Dear Bruce,

On 05/11/2010 04:57 AM, Bruce wrote:

> I would like to take a class, say for example Graph, and work with
> formal R-linear combinations of Graphs.
> The FormalSum only applies to numbers and the examples for
> CombinatorialFreeModule only have finite sets.
> 
> Can I do this? (Nicolas has said I can with CombinatorialFreeModule).

In principle, CombinatorialFreeModule is exactly the right tool for
this.  As Florent pointed out, this class has no difficulties with
infinite sets.  The problem is that the objects that make up your basis
must be immutable.   Almost all of the things that one might call
'combinatorial objects' in sage are immutable, in large part so that
they can be used in this way.  Unfortunately, that is not the case for
graphs.  So I don't know how to solve your problem.  Maybe someone else
knows how create a dummy class whose objects are immutable graphs?

Sorry I can't be of more help.

Best,
Jason

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