Xin, Guoce; Zhou, Yue Residue reduced form of a rational function as an iterated Laurent series. (English) Zbl 1284.05023 Electron. J. Comb. 20, No. 1, Research Paper P47, 23 p. (2013). Summary: Lipshitz showed that the diagonal of a D-finite power series is still D-finite, but his proof seems hard to implement. This paper may be regarded as the first step towards an efficient algorithm realizing Lipshitz’s theory. We show that the idea of a reduced form may be a big saving for computing the D-finite functional equation. For the residue in one variable of a rational function, we develop an algorithm for computing its minimal algebraic functional equation. MSC: 05A15 Exact enumeration problems, generating functions 13J05 Power series rings 16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras) Keywords:diagonal; residue; algebraic; D-finite Software:bs3np PDFBibTeX XMLCite \textit{G. Xin} and \textit{Y. Zhou}, Electron. J. Comb. 20, No. 1, Research Paper P47, 23 p. (2013; Zbl 1284.05023) Full Text: Link