Equivalences of Linear Functional Systems

Within the algebraic analysis approach to linear systems theory, we investigate the equivalence problem of linear functional systems, i.e., the problem of characterizing when all the solutions of two linear functional systems are in a one-to-one correspondence. To do that, we first provide a new characterization of isomorphic finitely presented modules in terms of inflations of their presentation matrices. We then prove several isomorphisms which are consequences of the unimodular completion problem. We then use these isomorphisms to complete and refine existing results concerning Serre's reduction problem. Finally, different consequences of these results are given. All the results obtained in this paper are algorithmic for rings for which Grobner basis techniques exist and the computations can be performed by the Maple packages OreModules and OreMorphisms.

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