Commentary on: solving symbolic equations with PRESS
ACM SIGSAM Bulletin
Towards a general theory of special functions
Communications of the ACM
On square-free decomposition algorithms
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Automatic symbolic solution of differential equations of first order and first degree
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Using basis computation to determine pseudo-multiplicative independence
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Simplification of radical expressions
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
ACM SIGSAM Bulletin
Implications of symbolic computation for the teaching of mathematics
ACM SIGSAM Bulletin
Course outline: Yale University, New Haven
ACM SIGSAM Bulletin
A discussion and implementation of Brown's REX simplification algorithm
ACM SIGSAM Bulletin
Rationally simplifying non-rational expressions
ACM SIGSAM Bulletin
Using matching in algebraic equation solving
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 1
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This thesis consists of essays on several aspects of the problem of algebraic simplification by computer. Since simplification is at the core of most algebraic manipulations, efficient and effective simplification procedures are essential to building useful computer systems for non-numerical mathematics. Efficiency is attained through carefully designed and engineered algorithms, heuristics, and data types, while effectiveness is assured through theoretical considerations. Chapter 1 is an introduction to the field of algebraic manipulation, and serves to place the following chapters in perspective. Chapter 2 reports on an original design for, and programming implementation of, a pattern matching system intended to recognize non-obvious occurrences of patterns within algebraic expressions. A user of such a system can "teach" the computer new simplification rules. Chapter 3 reports on new applications of standard mathematical algorithms used for canonical simplifications of rational expressions. These applications, in combinations, allow a computer system to contain a fair amount of expertise in several areas of algebraic manipulation. Chapter 4 reports on a new, practical, canonical simplification algorithm for radical expressions (i.e. algebraic expressions including roots of polynomials). The effectiveness of the procedure is assured through proofs of appropriate properties of these simplified expressions. Chapter 5 is a brief summary and a discussion of potential research areas. Two appendices describe MACSYMA, a computer system for symbolic manipulation, an effort of some dozen researchers (including the author) which has served as the vehicle for this work.