>
> In short, the Gröbner fan knows the correct ordering (in terms of a weight 
> vector) but Sage's output presents the basis with a different ordering. 
> This caused me no small amount of confusion. Is this a feature, or a bug?
>

I ran into this very same issue today -- to get a functionality out of this 
would be to provide a method for Gröbner fans that returns the leading 
monomials of a given reduced Gröbner basis with respect to the 
corresponding weight vector.

The only assumption that I would need to make is that the reduced Gröbner 
bases come in the same order the weight vectors come. Can anyone confirm 
that this is always the case?

Thanks, Christian

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