Hermite Normal Form
نویسندگان
چکیده
The 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 Z-matrices and K[x]-matrices are presented as well.
منابع مشابه
Lecture : Integer Programming , Spring 2010
2 Euclidean Algorithm and Hermite Normal Form 9 2.1 Sizes of Rational Numbers and Polynomial Complexity . . . . . . . . . . . . 9 2.2 Computing the GCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Computing the Hermite Normal Form . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Lattices and the Hermite Normal Form . . . . . . . . . . . . . . . . . . . . . 15 2.5 Dual ...
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عنوان ژورنال:
- Archive of Formal Proofs
دوره 2015 شماره
صفحات -
تاریخ انتشار 2015