On Sat, Mar 26, 2011 at 03:28:49AM -0700, Simon King wrote:
> I guess that F.basis() should have some index set. Here, it seems
> natural to me to choose M=FreeMonoid(3,['x','y','z']): If m is in M
> then F.basis()[m] returns the corresponding element of F.
>
> Is that the only requirement to F.basis()?
And it should model the basis of F; in particular here, we might want
to do things like:
for b in F.basis(): ...
The best is to implement ``basis`` using a Family, as is done in
CombinatorialFreeModule. In fact, we should probably lift this
definition to ModulesWithBasis, possibly adding a method
F.basis_keys() to encapsulate the current ``_basis_keys`` attribute of
CombinatorialFreeModule.
> Concerning compatibility: Rather than indexing the basis with the
> elements of M, one could index it by the words in the alphabet
> 'x','y','z'.
Or better: the elements of the FreeMonoid should really be words!
> Is there a protocol for doing conversion by changing the index set,
> yet?
Not yet.
> Such conversions could indeed facilitate consistency between
> different implementations of "the same" algebra.
Indeed!
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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