Table des matières
Integer Smith Form via the Valence :Experience with large sparse matrices from Homology
Smith form of an integer matrix A ? Zm x n
Motivation
Our Problem : Homology matrices Algebraic topology of simple graphs
4 ? 4 chessboard complex :boundary map of size 96 ? 72between dimensions 1 and 2with AAT and ATA
Smith form computation : State of the art
Idea : work with powers of primes
Contents
Valence Smith Form of a matrix A
Integer Valence computation
Integer minimum polynomial
Degree of the minimum polynomial
How many primes to use ?
Valence Smith Form of a matrix A
Reducing the set L when using B = ATA
Valence Smith Form of a matrix A
Local Smith Form at p : via elimination
Local Smith form at p : Blackbox
Last invariant factor at p : q-adic
Valence Smith Form of a matrix A
Linbox and Athapascan Experiments with Homology matrices
Linbox project (NSF-CNRS)University of Delaware, North Carolina State University, University of Western Ontario, University of Calgary, Laboratoire LMC, Laboratoire ID.
Which interface ?
Athapascan -1 : Parallel Application Programming Interface
Parallel Valence
Parallel Valence algorithm
Homology Valence-only parallel computation
Diapositive PPT
Parallel Wiedemann
Diapositive PPT
Wiedemann algorithm on SMP
Ranks mod 65521 : Wiedemann versus Gauß
Sequential Integer Smith form
Prospects
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Auteur:Jean-Guillaume Dumas
Messagerie: Jean-Guillaume.Dumas@imag.fr
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