On Thu, Dec 09, 2010 at 09:05:03PM +0100, Nicolas M. Thiery wrote:
>       Hi Paul,
> 
> On Wed, Dec 08, 2010 at 09:04:50AM +1100, Paul Bryan wrote:
> > I'm wondering if the best way to implement multi-symmetric functions
> > is as I've done so far, using SymmetricFunctionAlgebra as a model,
> > which means my MultiSymmetricFunctionAlgebra class extends
> > CombinatorialFreeModule in the category of GradedHopfAlgebrasWithBasis
> > or should I use the CombinatorialAlgebra class? Is there a reason why
> > SymmetricFunctionAlgebra doesn't extend CombinatorialAlgebra? Is it
> > historical, or for efficiency, or something else?
> 
>     sage: CombinatorialAlgebra?
>     Deprecated! Don't use!
> 
> Granted it's not very explicit :-)

It's not mentioned on the reference page. I haven't looked at the
code, perhaps it's mentioned there?

> Here is more detail about the story: CombinatorialAlgebra is an
> ancient rest from when Sage did not yet have categories. It's still
> used in a couple places that have not yet been refactored.
> CombinatorialFreeModule in the category of GradedHopfAlgebrasWithBasis
> is the right way to go! On the inheritance side you specify the data
> structure for the elements (CombinatorialFreeModule); on the category
> side you state the mathematical properties of the algebra (a graded
> hopf algebra).
> 

Excellent. I've done the right thing!

Cheers,
Paul.


> Cheers,
>                               Nicolas
> --
> Nicolas M. ThiƩry "Isil" <nthi...@users.sf.net>
> http://Nicolas.Thiery.name/
> 
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