Modular algorithms for computing Gröbner bases

Journal of Symbolic Computation

Volumn 35, Issue 4, 2003, Pages 403-419

  Arnold, Elizabeth A ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038743196     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0747-7171(02)00140-2     Document Type: Article

References (19)

1. Adams, W.W., Loustaunau, P., 1994. An Introduction to Gröbner Bases, American Mathematical Society, Providence, RI.
2. Arnold, E.A., 2000. Computing Gröbner Bases with Hilbert Lucky Primes, Ph.D. Dissertation, University of Maryland, College Park, MD.
3. Borosh, I., 1966. Exact solutions of linear equations with rational coefficients by congruence techniques. Mathematics of Computation 20, 107-112.
4. Buchberger, B., 1979. A criterion for detecting unnecessary reductions in the construction of Gröbner-bases, Lecture Notes in Computer Science, vol. 72, pp. 23-21.
5. Buchberger, B., 1985. Gröbner-bases: an algorithmic method in polynomial ideal theory, In: Multidimensional Systems Theory, pp. 184-232.
6. Capani, A., Niesi, G., Robbiano, L., 2001. CoCoA, a system for doing Computations in Commutative Algebra. Available via anonymous ftp from cocoa.dima.unige.it, ed. 4. 1.
7. Davenport, J.H., Siret, Y., Tournier, E., 1988. Computer Algebra: Systems and algorithms for algebraic computation, Academic Press.
8. Ebert, G.L., 1983. Some comments on the modular approach to Gröbner-bases. ACM SIGSAM Bulletin 17, 28-32.
9. Eisenbud, D., 1995. Commutative Algebra with a view toward Algebraic Geometry, Springer-Verlag.
10. Gebauer, R., Möller, H.M., 1988. On an installation of Buchberger's algorithm. Journal of Symbolic Computation 6, 275-286.
11. Gräbe, H., 1994. On lucky primes. Journal of Symbolic Computation 15, 199-209.
12. Kornerup, P., Gregory, R., 1983. Mapping integers and Hensel codes onto Farey fractions. Bit 23, 9-20.
13. Grayson, D., Stillman, M., 2000. Macaulay 2, Available via anonymous ftp from ftp.math.uiuc.edu,ed. 0.8.60.
14. Möller, H.M., Mora, R, 1984. Upper and lower bounds for the degree of Groebner bases, Eurosam '84, Lecture Notes in Computer Science, vol. 174, pp. 172-183.
15. Pauer, F., 1992. On lucky ideals for Gröbner basis computations. Journal of Symbolic Computation 14, 471-482.
16. Sasaki, T., Takeshima, T., 1989. A modular method for Gröbner-basis construction over ℚ and solving system of algebraic equations. Journal of Information Processing 12, 371-379.
17. Traverso, C., 1988. Gröbner Trace Algorithms, Proceedings ISSAC '88, Lecture notes in Computer Science, vol. 358, pp. 125-138.
18. Traverso, C., 1997. Hilbert functions and the Buchberger's algorithm. Journal of Symbolic Computation 22, 355-376.
19. Winkler, F., 1987. A p-adic approach to the computation of Gröbner bases. Journal of Symbolic Computation 6, 287-304.