An Algorithm to Compute Floating Point Groebner Bases
Kiyoshi Shirayanagi · Birkhäuser Boston eBooks · 1993
Gröbner basis (GB) techniques are a valuable tool for solving many problems in polynomial ideal theory. As is well known, the process of computing a GB may involve large numbers of intermediate coefficients - say from a field k - even when the final GB does not involve many coefficients. In fact, the cost of performing exact arithmetic in k with the intermediate coefficients is a major factor determining the computational cost of computing the GB. This paper proposes a new approach using floating point computation that can be applied when k is a subfield of the real numbers.1