Assuming that all of the coordinates of two Cayley-Dickson Hypercomplex numbers are non-negative integers less than a prime $p$, how quickly can we multiply these numbers? I'm also interested in what else is known about multiplication of two Cayley-Dickson hypercomplexes in a more general setting, to see what related results are known. I'm not a mathematician by trade, but am very interested in finding ways to perform computations faster, and my interests have led me here. I'm hoping that someone can provide me with some help or pointers...
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2$\begingroup$ You may want to clarify what you mean by a real number being an element in a finite field. $\endgroup$– S. Carnahan ♦May 17, 2016 at 16:45
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$\begingroup$ @S.Carnahan: Thanks! I tried to clarify - is there some more appropriate terminology to state that the components are essentially all non-negative integers? I recall coming across it in the literature, but the term escapes me. $\endgroup$– Matt GroffMay 17, 2016 at 17:03
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$\begingroup$ If you just say that all of the coordinates are non-negative integers, that would be least confusing. If there is a special term for this, I don't think it is universally accepted. $\endgroup$– S. Carnahan ♦May 18, 2016 at 4:51
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