Séminaire Calcul Formel

Presenting isomorphic finitely presented modules by equivalent matrices: a constructive approach

by Dr Cyrille Chenavier (Université de Limoges)




 A multidimensional linear system can be studied by means of its
associated module, presented by the unknown functions of this system
subject to the equations. Testing whether two linear systems/modules are
isomorphic (the so-called equivalence problem) is an important issue. In
this presentation, I will first recall from a previous work of
Thomas Cluzeau and Alban Quadrat an explicit characterisation for a
module morphism to be an isomorphism. Then, I will recall how they
obtained a constructive version of a result due to Fitting, which shows
how to enlarge matrices presenting isomorphic modules by blocks of zeros
and identities to get equivalent matrices. Finally, I will present an
inductive procedure for reducing the size of these two equivalent
matrices. It turns out that this procedure enables us to recover a result
due to Warfield.