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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$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   )r<   r=   r>   r?   r@   )rA   )rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   )
r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   )re   rf   )rg   rh   ri   rj   rk   rl   )rm   rn   ro   rp   rq   )rr   ) rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r€   r�   r‚   rƒ   r„   r…   r†   r‡   rˆ   r‰   rŠ   r‹   rŒ   r�   rŽ   r�   r�   r‘   r’   )r“   )r”   r•   r–   r—   r˜   )r™   rš   r›   rœ   r�   rž   rŸ   )r    r¡   r¢   r£   r¤   )r¥   r¦   r§   )r¨   )r©   rª   r«   r¬   )r­   r®   r¯   r°   N)ÄÚ__doc__Ú__all__Z	polytoolsr   r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   Z	polyfuncsr<   r=   r>   r?   r@   ZrationaltoolsrA   Z
polyerrorsrB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   Znumberfieldsr[   r\   r]   r^   r_   r`   ra   rb   rc   rd   Z	monomialsre   rf   Z	orderingsrg   rh   ri   rj   rk   rl   Zrootoftoolsrm   rn   ro   rp   rq   Z	polyrootsrr   Údomainsrs   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’   Úconstructorr“   Zspecialpolysr”   r•   r–   r—   r˜   Z
orthopolysr™   rš   r›   rœ   r�   rž   rŸ   Z
appellseqsr    r¡   r¢   r£   r¤   Zpartfracr¥   r¦   r§   Zpolyoptionsr¨   Zringsr©   rª   r«   r¬   Úfieldsr­   r®   r¯   r°   © r·   r·   úS/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/polys/__init__.pyÚ<module>   s†                                                                                                                                     ÂAôl
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