Residue Reduced Form of a Rational Function as an Iterated Laurent Series

Xin Guo Ce, Zhou Yue


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.


diagonal; residue; algebraic; D-finite

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