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Lattice of ℤ-module

2016; De Gruyter Open; Volume: 24; Issue: 1 Linguagem: Inglês

10.1515/forma-2016-0005

1898-9934

Yuichi Futa, Yasunari Shidama,

graph theory and CDMA systems

Summary In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9].