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| Smith normal form of Laurent Polynomial matrices https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2498 |
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| Author: | Yoann [ Wed Jun 03, 2015 1:35 am ] |
| Post subject: | Smith normal form of Laurent Polynomial matrices |
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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| Author: | levandov [ Thu Oct 01, 2015 4:17 pm ] |
| Post subject: | Re: Smith normal form of Laurent Polynomial matrices |
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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