# Symbolic Computation Group Seminar

2011 Sep 16 at 13:30

DC 1304

## Exact Linear Algebra in LinBox, a status report

B. David Saunders, University of Delaware, USA

LinBox is a C++ library for high performance exact linear algebra that has been in development for two decades. It was created to implement a family of algorithms known as blackbox methods. It has come to also encompass Gaussian elimination based methods. Problems solved include linear system solution, diophantine system solution, rank, determinant, minimal polynomial, characteristic polynomial, Frobenius form, Smith form, nullspace basis, sample nullspace.

For matrices over Z or Q, algorithms using homomorphic images dominate. In support of that LinBox has extensive capability for matrices over GF(q), where q is a word-size prime, as well as specialized features for q very small (such as 2, 3), and for q a prime power. Finally, there is some capability for matrices over Z/nZ.

In this talk I will sketch the core features of linbox, regarding both algorithms and software design. I will offer a ``to do'' list of developments in the works or soon to be started or wished that someone would start. For each list item, I will sketch the motivation and the issues that seem to be involved.