Eigenvector matrices as returned from the Casimir module.
Description
The Racah procedure will use the mapping and polynomials from the last time the MapHW procedure was run. Likewise, if MapHW has not been ran, an error will result.
The coefficents will be returned as a matrix. If P1 is from the first coupling scheme and P2 from the second, then the Racah coefficent in ith row and jth column will correspond to the overlap between vectors labeled by the ith set of eigenvalues from coupling scheme one and the jth set of eigenvalues from coupling scheme two.
It should be noted that Maple is not consistant in its ordering of eigenvalues and vectors, so attention should be given in the ordering of eigenvalues, i.e. if the matrix P1 is computed multiple times, the ordering may not be consistant. However, the ordering of the Racah coefficients always matches the ordering of the matrices given to it as input.