Hi Daniel,

On 2019-02-08, Daniel Krenn <kr...@aon.at> wrote:
> Let I be an ideal. Then I might want to compute something involving
> Groebner basis, e.g. computing I.variety().
> Now suppose one wants to select a particular algorithm for the
> computation of the Groebner basis. Then (due to caching) I use something
> along the lines of
>
>   GB = I.groebner_basis(algorithm='libsingular:slimgb')
>   I.groebner_basis.set_cache(GB)
>   I.variety()
>
> Is this the intended way of doing so?

I guess not. I would expect that I.groebner_basis uses caching
regardless of the used algorithm. Are you sure that this is not the
case?

Or do you say that I.groebner_basis sets a cache item for each possible
value of "algorithm" individually? That would probably be a bug (i.e.,
please open a ticket).

Why "probably"? *Reduced* Gröbner bases are unique, hence, they should
be cached independently of the algorithm used to compute them. But some
algorithms would only call *some* Gröbner basis, no *the* reduced
Gröbner basis. So, in these cases it makes sense to not automatically
cache the value.

Best regards,
Simon

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