On Wed, Feb 28, 2024 at 5:00 PM Nils Bruin <nbr...@sfu.ca> wrote: > On Wednesday 28 February 2024 at 08:03:45 UTC-8 Giacomo Pope wrote: > > > I don't know the history of this choice or what we should be doing > generally. -1 for polynomials with only positive degree seems like a > computer science workaround, but for the LaurentPolynomialRing it just > seems wrong? > > > I think it's more than just a CS workaround. It has its roots in dimension > considerations: the space of polynomials of degree at most d is > (d+1)-dimensional. WIth that convention, 0 having degree -1 makes perfect > sense. >
well, it's the convention used in Singular. But GAP and Macaulay2 use -infinity. The arguments for -infinity: 1) degree of the product should be the sum of degrees; so it's got to be infinite. 2) it should be -infinity, to make sense of the rule that if you do division f/g with remainder r, the degree of the remainder should be less than the deg(r)<=deg(f), but if r=0 then the only way to get this is to use -infinity. Dima > > For deg = - ord_infty it should definitely be -oo, though, and for Laurent > polynomials the dimension argument doesn't work. > > -- > 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/ac40d2e7-5e71-43e1-8914-869081f9bdd9n%40googlegroups.com > <https://groups.google.com/d/msgid/sage-devel/ac40d2e7-5e71-43e1-8914-869081f9bdd9n%40googlegroups.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/CAAWYfq0tSp1v%3D2t7m70hKkBF%3DtmWY4x54_vSWAza2hcxHJc4CQ%40mail.gmail.com.
