> From: William Stein <[email protected]>
> Date: Thu, 22 Oct 2009 14:14:41 -0700
>
> On Thu, Oct 22, 2009 at 2:02 PM, John H Palmieri <[email protected]>
> wrote:
> >
> >
> >
> > On Oct 22, 8:57 am, William Stein <[email protected]> wrote:
> >> On Thu, Oct 22, 2009 at 8:11 AM, John H Palmieri <[email protected]>
> >> 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
>
> William
>
> -- William
indeed. Note that one gets the same results in C:
#include <stdio.h>
#include <math.h>
int
main ()
{
double x = 0.0;
double y = 0.0;
double z = pow (x, y);
printf ("%f^%f=%f\n", x, y, z);
}
patate% gcc e.c -o e -lm
patate% ./e
0.000000^0.000000=1.000000
Paul Zimmermann
PS: Maple is inconsistent here:
|\^/| Maple 10 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2005
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> 0^0;
1
> 0.0^0.0;
Float(undefined)
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