Details:

Title
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 non-zero coefficients of Gmu and G are exactly the same. The practical usefulness of the algorithm is suggested by experimental results.
Length	20
ISSN	0378-4754
Copyright	Elsevier Science Ltd.
File
URL	dx.doi.org/10.1016/S0378-4754(96)00027-4
Language	English
Journal	Mathematics and Computers in Simulation
Series	Symbolic Computation, New Trends and Developments
Volume	42
Number	4-6
Pages	509-528
Publisher	Elsevier Science Ltd
Address	Amsterdam, The Netherlands, The Netherlands
Year	1996
Translation	No
Refereed	No