Frequently Asked Questions for the Packages of the Mgfun Family

Is it possible to obtain the elements of a computed Gröbner basis in terms of the elements of the original basis?

Yes! This is described by an example in the help page ?Groebner[Groebner_bases_for_modules]. However, this uses calculations of Gröbner bases for modules, whose code contains a bug in Maple V Release 5.

I understand that there is a demand for a separate command, and I will write such a command when I have time in a future version of Mgfun.

Is it possible to compute a generalized Smith normal form for a matrix over linear operators using Gröbner bases?

Hmm... What is definitely possible is to perform Gaussian elimination in a matrix by means of Gröbner bases for modules (see the bug concerning Maple V Release 5). But I do not know whether this extends to a diagonalization procedure. Any suggestion is welcome (Frederic.Chyzak@inria.fr).