o 3Ih@sHdZddlmZddlmZddlmZddlmZedddZ dS) zZ This module implements the Residue function and related tools for working with residues. )Mul)S)sympify)timethisresiduec Csddlm}ddlm}t|}|dkr||||}dD]}|j||d}||r2|dkr4nq|| |}|j rC|j }n|g}t j }|D]+} | |\} } t| } | t j|fvsl| jrf| jjsltd| | d|krv|| 7}qK|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.orderrsympy.simplify.radsimprrsubsnserieshasgetnremoveOis_AddargsrZero as_coeff_mulrOneis_Powexp is_IntegerNotImplementedError) exprxx0rrrsrresargcmr(U/home/air/sanwanet/gpt-api/venv/lib/python3.10/site-packages/sympy/series/residues.pyr s0 '   N) __doc__sympy.core.mulrsympy.core.singletonrsympy.core.sympifyrsympy.utilities.timeutilsrrr(r(r(r)s