Published in Proceedings of the 34th Conference on Decision and Control, New Orleans, LA, December 13, 1995, pages 303-306.
Copyright © 1995 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. The definitive version is available at http://dx.doi.org/10.1109/CDC.1995.478746.
NOTE: At the time of publication, the author Mark Stankus was not yet affiliated with Cal Poly.
If one reads a typical article on A,B,C,D systems in the control transactions, one finds that most of the algebra involved is non commutative rather than commutative. Thus, for symbolic computing to have much impact on linear systems research, one needs a program which will do non-commuting operations. Mathematica, Macsyma and Maple do not. We have a package, NCAlgebra, which runs under Mathematica which does the basic operations, block matrix manipulations and other things. The package might be seen as a competitor to a yellow pad. Like Mathematica the emphasis is on interaction with the program and flexibility.
The issue now is what types of “intelligence” to put in the package. [HSW] (CDC94) focused on procedures for simplifying complicated expressions automatically. In this talk we turn to a much more adventurous pursuit which is in a primitive stage. This is a highly computer assisted method for discovering certain types of theorems.
At the beginning of “discovering” a theorem, an engineering problem is often presented as a large system of matrix equations. The point is to isolate and to minimize what the user must do by running heavy algorithms. Often when viewing the output of the algorithm, one can see what additional hypothesis should be added to produce a useful theorem and what the relevant matrix quantities are.
Rather than use the word “algorithm”, we call our method a strategy since it allows for modest human intervention. We are under the impression that many theorems in engineering systems might be derivable in this way.