can be easily obtained for any specific value of $\br$ and $N$ through the use of algebro-geometric computer packages such as [Macaulay2]{} [@m2] (see appendix \[app:b\] for an example).

Another important aspect of this framework that we wish to emphasize is the ability to obtain an explicit basis of independent operators. This is simply the set of operators corresponding to the basis elements of the module, eq. . These are also easily output in a package such as [Macaulay2]{}—see Appendix \[app:b\] for an example.

In the next two sections we will proceed to address the specifics of computing $H_{\br}(R_{\br}^{G_{\br}}/I_{\br},t)$ in general, and obtain summed formulas for the generalized Hilbert series, eq. , for our one-dimensional EFT. We end this section with some observations that will be useful to keep in mind during the following. First, due to the equations of motion, the quotient ring in eq.  contains only a finite number of elements, and so the full generalized Hilbert series will be finitely generated. This is because the EOM bound the number of derivatives we can add to operator of the form $\ph_1^{r_1}\dots\ph_N^{r_N}$—one obvious consequence being $k_i\le r_i$, where $k_i$ denotes the number of derivatives acting on $\ph_i$. Second, it 