Hey Andrew,

My comment wasn't intended as a criticism of the code or of anyone:  it is 
> great that Mike, Nicolas, Christian and others developed this. Nor was it 
> meat as a complaint as I think that our general philosophy is that if you 
> don't like something then discuss and put a patch on trac.
>

I wasn't trying to imply you were, and I'm sorry if I did. I wanted to 
point out that it is a more general Sage issue beyond 
CombinatorialFreeModule, in the sense that it would be the same issues if 
we were trying to do this with (subclasses of) FreeModules, Rings or 
Algebras.

>
> Your second paragraph is really the point that I was making: given an 
> existing CombinatorialFreeModule, which by definition already has at least 
> one basis, it is hard for non-developers to define a new basis that plays 
> well with the existing ones. For me the coercions aren't really the issue, 
> it shouldn't be hard to streamline this and, in any case, to define a new 
> basis for a given module you have to say how it relates to an existing 
> basis.
>

The most basic/simple setup would be different parents (with perhaps some 
common (abstract) base class) with coercions between them and some common 
entry point.

>
> I have used the With Realizations framework quite a bit in my own code 
> and, of course, in the KL-basis machinery. For people developing code  I 
> think this is very workable, but I doubt that a non-developer would get 
> very far with it.
>

   There definitely is an entry barrier. I should also state that the 
WithRealizations framework also allows us to specify when particular 
morphisms are COB's (via the category of the Homset which we can't so 
easily do with ABC's).

>
> Down the track, what I would like to see is a way of *dynamically* adding 
> bases to a CombinatorialFreeModule without these new bases having to be 
> part of the sage source code. For example, it is possible to do this in 
> chevie. From my quick look at the manifold code, it seems that it allows 
> something in this direction. When I have time I'll see if I can find a way 
> of doing this...
>
> Ah I see what you're after. I guess what we could do is have a method to 
an invertible module morphism (on basis) which creates some generic 
subclass of CombinatorialFreeModule which uses this morphism to translate 
(co)multiplication for (co)algebras.

Best,
Travis

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