@inproceedings{79eb391a6da647fa91133c2ea921a8ef,
title = "Degree bounds for Gr{\"o}bner bases of low-dimensional polynomial ideals",
abstract = "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 Gr{\"o}bner basis for I is bounded by 2(1/2dn-r + d)2r. This is proved using the cone decompositions introduced by Dub{\'e} in [5]. Also, a lower bound of similar form is given.",
keywords = "Bner basis, Complexity, Gr{\"o}, Ideal dimension, Multivariate polynomial, Polynomial ideal",
author = "Mayr, {Ernst W.} and Stephan Ritscher",
year = "2010",
doi = "10.1145/1837934.1837945",
language = "English",
isbn = "9781450301503",
series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",
publisher = "Association for Computing Machinery (ACM)",
pages = "21--27",
booktitle = "Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010",
note = "2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010 ; Conference date: 25-07-2010 Through 28-07-2010",
}