Computational Aspects of the Short Resolution

Let $R:= \Bbbk[x_1,\ldots,x_{n}]$ be a polynomial ring over a field $\Bbbk$, $I \subset R$ be a homogeneous ideal with respect to a weight vector $ω= (ω_1,\ldots,ω_n) \in (\mathbb{Z}^+)^n$, and denote by $d$ the Krull dimension of $R/I$. In this paper we study graded free resolutions of $R/I$ as $A$