Factoring systems of linear PDEs with finite-dimensional solution spaces

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. Let L be a D-finite system with rational function coefficients. We present an algorithm for computing all hyperexponential solutions of L, and an algorithm for computing all D-finite systems whose coefficients are also rational functions, and whose solutions are contained in the solution space of L.