On 2019-02-08, Daniel Krenn <kr...@aon.at> wrote:
> Which algorithm does not return a *reduced* Gröbner basis?

Singular has some options that determine whether or not a reduced GB is
returned. I simply don't know (and have at the moment no time to look at
the code) whether this option is used. Also, IIRC, there is some toy
implementation of Buchberger's algorithm (which is mainly for teaching,
not for production), and I am not sure if it returns a reduced GB.

In any case, if the documentation says it returns a *reduced* GB, then
we certainly have a bug. Either a bug in the documentation (if in fact
the returned GB is not always reduced) or in caching (if it *is* the
reduced GB and isn't cached).

Best regards,
Simon

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