Abstract :
Bracket coefficients for polynomials are introduced. These are like specific precision floating point numbers together with error terms. Working in terms of bracket coefficients, an algorithm that computes a Gröbner basis with floating point coefficients is presented, and a new criterion for determining whether a bracket coefficient is zero is proposed. Given a finite set F of polynomials with real coefficients, let Gμ be the result of the algorithm for F and a precision value μ, and G be a true Gröbner basis of F. Then, as μ approaches infinity, Gμ converges to G coefficientwise. Moreover, there is a precision M such that if μ ≥ M, then the sets of monomials with non-zero coefficients of Gμ and G are exactly the same. The practical usefulness of the algorithm is suggested by experimental results.
