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Matrix of ℤ-module1

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Futa Y., Okazaki H., Shidama Y.

Formalized Mathematics

2015

tom 23

nr 1

29-49

In this article, we formalize a matrix of ℤ-module and its properties. Specially, we formalize a matrix of a linear transformation of ℤ-module, a bilinear form and a matrix of the bilinear form (Gramian matrix). We formally prove that for a finite-rank free ℤ-module V, determinant of its Gramian matrix is constant regardless of selection of its basis. ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattices [22] and coding theory [14]. Some theorems in this article are described by translating theorems in [24], [26] and [19] into theorems of ℤ-module.

Ograniczanie wyników

1 Formalized Mathematics

1 Futa Y.

1 Okazaki H.

1 Shidama Y.

1 2015

Wyniki wyszukiwania

Matrix of ℤ-module1