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.

翻译：在本文中,我们研究并联系到若干与多元营养体系的解析程度有关的变量,为通过格罗布纳基础方法估计解决多元等式体系的复杂性提供了一个严格的框架,我们的主要结果包括解析程度与最后秋季程度之间的联系,以及常规程度与卡斯特卢诺沃-孟德常规程度之间的联系。