A new Gröbner basis conversion method based on stabilization techniques

  • Authors:

  • Kiyoshi Shirayanagi;Hiroshi Sekigawa

  • Affiliations:

  • School of Science, Tokai University, 1117 Kitakaname, Hiratsuka-shi, Kanagawa, 259-1292, Japan;NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa, 243-0198, Japan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2008

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Abstract

We propose a new method for converting a Grobner basis w.r.t. one term order into a Grobner 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 Grobner basis from a floating-point Grobner 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.