Computer assistance in discovering formulas and theorems in system engineering
J. William Helton, M. Stankus · 2002
We deal with 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 using 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. The approach we use to manipulate large collections of equations is based largely on a noncommutative Grobner basis algorithm (GBA), and the program we use is based upon a GBA, called NCProcess.