
    \h                     `   S r / SQrSSKJrJrJrJrJrJrJ	r	J
r
JrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJ r J!r!J"r"J#r#J$r$J%r%J&r&J'r'J(r(J)r)J*r*J+r+J,r,J-r-J.r.J/r/J0r0J1r1J2r2J3r3J4r4J5r5J6r6J7r7J8r8J9r9J:r:J;r;J<r<J=r=  SSK>J?r?J@r@JArAJBrBJCrC  SSKDJErE  SSKFJGrGJHrHJIrIJJrJJKrKJLrLJMrMJNrNJOrOJPrPJQrQJRrRJSrSJTrTJUrUJVrVJWrWJXrXJYrYJZrZJ[r[J\r\J]r]J^r^J_r_  SSK`JaraJbrbJcrcJdrdJereJfrfJgrgJhrhJiriJjrj  SSKkJlrlJmrm  SS	KnJoroJprpJqrqJrrrJsrsJtrt  SS
KuJvrvJwrwJxrxJyryJzrz  SSK{J|r|  SSK}J~r~JrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJrJr  SSKJr  SSKJrJrJrJrJr  SSKJrJrJrJrJrJrJr  SSKJrJrJrJrJr  SSKJrJrJr  SSKJr  SSKJrJrJrJr  SSKJrJrJrJr  g)z:Polynomial manipulation algorithms and algebraic objects. )PolyPurePolypoly_from_exprparallel_poly_from_exprdegreetotal_degreedegree_listLCLMLTpdivprempquopexquodivremquoexquo
half_gcdexgcdexinvertsubresultants	resultantdiscriminant	cofactorsgcd_listgcdlcm_listlcm	terms_gcdtruncmoniccontent	primitivecompose	decomposesturmgff_listgffsqf_normsqf_partsqf_listsqffactor_listfactor	intervalsrefine_rootcount_roots	all_roots
real_rootsnrootsground_rootsnth_power_roots_polycancelreducedgroebneris_zero_dimensionalGroebnerBasispoly
symmetrizehornerinterpolaterational_interpolatevietetogetherBasePolynomialErrorExactQuotientFailedPolynomialDivisionFailedOperationNotSupportedHeuristicGCDFailedHomomorphismFailedIsomorphismFailedExtraneousFactorsEvaluationFailedRefinementFailedCoercionFailedNotInvertibleNotReversibleNotAlgebraicDomainErrorPolynomialErrorUnificationFailedGeneratorsErrorGeneratorsNeededComputationFailedUnivariatePolynomialErrorMultivariatePolynomialErrorPolificationFailedOptionError	FlagErrorminpolyminimal_polynomialprimitive_elementfield_isomorphismto_number_fieldisolate	round_twoprime_decompprime_valuationgalois_groupitermonomialsMonomiallexgrlexgrevlexilexigrlexigrevlexCRootOfrootofRootOfComplexRootOfRootSumrootsDomainFiniteFieldIntegerRingRationalField	RealFieldComplexFieldPythonFiniteFieldGMPYFiniteFieldPythonIntegerRingGMPYIntegerRingPythonRationalGMPYRationalFieldAlgebraicFieldPolynomialRingFractionFieldExpressionDomain	FF_pythonFF_gmpy	ZZ_pythonZZ_gmpy	QQ_pythonQQ_gmpyGFFFZZQQZZ_IQQ_IRRCCEXEXRAWconstruct_domainswinnerton_dyer_polycyclotomic_polysymmetric_polyrandom_polyinterpolating_polyjacobi_polychebyshevt_polychebyshevu_polyhermite_polyhermite_prob_polylegendre_polylaguerre_polybernoulli_polybernoulli_c_polygenocchi_poly
euler_poly
andre_polyapart
apart_listassemble_partfrac_listOptionsringxringvringsringfieldxfieldvfield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$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   )r=   r>   r?   r@   rA   )rB   )rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   )
r\   r]   r^   r_   r`   ra   rb   rc   rd   re   )rf   rg   )rh   ri   rj   rk   rl   rm   )rn   ro   rp   rq   rr   )rs   ) rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   )r   r   r   r   r   )r   r   r   r   r   r   r   )r   r   r   r   r   )r   r   r   )r   )r   r   r   r   )r   r   r   r   N)__doc____all__	polytoolsr   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   	polyfuncsr=   r>   r?   r@   rA   rationaltoolsrB   
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[   numberfieldsr\   r]   r^   r_   r`   ra   rb   rc   rd   re   	monomialsrf   rg   	orderingsrh   ri   rj   rk   rl   rm   rootoftoolsrn   ro   rp   rq   rr   	polyrootsrs   domainsrt   ru   rv   rw   rx   ry   rz   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   constructorr   specialpolysr   r   r   r   r   
orthopolysr   r   r   r   r   r   r   
appellseqsr   r   r   r   r   partfracr   r   r   polyoptionsr   ringsr   r   r   r   fieldsr   r   r   r        L/var/www/auris/envauris/lib/python3.13/site-packages/sympy/polys/__init__.py<module>r      s%   @?B	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	% % $      ' ' ' / B B H H / / / / / / / / / *9 9G G G    @ ?   , , 1 1r   