An Algorithm for Computing Relative Groebner Bases
Guanli Huang, Meng Zhou · Advances in intelligent systems research/Advances in Intelligent Systems Research · 2014
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.