Algorithm for multiplying two octonions

We consider algorithmic aspects of improving calculations of octonion product. Octonions together with quaternions represent a variety of hypercomplex numbers. An advantage of the suggested algorithm consists in decreased twice number of calculated real number products needed to compute the octonion product if compared to a straightforward naive way of performing the calculation. During synthesis of the discussed algorithm we use a fact that octonions product may be represented by a vector-matrix product. Such representation provides a possibility to discover repeating elements in the matrix structure and to use specific properties of their mutual placement to decrease the number of real number products needed to compute the octonion product