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 $L$, called a parallel telescoper, for several multivariate functions, such that the applications of $L$ 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.

19 pages

References in corpus (3)

• Creative Telescoping for Holonomic Functions
• Computing the differential Galois group of a one-parameter family of second order linear differential equations
• Hermite Reduction and Creative Telescoping for Hyperexponential Functions

Cited by in corpus (1)

• Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation