Three types of closure oracle have been considered: one that tests if a given element belongs to the closure of a given set, a second one that returns the closure of the set, and a third one that tests whether a given set is closed [REF].
A girth oracle takes as its input a set of matroid elements, and returns as its output a numerical value, the size of the smallest circuit within that set (or \scriptstyle +\infty if the given set is independent) [REF].