COMPARISON OF ALGORITHMS FOR THE SYMBOLIC COMPUTATION OF THE NP SPIN COEFFICIENTS AND CURVATURE COMPONENTS

Algorithms for the symbolic computation of the NP spin coefficients an d curvature components for a given null coframe based on the structura l equations of Cartan and the complex vectorial formalism of Debever a re described. The efficiency of the algorithms is compared theoretical ly and also empirically in a number of test cases using implementation s in the computer algebra system Maple. The test results confirm the t heoretical superiority of the algorithm based on Debever's formalism o ver the one based directly on Cartan's first structural equations for the computation of the spin coefficients both with respect to executio n time and storage requirements. The algorithm for the computation of the curvature components based on Debever's formalism is generally sup erior to the one based on Cartan's second structural equations but the advantage is not as marked as for the spin coefficients.