Some Recent Results on Solving and Factoring Differential and Difference Equations

After a brief introduction to KLMM and some research projects related to differential and difference equations, I'll describe three algorithms for handling linear partial differential and difference systems with finite-dimensional solution spaces. The first algorithm is for converting a first-order matrix system to a reflexive system, the second is for finding hyperexponential solutions of a reflexive system, and the third is for factoring a reflexive system.