> That's absolutely correct, and a point I make in my blog. One heuristic is 
> that GBs tend to have a large number of very small polynomials and so one 
> can dispatch larger arithmetic operations to a different back end safely 
> (converting to and from some other format on the fly). This is something 
> Singular already does, I believe.

I guess for a system like Sage it makes sense to use a default backend
that optimises for fast arithmetic. A GB computation is something one
expects to be long, so it seems OK to take a small amount of time
converting to a GB-optimised backend whenever a GB-computation is
called.

Best,
Johan

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