Lattice basis reduction : an introduction to the LLL algorithm and its applications /

First developed in the early 1980s by Lenstra, Lenstra, and Lovász, 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 adapte...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Bremner, Murray R.
Format: Electronic eBook
Language:Inglés
Published: Boca Raton, FL : CRC Press, ©2012.
Series:Monographs and textbooks in pure and applied mathematics.
Subjects:
Lattice theory > Textbooks.
Data reduction > Textbooks.
MATHEMATICS > Infinity.
MATHEMATICS > Logic.
Data reduction
Lattice theory
Electronic books.
Textbooks
Online Access:Texto completo (Requiere registro previo con correo institucional)
Table of Contents:
  • 1. Introduction to lattices
  • 2. Two-dimensional lattices
  • 3. Gram-Schmidt orthogonalization
  • 4. The LLL algorithm
  • 5. Deep insertions
  • 6. Linearly dependent vectors
  • 7. The knapsack problem
  • 8. Coppersmith's algorithm
  • 9. Diophantine approximation
  • 10. The Fincke-Pohst algorithm
  • 11. Kannan's algorithm
  • 12. Schnorr's algorithm
  • 13. NP-completeness
  • 14. The hermite normal form
  • 15. Polynomial factorization.

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