Factoring zero-dimensional ideals of linear partial differential operators
Ziming Li, Fritz Schwarz, Sergey Petrovich Tsarev · 2002
We present an algorithm for factoring a zero-dimensional left ideal in the ring Q(x, y) [∂x, ∂y], i.e. factoring a linear homogeneous partial differential system whose coefficients belong to Q(x, y), and whose solution space is finite-dimensional over Q. The algorithm computes all the zero-dimensional left ideals containing the given ideal. It generalizes the Beke-Schlesinger algorithm for factoring linear ordinary differential operators, and uses an algorithm for finding hyperexponential solutions of such ideals.