Bøker av Murray R. Bremner

First realized in the 1980s by Lenstra, Lenstra, and Lovasz, the LLL algorithm was originally intended to factor polynomials with rational coefficients. It improved upon the existing lattice reduction algorithm in order to solve integer linear programming problems and was later adapted for use in crypanalysis. This book provides an introduction

This book presents a systematic treatment of Gröbner bases in several contexts. The book builds up to the theory of Gröbner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. Throughout the book, both the mathematical theory and computational methods ar

This book presents a systematic treatment of Gröbner bases in several contexts. The book builds up to the theory of Gröbner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. Throughout the book, both the mathematical theory and computational methods are emphasized and numerous algorithms, examples, and exercises are provided to clarify and illustrate the concrete meaning of abstract theory.

First developed in the early 1980s by Lenstra, Lenstra, and Lov sz, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial factorization, and matrix canonical forms.