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 -