Algorithms for Large Integer Matrix Problems

Abstract. New algorithms are described and analysed for solving various problems associated with a large integer matrix: computing the Hermite form, computing a kernel basis, and solving a system of linear diophantine equations. The algorithms are space-efficient and for certain types of input matrices — for example, those arising during the computation of class groups and regulators — are faster than previous methods. Experiments with a prototype implementation support the running time analyses.

• Type: Conference
• Year: 2001
• Where: AAECC
• Authors: Mark Giesbrecht, Michael J. Jacobson Jr., Arne Storjohann
• Keywords: AAECC 2001, Algorithms, Large Integer Matrix, Linear Diophantine Equations, Prototype Implementation Support