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Residue reduced form of a rational function as an iterated Laurent series. (English) Zbl 1284.05023

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)

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