Factoring systems of linear PDEs with finite-dimensional solution spaces (Q1878482)

A D-finite system is a finite set of linear homogeneous partial differential equations in several independent and dependent variables, whose solution space is of finite dimension. The authors consider D-finite systems with coefficients in the field \(\mathbb{K} = \overline{Q}(x_{1},\dots,x_{n})\). They first give an algorithm to compute all hyper-exponential solutions of such a system, that is, solutions all of whose logarithmic partial derivatives lie in \(\mathbb{K}\). Then, they introduce some kind of extension to PDEs of the Beke-Schlesinger algorithm for factoring linear differential operators.