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TitleA new Gröbner basis conversion method based on stabilization techniques
Author(s) Hiroshi Sekigawa, Kiyoshi Shirayanagi
TypeArticle in Journal
AbstractWe propose a new method for converting a Gröbner basis w.r.t. one term order into a Gröbner basis w.r.t. another term order by using the algorithm stabilization techniques proposed by Shirayanagi and Sweedler. First, we guess the support of the desired Gröbner basis from a floating-point Gröbner basis by exploiting the supportwise convergence property of the stabilized Buchberger’s algorithm. Next, assuming this support to be correct, we use linear algebra, namely, the method of indeterminate coefficients to determine the exact values for the coefficients. Related work includes the FGLM algorithm and its modular version. Our method is new in the sense that it can be thought of as a floating-point approach to the linear algebra method. The results of Maple computing experiments indicate that our method can be very effective in the case of non-rational coefficients, especially the ones including transcendental constants.
KeywordsBasis conversion, Gröbner basis. Algorithm stabilization, Floating-point Gröbner basis, Symbolic and numeric computation
URL http://www.sciencedirect.com/science/article/pii/S0304397508006488
JournalTheoretical Computer Science
Pages311 - 317
NoteSymbolic-Numerical Computations
Translation No
Refereed No