On Wed, Apr 4, 2012 at 12:41 PM, Tom Bachmann <[email protected]> wrote:
>> Well, I actually had in mind to base my implementation of the Groebner
>> walk off these classes, this is why I was so eager about discussing
>> the topic.
>>
>
> I think this is the part which I really don't understand. Groebner basis
> code works for very specific rings (namely polynomial rings in finitely many
> commuting indeterminates, or certain special localisations thereof -- you
> probably know this better than I do) and does something very special - in
> your case taking a very specific list of elements of the ring, and turning
> them into another very specific list of elements. I don't see how an
> abstract ring framework will be of use here at all -- since the only ring
> your code works with is PolynomialRing anyway. It is not clear to me either
> how a class representing ideals is helpful for you -- as I see it, groebner
> bases are an implementation detail of ideals, so an ideal class creates
> groebner bases, but not the other way round.

Yes, right, I'm not going to use those classes in the implementation.

However, I will have to make my implementation available to the user,
and I choose to make it available via classes which represent the
corresponding concepts.

For example, instead of running compute_groebner_basis([generator1,
generator2, generator3]), I suggest writing
GroebnerBasis(Ideal([generator1, generator2, generator3)).

Sergiu

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