+
    ‹°³jÉ  ã                   ó  € R t . RNRNRNRNRNRNRNRNR	NR
NRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'NR(NR)NR*NR+NR,NR-NR.NR/NR0NR1NR2NR3NR4NR5NR6NR7NR8NR9NR:NR;NR<NR=NR>NR?NR@NRANRBNRCNRDNRENRFNRGNRHNRINRJNRKNRLNRMNRNNRONRPNRQNRRNRSNRTNRUNRVNRWNRXNRYNRZNR[NR\NR]NR^NR_NR`NRaNRbNRcNRdNReNRfNRgNRhNRiNRjNRkNRlNRmNRnNRoNRpNRqNRrNRsNRtNRuNRvNRwNRxNRyNRzNR{NR|NR}NR~NRNR€NR�NR‚NRƒNR„NR…NR†NR‡NRˆNR‰NRŠNR‹NRŒNR�NRŽNR�NR�NR‘NR’NR“NR”NR•NR–NR—NR˜NR™NRšNR›NRœNR�NRžNRŸNR NR¡NR¢NR£NR¤NR¥NR¦NR§NR¨NR©NRªNR«NR¬NR­NR®NR¯NR°Nt^R±IHtHtHtHtHtHtH	t	H
t
HtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtH t H!t!H"t"H#t#H$t$H%t%H&t&H't'H(t(H)t)H*t*H+t+H,t,H-t-H.t.H/t/H0t0H1t1H2t2H3t3H4t4H5t5H6t6H7t7H8t8H9t9H:t:H;t;H<t<H=t= ^R²I>H?t?H@t@HAtAHBtBHCtC ^R³IDHEtE ^R´IFHGtGHHtHHItIHJtJHKtKHLtLHMtMHNtNHOtOHPtPHQtQHRtRHStSHTtTHUtUHVtVHWtWHXtXHYtYHZtZH[t[H\t\H]t]H^t^H_t_ ^RµI`HataHbtbHctcHdtdHeteHftfHgtgHhthHitiHjtj ^R¶IkHltlHmtm ^R·InHotoHptpHqtqHrtrHstsHttt ^R¸IuHvtvHwtwHxtxHytyHztz ^R¹I{H|t| ^RºI}H~t~HtH€t€H�t�H‚t‚HƒtƒH„t„H…t…H†t†H‡t‡HˆtˆH‰t‰HŠtŠH‹t‹HŒtŒH�t�HŽtŽH�t�H�t�H‘t‘H’t’H“t“H”t”H•t•H–t–H—t—H˜t˜H™t™HštšH›t›HœtœH�t� ^R»IžHŸtŸ ^R¼I H¡t¡H¢t¢H£t£H¤t¤H¥t¥ ^R½I¦H§t§H¨t¨H©t©HªtªH«t«H¬t¬H­t­ ^R¾I®H¯t¯H°t°H±t±H²t²H³t³ ^R¿I´HµtµH¶t¶H·t· ^RÀI¸H¹t¹ ^RÁIºH»t»H¼t¼H½t½H¾t¾ ^RÂI¿HÀtÀHÁtÁHÂtÂHÃtÃ RÃ# )Äz:Polynomial manipulation algorithms and algebraic objects. ÚPolyÚPurePolyÚpoly_from_exprÚparallel_poly_from_exprÚdegreeÚtotal_degreeÚdegree_listÚLCÚLMÚLTÚpdivÚpremÚpquoÚpexquoÚdivÚremÚquoÚexquoÚ
half_gcdexÚgcdexÚinvertÚsubresultantsÚ	resultantÚdiscriminantÚ	cofactorsÚgcd_listÚgcdÚlcm_listÚlcmÚ	terms_gcdÚtruncÚmonicÚcontentÚ	primitiveÚcomposeÚ	decomposeÚsturmÚgff_listÚgffÚsqf_normÚsqf_partÚsqf_listÚsqfÚfactor_listÚfactorÚ	intervalsÚrefine_rootÚcount_rootsÚ	all_rootsÚ
real_rootsÚnrootsÚground_rootsÚnth_power_roots_polyÚcancelÚreducedÚgroebnerÚis_zero_dimensionalÚGroebnerBasisÚpolyÚ
symmetrizeÚhornerÚinterpolateÚrational_interpolateÚvieteÚtogetherÚBasePolynomialErrorÚExactQuotientFailedÚPolynomialDivisionFailedÚOperationNotSupportedÚHeuristicGCDFailedÚHomomorphismFailedÚIsomorphismFailedÚExtraneousFactorsÚEvaluationFailedÚRefinementFailedÚCoercionFailedÚNotInvertibleÚNotReversibleÚNotAlgebraicÚDomainErrorÚPolynomialErrorÚUnificationFailedÚGeneratorsErrorÚGeneratorsNeededÚComputationFailedÚUnivariatePolynomialErrorÚMultivariatePolynomialErrorÚPolificationFailedÚOptionErrorÚ	FlagErrorÚminpolyÚminimal_polynomialÚprimitive_elementÚfield_isomorphismÚto_number_fieldÚisolateÚ	round_twoÚprime_decompÚprime_valuationÚgalois_groupÚitermonomialsÚMonomialÚlexÚgrlexÚgrevlexÚilexÚigrlexÚigrevlexÚCRootOfÚrootofÚRootOfÚComplexRootOfÚRootSumÚrootsÚDomainÚFiniteFieldÚIntegerRingÚRationalFieldÚ	RealFieldÚComplexFieldÚPythonFiniteFieldÚGMPYFiniteFieldÚPythonIntegerRingÚGMPYIntegerRingÚPythonRationalÚGMPYRationalFieldÚAlgebraicFieldÚPolynomialRingÚFractionFieldÚExpressionDomainÚ	FF_pythonÚFF_gmpyÚ	ZZ_pythonÚZZ_gmpyÚ	QQ_pythonÚQQ_gmpyÚGFÚFFÚZZÚQQÚZZ_IÚQQ_IÚRRÚCCÚEXÚEXRAWÚconstruct_domainÚswinnerton_dyer_polyÚcyclotomic_polyÚsymmetric_polyÚrandom_polyÚinterpolating_polyÚjacobi_polyÚchebyshevt_polyÚchebyshevu_polyÚhermite_polyÚhermite_prob_polyÚlegendre_polyÚlaguerre_polyÚbernoulli_polyÚbernoulli_c_polyÚgenocchi_polyÚ
euler_polyÚ
andre_polyÚapartÚ
apart_listÚassemble_partfrac_listÚOptionsÚringÚxringÚvringÚsringÚfieldÚxfieldÚvfieldÚsfield);r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   )r=   r>   r?   r@   rA   )rB   )rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   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   rw   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£   r¤   r¥   )r¦   r§   r¨   )r©   )rª   r«   r¬   r­   )r®   r¯   r°   r±   N)ÄÚ__doc__Ú__all__Ú	polytoolsr   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   Ú	polyfuncsr=   r>   r?   r@   rA   ÚrationaltoolsrB   Ú
polyerrorsrC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   Únumberfieldsr\   r]   r^   r_   r`   ra   rb   rc   rd   re   Ú	monomialsrf   rg   Ú	orderingsrh   ri   rj   rk   rl   rm   Úrootoftoolsrn   ro   rp   rq   rr   Ú	polyrootsrs   Údomainsrt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r€   r�   r‚   rƒ   r„   r…   r†   r‡   rˆ   r‰   rŠ   r‹   rŒ   r�   rŽ   r�   r�   r‘   r’   r“   Úconstructorr”   Úspecialpolysr•   r–   r—   r˜   r™   Ú
orthopolysrš   r›   rœ   r�   rž   rŸ   r    Ú
appellseqsr¡   r¢   r£   r¤   r¥   Úpartfracr¦   r§   r¨   Úpolyoptionsr©   Úringsrª   r«   r¬   r­   Úfieldsr®   r¯   r°   r±   © ó    ÚU/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/polys/__init__.pyÚ<module>rÉ      s�  ðÙ @ð?Ø
ð?Øð?Ø(ð?Ø*Cð?ØEMð?àð?à!ð?à#'ð?à)-ð?à/3ð?à5;ð?à=Cð?àEKð?ð ð?ð ð?ð ð?ð "ð?ð $+ð?ð -9ð?ð ;Bð?ð DLð?ð ð	?ð !ð	?ð #1ð	?ð 3>ð	?ð @Jð	?ð
 
ð?ð
 ð?ð
 ð?ð
 *ð?ð
 ,3ð?ð
 5<ð?ð
 >Gð?ð ð?ð ð?ð (ð?ð *1ð?ð 3=ð?ð ?Dð?ð ð?ð ð?ð 'ð?ð ).ð?ð 0=ð?ð ?Gð?ð ð?ð ð?ð !.ð?ð 0;ð?ð =Ið?ð ð?ð ð?ð 5ð?ð 7?ð?ð AJð?ð ð?ð &ð?ð (7ð?ð 9?ð?ð ð?ð ð?ð *ð?ð ,Bð?ð DKð?ð ð?ð  ð!?ð  1ð!?ð  3Mð!?ð" ð#?ð" 2ð#?ð" 4Hð#?ð$ ð%?ð$ -ð%?ð$ /Að%?ð& ð'?ð& )ð'?ð& +:ð'?ð& <Kð'?ð( ð)?ð( "ð)?ð( $5ð)?ð( 7Jð)?ð* ð+?ð* *ð+?ð* ,?ð+?ð,  ð-?ð, "?ð-?ð. ð/?ð. (ð/?ð. *5ð/?ð2 ð3?ð2 $ð3?ð2 &9ð3?ð2 ;Nð3?ð4 ð5?ð4 !ð5?ð4 #.ð5?ð4 0>ð5?ð6 ð7?ð6 &ð7?ð: ð;?ð:  ð;?ð> 
ð??ð> ð??ð> ð??ð>  &ð??ð> (0ð??ð> 2<ð??ðB ðC?ðB ðC?ðB "ðC?ðB $3ðC?ðB 5>ðC?ðF ðG?ðJ ðK?ðJ ðK?ðJ +ðK?ðJ -<ðK?ðJ >IðK?ðL ðM?ðL (ðM?ðL *;ðM?ðN ðO?ðN +ðO?ðN -=ðO?ðP ðQ?ðP *ðQ?ðP ,<ðQ?ðP >MðQ?ðR ðS?ðR $ðS?ðR &/ðS?ðR 1<ðS?ðR >GðS?ðT ðU?ðT ðU?ðT !ðU?ðT #'ðU?ðT )-ðU?ðT /3ðU?ðT 5;ðU?ðT =CðU?ðT EIðU?ðV 	ðW?ðV ðW?ðV ðW?ðZ ð[?ð^ ð_?ð^ .ð_?ð^ 0@ð_?ð` ða?ð` (ða?ðd ðe?ðd %ðe?ðd '8ðe?ðd :Hðe?ðf ðg?ðf )ðg?ðf +:ðg?ðj ðk?ðj )ðk?ðj +:ðk?ðj <Hðk?ðl ðm?ðp ðq?ðp ðq?ðp 4ðq?ðt ðu?ðx ðy?ðx ðy?ðx ðy?ðx &ðy?ð| ð}?ð| ð}?ð|  ð}?ð| "*ð}?€÷B	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	ñ 	÷%õ %õ $÷÷ ÷ ÷ ÷ ÷ õ ÷'÷ '÷ '÷ /ç B× Bç HÕ Hå ÷/÷ /÷ /÷ /÷ /÷ /÷ /÷ /ó /õ *÷9õ 9÷G÷ Gñ G÷ õ  ÷ @Ñ ?å  ç ,Ó ,ç 1Õ 1rÇ   