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2023•arXiv (Cornell University)Open access

An upper bound for the solving degree in terms of the degree of regularity

Flavio Salizzoni

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Abstract

The solving degree is an important parameter for estimating the complexity of solving a system of polynomial equations. In this paper, we provide an upper bound for the solving degree in terms of the degree of regularity. We also show that this bound is optimal. As a direct consequence, we prove an upper bound for the last fall degree and a Macaulay bound.

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The solving degree is an important parameter for estimating the complexity of solving a system of polynomial equations. In this paper, we provide an upper bound for the solving degree in terms of the degree of regularity. We also show that this bound is optimal. As a direct consequence, we prove an upper bound for the last fall degree and a Macaulay bound.

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Available abstract

The solving degree is an important parameter for estimating the complexity of solving a system of polynomial equations. In this paper, we provide an upper bound for the solving degree in terms of the degree of regularity. We also show that this bound is optimal. As a direct consequence, we prove an upper bound for the last fall degree and a Macaulay bound.

Key concepts: Degree (music), Upper and lower bounds, Mathematics, Polynomial, Degree of a polynomial, Applied mathematics, Mathematical analysis, Physics

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