Re: [Axiom-mail] Expressions over finite fields

[Marcus Better]

> EXPR has the signature: 
>     Expression(R:OrderedSet)
> but if we ask about PrimeField(2):
>     PrimeField(2) has OrderedSet  ==>  false
> so Axiom will not allow you to build the type because 
> PrimeField(2) lacks the OrderedSet property.

The categories that are defined in algfunc.spad 
(AlgebraicallyClosedField, AlgebraicallyClosedFunctionSpace etc) all 
seem to impose the OrderedSet assumptions for the underlying domains.

I probably don't know the code well enough, but is this OrderedSet 
restriction really motivated? It would appear that most of these 
operations, such as rootsOf and friends, make perfect sense without 
OrderedSet.

For instance, it should be possible to apply these operations to 
PrimeField 2, as I have been trying to do, even though it is not an 
OrderedSet.

Unless someone tells me that I've got it all wrong here, I might just 
clone the code in algfunc.spad and see what happens.

Marcus

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Marcus Better
Department of Mathematics                      Tel. +46 8 164539
Stockholm University                           Fax +46 8 6126717
SE-106 91 Stockholm
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