On Thu, Oct 22, 2009 at 4:15 PM, Fredrik Johansson <fredrik.johans...@gmail.com> wrote: > > On Fri, Oct 23, 2009 at 12:51 AM, John H Palmieri > <jhpalmier...@gmail.com> wrote: >> >> On Oct 22, 2:14 pm, William Stein <wst...@gmail.com> wrote: >>> On Thu, Oct 22, 2009 at 2:02 PM, John H Palmieri <jhpalmier...@gmail.com> >>> wrote: >>> >>> >>> > On Oct 22, 8:57 am, William Stein <wst...@gmail.com> wrote: >>> >> On Thu, Oct 22, 2009 at 8:11 AM, John H Palmieri >>> >> <jhpalmier...@gmail.com> wrote: >>> >>> >> > Anyway, 0^0 is undefined in mathematics, so it's good that it's >>> >> > undefined in Sage. >>> >>> >> It's defined for Sage *integers*: >>> >>> >> sage: 0^0 >>> >> 1 >>> >>> > What about: >>> >>> > sage: 0.000^0.000 >>> > 1.00000000000000 >>> >>> > Shouldn't this be undefined? >>> >>> > John >>> >>> Sage's behavior for 0.0^0.0 is determined by MPFR's, and MPFR follows >>> "the ISO C99 standard for the pow function" as explained here: >>> >>> http://www.mpfr.org/mpfr-current/mpfr.html >>> >>> In particular, see the rule that "pow(x, ±0) returns 1 for any x, even >>> a NaN." Indeed: >>> >>> sage: RR('NaN')^0 >>> 1.00000000000000 >> >> Wow, I thought Sage did math. The mathematical standard for 0^0 (for >> real numbers) is that it doesn't exist, right? Or did I miss a memo >> somewhere? What about these: > > What do you mean by "mathematical standard"? A perfectly valid view is > that 0^0 = 1 and that the function f(x,y) = x^y simply is > discontinuous.
Also, 0^x is discontinuous. > >> sage: CC(0)^CC(0) >> NaN - NaN*I >> sage: 0^CC(0) >> NaN - NaN*I >> sage: CC(0)^0 >> ArithmeticError: 0^0 is undefined. >> sage: CC(Infinity)^0 >> 1.00000000000000 >> sage: CC(Infinity)^CC(0) >> NaN - NaN*I > > The inconsistency is surely not good. > > Fredrik > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
