Scratchpad's view of algebra I: Basic commutative algebra

James H Davenport, B. M. Trager

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Abstract

While computer algebra systems have dealt with polynomials and rational functions with integer coefficients for many years, dealing with more general constructs from commutative algebra is a more recent problem. In this paper we explain how one system solves this problem, what types and operators it is necessary to introduce and, in short, how one can construct a computational theory of commutative algebra. Of necessity, such a theory is rather different from the conventional, non-constructive, theory. It is also somewhat different from the theories of Seidenberg [1974] and his school, who are not particularly concerned with practical questions of efficiency.
Original languageEnglish
Title of host publicationDesign and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings
Place of PublicationBerlin
PublisherSpringer
Pages40-54
ISBN (Print)9783540525318
DOIs
Publication statusPublished - 1990
EventDesign and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 - Capri, Italy
Duration: 9 Apr 199011 Apr 1990

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume429/1990
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceDesign and Implementation of Symbolic Computation Systems: International Symposium DISCO '90
CountryItaly
CityCapri
Period9/04/9011/04/90

Fingerprint

Basic Algebra
Commutative Algebra
Algebra
Computer algebra system
Polynomial function
Rational function
Integer
Necessary
Coefficient
Operator

Cite this

Davenport, J. H., & Trager, B. M. (1990). Scratchpad's view of algebra I: Basic commutative algebra. In Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings (pp. 40-54). (Lecture Notes in Computer Science; Vol. 429/1990). Berlin: Springer. https://doi.org/10.1007/3-540-52531-9_122

Scratchpad's view of algebra I: Basic commutative algebra. / Davenport, James H; Trager, B. M.

Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings. Berlin : Springer, 1990. p. 40-54 (Lecture Notes in Computer Science; Vol. 429/1990).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Davenport, JH & Trager, BM 1990, Scratchpad's view of algebra I: Basic commutative algebra. in Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings. Lecture Notes in Computer Science, vol. 429/1990, Springer, Berlin, pp. 40-54, Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 , Capri, Italy, 9/04/90. https://doi.org/10.1007/3-540-52531-9_122
Davenport JH, Trager BM. Scratchpad's view of algebra I: Basic commutative algebra. In Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings. Berlin: Springer. 1990. p. 40-54. (Lecture Notes in Computer Science). https://doi.org/10.1007/3-540-52531-9_122
Davenport, James H ; Trager, B. M. / Scratchpad's view of algebra I: Basic commutative algebra. Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings. Berlin : Springer, 1990. pp. 40-54 (Lecture Notes in Computer Science).
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