The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
A Sorting Algorithm for Polynomial Multiplication
Journal of the ACM (JACM)
ACM SIGSAM Bulletin
LISP 1.5 Programmer's Manual
Parallel multiplication and powering of polynomials
Journal of Symbolic Computation
Canonical representations in Lisp and applications to computer algebra systems
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Lively linear Lisp: “look ma, no garbage!”
ACM SIGPLAN Notices
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Design of a Lisp machine - FLATS
LFP '82 Proceedings of the 1982 ACM symposium on LISP and functional programming
FLATS, a machine for numerical, symbolic and associative computing
ISCA '79 Proceedings of the 6th annual symposium on Computer architecture
Universal classes of hash functions (Extended Abstract)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
In memoriam: Professor Eiichi Goto
ACM SIGSAM Bulletin
Evaluation of Associative Memory Using Parallel Chained Hashing
IEEE Transactions on Computers
Flats, a machine for numerical, symbolic and associative computing
IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 2
Ways to implement computer algebra compactly
ACM Communications in Computer Algebra
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In this paper, time complexities of operation on “sets” and “ordered n-tuples” based on a hashing table search technique are presented as “Hashing LEMMAs” and are applied to formula manipulation. Unique normal forms for multivariate symbolic formulas resulting in O(1) time complexity for identity checks are presented. The logarithmic factor log2N, characteristic to sorting algorithms, is shown to all disappear from time complexities of polynomial manipulations. Actual implementation of the hashing technique is outlined and actual timing data are presented in the appendix.