See http://en.wikipedia.org/wiki/Z-transform for the z-transform (used frequently in discrete signal processing). Not seeking solutions to differential equations! I need to solve systems of coupled difference equations (the same wiki link describes difference equations too). Memory limitations in Mathematica and Maple, limit explicit solutions to about 4 coupled difference equations and I was hoping to solve 5 or more such equations with SAGE, after seeing some of it's capabilities on the benchmark page.