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.
@article{10_37236_2909,
author = {Xin Guo Ce and Zhou Yue},
title = {Residue reduced form of a rational function as an iterated {Laurent} series},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {1},
doi = {10.37236/2909},
zbl = {1284.05023},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2909/}
}
TY - JOUR
AU - Xin Guo Ce
AU - Zhou Yue
TI - Residue reduced form of a rational function as an iterated Laurent series
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2909/
DO - 10.37236/2909
ID - 10_37236_2909
ER -
%0 Journal Article
%A Xin Guo Ce
%A Zhou Yue
%T Residue reduced form of a rational function as an iterated Laurent series
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2909/
%R 10.37236/2909
%F 10_37236_2909
Xin Guo Ce; Zhou Yue. Residue reduced form of a rational function as an iterated Laurent series. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2909
