Hi Yoann,
it is in principle possible but there's no ready-to-use solution (as far as
I can see). The technology is described in two papers:
Viktor Levandovskyy and Kristina Schindelar : Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases . Journal of Symbolic Computation 47,10 (2012), 1214-1232
http://dx.doi.org/10.1016/j.jsc.2011.12.042Viktor Levandovskyy and Kristina Schindelar : Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases . Journal of Symbolic Computation 46,5 (2011), 595-608
http://dx.doi.org/10.1016/j.jsc.2010.10.009and implemented in jacobson_lib (see D.11 System and Control theory
in the Manual). Actually the procedure smith from jacobson_lib
has a built-in restriction that the basering should contain only one
variable. However, this is not crucial for the Laurent situation, since
the latter is a PID. One has to look at the code; it makes an interesting
research+implementation project (do you wish to embark
on that?). Feel free to contact me.
Cheers,
Viktor Levandovskyy