On 2017-10-17 11:49, Luca De Feo wrote:
>> It takes I as the generators of the ideal and uses that as the reduction
>> set.
> 
> That's not a definition. I'm in front of a class asking what this
> function does, and I'm unable to give a mathematical definition of
> what Sage means by "reduction" modulo something that's not a Groebner
> basis.
> 
>> What it does is probably do the reduction using the list in reverse order
>> for this case.
> 
> "Probably" is not a mathematical definition. Besides, I think it's
> more complicated than that.
> 
> Am I the only one who's regularly embarassed explaining Sage's quirks
> to an audience of beginners (or not beginners)?

+1 for doing something.

What about the following fix: When the input is a list/tuple, we check
if it is a Groebner basis or not. If it is, do the computation, if not,
print a warning or raise an error.

Testing if something is a Groebner basis could be done by converting the
list to an object of
<class
'sage.rings.polynomial.multi_polynomial_sequence.PolynomialSequence_generic'>
and use its method .is_groebner()

Daniel

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