An algorithm for the algebraic classification of the symmetric (3,1)-spinor

We present a detailed classification of the symmetric (3, 1)-spinor accordi ng to its factorization properties, analogously with the Petrov classificat ion of the (4, 0)-spinor, and present an efficient algorithm, suitable for implementation on a computer, for performing such a classification. One app lication would be for the classification of spacetimes with torsion, since the symmetric part of the torsion spinor is a symmetric (3, 1)-spinor. This algorithm can also be applied to the Lanczos spinor potential of the Weyl curvature spinor.