[ACM Press the 2010 International Symposium - Munich, Germany (2010.07.25-2010.07.28)] Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation - ISSAC '10 - Degree bounds for Gröbner bases of low-dimensional polynomial ideals

✍ Scribed by Mayr, Ernst W.; Ritscher, Stephan

• Book ID: 121440016
• Publisher: ACM Press
• Year: 2010
• Weight: 748 KB
• Category: Article
• ISBN: 1450301509
• DOI: 10.1145/1837934.1837945

✦ Synopsis

Let K[X] be a ring of multivariate polynomials with coefficients in a field K, and let f1, . . . , fs be polynomials with maximal total degree d which generate an ideal I of dimension r. Then, for every admissible ordering, the total degree of polynomials in a Gröbner basis for I is bounded by

. This is proved using the cone decompositions introduced by Dubé in [5]. Also, a lower bound of similar form is given.