On 20-Mar-10, at 8:50 AM, John Cremona wrote:
I would say that you should never test for primality unless specifically required, e.g. if the user asks is_field() (after which the category could be upgraded? I don't know if that is possible). I would always use GF(p) rather than IntegerMod(p) for when I know p is prime. it is is vital in teaching primality tests and the like that one can form IntegerModRing(n) without knowing (or automatically testing behind the scenes) whether or not n is prime. There are surely many other similar situations, for example when constructing a commutative ring it might be expensive to determine whether or not it is an Integral Domain.
+1, I agree with John: no primality testing unless I ask for it, and even then I would like to be able to specify the category and override it.
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