YAP (was Re: Proposal: Remove Show and Eq superclasses of Num)
R.Paterson at city.ac.uk
Tue Oct 18 01:19:18 CEST 2011
Balazs Komuves writes:
> Rings with unity have a canonical map, actually a ring homomorphism (but not
> necessarily injection) from the integers, namely for the natural integer N, you
> add together the unit element with itself N times. For negative N, you take the
> additive inverse.
> For fields, you would try to extend this to rationals; however, it seems that because
> of the non-injectivity of the above, this won't always work. Example: finite fields.
> In a finite field of order P, we would have f(N/P) = f(N)/f(P) = f(N)/0 which is not defined.
Good point. Mind you we already have this with Ratio Int and friends.
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