Parallel telescoping and parameterized Picard-Vessiot theory

Shaoshi Chen, Ruyong Feng, Ziming Li, Michael F. Singer
2014 Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14  
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 application of L to the functions yields partial derivatives of a single function. We present a necessary and sufficient condition guaranteeing the existence of parallel telescopers for differentially finite functions, and develop an
more » ... 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.
doi:10.1145/2608628.2608638 dblp:conf/issac/ChenFLS14 fatcat:iqpzeq4rizfipndqtda3rmuo6i