I'd be OK with raising an exception or with -oo, but it should be uniform, and I think it should be the same for polynomials, Laurent polynomials and in the same spirit for degree and valuation.
It might be best to raise an exception, because this ensures that the zero polynomial gets special treatment. Martin On Thursday 29 February 2024 at 22:54:20 UTC+1 Nils Bruin wrote: > On Thursday 29 February 2024 at 11:15:21 UTC-8 Dima Pasechnik wrote: > > How about using something like https://github.com/NeilGirdhar/extended_int > ? > (Even better, do a PEP to have such a thing in Python proper...) > In old, totally duck-typed, Python this didn't really matter, but nowadays > it does make > a perfect sense. > > At the moment, I think most degree functions do their best to return sage > Integer objects; mainly so that coercion works well with them. So whatever > solution we use should probably be based on objects that naturally live in > the sage hierarchy. We do have an infinity object in sage and it already > gets used for valuations. > > Incidentally: > > sage: R.<x>=LaurentSeriesRing(QQ) > sage: z=R(0) > sage: z.valuation() > +Infinity > sage: z.degree() > -1 > > I don't quite know why laurent series have a degree defined at all, but > they're keeping to the deg(0)=-1 convention. > > Incidentally: > > sage: A.<x>=QQ[] > sage: B.<y>=LaurentPolynomialRing(QQ) > sage: x.valuation(oo) > -1 > sage: y.valuation(oo) > 1 > so polynomial rings have a valuation (that will return +oo when > appropriate), but on LaurentPolynomialRing this gets silently broken: the > argument simply gets ignored and the valuation at 0 is returned. So I guess > you can get a well-behaving degree with > > f=0*y > -f(1/y).valuation() > -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/ec50bffa-37ef-4bee-9095-09e738be1842n%40googlegroups.com.
