This computer - algebraic and system - theoretic project deals with time-varying continuous linear systems in the
engineering sense or, in mathematical language, with implicit systems of ordinary linear differential equations,
their solutions in suitable vector spaces of signals and their solution spaces, called linear systems or behaviours
(Willems 86). Discrete and multidimensional linear systems of difference resp. partial differential or difference
equations with variable coefficients will be considered as far as possible.
The principal goal is to determine the properties of these systems and behaviours by means of effective algorithms
for finitely generated modules over suitable rings of linear differential or difference operators and to implement
these algorithms in a computer algebra system (CAS), probably Axiom, in order to also obtain quantitative results.
Of course, other existing CAS in this area will be screened and used if possible and necessary. The theoretical
background is the theory of D-modules and that of hyperfunctions according to Sato.
The results and implementations should be interesting not only for system theorists and electrical engineers. but
also for specialists in noncommutative ring and module theory who want to see effective computations and
applications for a prototypical class of rings.