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Mutliplication of base units - Printable Version

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Mutliplication of base units - Xorter - 10/02/2016

We have number sets R^(2^N) like complexes, quaternions, octonions, sedenions ... etc. . These have base units from i[0]=1 over i[1], i[2], i[3] ... to i[n].
I am interested in the sign of the multiplication of these units.
Here is a multiplication table: https://en.wikipedia.org/wiki/Sedenion
i[q] * i[p] = R * i[r], where R is the sign
I would like to know what R is.
R = ?