Space-efficient Gröbner basis computation without degree bounds

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn , Issue , 2011, Pages 257-264

  Mayr, Ernst W ^a   Ritscher, Stephan ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Gr bner basis; ideal dimension; macaulay matrix; multivariate polynomial; polynomial ideal; s criterion; space complexity

Indexed keywords

IDEAL DIMENSION; MATRIX; MULTIVARIATE POLYNOMIAL; S-CRITERION; SPACE COMPLEXITY;

POLYNOMIALS;

ALGORITHMS;

EID: 79959630960     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1993886.1993926     Document Type: Conference Paper

References (19)

1. A. Borodin. On relating time and space to size and depth. SIAM Journal on Computing, 6(4):733-744, 1977.
2. A. Borodin, S. Cook, and N. Pippenger. Parallel computation for well-endowed rings and space-bounded probabilistic machines. Information and Control, 58(1-3):113-136, 1983. (Pubitemid 14600674) (Pubitemid 14600674)
3. B. Buchberger. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, Universität Innsbruck, Austria, 1965.
4. B. Buchberger. Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Journal of Symbolic Computation, 41(3-4):475-511, 2006.
5. A. Y. Chiu. Complexity of Parallel Arithmetic Using the Chinese Remainder Representation. PhD thesis, The University of Wisconsin-Milwaukee, WI, USA, 1995.
6. D. A. Cox, J. B. Little, and D. O'Shea. Ideals, Varieties, and Algorithms. Springer New York, 1992.
7. D. A. Cox, J. B. Little, and D. O'Shea. Using Algebraic Geometry. Springer, 2005.
8. A. Dickenstein, N. Fitchas, M. Giusti, and C. Sessa. The membership problem for unmixed polynomial ideals is solvable in single exponential time. Discrete Applied Mathematics, 33(1-3):73-94, 1991.
9. T. W. Dubé. The Structure of Polynomial Ideals and Gröbner Bases. SIAM Journal on Computing, 19(4):750-773, 1990.
10. J. C. Faugère. A new efficient algorithm for computing Gröbner bases (F4). Journal of Pure Applied Algebra, 139:61-88, 1999.
11. J. C. Faugère. A new efficient algorithm for computing Gröbner bases without reduction to zero (F5). In Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, pages 75-83. ACM, 2002.
12. G. Hermann. Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Mathematische Annalen, 95(1):736-788, 1926.
13. M. Kratzer. Computing the dimension of a polynomial ideal and membership in low-dimensional ideals. Master's thesis, Technische Universität München, Germany, October 2008.
14. M. Kreuzer and L. Robbiano. Computational Commutative Algebra 1. Springer, 2000.
15. M. Kreuzer and L. Robbiano. Computational Commutative Algebra 2. Springer, 2005.
16. T. Krick and A. Logar. Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals. In Effective Methods in Algebraic Geometry, pages 203-216. Birkhauser, 1991.
17. K. Kühnle and E. W. Mayr. Exponential space computation of Gröbner bases. In Proceedings of the 1996 international symposium on Symbolic and algebraic computation, pages 63-71. ACM New York, NY, USA, 1996.
18. E. W. Mayr and A. R. Meyer. The complexity of the word problems for commutative semigroups and polynomial ideals. Advances in Mathematics, 46(3):305-329, 1982.
19. E. W. Mayr and S. Ritscher. Degree bounds for Gröbner bases of low-dimensional polynomial ideals. In Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, pages 21-27. ACM, 2010.