  )r›   rO  r(  rT  rÄ  s   &&& r/  r›   ÚIPolys.dup_ff_lcm°  rÌ  r3  c                	óŽ   € \        V P                  V4      V P                  V4      V P                  4      pV P                  V4      # r+  )rœ   rO  r(  rT  rÄ  s   &&& r/  rœ   ÚIPolys.dup_lcm³  rÆ  r3  c                	ó²   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      pV P	                  V4      # rR  )r�   rO  r'  r(  rT  rÄ  s   &&& r/  r�   ÚIPolys.dmp_rr_lcm¶  ó?   € Ü�t—}‘} QÓ'¨¯©°qÓ)9¸4¿:¹:Àa½<ÈÏÉÓUˆØ�‰˜qÓ!Ð!r3  c                	ó²   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      pV P	                  V4      # rR  )rž   rO  r'  r(  rT  rÄ  s   &&& r/  rž   ÚIPolys.dmp_ff_lcm¹  rÓ  r3  c                	ó²   € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  4      pV P	                  V4      # rR  )rŸ   rO  r'  r(  rT  rÄ  s   &&& r/  rŸ   ÚIPolys.dmp_lcm¼  rÉ  r3  c                	óP   € \        V P                  V4      V P                  4      pV# r+  )rc   rO  r(  ©r-  rX  Úconts   && r/  rc   ÚIPolys.dup_contentÀ  s    € Ü˜4Ÿ=™=¨Ó+¨T¯[©[Ó9ˆØˆr3  c                	ót   € \        V P                  V4      V P                  4      w  r#W P                  V4      3# r+  )re   rO  r(  rT  ©r-  rX  rÚ  Úprims   &&  r/  re   ÚIPolys.dup_primitiveÃ  s/   € Ü" 4§=¡=°Ó#3°T·[±[ÓA‰
ˆØ—_‘_ TÓ*Ð*Ð*r3  c                	óÐ   € \        V P                  V4      V P                  ^,
          V P                  4      p\	        V\
        4      '       d   V R,          P                  V4      # V# r+  )r    rO  r'  r(  rI  rö  rT  rÙ  s   && r/  r    ÚIPolys.dmp_contentÇ  sL   € Ü˜4Ÿ=™=¨Ó+¨T¯Z©Z¸­\¸4¿;¹;ÓGˆÜ�dœD×!Ò!Ø˜•8×&Ñ& tÓ,Ð,àˆKr3  c                	ó  € \        V P                  V4      V P                  ^,
          V P                  4      w  r#\	        V\
        4      '       d*   V R,          P                  V4      V P                  V4      3# W P                  V4      3# r+  )r¡   rO  r'  r(  rI  rö  rT  rÝ  s   &&  r/  r¡   ÚIPolys.dmp_primitiveÍ  si   € Ü" 4§=¡=°Ó#3°T·Z±ZÀµ\À4Ç;Á;ÓO‰
ˆÜ�dœD×!Ò!Ø˜•H×'Ñ'¨Ó-¨t¯©¸tÓ/DÐEÐEàŸ/™/¨$Ó/Ð0Ð0r3  c                	ót   € \        V P                  V4      V P                  ^,
          V P                  4      pV# rR  )rd   rO  r'  r(  rÙ  s   && r/  rd   ÚIPolys.dmp_ground_contentÔ  s*   € Ü! $§-¡-°Ó"2°D·J±J¸qµLÀ$Ç+Á+ÓNˆØˆr3  c                	ó˜   € \        V P                  V4      V P                  ^,
          V P                  4      w  r#W P	                  V4      3# rR  )rf   rO  r'  r(  rT  rÝ  s   &&  r/  rf   ÚIPolys.dmp_ground_primitive×  s9   € Ü)¨$¯-©-¸Ó*:¸D¿J¹JÀq½LÈ$Ï+É+ÓV‰
ˆØ—o‘o dÓ+Ð,Ð,r3  c                	ó  € \        V P                  V4      V P                  V4      V P                  VR 7      pV'       g)   Vw  rVrxWVV P                  V4      V P                  V4      3# Vw  rxV P                  V4      V P                  V4      3# )©Úinclude)r¢   rO  r(  rT  ©	r-  rX  r•  rê  r,  ÚcfÚcgrE  rF  s	   &&&&     r/  r¢   ÚIPolys.dup_cancelÛ  sx   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇÁÐU\Ô]ˆßØ!‰LˆB�AØ˜DŸO™O¨AÓ.°·±ÀÓ0BÐCÐCà‰DˆAØ—O‘O AÓ&¨¯©¸Ó(:Ð;Ð;r3  c                	ó@  € \        V P                  V4      V P                  V4      V P                  ^,
          V P                  VR7      pV'       g)   Vw  rVrxWVV P	                  V4      V P	                  V4      3# Vw  rxV P	                  V4      V P	                  V4      3# )rS  ré  )r£   rO  r'  r(  rT  rë  s	   &&&&     r/  r£   ÚIPolys.dmp_cancelã  s‚   € Ü˜DŸM™M¨!Ó,¨d¯m©m¸AÓ.>ÀÇ
Á
È1ÅÈdÏkÉkÐcjÔkˆßØ!‰LˆB�AØ˜DŸO™O¨AÓ.°·±ÀÓ0BÐCÐCà‰DˆAØ—O‘O AÓ&¨¯©¸Ó(:Ð;Ð;r3  c           	     	óâ   € \        V P                  V4      \        \        V P                  V4      4      V P                  4      pV UUu. uF  w  r4V P                  V4      V3NK  	  upp# u uppi r+  )r¤   rO  rö  r÷  r(  rT  ©r-  rX  Úfactorsr•  Úks   &&&  r/  r¤   ÚIPolys.dup_trial_divisionì  sX   € Ü$ T§]¡]°1Ó%5´t¼CÀÇÁÈwÓ<WÓ7XÐZ^×ZeÑZeÓfˆÙ5<Ô>±W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>s   Á	A+c           	     	ó  € \        V P                  V4      \        \        V P                  V4      4      V P                  ^,
          V P
                  4      pV UUu. uF  w  r4V P                  V4      V3NK  	  upp# u uppi rR  )r¥   rO  rö  r÷  r'  r(  rT  rò  s   &&&  r/  r¥   ÚIPolys.dmp_trial_divisionï  sg   € Ü$ T§]¡]°1Ó%5´t¼CÀÇÁÈwÓ<WÓ7XÐZ^×ZdÑZdÐefÕZfÐhl×hsÑhsÓtˆÙ5<Ô>±W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>s   ÁA=c                	óL   € \        V P                  V4      V P                  4      # r+  )r¦   rO  r(  r‰  s   &&r/  r¦   ÚIPolys.dup_zz_mignotte_boundó  s   € Ü$ T§]¡]°1Ó%5°t·{±{ÓCÐCr3  c                	óp   € \        V P                  V4      V P                  ^,
          V P                  4      # rR  )r§   rO  r'  r(  r‰  s   &&r/  r§   ÚIPolys.dmp_zz_mignotte_boundõ  s&   € Ü$ T§]¡]°1Ó%5°t·z±zÀ!µ|ÀTÇ[Á[ÓQÐQr3  c           
     	ó  € V P                   p\        W! V4      V! V4      V! V4      V! V4      V! V4      V P                  4      w  r‰r«V P                  V4      V P                  V	4      V P                  V
4      V P                  V4      3# r+  )rO  r¨   r(  rT  )r-  r  rX  r•  r¡  rp  rv  ÚDrF  r­  ÚSÚTs   &&&&&&&     r/  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_r3  c           
     	ó¶   € V P                   p\        W! V4      \        \        WS4      4      W@P                  4      p\        \        V P
                  V4      4      # r+  )rO  r©   rö  r÷  r(  rT  )r-  r8  rX  Úf_listÚlrý  rù  s   &&&&&  r/  r©   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0r3  c                	ó¦   € \        V P                  V4      V P                  4      pV UUu. uF  w  r4V P                  V4      V3NK  	  upp# u uppi r+  )rª   rO  r(  rT  rò  s   &&   r/  rª   ÚIPolys.dup_zz_zassenhaus  sC   € Ü# D§M¡M°!Ó$4°d·k±kÓBˆÙ5<Ô>±W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>ó   «Ac                	óL   € \        V P                  V4      V P                  4      # r+  )r«   rO  r(  r‰  s   &&r/  r«   ÚIPolys.dup_zz_irreducible_p  ó   € Ü# D§M¡M°!Ó$4°d·k±kÓBÐBr3  c                	óP   € \        V P                  V4      V P                  VR 7      # ))Úirreducible)r¬   rO  r(  )r-  rX  r  s   &&&r/  r¬   ÚIPolys.dup_cyclotomic_p  s   € Ü §¡¨aÓ 0°$·+±+È;ÔWÐWr3  c                	óN   € \        WP                  4      pV P                  V4      # r+  )r­   r(  rT  )r-  rƒ  rE  s   && r/  r­   ÚIPolys.dup_zz_cyclotomic_poly	  s   € Ü" 1§k¡kÓ2ˆØ�‰˜qÓ!Ð!r3  c                	ó–   € \        V P                  V4      V P                  4      pVf   V# \        \	        V P
                  V4      4      # r+  )r®   rO  r(  rö  r÷  rT  r_  s   && r/  r®   ÚIPolys.dup_zz_cyclotomic_factor  s;   € Ü)¨$¯-©-¸Ó*:¸D¿K¹KÓHˆØŠ>ØˆMäœ˜DŸO™O¨VÓ4Ó5Ð5r3  c                	ó.   € \        WW0P                  4      # r+  )r±   r(  )r-  ÚEÚcsÚcts   &&&&r/  r±   ÚIPolys.dmp_zz_wang_non_divisors  s   € Ü'¨¨r·;±;Ó?Ð?r3  c           
     	óÐ  € V R ,          pV UU	u. uF  w  r‰VP                  V4      V	3NK  	  ppp	V R,          p
\        \        V
P                   V4      4      p\        V P                  V4      W#WEW`P                  ^,
          V P
                  4      w  rpV P                  V4      \        \        V
P                  V4      4      \        \        VP                  V4      4      3# u up	pi )r  ºNrS  N)rO  rö  r÷  r²   r'  r(  rT  )r-  rX  rÿ  r  r  r­  r4  Úmvrv  rô  ÚuvÚHHÚCCs   &&&&&&&      r/  r²   ÚIPolys.dmp_zz_wang_lead_coeffs  s·   € Ø�"�XˆÙ./Ô1©a¡d aˆr�{‰{˜1‹~˜qÓ!©aˆÑ1Ø�"�XˆÜ”�R—[‘[ !Ó$Ó%ˆÜ+¨D¯M©M¸!Ó,<¸aÀQÈ1ÏjÉjÐYZÍlÐ\`×\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¨   € \        \        \        V P                  V4      4      W#V P                  4      p\        \        V P
                  V4      4      # r+  )r³   rö  r÷  rO  r(  rT  )r-  rE  r  r8  r,  s   &&&& r/  r³   ÚIPolys.dup_zz_diophantine%  s:   € Ü#¤D¬¨T¯]©]¸AÓ)>Ó$?ÀÀtÇ{Á{ÓSˆÜ”C˜Ÿ™¨Ó0Ó1Ð1r3  c           	     	óì   € \        \        \        V P                  V4      4      V P                  V4      W4WPP                  ^,
          V P
                  4      p\        \        V P                  V4      4      # rR  )r´   rö  r÷  rO  r'  r(  rT  )r-  rE  rY  r4  rC  r8  r,  s   &&&&&& r/  r´   ÚIPolys.dmp_zz_diophantine*  sX   € Ü#¤D¬¨T¯]©]¸AÓ)>Ó$?ÀÇÁÈqÓAQÐSTÐYZ×\fÑ\fÐghÕ\hÐjn×juÑjuÓvˆÜ”C˜Ÿ™¨Ó0Ó1Ð1r3  c           	     	óR  € V R ,          pV R,          p\        \        VP                  V4      4      p\        \        VP                  V4      4      p\        V P                  V4      W#WEV P                  ^,
          V P
                  4      p\        \        V P                  V4      4      # )r  r  )rö  r÷  rO  rµ   r'  r(  rT  )	r-  rX  r­  r  r4  r8  r  r  r,  s	   &&&&&&   r/  rµ   Ú!IPolys.dmp_zz_wang_hensel_lifting/  s   € Ø�"�XˆØ�"�XˆÜ”�R—[‘[ !Ó$Ó%ˆÜ”#�b—k‘k 2Ó&Ó'ˆÜ+¨D¯M©M¸!Ó,<¸aÀQÈ4Ï:É:ÐVWÍ<ÐY]×YdÑYdÓeˆÜ”C˜Ÿ™¨Ó0Ó1Ð1r3  c                	ó¾   € \        V P                  V4      V P                  ^,
          V P                  W#R7      pV Uu. uF  qPP	                  V4      NK  	  up# u upi )rS  )ÚmodÚseed)r¶   rO  r'  r(  rT  )r-  rX  r%  r&  ró  r•  s   &&&&  r/  r¶   ÚIPolys.dmp_zz_wang7  sF   € Ü˜dŸm™m¨AÓ.°·
±
¸1µ¸d¿k¹kÈsÔ^ˆÙ-4Ó6©W¨—‘ Ö#©WÑ6Ð6ùÒ6s   ¾Ac                	óœ   € \        V P                  V4      V P                  4      w  r#Y# Uu. uF  q@P                  V4      NK  	  up3# u upi r+  )r¯   rO  r(  rT  )r-  rX  Úcoeffró  r•  s   &&   r/  r¯   ÚIPolys.dup_zz_factor_sqf;  sA   € Ü*¨4¯=©=¸Ó+;¸T¿[¹[ÓI‰ˆØ°WÓ>±W°Ÿ™¨Ö+±WÑ>Ð?Ð?ùÒ>s   ¬A	c                	ó¬   € \        V P                  V4      V P                  4      w  r#Y# UUu. uF  w  rEV P                  V4      V3NK  	  upp3# u uppi r+  )r°   rO  r(  rT  ©r-  rX  r)  ró  r•  rô  s   &&    r/  r°   ÚIPolys.dup_zz_factor?  óJ   € Ü& t§}¡}°QÓ'7¸¿¹ÓE‰ˆØ¸WÔF¹W±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFó   ­Ac                	óÐ   € \        V P                  V4      V P                  ^,
          V P                  4      w  r#Y# UUu. uF  w  rEV P	                  V4      V3NK  	  upp3# u uppi rR  )r·   rO  r'  r(  rT  r,  s   &&    r/  r·   ÚIPolys.dmp_zz_factorB  óT   € Ü& t§}¡}°QÓ'7¸¿¹ÀA½ÀtÇ{Á{ÓS‰ˆØ¸WÔF¹W±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFó   ¿A"c                	ó¬   € \        V P                  V4      V P                  4      w  r#Y# UUu. uF  w  rEV P                  V4      V3NK  	  upp3# u uppi r+  )r¸   rO  r(  rT  r,  s   &&    r/  r¸   ÚIPolys.dup_qq_i_factorF  óJ   € Ü(¨¯©°qÓ)9¸4¿;¹;ÓG‰ˆØ¸WÔF¹W±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFr/  c                	óÐ   € \        V P                  V4      V P                  ^,
          V P                  4      w  r#Y# UUu. uF  w  rEV P	                  V4      V3NK  	  upp3# u uppi rR  )rº   rO  r'  r(  rT  r,  s   &&    r/  rº   ÚIPolys.dmp_qq_i_factorI  óT   € Ü(¨¯©°qÓ)9¸4¿:¹:Àa½<ÈÏÉÓU‰ˆØ¸WÔF¹W±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFr3  c                	ó¬   € \        V P                  V4      V P                  4      w  r#Y# UUu. uF  w  rEV P                  V4      V3NK  	  upp3# u uppi r+  )r¹   rO  r(  rT  r,  s   &&    r/  r¹   ÚIPolys.dup_zz_i_factorM  r6  r/  c                	óÐ   € \        V P                  V4      V P                  ^,
          V P                  4      w  r#Y# UUu. uF  w  rEV P	                  V4      V3NK  	  upp3# u uppi rR  )r»   rO  r'  r(  rT  r,  s   &&    r/  r»   ÚIPolys.dmp_zz_i_factorP  r9  r3  c                	ó¬   € \        V P                  V4      V P                  4      w  r#Y# UUu. uF  w  rEV P                  V4      V3NK  	  upp3# u uppi r+  )r¼   rO  r(  rT  r,  s   &&    r/  r¼   ÚIPolys.dup_ext_factorT  sJ   € Ü'¨¯©°aÓ(8¸$¿+¹+ÓF‰ˆØ¸WÔF¹W±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFr/  c                	óÐ   € \        V P                  V4      V P                  ^,
          V P                  4      w  r#Y# UUu. uF  w  rEV P	                  V4      V3NK  	  upp3# u uppi rR  )r½   rO  r'  r(  rT  r,  s   &&    r/  r½   ÚIPolys.dmp_ext_factorW  sT   € Ü'¨¯©°aÓ(8¸$¿*¹*ÀQ½,ÈÏÉÓT‰ˆØ¸WÔF¹W±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFr3  c                	ó¬   € \        V P                  V4      V P                  4      w  r#Y# UUu. uF  w  rEV P                  V4      V3NK  	  upp3# u uppi r+  )r¾   rO  r(  rT  r,  s   &&    r/  r¾   ÚIPolys.dup_gf_factor[  r.  r/  c                	óÐ   € \        V P                  V4      V P                  ^,
          V P                  4      w  r#Y# UUu. uF  w  rEV P	                  V4      V3NK  	  upp3# u uppi rR  )r¿   rO  r'  r(  rT  r,  s   &&    r/  r¿   ÚIPolys.dmp_gf_factor^  r2  r3  c                	ó¬   € \        V P                  V4      V P                  4      w  r#Y# UUu. uF  w  rEV P                  V4      V3NK  	  upp3# u uppi r+  )rÀ   rO  r(  rT  r,  s   &&    r/  rÀ   ÚIPolys.dup_factor_listb  r6  r/  c                	ó¦   € \        V P                  V4      V P                  4      pV UUu. uF  w  r4V P                  V4      V3NK  	  upp# u uppi r+  )rÁ   rO  r(  rT  rò  s   &&   r/  rÁ   ÚIPolys.dup_factor_list_includee  sC   € Ü)¨$¯-©-¸Ó*:¸D¿K¹KÓHˆÙ5<Ô>±W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>r  c                	óÐ   € \        V P                  V4      V P                  ^,
          V P                  4      w  r#Y# UUu. uF  w  rEV P	                  V4      V3NK  	  upp3# u uppi rR  )rÂ   rO  r'  r(  rT  r,  s   &&    r/  rÂ   ÚIPolys.dmp_factor_listi  r9  r3  c                	óÊ   € \        V P                  V4      V P                  ^,
          V P                  4      pV UUu. uF  w  r4V P	                  V4      V3NK  	  upp# u uppi rR  )rÃ   rO  r'  r(  rT  rò  s   &&   r/  rÃ   ÚIPolys.dmp_factor_list_includel  sM   € Ü)¨$¯-©-¸Ó*:¸D¿J¹JÀq½LÈ$Ï+É+ÓVˆÙ5<Ô>±W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>ó   ½Ac                	óL   € \        V P                  V4      V P                  4      # r+  )rÄ   rO  r(  r‰  s   &&r/  rÄ   ÚIPolys.dup_irreducible_pp  s   € Ü  §¡¨qÓ!1°4·;±;Ó?Ð?r3  c                	óp   € \        V P                  V4      V P                  ^,
          V P                  4      # rR  )rÅ   rO  r'  r(  r‰  s   &&r/  rÅ   ÚIPolys.dmp_irreducible_pr  s&   € Ü  §¡¨qÓ!1°4·:±:¸aµ<ÀÇÁÓMÐMr3  c                	óŠ   € \        V P                  V4      V P                  4      p\        \	        V P
                  V4      4      # r+  )rÆ   rO  r(  rö  r÷  rT  )r-  rX  Úseqs   && r/  rÆ   ÚIPolys.dup_sturmu  s1   € Ü˜Ÿ™ aÓ(¨$¯+©+Ó6ˆÜ”C˜Ÿ™¨Ó-Ó.Ð.r3  c                	óL   € \        V P                  V4      V P                  4      # r+  )rØ   rO  r(  r‰  s   &&r/  rØ   ÚIPolys.dup_sqf_py  s   € Ü˜Ÿ™ qÓ)¨4¯;©;Ó7Ð7r3  c                	óp   € \        V P                  V4      V P                  ^,
          V P                  4      # rR  )rÙ   rO  r'  r(  r‰  s   &&r/  rÙ   ÚIPolys.dmp_sqf_p{  s&   € Ü˜Ÿ™ qÓ)¨4¯:©:°a­<¸¿¹ÓEÐEr3  c                	ó®   € \        V P                  V4      V P                  ^,
          V P                  4      pV P	                  4       P                  V4      # rR  )rÚ   rO  r'  r(  r8  rT  r‚  s   && r/  rÚ   ÚIPolys.dmp_norm~  s=   € Ü�T—]‘] 1Ó% t§z¡z°!¥|°T·[±[ÓAˆØ�~‰~Ó×*Ñ*¨1Ó-Ð-r3  c                	ó²   € \        V P                  V4      V P                  4      w  r#pW P                  V4      V P	                  4       P                  V4      3# r+  )rÛ   rO  r(  rT  r8  ©r-  rX  rp  rE  ÚRs   &&   r/  rÛ   ÚIPolys.dup_sqf_norm‚  sE   € Ü˜tŸ}™}¨QÓ/°·±Ó=‰ˆˆaØ—?‘? 1Ó% t§~¡~Ó'7×'BÑ'BÀ1Ó'EÐFÐFr3  c                	óÖ   € \        V P                  V4      V P                  ^,
          V P                  4      w  r#pW P	                  V4      V P                  4       P	                  V4      3# rR  )rÜ   rO  r'  r(  rT  r8  r]  s   &&   r/  rÜ   ÚIPolys.dmp_sqf_norm…  sO   € Ü˜tŸ}™}¨QÓ/°·±¸Aµ¸t¿{¹{ÓK‰ˆˆaØ—?‘? 1Ó% t§~¡~Ó'7×'BÑ'BÀ1Ó'EÐFÐFr3  c                	ój   € V P                  \        V P                  V4      V P                  4      4      # r+  )rT  rÝ   rO  r(  r‰  s   &&r/  rÝ   ÚIPolys.dup_gf_sqf_part‰  ó%   € Ø�‰œ¨t¯}©}¸QÓ/?ÀÇÁÓMÓNÐNr3  c                	ój   € V P                  \        V P                  V4      V P                  4      4      # r+  )rT  rÞ   rO  r(  r‰  s   &&r/  rÞ   ÚIPolys.dmp_gf_sqf_part‹  rd  r3  c                	ój   € V P                  \        V P                  V4      V P                  4      4      # r+  )rT  rß   rO  r(  r‰  s   &&r/  rß   ÚIPolys.dup_sqf_part�  s%   € Ø�‰œ|¨D¯M©M¸!Ó,<¸d¿k¹kÓJÓKÐKr3  c                	óŽ   € V P                  \        V P                  V4      V P                  ^,
          V P                  4      4      # rR  )rT  rà   rO  r'  r(  r‰  s   &&r/  rà   ÚIPolys.dmp_sqf_part�  s/   € Ø�‰œ|¨D¯M©M¸!Ó,<¸d¿j¹jÈ½lÈDÏKÉKÓXÓYÐYr3  c                	ó°   € \        V P                  V4      V P                  VR 7      w  r4Y4 UUu. uF  w  rVV P                  V4      V3NK  	  upp3# u uppi ©©Úall)rá   rO  r(  rT  ©r-  rX  rn  r)  ró  r•  rô  s   &&&    r/  rá   ÚIPolys.dup_gf_sqf_list’  sL   € Ü(¨¯©°qÓ)9¸4¿;¹;ÈCÔP‰ˆØ¸WÔF¹W±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFó   ¯Ac                	óÔ   € \        V P                  V4      V P                  ^,
          V P                  VR7      w  r4Y4 UUu. uF  w  rVV P	                  V4      V3NK  	  upp3# u uppi ©rS  rm  )râ   rO  r'  r(  rT  ro  s   &&&    r/  râ   ÚIPolys.dmp_gf_sqf_list•  sW   € Ü(¨¯©°qÓ)9¸4¿:¹:Àa½<ÈÏÉÐZ]Ô^‰ˆØ¸WÔF¹W±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFó   ÁA$c                	ó°   € \        V P                  V4      V P                  VR 7      w  r4Y4 UUu. uF  w  rVV P                  V4      V3NK  	  upp3# u uppi rl  )rã   rO  r(  rT  ro  s   &&&    r/  rã   ÚIPolys.dup_sqf_list™  sL   € Ü% d§m¡m°AÓ&6¸¿¹ÈÔM‰ˆØ¸WÔF¹W±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFrq  c                	óª   € \        V P                  V4      V P                  VR 7      pV UUu. uF  w  rEV P                  V4      V3NK  	  upp# u uppi rl  )rä   rO  r(  rT  ©r-  rX  rn  ró  r•  rô  s   &&&   r/  rä   ÚIPolys.dup_sqf_list_includeœ  sE   € Ü& t§}¡}°QÓ'7¸¿¹È#ÔNˆÙ5<Ô>±W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>s   ­Ac                	óÔ   € \        V P                  V4      V P                  ^,
          V P                  VR7      w  r4Y4 UUu. uF  w  rVV P	                  V4      V3NK  	  upp3# u uppi rs  )rå   rO  r'  r(  rT  ro  s   &&&    r/  rå   ÚIPolys.dmp_sqf_listŸ  sW   € Ü% d§m¡m°AÓ&6¸¿
¹
À1½ÀdÇkÁkÐWZÔ[‰ˆØ¸WÔF¹W±T°Q˜$Ÿ/™/¨!Ó,¨aÓ0¹WÒFÐGÐGùÓFru  c                	óÎ   € \        V P                  V4      V P                  ^,
          V P                  VR7      pV UUu. uF  w  rEV P	                  V4      V3NK  	  upp# u uppi rs  )ræ   rO  r'  r(  rT  ry  s   &&&   r/  ræ   ÚIPolys.dmp_sqf_list_include¢  sP   € Ü& t§}¡}°QÓ'7¸¿¹ÀA½ÀtÇ{Á{ÐX[Ô\ˆÙ5<Ô>±W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>s   ¿A!c                	ó¦   € \        V P                  V4      V P                  4      pV UUu. uF  w  r4V P                  V4      V3NK  	  upp# u uppi r+  )rç   rO  r(  rT  rò  s   &&   r/  rç   ÚIPolys.dup_gff_list¦  sC   € Ü˜tŸ}™}¨QÓ/°·±Ó=ˆÙ5<Ô>±W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>r  c                	óÊ   € \        V P                  V4      V P                  ^,
          V P                  4      pV UUu. uF  w  r4V P	                  V4      V3NK  	  upp# u uppi rR  )rè   rO  r'  r(  rT  rò  s   &&   r/  rè   ÚIPolys.dmp_gff_list©  sM   € Ü˜tŸ}™}¨QÓ/°·±¸Aµ¸t¿{¹{ÓKˆÙ5<Ô>±W©T¨Q�$—/‘/ !Ó$ aÓ(±WÒ>Ð>ùÓ>rN  c                	óL   € \        V P                  V4      V P                  4      # r+  )rÇ   rO  r(  r‰  s   &&r/  rÇ   ÚIPolys.dup_root_upper_bound­  r
  r3  c                	óL   € \        V P                  V4      V P                  4      # r+  )rÈ   rO  r(  r‰  s   &&r/  rÈ   ÚIPolys.dup_root_lower_bound¯  r
  r3  c                	óP   € \        V P                  V4      W P                  VR 7      # ))Úfast)rÉ   rO  r(  )r-  rX  ÚMrˆ  s   &&&&r/  rÉ   Ú IPolys.dup_step_refine_real_root²  s   € Ü(¨¯©°qÓ)9¸1¿k¹kÐPTÔUÐUr3  c                	óT   € \        V P                  V4      W P                  W4WVVR 7      # ))ÚepsÚstepsÚdisjointrˆ  Úmobius)rÊ   rO  r(  )r-  rX  r‰  rŒ  r�  rŽ  rˆ  r�  s   &&&&&&&&r/  rÊ   Ú!IPolys.dup_inner_refine_real_root´  s/   € Ü)¨$¯-©-¸Ó*:¸A¿{¹{ÐPSÐksð  HNô  Oð  	Or3  c                	óT   € \        V P                  V4      W#V P                  WEWgR 7      # ©)rŒ  r�  rŽ  rˆ  )rË   rO  r(  ©r-  rX  rp  rv  rŒ  r�  rŽ  rˆ  s   &&&&&&&&r/  rË   Ú!IPolys.dup_outer_refine_real_root¶  s*   € Ü)¨$¯-©-¸Ó*:¸AÀ$Ç+Á+ÐSVÐnvô  Cð  	Cr3  c                	óT   € \        V P                  V4      W#V P                  WEWgR 7      # r’  )rÌ   rO  r(  r“  s   &&&&&&&&r/  rÌ   ÚIPolys.dup_refine_real_root¸  s#   € Ü# D§M¡M°!Ó$4°a¸D¿K¹KÈSÐhpÔ|Ð|r3  c                	óP   € \        V P                  V4      V P                  W#R 7      # ))rŒ  rˆ  )rÍ   rO  r(  )r-  rX  rŒ  rˆ  s   &&&&r/  rÍ   Ú#IPolys.dup_inner_isolate_real_rootsº  s   € Ü+¨D¯M©M¸!Ó,<¸d¿k¹kÈsÔ^Ð^r3  c           
     	óT   € \        V P                  V4      V P                  W#WEVR 7      # ))rŒ  ÚinfÚsuprˆ  r�  )rÎ   rO  r(  )r-  rX  rŒ  rš  r›  rˆ  r�  s   &&&&&&&r/  rÎ   Ú'IPolys.dup_inner_isolate_positive_roots¼  ó/   € Ü/°·±¸aÓ0@À$Ç+Á+ÐSVÐehð  }Cô  Dð  	Dr3  c           
     	óT   € \        V P                  V4      V P                  W#WEVR 7      # ))rš  r›  rŒ  rˆ  r�  )rÏ   rO  r(  )r-  rX  rš  r›  rŒ  rˆ  r�  s   &&&&&&&r/  rÏ   Ú'IPolys.dup_inner_isolate_negative_roots¾  r�  r3  c           
     	óT   € \        V P                  V4      V P                  W#WEVR 7      # ©)rŒ  rš  r›  rˆ  Úblackbox)rÐ   rO  r(  ©r-  rX  rŒ  rš  r›  rˆ  r¢  s   &&&&&&&r/  rÐ   Ú!IPolys.dup_isolate_real_roots_sqfÀ  s.   € Ü)¨$¯-©-¸Ó*:¸D¿K¹KÈSÐ_bð  yAô  Bð  	Br3  c           
     	óT   € \        V P                  V4      V P                  W#WEVR 7      # ))rŒ  rš  r›  Úbasisrˆ  )rÑ   rO  r(  )r-  rX  rŒ  rš  r›  r¦  rˆ  s   &&&&&&&r/  rÑ   ÚIPolys.dup_isolate_real_rootsÂ  s$   € Ü% d§m¡m°AÓ&6¸¿¹ÈÐ[^ÐrvÔwÐwr3  c                	óp   € \        \        \        V P                  V4      4      V P                  W#WEWgR 7      # ))rŒ  rš  r›  Ústrictr¦  rˆ  )rÒ   rö  r÷  rO  r(  )r-  rù  rŒ  rš  r›  r©  r¦  rˆ  s   &&&&&&&&r/  rÒ   Ú"IPolys.dup_isolate_real_roots_listÄ  s6   € Ü*¬4´°D·M±MÀ5Ó0IÓ+JÈDÏKÉKÐ]`Ðorð  JOô  [ð  	[r3  c                	óP   € \        V P                  V4      V P                  W#R 7      # ))rš  r›  )rÓ   rO  r(  )r-  rX  rš  r›  s   &&&&r/  rÓ   ÚIPolys.dup_count_real_rootsÆ  s   € Ü# D§M¡M°!Ó$4°d·k±kÀsÔTÐTr3  c                	óR   € \        V P                  V4      V P                  W#VR 7      # ))rš  r›  Úexclude)rÔ   rO  r(  )r-  rX  rš  r›  r®  s   &&&&&r/  rÔ   ÚIPolys.dup_count_complex_rootsÈ  s!   € Ü& t§}¡}°QÓ'7¸¿¹È#Ð`gÔhÐhr3  c           	     	óR   € \        V P                  V4      V P                  W#WER 7      # ))rŒ  rš  r›  r¢  )rÕ   rO  r(  )r-  rX  rŒ  rš  r›  r¢  s   &&&&&&r/  rÕ   Ú$IPolys.dup_isolate_complex_roots_sqfÊ  s"   € Ü,¨T¯]©]¸1Ó-=¸t¿{¹{ÐPSÐbeÔyÐyr3  c           
     	óT   € \        V P                  V4      V P                  W#WEVR 7      # r¡  )rÖ   rO  r(  r£  s   &&&&&&&r/  rÖ   Ú IPolys.dup_isolate_all_roots_sqfÌ  s*   € Ü(¨¯©°qÓ)9¸4¿;¹;ÈCÐ^aÐwô  Að  	Ar3  c           	     	óR   € \        V P                  V4      V P                  W#WER 7      # ))rŒ  rš  r›  rˆ  )r×   rO  r(  )r-  rX  rŒ  rš  r›  rˆ  s   &&&&&&r/  r×   ÚIPolys.dup_isolate_all_rootsÎ  s!   € Ü$ T§]¡]°1Ó%5°t·{±{ÈÐZ]ÔiÐir3  c           	     	ó�   € ^ RI Hp \        \        V P                  V! V P
                  ^,
          V P                  4      4      4      # )rG  )Údmp_fateman_poly_F_1)Úsympy.polys.specialpolysr·  Útupler÷  rT  r'  r(  )r-  r·  s   & r/  Úfateman_poly_F_1ÚIPolys.fateman_poly_F_1Ñ  ó/   € ÝAÜ”S˜Ÿ™Ñ*>¸t¿z¹zÈ!½|ÈTÏ[É[Ó*YÓZÓ[Ð[r3  c           	     	ó�   € ^ RI Hp \        \        V P                  V! V P
                  ^,
          V P                  4      4      4      # )rG  )Údmp_fateman_poly_F_2)r¸  r¾  r¹  r÷  rT  r'  r(  )r-  r¾  s   & r/  Úfateman_poly_F_2ÚIPolys.fateman_poly_F_2Ô  r¼  r3  c           	     	ó�   € ^ RI Hp \        \        V P                  V! V P
                  ^,
          V P                  4      4      4      # )rG  )Údmp_fateman_poly_F_3)r¸  rÂ  r¹  r÷  rT  r'  r(  )r-  rÂ  s   & r/  Úfateman_poly_F_3ÚIPolys.fateman_poly_F_3×  r¼  r3  c           	     	óÔ   € \        V P                  V4      P                  4        Uu. uF1  q P                  P                  P                  W P                  4      NK3  	  up4      # u upi r+  )rì   rL  rO  r(  Údomre  )r-  r<  rY  s   && r/  Úto_gf_denseÚIPolys.to_gf_denseÛ  sI   € ÜÈ4Ï9É9ÐU\ÓK]×KfÑKfÔKhÓjÑKhÀaŸ+™+Ÿ/™/×1Ñ1°!·[±[ÖAÑKhÑjÓkÐkùÒjs   §7A%c                	ó‚   € V P                  \        WP                  ^,
          V P                  P                  4      4      # rR  )rD  rR   r'  r(  rÆ  r;  s   &&r/  Úfrom_gf_denseÚIPolys.from_gf_denseÞ  s(   € Ø�~‰~œk¨'·:±:¸aµ<ÀÇÁÇÁÓQÓRÐRr3  c                	ó6   € \        V P                  V4      4      # r+  )ré   rÇ  r‰  s   &&r/  ré   ÚIPolys.gf_degreeá  s   € Ü˜×)Ñ)¨!Ó,Ó-Ð-r3  c                	ó`   € \        V P                  V4      V P                  P                  4      # r+  )rê   rÇ  r(  rÆ  r‰  s   &&r/  rê   ÚIPolys.gf_LCä  ó"   € Ü�T×%Ñ% aÓ(¨$¯+©+¯/©/Ó:Ð:r3  c                	ó`   € \        V P                  V4      V P                  P                  4      # r+  )rë   rÇ  r(  rÆ  r‰  s   &&r/  rë   ÚIPolys.gf_TCæ  rÐ  r3  c                	óT   € V P                  \        V P                  V4      4      4      # r+  )rÊ  rì   rÇ  r‰  s   &&r/  rì   ÚIPolys.gf_stripé  s#   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>Ó"?Ó@Ð@r3  c                	ó~   € V P                  \        V P                  V4      V P                  P                  4      4      # r+  )rÊ  rì   rÇ  r(  r%  r‰  s   &&r/  Úgf_truncÚIPolys.gf_truncë  s-   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>ÀÇÁÇÁÓ"PÓQÐQr3  c                	ó¨   € V P                  \        V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  rì   rÇ  r(  r%  rÆ  r‰  s   &&r/  Ú	gf_normalÚIPolys.gf_normalí  ó<   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>ÀÇÁÇÁÐQU×Q\ÑQ\×Q`ÑQ`Ó"aÓbÐbr3  c                	óˆ   € V P                  \        WP                  P                  V P                  P                  4      4      # r+  )rÊ  rí   r(  r%  rÆ  r‰  s   &&r/  rí   ÚIPolys.gf_from_dictð  s*   € Ø×!Ñ!¤,¨q·+±+·/±/À4Ç;Á;Ç?Á?Ó"SÓTÐTr3  c                	ód   € \        V P                  V4      V P                  P                  VR 7      # ©)Ú	symmetric)rî   rÇ  r(  r%  ©r-  rX  rà  s   &&&r/  rî   ÚIPolys.gf_to_dictò  s$   € Ü˜$×*Ñ*¨1Ó-¨t¯{©{¯©È)ÔTÐTr3  c                	ó^   € V P                  \        WP                  P                  4      4      # r+  )rÊ  rï   r(  r%  r‰  s   &&r/  rï   ÚIPolys.gf_from_int_polyõ  s!   € Ø×!Ñ!Ô"2°1·k±k·o±oÓ"FÓGÐGr3  c                	ód   € \        V P                  V4      V P                  P                  VR 7      # rß  )rð   rÇ  r(  r%  rá  s   &&&r/  rð   ÚIPolys.gf_to_int_poly÷  s$   € Ü˜d×.Ñ.¨qÓ1°4·;±;·?±?ÈiÔXÐXr3  c                	ó¨   € V P                  \        V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  rñ   rÇ  r(  r%  rÆ  r‰  s   &&r/  rñ   ÚIPolys.gf_negú  ó7   € Ø×!Ñ!¤&¨×)9Ñ)9¸!Ó)<¸d¿k¹k¿o¹oÈtÏ{É{ÏÉÓ"_Ó`Ð`r3  c                	ó¨   € V P                  \        V P                  V4      W P                  P                  V P                  P
                  4      4      # r+  )rÊ  rò   rÇ  r(  r%  rÆ  r'  s   &&&r/  rò   ÚIPolys.gf_add_groundý  ó<   € Ø×!Ñ!¤-°×0@Ñ0@ÀÓ0CÀQÏÉÏÉÐY]×YdÑYd×YhÑYhÓ"iÓjÐjr3  c                	ó¨   € V P                  \        V P                  V4      W P                  P                  V P                  P
                  4      4      # r+  )rÊ  ró   rÇ  r(  r%  rÆ  r'  s   &&&r/  ró   ÚIPolys.gf_sub_groundÿ  rì  r3  c                	ó¨   € V P                  \        V P                  V4      W P                  P                  V P                  P
                  4      4      # r+  )rÊ  rô   rÇ  r(  r%  rÆ  r'  s   &&&r/  rô   ÚIPolys.gf_mul_ground  rì  r3  c                	ó¨   € V P                  \        V P                  V4      W P                  P                  V P                  P
                  4      4      # r+  )rÊ  rõ   rÇ  r(  r%  rÆ  r'  s   &&&r/  rõ   ÚIPolys.gf_quo_ground  rì  r3  c                	óÈ   € V P                  \        V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  rö   rÇ  r(  r%  rÆ  r”  s   &&&r/  rö   ÚIPolys.gf_add  óN   € Ø×!Ñ!¤&¨×)9Ñ)9¸!Ó)<¸d×>NÑ>NÈqÓ>QÐSW×S^ÑS^×SbÑSbÐdh×doÑdo×dsÑdsÓ"tÓuÐur3  c                	óÈ   € V P                  \        V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r÷   rÇ  r(  r%  rÆ  r”  s   &&&r/  r÷   ÚIPolys.gf_sub  rõ  r3  c                	óÈ   € V P                  \        V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  rø   rÇ  r(  r%  rÆ  r”  s   &&&r/  rø   ÚIPolys.gf_mul
  rõ  r3  c                	ó¨   € V P                  \        V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  rù   rÇ  r(  r%  rÆ  r‰  s   &&r/  rù   ÚIPolys.gf_sqr  ré  r3  c           	     	óè   € V P                  \        V P                  V4      V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  rú   rÇ  r(  r%  rÆ  r   s   &&&&r/  rú   ÚIPolys.gf_add_mul  ó{   € Ø×!Ñ!¤*¨T×-=Ñ-=¸aÓ-@À$×BRÑBRÐSTÓBUÐW[×WgÑWgÐhiÓWjÐlp×lwÑlw×l{Ñl{ð  ~B÷  ~Iñ  ~I÷  ~Mñ  ~Mó  #Nó  Oð  	Or3  c           	     	óè   € V P                  \        V P                  V4      V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  rû   rÇ  r(  r%  rÆ  r   s   &&&&r/  rû   ÚIPolys.gf_sub_mul  rþ  r3  c           
     	óÄ   € V P                  \        \        \        V P                  V4      4      V P
                  P                  V P
                  P                  4      4      # r+  )rÊ  rü   rö  r÷  rÇ  r(  r%  rÆ  )r-  rE  s   &&r/  rü   ÚIPolys.gf_expand  sC   € Ø×!Ñ!¤)¬D´°T×5EÑ5EÀqÓ1IÓ,JÈDÏKÉKÏOÉOÐ]a×]hÑ]h×]lÑ]lÓ"mÓnÐnr3  c                	óò   € \        V P                  V4      V P                  V4      V P                  P                  V P                  P                  4      w  r4V P                  V4      V P                  V4      3# r+  )rý   rÇ  r(  r%  rÆ  rÊ  r¸  s   &&&  r/  rý   ÚIPolys.gf_div  s`   € Ü�d×&Ñ& qÓ)¨4×+;Ñ+;¸AÓ+>ÀÇÁÇÁÐQU×Q\ÑQ\×Q`ÑQ`Óa‰ˆØ×!Ñ! !Ó$ d×&8Ñ&8¸Ó&;Ð;Ð;r3  c                	óÈ   € V P                  \        V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  rþ   rÇ  r(  r%  rÆ  r”  s   &&&r/  rþ   ÚIPolys.gf_rem  rõ  r3  c                	óÈ   € V P                  \        V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  rÿ   rÇ  r(  r%  rÆ  r”  s   &&&r/  rÿ   ÚIPolys.gf_quo  rõ  r3  c                	óÈ   € V P                  \        V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r   rÇ  r(  r%  rÆ  r”  s   &&&r/  r   ÚIPolys.gf_exquo  óO   € Ø×!Ñ!¤(¨4×+;Ñ+;¸AÓ+>À×@PÑ@PÐQRÓ@SÐUY×U`ÑU`×UdÑUdÐfj×fqÑfq×fuÑfuÓ"vÓwÐwr3  c                	ó~   € V P                  \        V P                  V4      W P                  P                  4      4      # r+  )rÊ  r  rÇ  r(  rÆ  r‚  s   &&&r/  r  ÚIPolys.gf_lshift!  ó-   € Ø×!Ñ!¤)¨D×,<Ñ,<¸QÓ,?ÀÇKÁKÇOÁOÓ"TÓUÐUr3  c                	ó~   € V P                  \        V P                  V4      W P                  P                  4      4      # r+  )rÊ  r  rÇ  r(  rÆ  r‚  s   &&&r/  r  ÚIPolys.gf_rshift#  r  r3  c                	ó¨   € V P                  \        V P                  V4      W P                  P                  V P                  P
                  4      4      # r+  )rÊ  r  rÇ  r(  r%  rÆ  r‚  s   &&&r/  r  ÚIPolys.gf_pow&  s<   € Ø×!Ñ!¤&¨×)9Ñ)9¸!Ó)<¸aÇÁÇÁÐRV×R]ÑR]×RaÑRaÓ"bÓcÐcr3  c           	     	óÈ   € V P                  \        V P                  V4      W P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r  rÇ  r(  r%  rÆ  )r-  rX  rƒ  r•  s   &&&&r/  r  ÚIPolys.gf_pow_mod(  sO   € Ø×!Ñ!¤*¨T×-=Ñ-=¸aÓ-@À!×EUÑEUÐVWÓEXÐZ^×ZeÑZe×ZiÑZiÐko×kvÑkv×kzÑkzÓ"{Ó|Ð|r3  c                	ó  € \        V P                  V4      V P                  V4      V P                  P                  V P                  P                  4      w  r4pV P                  V4      V P                  V4      V P                  V4      3# r+  )r  rÇ  r(  r%  rÆ  rÊ  )r-  rX  r•  r¡  ÚcffÚcfgs   &&&   r/  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Vr3  c                	óÈ   € V P                  \        V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r  rÇ  r(  r%  rÆ  r”  s   &&&r/  r  ÚIPolys.gf_gcd.  rõ  r3  c                	óÈ   € V P                  \        V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r  rÇ  r(  r%  rÆ  r”  s   &&&r/  r  ÚIPolys.gf_lcm0  rõ  r3  c                	óÈ   € V P                  \        V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r  rÇ  r(  r%  rÆ  r”  s   &&&r/  r  ÚIPolys.gf_gcdex2  r  r3  c                	ó¨   € V P                  \        V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r	  rÇ  r(  r%  rÆ  r‰  s   &&r/  r	  ÚIPolys.gf_monic5  rÛ  r3  c                	ó¨   € V P                  \        V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r
  rÇ  r(  r%  rÆ  r‰  s   &&r/  r
  ÚIPolys.gf_diff7  s<   € Ø×!Ñ!¤'¨$×*:Ñ*:¸1Ó*=¸t¿{¹{¿¹ÐPT×P[ÑP[×P_ÑP_Ó"`ÓaÐar3  c                	óŠ   € \        V P                  V4      W P                  P                  V P                  P                  4      # r+  )r  rÇ  r(  r%  rÆ  r'  s   &&&r/  r  ÚIPolys.gf_eval:  s,   € Ü�t×'Ñ'¨Ó*¨A¯{©{¯©ÀÇÁÇÁÓPÐPr3  c                	óŠ   € \        V P                  V4      W P                  P                  V P                  P                  4      # r+  )r  rÇ  r(  r%  rÆ  )r-  rX  r4  s   &&&r/  r  ÚIPolys.gf_multi_eval<  s,   € Ü˜T×-Ñ-¨aÓ0°!·[±[·_±_ÀdÇkÁkÇoÁoÓVÐVr3  c                	óÈ   € V P                  \        V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r  rÇ  r(  r%  rÆ  r”  s   &&&r/  r  ÚIPolys.gf_compose?  sO   € Ø×!Ñ!¤*¨T×-=Ñ-=¸aÓ-@À$×BRÑBRÐSTÓBUÐW[×WbÑWb×WfÑWfÐhl×hsÑhs×hwÑhwÓ"xÓyÐyr3  c           	     	óè   € V P                  \        V P                  V4      V P                  V4      V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r  rÇ  r(  r%  rÆ  )r-  r•  r¡  rX  s   &&&&r/  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r3  c           	     	ó>  € V P                  V4      pV P                  V4      pV P                  V4      pV P                  V4      p\        WW4WPP                  P                  V P                  P                  4      w  rgV P                  V4      V P                  V4      3# r+  )rÇ  r  r(  r%  rÆ  rÊ  )r-  r(  ÚbrY  rƒ  rX  ÚUÚVs   &&&&&&  r/  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;r3  c                	óˆ   € V P                  \        WP                  P                  V P                  P                  4      4      # r+  )rÊ  r  r(  r%  rÆ  ©r-  rƒ  s   &&r/  r  ÚIPolys.gf_randomL  s*   € Ø×!Ñ!¤)¨A¯{©{¯©ÀÇÁÇÁÓ"PÓQÐQr3  c                	óˆ   € V P                  \        WP                  P                  V P                  P                  4      4      # r+  )rÊ  r  r(  r%  rÆ  r1  s   &&r/  r  ÚIPolys.gf_irreducibleN  s*   € Ø×!Ñ!¤.°·K±K·O±OÀTÇ[Á[Ç_Á_Ó"UÓVÐVr3  c                	óŠ   € \        V P                  V4      V P                  P                  V P                  P                  4      # r+  )r  rÇ  r(  r%  rÆ  r‰  s   &&r/  r  ÚIPolys.gf_irred_p_ben_orQ  s,   € Ü  ×!1Ñ!1°!Ó!4°d·k±k·o±oÀtÇ{Á{ÇÁÓWÐWr3  c                	óŠ   € \        V P                  V4      V P                  P                  V P                  P                  4      # r+  )r  rÇ  r(  r%  rÆ  r‰  s   &&r/  r  ÚIPolys.gf_irred_p_rabinS  ó,   € Ü × 0Ñ 0°Ó 3°T·[±[·_±_ÀdÇkÁkÇoÁoÓVÐVr3  c                	óŠ   € \        V P                  V4      V P                  P                  V P                  P                  4      # r+  )r  rÇ  r(  r%  rÆ  r‰  s   &&r/  r  ÚIPolys.gf_irreducible_pU  r9  r3  c                	óŠ   € \        V P                  V4      V P                  P                  V P                  P                  4      # r+  )r  rÇ  r(  r%  rÆ  r‰  s   &&r/  r  ÚIPolys.gf_sqf_pW  s,   € Ü˜×(Ñ(¨Ó+¨T¯[©[¯_©_¸d¿k¹k¿o¹oÓNÐNr3  c                	ó¨   € V P                  \        V P                  V4      V P                  P                  V P                  P
                  4      4      # r+  )rÊ  r  rÇ  r(  r%  rÆ  r‰  s   &&r/  r  ÚIPolys.gf_sqf_partZ  s<   € Ø×!Ñ!¤+¨d×.>Ñ.>¸qÓ.AÀ4Ç;Á;Ç?Á?ÐTX×T_ÑT_×TcÑTcÓ"dÓeÐer3  c                	óê   € \        V P                  V4      V P                  P                  V P                  P                  4      w  r4Y4 UUu. uF  w  rVV P                  V4      V3NK  	  upp3# u uppi r+  )r  rÇ  r(  r%  rÆ  rÊ  ro  s   &&&    r/  Úgf_sqf_listÚIPolys.gf_sqf_list\  s\   € Ü$ T×%5Ñ%5°aÓ%8¸$¿+¹+¿/¹/È4Ï;É;Ï?É?Ó[‰ˆØ¸wÔH¹w±t°q˜×+Ñ+¨AÓ.°Ó2¹wÒHÐHÐHùÓHó   ÁA/c                	óŠ   € \        V P                  V4      V P                  P                  V P                  P                  4      # r+  )r  rÇ  r(  r%  rÆ  r‰  s   &&r/  r  ÚIPolys.gf_Qmatrix`  s,   € Ü˜$×*Ñ*¨1Ó-¨t¯{©{¯©ÀÇÁÇÁÓPÐPr3  c                	óÔ   € \        V P                  V4      V P                  P                  V P                  P                  4      pV Uu. uF  q0P                  V4      NK  	  up# u upi r+  )r  rÇ  r(  r%  rÆ  rÊ  ©r-  rX  ró  r•  s   &&  r/  r  ÚIPolys.gf_berlekampb  óL   € Ü˜t×/Ñ/°Ó2°D·K±K·O±OÀTÇ[Á[Ç_Á_ÓUˆÙ07Ó9±¨1×#Ñ# AÖ&±Ñ9Ð9ùÒ9ó   Á	A%c                	óä   € \        V P                  V4      V P                  P                  V P                  P                  4      pV UUu. uF  w  r4V P                  V4      V3NK  	  upp# u uppi r+  )r  rÇ  r(  r%  rÆ  rÊ  rò  s   &&   r/  r  ÚIPolys.gf_ddf_zassenhausf  sU   € Ü# D×$4Ñ$4°QÓ$7¸¿¹¿¹È$Ï+É+Ï/É/ÓZˆÙ8?ÔA¹±°�$×$Ñ$ QÓ'¨Ó+¹ÒAÐAùÓAó   Á
A,c                	óÔ   € \        V P                  V4      V P                  P                  V P                  P                  4      pV Uu. uF  q@P                  V4      NK  	  up# u upi r+  )r  rÇ  r(  r%  rÆ  rÊ  ©r-  rX  rƒ  ró  r•  s   &&&  r/  r  ÚIPolys.gf_edf_zassenhausi  sL   € Ü# D×$4Ñ$4°QÓ$7¸¿¹¿¹È$Ï+É+Ï/É/ÓZˆÙ07Ó9±¨1×#Ñ# AÖ&±Ñ9Ð9ùÒ9rJ  c                	óä   € \        V P                  V4      V P                  P                  V P                  P                  4      pV UUu. uF  w  r4V P                  V4      V3NK  	  upp# u uppi r+  )r  rÇ  r(  r%  rÆ  rÊ  rò  s   &&   r/  r  ÚIPolys.gf_ddf_shoupm  sU   € Ü˜t×/Ñ/°Ó2°D·K±K·O±OÀTÇ[Á[Ç_Á_ÓUˆÙ8?ÔA¹±°�$×$Ñ$ QÓ'¨Ó+¹ÒAÐAùÓArM  c                	óÔ   € \        V P                  V4      V P                  P                  V P                  P                  4      pV Uu. uF  q@P                  V4      NK  	  up# u upi r+  )r  rÇ  r(  r%  rÆ  rÊ  rO  s   &&&  r/  r  ÚIPolys.gf_edf_shoupp  rI  rJ  c                	óÔ   € \        V P                  V4      V P                  P                  V P                  P                  4      pV Uu. uF  q0P                  V4      NK  	  up# u upi r+  )r  rÇ  r(  r%  rÆ  rÊ  rG  s   &&  r/  r  ÚIPolys.gf_zassenhaust  sL   € Ü × 0Ñ 0°Ó 3°T·[±[·_±_ÀdÇkÁkÇoÁoÓVˆÙ07Ó9±¨1×#Ñ# AÖ&±Ñ9Ð9ùÒ9rJ  c                	óÔ   € \        V P                  V4      V P                  P                  V P                  P                  4      pV Uu. uF  q0P                  V4      NK  	  up# u upi r+  )r  rÇ  r(  r%  rÆ  rÊ  rG  s   &&  r/  r  ÚIPolys.gf_shoupw  sL   € Ü˜4×+Ñ+¨AÓ.°·±·±ÀÇÁÇÁÓQˆÙ07Ó9±¨1×#Ñ# AÖ&±Ñ9Ð9ùÒ9rJ  c                	óÞ   € \        V P                  V4      V P                  P                  V P                  P                  VR 7      w  r4Y4 Uu. uF  qPP                  V4      NK  	  up3# u upi ))Úmethod)r  rÇ  r(  r%  rÆ  rÊ  )r-  rX  rZ  r)  ró  r•  s   &&&   r/  r  ÚIPolys.gf_factor_sqf{  sV   € Ü& t×'7Ñ'7¸Ó':¸D¿K¹K¿O¹OÈTÏ[É[Ï_É_ÐekÔl‰ˆØ°wÓ@±w°!×*Ñ*¨1Ö-±wÑ@Ð@Ð@ùÒ@s   ÁA*c                	óê   € \        V P                  V4      V P                  P                  V P                  P                  4      w  r#Y# UUu. uF  w  rEV P                  V4      V3NK  	  upp3# u uppi r+  )r   rÇ  r(  r%  rÆ  rÊ  r,  s   &&    r/  r   ÚIPolys.gf_factor~  s\   € Ü" 4×#3Ñ#3°AÓ#6¸¿¹¿¹ÈÏÉÏÉÓY‰ˆØ¸wÔH¹w±t°q˜×+Ñ+¨AÓ.°Ó2¹wÒHÐHÐHùÓHrC  r,  )NNN)F)T)NN)NNNFF)NNNF)NF)NNNFFFr+  (.  Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__Ú__annotations__r0  r5  r8  r=  r@  rD  rL  rO  rT  r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rS   rT   rV   rW   rX   rU   rY   rZ   r[   r]   r\   r^   r_   r`   ra   rb   rg   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‚   r†   rƒ   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   rc   re   r    r¡   rd   rf   r¢   r£   r¤   r¥   r¦   r§   r¨   r©   rª   r«   r¬   r­   r®   r±   r²   r³   r´   rµ   r¶   r¯   r°   r·   r¸   rº   r¹   r»   r¼   r½   r¾   r¿   rÀ   rÁ   rÂ   rÃ   rÄ   rÅ   rÆ   rØ   rÙ   rÚ   rÛ   rÜ   rÝ   rÞ   rß   rà   rá   râ   rã   rä   rå   ræ   rç   rè   rÇ   rÈ   rÉ   rÊ   rË   rÌ   rÍ   rÎ   rÏ   rÐ   rÑ   rÒ   rÓ   rÔ   rÕ   rÖ   r×   rº  r¿  rÃ  rÇ  rÊ  ré   rê   rë   rì   rÖ  rÙ  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  rA  r  r  r  r  r  r  r  r  r  r   Ú__static_attributes__r,  r3  r/  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ò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ò Ir3  r#  N(0  Ú__doc__Ú
__future__r   Útypingr   Úsympy.core.exprr   Úsympy.polys.domains.domainr   Úsympy.polys.orderingsr   rH  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.   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   Úsympy.polys.densebasicrI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   Úsympy.polys.densetoolsrS   rT   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   Úsympy.polys.euclidtoolsrw   rx   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£   Úsympy.polys.factortoolsr¤   r¥   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   Úsympy.polys.rootisolationrÆ   rÇ   rÈ   rÉ   rÊ   rË   rÌ   rÍ   rÎ   rÏ   rÐ   rÑ   rÒ   rÓ   rÔ   rÕ   rÖ   r×   Úsympy.polys.sqfreetoolsrØ   rÙ   rÚ   rÛ   rÜ   rÝ   rÞ   rß   rà   rá   râ   rã   rä   rå   ræ   rç   rè   Úsympy.polys.galoistoolsré   rê   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   Úsympy.utilitiesr!  r#  r,  r3  r/  Ú<module>rs     sO  ðÙ >å "å  ç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 óOIr3  