Peter, isn't your concern actually defining the scope of a (set of) evaluation?I agree with you that making the scope of evaluation is fundamental for computation but maybe it should be considered as such and not considered within the object? I would mean something such as :
evaluate-with-setting( inverse-morphism(xx), setting(base-ring, known-statements))
Among meaningful features of this approach is the fact that setting could be actually transmitted by reference (you and I knowing that group G part of context is actually finite but not needing to repeat it, that this module is noetherian...).
paul PS: that is a whole core discussion! Le 18-sept.-08 à 09:57, Peter Horn a écrit :
Point taken, but in our case we don't really like to distinguish between what you call "simple things" and the rest -- that would just make things more complicated for us ;) Your x+1 may very well be a polynomial in x, y, and z over QQ. This information is lost, but essential! Just an example: If you say x^2-2, it may be irreducible if you take QQ as ground-ring but reducible if you choose RR. So this is incredibly important, and the very same is true about matices, if you think of inversion, eigenvalues and the like.
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