Hermite Normal Form
ISSN: 2150-914X
Argitalpen urtea: 2015
Alea: 2015
Orrialdeak: 1-54
Mota: Artikulua
Beste argitalpen batzuk: Archive of Formal Proofs
Lotura duten proiektuak
Laburpena
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.