Figuring out if a multivector is decomposable

Gene wrote this on the page "The wedgie" on the wiki:
> In the 7-limit case, if we wedge a prospective rank two multival W = <<a b c d e f|| with itself, we obtain W∧W = 2(af-be+cd). The quantity af-be+cd is the Pfaffian of the wedgie

So I found the Wikipedia page on Pfaffians at
http://en.wikipedia.org/wiki/Pfaffian

So it looks like, for a grade-2 multivectors, I can just convert the
multivector back into an antisymmetric matrix and compute its
determinant. If the determinant is 0 (and hence is square root is 0),
then it's a Bona Fide Wedgie (tm), and if it isn't then we know that
it's not totally decomposable.

Is there some generalization of this to higher-grade wedgies as well?

-Mike