B e‹d¥ã@sHdZddlmZddlmZddlmZddlmZedƒdd„ƒZ dS) zZ This module implements the Residue function and related tools for working with residues. é)ÚMul)ÚS)Úsympify)ÚtimethisÚresiduec Csøddlm}ddlm}t|ƒ}|dkr8| |||¡}x2dD]*}|j||d}| |¡rf| ¡dkr>Pq>W||  ¡|ƒ}|j rˆ|j }n|g}t j }x^|D]V} |  |¡\} } t| Ž} | t j|fksÜ| jrÐ| jjsÜtd| ƒ‚| d|krš|| 7}qšW|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 )Zsympy.series.orderrZsympy.simplify.radsimprrÚsubsZnseriesÚhasZgetnZremoveOZis_AddÚargsrZZeroZ as_coeff_mulrZOneZis_PowÚexpZ is_IntegerÚNotImplementedError) ÚexprÚxZx0rrrÚsrÚresÚargÚcÚm©rúb/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/sympy/series/residues.pyr s,'       N) Ú__doc__Zsympy.core.mulrZsympy.core.singletonrZsympy.core.sympifyrZsympy.utilities.timeutilsrrrrrrÚs