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simplify_full development

Hi! Could someone elaborate on the status of the simplification routines in SAGE? I've noticed that the simplify_full can't exactly be said to compete with e.g. mathematica's corresponding FullSimplify...

I don't know if the simplify functions operate as replacement rules or such, but if they do, I might be able to contribute in the development (I'm not much of a programmer though).

So could someone please explain about how simplify_full and other simplification functions work, and how I and others can participate? This post could work as an info for all who want to take part!