Solving degree, last fall degree, and related invariants

12/10/2021

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by   Alessio Caminata, et al.

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In this paper we study and relate several invariants connected to the solving degree of a polynomial system. This provides a rigorous framework for estimating the complexity of solving a system of polynomial equations via Groebner bases methods. Our main results include a connection between the solving degree and the last fall degree and one between the degree of regularity and the Castelnuovo-Mumford regularity.