On 2017-10-17, Luca De Feo <de...@lix.polytechnique.fr> 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.
Why do they expect you to be able to? Unless it is a class on commutative algebra. >> 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. I agree on that part of your statement. When implementing polynomial reduction, the result (if you reduce by a list of polynomials that do not form a Gröbner basis) will depend on the order in which the reductions are done - hence, the outcome is not uniquely determined by the underlying mathematics but by implementation details. Not uncommon, if the result isn't unique. > Am I the only one who's regularly embarassed explaining Sage's quirks > to an audience of beginners (or not beginners)? Are your students the only ones that are embarassed if the teacher tells them that they are looking at a method which can only be understood with a background in some specific subfield of maths (such as number fields, commutative algebra, group theory, topology)? My students certainly wouldn't be embarassed. Cheers, Simon -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
