English

Solving degree, last fall degree, and related invariants

Cryptography and Security 2022-06-02 v2 Symbolic Computation Commutative Algebra

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 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.

Keywords

Cite

@article{arxiv.2112.05579,
  title  = {Solving degree, last fall degree, and related invariants},
  author = {Alessio Caminata and Elisa Gorla},
  journal= {arXiv preprint arXiv:2112.05579},
  year   = {2022}
}

Comments

Final version. To appear in Journal of Symbolic Computation