Ë ¬Ú“i¥ãóT—dZddlmZddlmZddlmZddlmZed«d„«Z y) zZ This module implements the Residue function and related tools for working with residues. é)ÚMul)ÚS)Úsympify)ÚtimethisÚresiduecóX—ddlm}ddlm}t |«}|dk7r|j |||z«}dD];}|j ||¬«}|j|«r|j«dk\sŒ;n|j«|«}|jr |j}n|g}tj}|D]p} | j|«\} } t| Ž} | tj |fvs0| j"r| j$j&st)d| z«‚| d|z k(sŒl|| z }Œr|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)ÚOrder)Úcollect)réééééé )Únzterm of unexpected form: %sr )Úsympy.series.orderr Úsympy.simplify.radsimpr rÚsubsÚnseriesÚhasÚgetnÚremoveOÚis_AddÚargsrÚZeroÚ as_coeff_mulrÚOneÚis_PowÚexpÚ is_IntegerÚNotImplementedError) ÚexprÚxÚx0r r rÚsrÚresÚargÚcÚms úr2s1ðñõ Ý"Ý&Ý.ñ ˆ)Óñ<óñ<r+