A new view on HJLS and PSLQ: sums and projections of lattices

Authors:
Jingwei Chen;Damien Stehlé;Gilles Villard
Affiliations:
Chengdu Institute of Computer Application, CAS, Chengdu, China;CNRS, ENS de Lyon, Inria UCBL, Université de Lyon, Laboratoire LIP, Lyon, France;CNRS, ENS de Lyon, Inria UCBL, Université de Lyon, Laboratoire LIP, Lyon, France
Venue:
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Year:
2013

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Abstract

The HJLS and PSLQ algorithms are the de facto standards for discovering non-trivial integer relations between a given tuple of real numbers. In this work, we provide a new interpretation of these algorithms, in a more general and powerful algebraic setup: we view them as special cases of algorithms that compute the intersection between a lattice and a vector subspace. Further, we extract from them the first algorithm for manipulating finitely generated additive subgroups of a euclidean space, including projections of lattices and finite sums of lattices. We adapt the analyses of HJLS and PSLQ to derive correctness and convergence guarantees.