Geodesic
Computer generated natural inner automorphisms of Cayley's algebra
Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 187-189

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This paper results from the design and development of computer software for lengthy computations with Cayley's algebra C over the field of reals. The algebra C is 8-dimensional over the reals and is not associative. Integer elements of C are defined and can be stored as integer arrays. The problem of solving linear equations αξ = β in C is implemented by using the equation where is the conjugate and N(α) is the non-zero norm of α. Programming multiplication of Cayley numbers is comparable in difficulty to programming matrix multiplication for matrices with eight rows and eight columns. 
Lamont, P. J. C. Computer generated natural inner automorphisms of Cayley's algebra. Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 187-189. doi: 10.1017/S0017089500004961
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