An efficient algorithm for the Riemannian 10j symbols

The 10j symbol is a spin network that appears in the partition function for the Barrett-Crane model of Riemannian quantum gravity. Elementary methods of calculating the 10j symbol require O(j(9)) or more operations and O(j(2)) or more space, where j is the average spin. We present an algorithm that computes the 10j symbol using O(j(5)) operations and O(j(2)) space, and a variant that uses O(j(6)) operations and a constant amount of space. An implementation has been made available on the web.