Computation of Macaulay Constants and Degree Bounds
for Gröbner Bases
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Co-author(s): Amir Hashemi and Hossein Parnian |
Reference: Journal of Symbolic Computation, 111 (2022) 44-60 |
Description: This paper continues and extends our previous works
[40,
46]
.
Following an approach developed by Dube and by applying the Hilbert series
method, we provide an efficient algorithm to compute the Macaulay constants of a monomial ideal
without computing any exact cone decomposition of the corresponding quotient ring. Combining
it with a method proposed by Mayr and Ritscher, we derive a new upper bound for the
maximum degree of the elements of any reduced Gröbner basis of an ideal generated by a set
of homogeneous polynomials which depends on Krull dimension and the maximal degree of a generator
of the considered ideal. |
PDF File: (257 kB)
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