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.
The object SquarefreeOnly is a symbol.