Posted Jul 1, 1996

Computer Assistance in Discovering Formulas and Theorems in System Engineering

By J. William Helton and Mark Stankus

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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 noncommuting 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.

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