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研究生学术研讨会:Simpler termination proof of generalized algorithm for computing Gröbner bases

发布时间:2014-03-14 浏览:

http://ste.xidian.edu.cn/seminar/?p=13

报告题目:
Simpler termination proof of generalized algorithm for
computing Gröbner bases
报告时间:2014-03-21 11:00:00
报告地点:老科技楼B301
报告人:潘森杉
导师:胡予濮
报告摘要:A more generalized F5GEN algorithm than the previous version is proposed in this paper. This F5GEN algorithm can cover popular non-incremental algorithms. Furthermore, it also covers F5 when inputs are homogeneous polynomials. That is, if F5 with breaking ties among Rules of the same degree are considered as instances, F5GEN contains all possible instances of F5. Much simpler termination proof here is a convenient tool for us to deal with other algorithms. We give an example showing that a F5GEN’s instance does not belong to F5. Moreover, this instance can generate a smaller basis than any instance of F5, which is non-trivial since it was not ensured that F5GEN has any better algorithm than F5 just because F5GEN is more general.
支撑材料:1、 Pan, S., Hu, Y., Wang, B.: The termination of the F5 algorithm revisited. In Proc. ISSAC ’13, pp. 291–298. New York, USA (2013).