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    RG5d                     @   s8  d Z g dZddl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'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z< ddl=m>Z>m?Z?m@Z@mAZAmBZB ddlCmDZD ddlEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^ ddl_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZh ddlimjZjmkZk dd	llmmZmmnZnmoZompZpmqZqmrZr dd
lsmtZtmuZumvZvmwZwmxZx ddlymzZz ddl{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ ddlmZ ddlmZmZmZmZmZ ddlmZmZmZmZmZmZ ddlmZmZmZ ddlmZ ddlmZmZmZmZ ddlmZmZmZmZ dS )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
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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legendre_polylaguerre_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$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   )r;   r<   r=   r>   r?   )r@   )rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   )	rZ   r[   r\   r]   r^   r_   r`   ra   rb   )rc   rd   )re   rf   rg   rh   ri   rj   )rk   rl   rm   rn   ro   )rp   ) rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r   )r   r   r   r   r   )r   r   r   r   r   r   )r   r   r   )r   )r   r   r   r   )r   r   r   r   N)__doc____all__Z	polytoolsr   r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   Z	polyfuncsr;   r<   r=   r>   r?   Zrationaltoolsr@   Z
polyerrorsrA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   ZnumberfieldsrZ   r[   r\   r]   r^   r_   r`   ra   rb   Z	monomialsrc   rd   Z	orderingsre   rf   rg   rh   ri   rj   Zrootoftoolsrk   rl   rm   rn   ro   	polyrootsrp   domainsrq   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   constructorr   Zspecialpolysr   r   r   r   r   Z
orthopolysr   r   r   r   r   r   Zpartfracr   r   r   Zpolyoptionsr   Zringsr   r   r   r   fieldsr   r   r   r    r   r   P/var/www/html/django/DPS/env/lib/python3.9/site-packages/sympy/polys/__init__.py<module>   s$   >
l
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