@inproceedings{10.1145/1837934.1837945,
    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.},
    Address = {New York, NY, USA},
    Author = {Mayr, Ernst W. and Ritscher, Stephan},
    BookTitle = {Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation},
    File = {Degree Bounds for Gröbner Bases of Low-Dimensional Polynomial Ideals.pdf},
    ISBN = {9781450301503},
    Keywords = {ideal dimension, complexity, Gr\"{o}bner basis, polynomial ideal, multivariate polynomial},
    Location = {Munich, Germany},
    Pages = {21--27},
    Publisher = {Association for Computing Machinery},
    Series = {ISSAC '10},
    Title = {Degree Bounds for Gr\"{o}Bner Bases of Low-Dimensional Polynomial Ideals},
    URL = {https://doi.org/10.1145/1837934.1837945},
    Year = {2010},
    bdsk-url-1 = {https://doi.org/10.1145/1837934.1837945},
    date-added = {2021-11-19 13:27:37 +0100},
    date-modified = {2021-11-19 13:27:37 +0100},
    numpages = {7},
    doi = {10.1145/1837934.1837945}
}

@inproceedings{10.1145/1837934.1837945, 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.}, Address = {New York, NY, USA}, Author = {Mayr, Ernst W. and Ritscher, Stephan}, BookTitle = {Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation}, File = {Degree Bounds for Gröbner Bases of Low-Dimensional Polynomial Ideals.pdf}, ISBN = {9781450301503}, Keywords = {ideal dimension, complexity, Gr\"{o}bner basis, polynomial ideal, multivariate polynomial}, Location = {Munich, Germany}, Pages = {21--27}, Publisher = {Association for Computing Machinery}, Series = {ISSAC '10}, Title = {Degree Bounds for Gr\"{o}Bner Bases of Low-Dimensional Polynomial Ideals}, URL = {https://doi.org/10.1145/1837934.1837945}, Year = {2010}, bdsk-url-1 = {https://doi.org/10.1145/1837934.1837945}, date-added = {2021-11-19 13:27:37 +0100}, date-modified = {2021-11-19 13:27:37 +0100}, numpages = {7}, doi = {10.1145/1837934.1837945} }