Paper 7: Constructing the split octonions by Donald E. Taylor The code for this paper takes around 10 seconds to run on a 64-bit 2.6GHz AMD processor. Changes since book release: V2.13: The intrinsic SemiSimpleType has been renamed to SemisimpleType. A minor change has been made to adjust for the fact that CartanMatrix now returns a matrix over the integers, rather than the rationals.