An efficient algorithm for the Riemannian 10 j symbols

The 10 j 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 10 j symbol require ( j 9 ) or more operations and ( j 2 ) or more space, where j is the average spin. We present an algorithm that computes the 10 j symbol using ( j 5 ) operations and ( j 2 ) space, and a variant that uses ( j 6 ) operations and a constant amount of space. An implementation has been made available on the web.