> Why not a middle ground?

Indeed. I like this idea a lot. +1

I think that Raoul's post takes care of the requirement of the list. Also, 
I will still take some time to write the proposal on the wiki. First, I 
want to be really clear on exactly what to implement and, more importantly, 
how to implement.

And sure, we can implement all things on a Cn over C vector space.

Raoul also mentioned the 7 dimensional cross product.

> Maybe one could even fill up R4,R5,R6 to R7? But that 
> I never tried.

Neither have I. So, let me. Though a first glance at Cayley's sample 
multiplication table (in the wikipedia page mentioned) reveals that the 7 
dimensional cross product may generalize all the way down to 1 dimension. 
This I say because the cross product of ei, i=1, 2, 3, is same as for cross 
product in R3. So, this looks hopeful.

Anyway, in the meantime, I have been jotting down ideas as they come to me 
on a whiteboard and copying them down in a notebook. Right now, I am trying 
to deal with coordinate systems and how best to implement them in a class. 
Some ideas include user defined bases, conversion matrices between 
different coordinate systems, conversion between different bases etc. After 
I have a basic visualization of the structure of the coordinate system 
class, I'll post my ideas here. Then, next thing I will focus on is the 
concept of Reference Frames and a world based coordinate origin. Until 
then, please feel free to post any ideas/suggestions/opinions, however 
small, over here.

Thanks for the valuable inputs everyone. Much appreciated.

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