On Fri, Mar 1, 2024 at 10:24 AM John Cremona <john.crem...@gmail.com> wrote:
> > > On Fri, 1 Mar 2024 at 10:04, Dima Pasechnik <dimp...@gmail.com> wrote: > >> >> >> On 1 March 2024 09:07:26 GMT, 'Martin R' via sage-devel < >> sage-devel@googlegroups.com> wrote: >> >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. >> >> Exceptions are expensive, performance-wise, and using them as a regular >> means of controlling the flow of the algorithm execution is not a good idea. >> A simple if/then/else is much cheaper. >> > > Isn't this suggestion to have f.degree() raise an exception when f is > zero, but also then that any code which needs the degree to treat 0 as a > special case (where that makes sense)? To it would be the caller's > responsibility to do that with a test of f.is_zero() or whatever, rather > than by seeing if an exception is triggered. > Letting degree(0) throw an exception means that every place where you want to test whether the degree of fg satisfies something needs a testing whether f or g is 0, in order to avoid an exception. OTOH, setting the degree of 0 to be -oo has an obvious advantage: it automaticlly gives mathematically correct degree of fg, by using degree(fg)=degree(f)+degree(g), regardless of f or g being 0. And checking the degree is (or at least ought to be) faster than comparing for equality to 0. Yes, it requires a change of the mental picture somehow. But same applies for e.g. using projective setting instead of affine one in geometry: you don't need to throw a mental exception as soon as you get parallel lines :-) Dima > > John > > >> >> Dima >> > >> >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/D20DACD9-8D5A-48F4-81F5-141CF0181BA1%40gmail.com >> . >> > -- > 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/CAD0p0K45r2ishqx4kzEwuVF9%3DYDtojjteBn3snKMkGj8ijb72g%40mail.gmail.com > <https://groups.google.com/d/msgid/sage-devel/CAD0p0K45r2ishqx4kzEwuVF9%3DYDtojjteBn3snKMkGj8ijb72g%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- 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/CAAWYfq0zF8ARVr_FbbKd7WAhM8t6cBSqegXZzKsSSx1Au5mFMw%40mail.gmail.com.
