Email Gateway (Aug 22 2022 at 10:49): Email Gateway (Aug 22 2022 at 10:49):From: Larry Paulson <lp15@cam.ac.uk>
From the abstract:
"Hermite Normal Form is a canonical matrix analogue of Reduced Echelon Form, but involving matrices over more general rings. In this work we formalise an algorithm to compute the Hermite Normal Form of a matrix by means of elementary row operations, taking advantage of the Echelon Form AFP entry. We have proven the correctness of such an algorithm and refined it to immutable arrays. Furthermore, we have also formalised the uniqueness of the Hermite Normal Form of a matrix. Code can be exported and some examples of execution involving integer matrices and polynomial matrices are presented as well."
It is online here:
http://afp.sourceforge.net/entries/Hermite.shtml
Many thanks to Jose Divasón and Jesús Aransay for this entry, which continues their extensive development of matrix theory.
Larry Paulson
Last updated: Apr 19 2024 at 20:15 UTC