Results 11  20
of
349
Analysis of PSLQ, An Integer Relation Finding Algorithm
 Mathematics of Computation
, 1999
"... Let K be either the real, complex, or quaternion number system and let O(K) be the corresponding integers. Let × = (Xl, • • • , ×n) be a vector in K n. The vector × has an integer relation if there exists a vector m = (ml,..., mn) E O(K) n, m = _ O, such that mlx I + m2x 2 +... + mnXn = O. In th ..."
Abstract

Cited by 69 (27 self)
 Add to MetaCart
Let K be either the real, complex, or quaternion number system and let O(K) be the corresponding integers. Let × = (Xl, • • • , ×n) be a vector in K n. The vector × has an integer relation if there exists a vector m = (ml,..., mn) E O(K) n, m = _ O, such that mlx I + m2x 2 +... + mnXn = O. In this paper we define the parameterized integer relation construction algorithm PSLQ(r), where the parameter rcan be freely chosen in a certain interval. Beginning with an arbitrary vector X = (Xl,..., Xn) _ K n, iterations of PSLQ(r) will produce lower bounds on the norm of any possible relation for X. Thus PS/Q(r) can be used to prove that there are no relations for × of norm less than a given size. Let M x be the smallest norm of any relation for ×. For the real and complex case and each fixed parameter rin a certain interval, we prove that PSLQ(r) constructs a relation in less than O(fl 3 + n 2 log Mx) iterations.
lrs: A Revised Implementation of the Reverse Search Vertex Enumeration Algorithm
 Polytopes – Combinatorics and Computation
, 2000
"... This paper describes an improved implementation of the reverse search vertex enumeration/convex hull algorithm for ddimensional convex polyhedra. The implementation uses a lexicographic ratio test to resolve degeneracy, works on bounded or unbounded polyhedra and uses exact arithmetic with all int ..."
Abstract

Cited by 58 (3 self)
 Add to MetaCart
(Show Context)
This paper describes an improved implementation of the reverse search vertex enumeration/convex hull algorithm for ddimensional convex polyhedra. The implementation uses a lexicographic ratio test to resolve degeneracy, works on bounded or unbounded polyhedra and uses exact arithmetic with all integer pivoting. It can also be used to compute the volume of the convex hull of a set of points. For a polyhedron with m inequalities in d variables and known extreme point, it finds all bases in time O(md2) per basis. This implementation can handle problems of quite large size, especially for simple polyhedra (where each basis corresponds to a vertex and the complexity reduces to O(md) per vertex). Computational experience is included in the paper, including a comparison with an earlier implementation. 1.
Testing Modules for Irreducibility
 J. Austral. Math. Soc. Ser. A
, 1994
"... A practical method is described for deciding whether or not a finitedimensional module for a group over a finite field is reducible or not. In the reducible case, an explicit submodule is found. The method is a generalisation of the ParkerNorton `Meataxe' algorithm, but it does not depend for ..."
Abstract

Cited by 46 (2 self)
 Add to MetaCart
A practical method is described for deciding whether or not a finitedimensional module for a group over a finite field is reducible or not. In the reducible case, an explicit submodule is found. The method is a generalisation of the ParkerNorton `Meataxe' algorithm, but it does not depend for its efficiency on the field being small. The principal tools involved are the calculation of the nullspace and the characteristic polynomial of a matrix over a finite field, and the factorisation of the latter. Related algorithms to determine absolute irreducibility and module isomorphism for irreducibles are also described. Details of an implementation in the GAP system, together with some performance analyses are included. 1991 Mathematics subject classification (Amer. Math. Soc.): 20C40, 2004. 1 Introduction The purpose of this paper is to describe a practical method for deciding whether or not a finite dimensional FGmodule M is irreducible, where F = GF (q) is a finite field and G is a fi...
Enclaves: Enabling Secure Collaboration over the Internet
 IEEE Journal on Selected Areas in Communications
, 1996
"... The rapid expansion of the Internet means that users increasingly want to interact with each other. Due to the openness and unsecure nature of the net, users often have to rely on firewalls to protect their connections. Firewalls, however, make realtime interaction and collaboration more difficult. ..."
Abstract

Cited by 41 (0 self)
 Add to MetaCart
(Show Context)
The rapid expansion of the Internet means that users increasingly want to interact with each other. Due to the openness and unsecure nature of the net, users often have to rely on firewalls to protect their connections. Firewalls, however, make realtime interaction and collaboration more difficult. Firewalls are also complicated to configure and expensive to install and maintain, and are inaccessible to small home offices and mobile users. The Enclaves approach is to transform user machines into "enclaves," which are protected from outside interference and attacks. Using Enclaves, a group of collaborators can dynamically form a secure virtual subnet within which to conduct their joint business. This paper describes the design and implementation of the Enclaves toolkit, and some applications we have built using the toolkit. 1 Motivation Most user interaction and collaboration over the Internet have been primarily via electronic mail. More recently, groupware applications including tel...
A recognition algorithm for special linear groups
 Proc. London Math. Soc
, 1992
"... Neubiiser asked for an efficient algorithm to decide whether the subgroup of the general linear group GL(d, q) generated by a given set X of nonsingular d X d matrices over a finite field ¥q contains the special linear group SL(rf, q). ..."
Abstract

Cited by 40 (1 self)
 Add to MetaCart
Neubiiser asked for an efficient algorithm to decide whether the subgroup of the general linear group GL(d, q) generated by a given set X of nonsingular d X d matrices over a finite field ¥q contains the special linear group SL(rf, q).
TestU01: A C library for empirical testing of random number generators
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 2007
"... We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several ot ..."
Abstract

Cited by 35 (1 self)
 Add to MetaCart
We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several others tests proposed in the literature, and some original ones. Predefined tests suites for sequences of uniform random numbers over the interval (0, 1) and for bit sequences are available. Tools are also offered to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator’s period length, before the generator starts to fail the test systematically. Finally, the library provides various types of generators implemented in generic form, as well as many specific generators proposed in the literature or found in widelyused software. The tests can be applied to instances of the generators predefined in the library, or to userdefined generators, or to streams of random numbers produced by any kind of device or stored in files. Besides introducing TestU01, the paper provides a survey and a classification of statistical tests for RNGs. It also applies batteries of tests to a long list of widely used RNGs.
Uniform Random Generation of Decomposable Structures Using FloatingPoint Arithmetic
 THEORETICAL COMPUTER SCIENCE
, 1997
"... The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to floatingpoint arithmetic. The resulting ADZ method enables one to generate decomposable data structures  both labelled or unlabelled  uniformly at random, ..."
Abstract

Cited by 34 (2 self)
 Add to MetaCart
The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to floatingpoint arithmetic. The resulting ADZ method enables one to generate decomposable data structures  both labelled or unlabelled  uniformly at random, in expected O(n 1+ffl ) time and space, after a preprocessing phase of O(n 2+ffl ) time, which reduces to O(n 1+ffl ) for contextfree grammars.
Constructing hyperelliptic curves of genus 2 suitable for cryptography
 Math. Comp
, 2003
"... Abstract. In this article we show how to generalize the CMmethod for elliptic curves to genus two. We describe the algorithm in detail and discuss the results of our implementation. 1. ..."
Abstract

Cited by 31 (2 self)
 Add to MetaCart
(Show Context)
Abstract. In this article we show how to generalize the CMmethod for elliptic curves to genus two. We describe the algorithm in detail and discuss the results of our implementation. 1.