An Algorithm for Computing Relative Groebner Bases
Guanli Huang, Meng Zhou
Available Online March 2014.
- https://doi.org/10.2991/mce-14.2014.46How to use a DOI?
- Computer aided design; relative Groebner basis; difference differential module; dimension polynomials; termination of algorithm.
- In this paper we improve the computer algorithm of Zhou and Winkler for computing relative Groebner bases which used in Computer aided design and Robotics, etc. We introduce the concept of difference differential degree compatibility on generalized term orders. Then we prove that in the process of the algorithm the polynomials with higher and higher degree wouldn't be produced, if the term orders are difference differential degree compatibility. We present a condition on the generalized orders and prove that under the condition the algorithm for computing relative Groebner bases will terminate. And then the relative Groebner bases exist under the condition. Due to the algorithm is used as the main tool for algorithmic computation of many engineering and technique problems, we conclude that our result improve the algorithm and guarantee the algorithm effective works in solving verious problems of science and technology.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - CONF AU - Guanli Huang AU - Meng Zhou PY - 2014/03 DA - 2014/03 TI - An Algorithm for Computing Relative Groebner Bases BT - 2014 International Conference on Mechatronics, Control and Electronic Engineering (MCE-14) PB - Atlantis Press SP - 211 EP - 214 SN - 1951-6851 UR - https://doi.org/10.2991/mce-14.2014.46 DO - https://doi.org/10.2991/mce-14.2014.46 ID - Huang2014/03 ER -