This package computes maximal vectors, the Frobenius normal form and
the Jordan-Chevalley decomposition of a (square) matrix over any field
that is available in GAP. In particular, it extends the already existing
GAP function MininmalPolynomial by computing also a vector whose local
minimal polynomial is equal to the minimal polynomial of a given matrix.
To install the package, just unpack the tar file inside the pkg directory of your GAP installation.
Then you can load the package into GAP by typing LoadPackge("nofoma");
The algorithms in this package are based on, and a combination of:
- K. Bongartz, A direct approach to the rational normal form, preprint available at arXiv:1410.1683.
- M. Neunhoeffer and C. E. Praeger, Computing minimal polynomials of matrices, LMS J. Comput. Math. 11 (2008), 252-279;
- M. Geck, On Jacob's construction of the rational canonical form, Electron. J. Linear Algebra 36 (2020), 177-182.
- M. Geck, On the Jordan-Chevalley decomposition of a matrix, preprint.
If you have any bug reports, feature requests, or suggestions, then please tell us via the issue tracker on GitHub.
The nofoma package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.