There may be case for leaving deg(0) undefined both for polynomials and Laurent polynomials (and power series and Laurent series): it's at best a shorthand (pace Nils' comment about dimensions) and needs to be handled separately in code. So calling deg(0) could raise a ValueError or ArithmeticError (just as "factor(0)" does)?
John On Thu, 29 Feb 2024 at 16:34, Oscar Benjamin <oscar.j.benja...@gmail.com> wrote: > I recently reviewed cases in the sympy polys code that handle the > degree of a zero polynomial: > https://github.com/sympy/sympy/pull/25784 > > My conclusion is that it is sometimes useful that deg(0) < deg(p) for > p != 0 but otherwise it is not really possible to use the value of > deg(0) for anything meaningful in practice. Generally if deg(p) is > needed then the zero polynomial needs special handling that no > particular value of deg(0) helps with. I would prefer that deg(0) = -1 > just so that the deg() function has a well defined type. > > For Laurent polynomials I am not sure that I would define a degree() > method or if I did that it would be defined as the exponent of the > leading term. It isn't clear to me when that notion of degree would be > useful: it doesn't seem like it would generalise the ways that degree > is typically used for ordinary polynomials. > > On Thu, 29 Feb 2024 at 10:57, Giacomo Pope <giacomop...@gmail.com> wrote: > > > > There seem to be two things we could do here: > > > > 1. Have some form of vote / discussion on whether the degree of the zero > polynomial should *ever* be -1 > > 2. Modify the degree calls for the LaurentSeries and > LaurentPolynomialRing (maybe other Laurent* which I am unfamiliar with) to > have the zero polynomial have degree -Infinity. > > > > Option 1 may be cleaner in the long run, but I assume will cause issues > for more people in the short term. Option 2 seems fairly harmless and > there's no good argument for degree -1 in this case. > > > > If anyone is interested in option 2, I will find time to make a PR to do > this, but I will not start this work without other people's input as this > is not code I am familiar with using and so I don't know what people could > be relying on. > > On Wednesday, February 28, 2024 at 6:41:48 PM UTC Dima Pasechnik wrote: > >> > >> 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+...@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 > . > > > > -- > > 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/6d95b253-fb17-4e2f-a61c-c723737774e8n%40googlegroups.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/CAHVvXxRe119u%3Dy-xk1O-BvWH_f1xxnHsuQCzZm_4xYRD-_NEFw%40mail.gmail.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/CAD0p0K5H2ne3XYrAL1ShXXCVfan67LMtw6%3DtfKy5PF%2BhLPNSGA%40mail.gmail.com.
