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TitleDimension-dependent bounds for Gröbner bases of polynomial ideals
Author(s) Ernst W. Mayr, Stephan Ritscher
TypeArticle in Journal
AbstractGiven a basis F of a polynomial ideal I in K [x_1, ,x_n] with degrees deg(F) ≤ d , the degrees of the reduced Gröbner basis G w.r.t. any admissible monomial ordering are known to be double exponential in the number of indeterminates in the worst case, i.e.  deg(G) = d^2^Θ(n). This was established in Mayr and Meyer (1982) andDubé (1990). We modify both constructions in order to give worst case bounds depending on the ideal dimension proving that deg(G) = d^n^Θ(1)2^Θ(r) for r -dimensional ideals (in the worst case).
KeywordsPolynomial ideal, Ideal dimension, Regular sequence, Noether normalization, Cone decomposition
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717111002112
LanguageEnglish
JournalJournal of Symbolic Computation
Volume49
Number0
Pages78 - 94
Year2013
NoteThe International Symposium on Symbolic and Algebraic Computation
Edition0
Translation No
Refereed No
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