A new incremental algorithm for computing Groebner bases. (English) Zbl 1321.68531
Watt, Stephen M. (ed.), Proceedings of the 35th international symposium on symbolic and algebraic computation, ISSAC 2010, Munich, Germany, July 25–28, 2010. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0150-3). 13-19 (2010).
MSC:
| 68W30 | Symbolic computation and algebraic computation |
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
References:
| [1] | B. Buchberger, Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, PhD thesis, Innsbruck, 1965. · Zbl 1245.13020 |
| [2] | B. Buchberger, “A Criterion for Detecting Unnecessary Reductions in the Construction of Gröbner Basis,” In Proc. EUROSAM 79 (1979), vol. 72 of Lect. Notes in Comp. Sci., Springer Verlag, 3-21. · Zbl 0417.68029 |
| [3] | B. Buchberger, “Gröbner Bases: an Algorithmic Method in Polynomial Ideal Theory,” In Recent trends in multidimensional system theory, Ed. Bose, 1985. |
| [4] | J. Buchmann, D. Cabarcas, J. Ding, M. S. E. Mohamed, “Flexible Partial Enlargement to Accelerate Grobner Basis Computation over F2,” AFRICACRYPT 2010, May 03-06, 2010, Stellenbosch, South Africa, to be published in LNCS by Springer 10.1007/978-3-642-12678-9_5 |
| [5] | N. Courtois, A. Klimov, J. Patarin, and A. Shamir, “Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations,” in Proceedings of International Conference on the Theory and Application of Cryptographic Techniques (EUROCRYPT), volume 1807 of Lecture Notes in Computer Science, pages 392-407, Bruges, Belgium, May 2000. Springer. · Zbl 1082.94514 |
| [6] | D. Cox, J. Little and D. O’Shea, Using algebraic geometry, Graduate Texts in Mathematics, 185. Springer-Verlag, New York, 1998. · Zbl 0920.13026 |
| [7] | J. Ding, J. Buchmann, M. S. E. Mohamed, W. S. A. M. Mohamed, R. Weinmann, “Mutant XL,” First International Conference on Symbolic Computation and Cryptography, SCC 2008 |
| [8] | C. Eder and J. Perry, “F5C: a variant of Faugère”s F5 algorithm with reduced Gröbner bases,” arXiv: 0906.2967v5, July 2009. |
| [9] | J.-C. Faugère, “A new efficient algorithm for computing Gröbner bases (F4),” Effective methods in algebraic geometry (Saint-Malo, 1998), J. Pure Appl. Algebra 139 (1999), no. 1-3, 61-88. · Zbl 0930.68174 |
| [10] | J.-C. Faugère, “A new efficient algorithm for computing Gröbner bases without reduction to zero (F5),” Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, 75-83 (electronic), ACM, New York, 2002. 10.1145/780506.780516 · Zbl 1072.68664 |
| [11] | A. Joux and V. Vitse, “A variant of the F4 algorithm,” preprint 2010. http://eprint.iacr.org/2010/158. |
| [12] | A. Kehrein and M. Kreuzer, “Computation of Border Bases,” J. Pure Appl. Algebra 205 (2006), 279-295. · Zbl 1097.13036 |
| [13] | D. Lazard, “Gaussian Elimination and Resolution of Systems of Algebraic Equations,” in Proc. EUROCAL 83 (1983), vol. 162 of Lect. Notes in Comp. Sci, 146-157. · Zbl 0539.13002 |
| [14] | F. Macaulay, “Some formulae in elimination,” Proceedings of London Mathematical Society (1902), 3-38. |
| [15] | M. S. E. Mohamed, D. D. Cabarcas, J. Ding, J. Buchmann and S. Bulygin, “MXL3: An efficient algorithm for computing Groebner bases of zero-dimensional ideals,” the 12th International Conference on Information Security and Cryptology (ICISC 2009), Dec. 2009, Seoul, Korea. (To be published in LNCS by Springer). |
| [16] | M. S. E. Mohamed, W. S. A. E. Mohamed, J. Ding, J. Buchmann, “MXL2: Solving Polynomial Equations over GF(2) Using an Improved Mutant Strategy,” PQCrypto 2008: 203-215, LNCS 5299, Springer 2008 10.1007/978-3-540-88403-3_14 · Zbl 1177.11094 |
| [17] | Y. Sun and D. K. Wang, “A New Proof of the F5 Algorithm,” preprint 2009. http://www.mmrc.iss.ac.cn/pub/mm28.pdf/06-F5Proof.pdf |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
