� ��g���b�dZddlmZddlmZddlmZddlmZed��d���Z dS) zZ This module implements the Residue function and related tools for working with residues. �)�Mul)�S)�sympify)�timethis�residuec�Z�ddlm}ddlm}t |��}|dkr|�|||z��}dD]H}|�||���}|�|��r|���dkrn�I||� ��|��}|j r|j }n|g}tj }|D]f} | �|��\} } t| �} | tj|fvs%| jr | jjst)d| z���| d|z kr|| z }�g|S)a Finds the residue of ``expr`` at the point x=x0. The residue is defined as the coefficient of ``1/(x-x0)`` in the power series expansion about ``x=x0``. Examples ======== >>> from sympy import Symbol, residue, sin >>> x = Symbol("x") >>> residue(1/x, x, 0) 1 >>> residue(1/x**2, x, 0) 0 >>> residue(2/sin(x), x, 0) 2 This function is essential for the Residue Theorem [1]. References ========== .. [1] https://en.wikipedia.org/wiki/Residue_theorem r)�Order)�collect)r������ )�nzterm of unexpected form: %sr )�sympy.series.orderr �sympy.simplify.radsimpr r�subs�nseries�has�getn�removeO�is_Add�argsr�Zero� as_coeff_mulr�One�is_Pow�exp� is_Integer�NotImplementedError) �expr�x�x0r r r�sr�res�arg�c�ms �e/home/asafur/pinokio/api/open-webui.git/app/env/lib/python3.11/site-packages/sympy/series/residues.pyrr s[��N)�(�(�(�(�(�.�.�.�.�.�.� �4�=�=�D� �Q�w�w��y�y��A��F�#�#�� $���� �L�L��a�L� � ���u�u�U�|�|� �q�v�v�x�x�1�}�}� �E� -���� � � � �Q���A��x���v����s�� �&�C���������"�"���1� ��G���a�e�Q�Z���A�H����1A��%�&C�a�&G�H�H� H� ��!��8�8� �1�H�C�� �J�N) �__doc__�sympy.core.mulr�sympy.core.singletonr�sympy.core.sympifyr�sympy.utilities.timeutilsrr�r+r*�<module>r2s����� ������"�"�"�"�"�"�&�&�&�&�&�&�.�.�.�.�.�.� ��)���<�<���<�<�<r+
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