Given a multivector $A \in {\mathbb G}^{p,q}$, is there an algorithm by which one can determine whether $A$ is a blade? Page 533 of Geometric Algebra for Computer Science (Dorst, Fontijne, & Mann, 2007) suggests a method when $A$ is known to be a versor, but what if that condition doesn't hold?
Within a space with indefinite signature $(p,q)$, it is possible to have a blade which isn't a versor. An example is $A = ({\mathbf e}_0 + {\mathbf e}_1) \wedge{\mathbf e}_2 = ({\mathbf e}_0 + {\mathbf e}_1){\mathbf e}_2 \in {\mathbb G}^{1,3}$, Hestenes' spacetime algebra. $A$ is a 2-blade but is not a versor, the disqualification arising because of the factor ${\mathbf e}_0 + {\mathbf e}_1$, which is a null vector.
