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 Post subject: Smith normal form of Laurent Polynomial matrices
PostPosted: Wed Jun 03, 2015 1:35 am 
Hi,

I need help to diagonalize a matrix with entries Laurent polynomial. Hence, I work with matrices in the PID Q[t,t^{-1}]. Does anybody know how can I do?
Because I found documentation about the diagonalization of matrices but not on the Laurent polynomial ring, which I don't know how to declare on Singular!

Thank you very much for your help,

Yoann


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 Post subject: Re: Smith normal form of Laurent Polynomial matrices
PostPosted: Thu Oct 01, 2015 4:17 pm 

Joined: Thu Aug 11, 2005 8:03 pm
Posts: 37
Location: RWTH Aachen, Germany
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.2011.12.042

Viktor 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.2010.10.009

and 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


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