getGVDIdeal(I, L)
The purpose of getGVDIdeal is to return the ideal generated by a sequence of choices of $C$ or $N$ ideals and corresponding choices of indeterminates $y$.
Given an ideal $I$ and variable $y_1$ in $R = k[x_1,\ldots,x_n]$, we can compute the ideals $C_{y_1,I}$ and $N_{y_1,I}$ (see isGVD for the definition of these ideals). But then for each of these ideals in the ring $R = k[x_1,\ldots,\hat{y_1},\ldots,x_n]$, we can then pick a new variable $y_2$ to form the ideals $C_{y_2,C_{y_1,I}}$, $C_{y_2,N_{y_1,I}}$, $N_{y_2,C_{y_1,I}}$ or $N_{y_2,N_{y_1,I}}$. This process can be continued by now picking a new variable $y_3$, and finding either the $C$ or $N$ ideals of these ideals.
The input syntax is best explained via example. The following is [KR, Example 2.16]. We are given the ideal $I$. The input tells us to first find $C_{y,I}$ of $I$. Then we find $N_{s,C_{y,I}}$.



[KR] P. Klein and J. Rajchgot. Geometric Vertex Decomposition and Liaison. Forum of Math, Sigma, 9 (2021) e70:123.
The object getGVDIdeal is a method function with options.