Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
On rank properties of Toeplitz matrices over finite fields
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Sign determination in residue number systems
Theoretical Computer Science - Special issue on real numbers and computers
On Wiedemann's Method of Solving Sparse Linear Systems
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
An output-sensitive variant of the baby steps/giant steps determinant algorithm
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Early termination over small fields
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Smith normal form of dense integer matrices fast algorithms into practice
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Numerical techniques for computing the inertia of products of matrices of rational numbers
Proceedings of the 2007 international workshop on Symbolic-numeric computation
On the generation of positivstellensatz witnesses in degenerate cases
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
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A key step in the computation of the unitary dual of a Lie group is the determination if certain rational symmetric matrices are positive semi-definite. The size of some of the computations dictates that high performance integer matrix computations be used. We explore the feasibility of this approach by developing three algorithms for integer symmetric matrix signature and studying their performance both asymptotically and experimentally on a particular matrix family constructed from the exceptional Weyl group E8. We conclude that the computation is doable, with a parallel implementation needed for the largest representations.