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 Gröbner 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.
Solving degree, last fall degree, and related invariants
Caminata A.;Gorla E.
2022-01-01
Abstract
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 Gröbner 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.
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Caminata, Gorla - Solving degree, last fall degree, and related invariants [Journal of Symbolic Computation].pdf
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