Dividing quaternions about quaternion HOT 4 CLOSED

You've copied the wikipedia entry incorrectly, in one very important way. The notation

is indeed ambiguous, as wikipedia says; on the other hand the notation p/q is not ambiguous; that is clearly equivalent to p * q^{-1}. This is pretty standard notation in non-commutative groups.

However, if you are unhappy with this or have trouble remembering it, you are welcome to just use explicit multiplication:

p * q.inverse()

or

q.inverse() * p

from quaternion.

Thanks, this gives me an idea on how to do this operation. However, it remains unclear to me what rationale lies behind the fact that the code p/q is analogous to only one of the possible divisions, p * q^{-1}, and why the other one is not presented as clear. Possibly there is a reason for that, but I am not well-accustomed to the underlying theory and computational math, it could be I am missing something rather simple and well-known. Is this one of the possible divisions considered to be somehow superior over the other one? (can't find any mention on this in papers)

from quaternion.

I'm not saying that one is superior; they're different quantities that you need in different situations. You have to decide which one you need for any given application.

All I'm saying is that p/q is defined as p * q.inverse(). The reason is that this particular notation makes clear typographically that p is on the left and q is on the right, leading to a standard order of operations in which the corresponding multiplication (involving the inverse) is in the same order. Here is a wikipedia reference supporting my claim; here is Mathematica's; I'm sure I could find others in the mathematical literature.

On the other hand, the "p over q" notation is left-right symmetric, so there's no clear choice as to which one should come first in the multiplication. And since either choice could be the correct one for some application, we just don't use that notation for non-commutative division. (Plus, python code is one-dimensional, so we don't really have that option.)

from quaternion.

This information is much appreciated! It brings clarity and explanation.

from quaternion.