Lattice of ℤ-module

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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].

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Formalized Mathematics

(a computer assisted approach)

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Source Normalized Impact per Paper (SNIP) 2017: 0.237



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researchers in the fields of formal methods and computer-checked mathematics

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