The goal of this project is the improvement of the implemented and available software for solution of a variety of matrix computation problems, including solution of systems of parameterized linear equations, solution of systems of linear equations over a polynomial function domain, matrix normal form computations, and determination of matrix similarity and equivalence. Such tools are a heavily used portion of computer algebra packages such as Maple, Mathematica, and Magma. Also they are relevant to custom large scale applications. The research will focus on (1) algorithm design, (2) parallel and distributed implementation, and (3) use of heuristics. An explicit goal of this work is to provide implementations that are directly usable by the scientific community. Such implementations will include stand-alone portable codes and code to be included in the libraries of one or more of the generally available computer algebra systems. In this sense this work will enhance the problem solving environments available for scientific and engineering computation.
