In this article we formalize a free ℤ-module and its rank. We formally prove that for a free finite rank ℤ-module V , the number of elements in its basis, that is a rank of the ℤ-module, is constant regardless of the selection of its basis. ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [15]. Some theorems in this article are described by translating theorems in [21] and [8] into theorems of Z-module.
@article{bwmeta1.element.doi-10_2478_v10037-012-0033-x,
author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama},
title = {Free $\mathbb{Z}$-module},
journal = {Formalized Mathematics},
volume = {20},
year = {2012},
pages = {275-280},
zbl = {06213848},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0033-x}
}
Yuichi Futa; Hiroyuki Okazaki; Yasunari Shidama. Free ℤ-module. Formalized Mathematics, Tome 20 (2012) pp. 275-280. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0033-x/
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