Talk:Geometric algebra: Difference between revisions
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:::No, I combine them with the geometric product. Let me remind you that quaternions here are used as a special case of a more general structure, the geometric algebra.--[[User:Grondilu|Grondilu]] ([[User talk:Grondilu|talk]]) 22:43, 17 October 2015 (UTC)
== Task still needs something... ==
Re-reading the task, and the implementation you have, I think the task needs some additional qualification.
Specifically, it's entirely possible to satisfy
:<math>\begin{array}{c}
(ab)c = a(bc)\\
a(b+c) = ab+ac\\
(a+b)c = ac+bc\\
\forall \mathbf{x}\in\mathcal{V},\,\mathbf{x}^2\in\R
\end{array}</math>
in a fashion which does not support quaternion multiplication. For example, an algebra where <math>\forall \mathbf{x}\in\mathcal{V},\forall \mathbf{y}\in\mathcal{V},\,\mathbf{xy}\in\R</math> would not support quaternions but would completely satisfy the given constraints.
And, in fact, there are arbitrarily many complex rules one could apply to achieve quaternion multiplication and still satisfy those constraints. This means that the specification is incomplete. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 22:49, 17 October 2015 (UTC)
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