Parallel Telescoping and Parameterized Picard--Vessiot Theory
Abstract
Parallel telescoping is a natural generalization of differential creative-telescoping for single integrals to line integrals. It computes a linear ordinary differential operator , called a parallel telescoper, for several multivariate functions, such that the applications of to the functions yield antiderivatives of a single function. We present a necessary and sufficient condition guaranteeing the existence of parallel telescopers for differentially finite functions, and develop an algorithm to compute minimal ones for compatible hyperexponential functions. Besides computing annihilators of parametric line integrals, we use the parallel telescoping for determining Galois groups of parameterized partial differential systems of first order.
Cite
@article{arxiv.1401.4666,
title = {Parallel Telescoping and Parameterized Picard--Vessiot Theory},
author = {Shaoshi Chen and Ruyong Feng and Ziming Li and Michael F. Singer},
journal= {arXiv preprint arXiv:1401.4666},
year = {2014}
}
Comments
19 pages