COMPUTER SIMPLIFICATION OF FORMULAS IN LINEAR-SYSTEMS THEORY

Currently, the three most popular commercial computer algebra systems are Mathematica, Maple, and MACSYMA. These systems provide a wide vari ety of symbolic computation facilities for commutative algebra and con tain implementations of powerful algorithms in that domain. The Grobne r Basis Algorithm, for example, is an important tool used in computati on with commutative algebras and in solving systems of polynomial equa tions, On the other hand, most of the computation involved in linear c ontrol theory is performed on matrices, and these do not commute, A ty pical issue of IEEE TRANSACTIONS ON AUTOMATIC CONTROL is full of linea r systems and computations with their coefficient matrices A B C D's o r partitions of them into block matrices, Mathematica, Maple, and MACS YMA are weak in the area of noncommutative operations, They allow a us er to declare an operation to be noncommutative but provide very fem c ommands for manipulating such operations and no powerful algorithmic t ools, It is the purpose of this paper to report on applications of a p owerful tool, a noncommutative version of the Grobner Basis algorithm, The commutative version of this algorithm is implemented in most majo r computer algebra packages, The noncommutative version is relatively new: [5].