Section: New Results

Serre's reduction of linear functional systems and related problems

Participants : Alban Quadrat, Thomas Cluzeau [ENSIL, Univ. Limoges] .

Given a linear multidimensional system (e.g., ordinary/partial differential systems, differential time-delay systems, difference systems), Serre's reduction aims at finding an equivalent linear multidimensional system which contains fewer equations and fewer unknowns. Finding Serre's reduction of a linear multidimensional system can generally simplify the study of structural properties and of different numerical analysis issues, and it can sometimes help solving the linear multidimensional system in closed form. The connection between Serre's reduction and the decomposition problem [94] , which aims at finding an equivalent linear functional system which is defined by a block diagonal matrix of functional operators, is algorithmically studied in [41] , [42] . Moreover, a characterization of isomorphic finitely presented modules in terms of certain inflations of their presentation matrices is obtained in [42] . This result yields a connection between a certain matrix completion problem and Serre's reduction [42] .