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    9%e                     @   s  d Z ddddddddd	d
dddddddddddddddddddddd d!d"d#d$d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d8d9d:d;d<d=d>d?d@dAdBdCdDdEdFdGdHdIdJdKdLdMdNdOdPdQdRdSdTdUdVdWdXdYdZd[d\d]d^d_d`dadbdcdddedfdgdhdidjdkdldmdndodpdqdrdsdtdudvdwdxdydzd{d|d}d~dddddddddddddddddddddddddddddddddddddddddddddddddgZddlmZmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$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< ddl=m>Z>m?Z?m@Z@mAZAmBZB ddlCmDZD ddlEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^ ddl_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZi ddljmkZkmlZl ddlmmnZnmoZompZpmqZqmrZrmsZs ddltmuZumvZvmwZwmxZxmyZy ddlzm{Z{ ddl|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ ddlmZ ddlmZmZmZmZmZ ddlmZmZmZmZmZmZmZ ddlmZmZmZmZmZ ddlmZmZmZ ddlmZ ddlmZmZmZmZ ddlmZmZmZmZ dS )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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.   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   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$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   Z	polyfuncsr;   r<   r=   r>   r?   Zrationaltoolsr@   Z
polyerrorsrA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   ZnumberfieldsrZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   Z	monomialsrd   re   Z	orderingsrf   rg   rh   ri   rj   rk   Zrootoftoolsrl   rm   rn   ro   rp   Z	polyrootsrq   domainsrr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   constructorr   Zspecialpolysr   r   r   r   r   Z
orthopolysr   r   r   r   r   r   r   Z
appellseqsr   r   r   r   r   Zpartfracr   r   r   Zpolyoptionsr   Zringsr   r   r   r   fieldsr   r   r   r    r   r   S/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/polys/__init__.py<module>   s                                                                                                                                    A
l
0 $