Some criteria for Gröbner bases and their applications. (May 2019) - Liu, Jinwang; Li, Dongmei; Liu, Weijun
Abstract: We consider the following two problems: Let f and g be two polynomials over a field K . P1. When is { f + s, g + t } a Gröbner basis for all s, t ∈ K ? P2. When is { f λ, g σ } a Gröbner basis for all λ, σ ∈ N ? We provide a simpler proof of Hoon's criterion for P1 and a new criterion for P2. The two criteria are applied to the theory of Gröbner bases under composition.