Details:
Title  Floating point Gröbner bases  Author(s)  Kiyoshi Shirayanagi  Type  Article in Journal  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 Grobner 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 Gmu be the result of the algorithm for F and a precision value mu, and G be a true Grobner basis of F. Then, as mu approaches infinity, Gmu converges to G coefficientwise. Moreover, there is a precisionM such that if mu >= M, then the sets of monomials with nonzero coefficients of Gmu and G are exactly the same. The practical usefulness of the algorithm is suggested by experimental results.  Length  20  ISSN  03784754  Copyright  Elsevier Science Ltd. 
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 URL 
dx.doi.org/10.1016/S03784754(96)000274 
Language  English  Journal  Mathematics and Computers in Simulation  Series  Symbolic Computation, New Trends and Developments  Volume  42  Number  46  Pages  509528  Publisher  Elsevier Science Ltd  Address  Amsterdam, The Netherlands, The Netherlands  Year  1996  Translation 
No  Refereed 
No 
