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TitleFloating point Gröbner bases
Author(s) Kiyoshi Shirayanagi
TypeArticle in Journal
AbstractBracket 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.
Length20
ISSN0378-4754
CopyrightElsevier Science Ltd.
File
URL dx.doi.org/10.1016/S0378-4754(96)00027-4
LanguageEnglish
JournalMathematics and Computers in Simulation
SeriesSymbolic Computation, New Trends and Developments
Volume42
Number4-6
Pages509-528
PublisherElsevier Science Ltd
AddressAmsterdam, The Netherlands, The Netherlands
Year1996
Translation No
Refereed No
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