arXiv subjects

Shaoshi Chen

Publications and source records attributed to Shaoshi Chen.

57 records · Page 4Linked to original sources

arXiv2012

Telescopers for Rational and Algebraic Functions via Residues

We show that the problem of constructing telescopers for functions of m variables is equivalent to the problem of constructing telescopers for algebraic functions of m -1 variables and present a new algorithm to construct telescopers for algebraic functions of two variables. These considerations are based on analyzing the residues of the input. According to experiments, the resulting algorithm for rational functions of three variables is faster than known algorithms, at least in some examples of combinatorial interest. The algorithm for algebraic functions implies a new bound on the order of the telescopers.

cs.SC↗

arXiv2012

Order-Degree Curves for Hypergeometric Creative Telescoping

Creative telescoping applied to a bivariate proper hypergeometric term produces linear recurrence operators with polynomial coefficients, called telescopers. We provide bounds for the degrees of the polynomials appearing in these operators. Our bounds are expressed as curves in the (r,d)-plane which assign to every order r a bound on the degree d of the telescopers. These curves are hyperbolas, which reflect the phenomenon that higher order telescopers tend to have lower degree, and vice versa.

cs.SC↗

arXiv2011

A Note on Lipshitz's Lemma 3

In this note, we give a remark on the proof of Lemma 3 in Lipshitz's paper "The diagonal of a D-Finite power series is D-Finite". This remark is motivated by the observation that the statement from line -8 to -3 on page 375 of that paper seems not completely correct.

math.RA↗