Johannes Grabmeier wrote:
>
> I started a revision of the field stuff. E.g. Simple algebraic
> extensions are MonogenicAlgebra 's, so I included this and learnt, that
> in this case one inherits DifferentialExtension with more differential
> operators.
> I think noone needs them (please indicate, if there are other
> opionons). Actuallly, I also do not know, why we have a trivial
> differential operator ( 0) in FiniteFieldCategory, because this category
> claims to inherit vom DifferentialRing. Can anyone tell me, who needs
> this, otherwise I would like to drop it.
This is mainy issue of consistency: we build structures by recursion,
so trivial cases are necessary as base case. Also, we like to
use generic algorithms and they may need such trivial operations.
So definitely they should be present.
> In any case, some domains have
> functions inherited, which are no longer needed. E.g.
> We have a degree function with values in OnePointCompletion
> PositiveInteger to allow the degree of a transcendent element to be
> infinite. However, in an algebraic extension of a finite field we never
> have a transcendent element, hence degree should map to PositiveInteger.
> So I want to drop the inherited degree function, because it is
> superfluous. .
>
> A suggestion an question to the compiler specialists: Similar to "with"
> can't we have a "without" to drop Categories or single functions.
Again, such inherited functions must be present for consitency:
they may be called by generic routines from categories. It would
be nice to be able to tell compiler and interpreter that they
are "second class" and overload resolution should strongly
prefer other version, but ATM even this is not possible.
--
Waldek Hebisch
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