Hi Luca,

On 2017-10-18, Luca De Feo <de...@lix.polytechnique.fr> wrote:
> I hate to sound snarky, but...

No offence taken...

> Yet, none of us seems to be able to second guess what kind of normal
> form is actually implemented by .reduce() (Singular's kNF, actually).
> And from the answers to this thread, it seems to me that neither Sage
> devs can.

I agree that Sage devs don't (need to) know what *exact* algorithm is
used. But at least it is clear that the .reduce() method does polynomial
reductions and continues till no further reduction is possible; all this
for a fixed monomial ordering (determined by the polynomial ring), in
*some* order of execution that is considered an implementation detail
and is thus not necessarily backwards compatible or compatible with an
order of execution proposed in the literature.

Best regards,
Simon


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