Integer Smith form via the valence: experience with large sparse matrices from homology

Authors:
Jean-Guillaume Dumas;B. David Saunders;Gilles Villard
Affiliations:
Unitée Informatique et, Distribution, B.P. 53 X, 38041, Grenoble Cedex, France;Department of Computer and Information Sciences, University of Delaware, Newark, Delaware;Laboratoire de Modélisation et, Calcul, IMAG, BP 53 F, 38041, Grenoble cedex 9, France
Venue:
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Year:
2000

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Abstract

We present a new algorithm to compute the Integer Smith normal form of large sparse matrices. We reduce the computation of the Smith form to independent, and therefore parallel, computations modulo powers of word-size primes. Consequently, the algorithm does not suffer from coefficient growth. We have implemented several variants of this algorithm (Elimination and/or Black-Box techniques) since practical performance depends strongly on the memory available. Our method has proven useful in algebraic topology for the computation of the homology of some large simplicial complexes.