TY - GEN

T1 - Scratchpad's view of algebra I: Basic commutative algebra

AU - Davenport, James H

AU - Trager, B. M.

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

UR - http://dx.doi.org/10.1007/3-540-52531-9_122

U2 - 10.1007/3-540-52531-9_122

DO - 10.1007/3-540-52531-9_122

M3 - Chapter in a published conference proceeding

SN - 9783540525318

T3 - Lecture Notes in Computer Science

SP - 40

EP - 54

BT - Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90 Capri, Italy, April 10–12, 1990 Proceedings

PB - Springer

CY - Berlin

T2 - Design and Implementation of Symbolic Computation Systems: International Symposium DISCO '90

Y2 - 9 April 1990 through 11 April 1990

ER -