> 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)?

Luca

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