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Excerpt from Lecture Notes on Lattices, Bases, and the Reduction Problem: Expository Notes The subject of geometry of numbers was developed by Minkowski around the turn of the century. This has been a classical tool in subjects such as integral quadratic forms, diophantine approximations. However, it occupied its renewed role as a powerful tool in Computer Science, after h.w. Lenstra used it to give a polynomial time algorithm for the Integer Programming (feasibility) Problem for fixed number of variables. Since then it has been used to give efficient algorithms in as diverse areas as simultaneous diophan tine approximations, cryptography, solvability by radicals, low density subset sum problem, computing with algebraic numbers, factorization of polynomi als over finite fields. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.