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    7^(hÉ  ã                   ó`  — d Z g d¢ZddlmZmZmZmZmZmZm	Z	m
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mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z= ddl>m?Z?m@Z@mAZAmBZBmCZC ddlDmEZE ddlFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_ ddl`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZj ddlkmlZlmmZm dd	lnmoZompZpmqZqmrZrmsZsmtZt dd
lumvZvmwZwmxZxmyZymzZz ddl{m|Z| ddl}m~Z~mZm€Z€m�Z�m‚Z‚mƒZƒm„Z„m…Z…m†Z†m‡Z‡mˆZˆm‰Z‰mŠZŠm‹Z‹mŒZŒm�Z�mŽZŽm�Z�m�Z�m‘Z‘m’Z’m“Z“m”Z”m•Z•m–Z–m—Z—m˜Z˜m™Z™mšZšm›Z›mœZœm�Z� ddlžmŸZŸ ddl m¡Z¡m¢Z¢m£Z£m¤Z¤m¥Z¥ ddl¦m§Z§m¨Z¨m©Z©mªZªm«Z«m¬Z¬m­Z­ ddl®m¯Z¯m°Z°m±Z±m²Z²m³Z³ ddl´mµZµm¶Z¶m·Z· ddl¸m¹Z¹ ddlºm»Z»m¼Z¼m½Z½m¾Z¾ ddl¿mÀZÀmÁZÁmÂZÂmÃZÃ y)z: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sfieldé   );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    úR/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/polys/__init__.pyú<module>rÊ      s%  ðÙ @ò?€÷B	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	÷ 	ñ 	÷%õ %õ $÷÷ ÷ ÷ ÷ ÷ õ ÷'÷ '÷ '÷ /ç B× Bç HÕ Hå ÷/÷ /÷ /÷ /÷ /÷ /÷ /÷ /ó /õ *÷9õ 9÷G÷ Gñ G÷ õ  ÷ @Ñ ?å  ç ,Ó ,ç 1Ô 1rÈ   