[LRUG] Abstract algebra slides

[Tom Stuart]

Hi Matthew,

On 9 Jul 2009, at 16:07, Matthew Willson wrote:
> Some comments from another ex-math-dude that might clarify or confuse:

Thanks for your comments, and for providing some extra (much-needed)  
mathematical detail. I wish I'd been able to be less superficial,  
although I see from the video that I overran my intended slot by ten  
minutes, so perhaps the superficiality was for the best.

> There may be some confusion, language-wise, between the programming  
> concept of a vector and the mathematical notion of a vector space

This is a good point. We don't really call them vectors in Ruby, but  
yes, if you're a recovering C++ or Java programmer this may well  
present an extra confusing problem on top of all the other confusing  
problems you already presumably have.

> One other thing is that the 'vector division' operation you have in  
> the vector space interface seems a little odd to me (it's not part  
> of the standard structure of a vector space structure, for one, but  
> also why offer vector division but not vector multiplication?).

You're quite right about this. It's just a piece of the application  
domain leaking through. I almost took it out of the library for the  
reasons you mention, but couldn't quite convince myself that it was  
harmful enough to warrant removal when it's something I use every day.  
I probably would remove it if anyone else actually started using the  
library because it's mathematically embarrassing.

Ditto for the partial order: clearly not part of the mathematical  
structure in question, but so obviously useful that I couldn't resist  
chucking it in for my own selfish/pragmatic purposes. It's tempting to  
make people mix it in manually.

Cheers,
-Tom