The algorithm for findOneStepGVD comprises two steps. First, it checks the given generators for the given ideal $I$ and creates a list of all indeterminates which appear squarefree in all of the generators. For each of the remaining variables $y$, it then computes a Gröbner basis for $I$ with respect to a $y$-compatible monomial order. If $y$ appears in the elements of the Gröbner basis with only degree zero or degree one, then we have a geometric vertex decomposition, and $y$ is appended to the list of indeterminates.

If SquarefreeOnly=>true, then only the first half of the algorithm runs. This option is used by the isGVD and isWeaklyGVD functions to avoid unnecessary duplicate computations of Gröbner bases.

- findOneStepGVD -- for which indeterminates does there exist a geometric vertex decomposition

- findOneStepGVD(...,SquarefreeOnly=>...)

The object SquarefreeOnly is a symbol.