Fast error-free algorithms for polynomial matrix computations

Highly efficient, error-free algorithms are developed for most of the important computations needed in linear systems over fields or rings. It is shown that the structure of the underlying rings and modules is critical in designing such algorithms. The algorithms compute exact Hermite forms of polynomial matrices in the MACSYMA and Mathematica computer algebra languages. A suite of auxiliary programs were written which call on triangularization procedures in order to perform the more high-level tasks arising in the frequency-domain approach to control system synthesis. Simulations were conducted with MACSYMA code running on Texas Instruments Explorer II, and performance results for the triangularization of polynomial matrices are given