On Jan 3, 5:05 pm, "William Stein" <wst...@gmail.com> wrote:
> On Sat, Jan 3, 2009 at 4:48 PM, mabshoff
>
>
>
> <michael.absh...@mathematik.uni-dortmund.de> wrote:
>
> > On Jan 3, 4:33 pm, calcp...@aol.com wrote:
>
> > Hi AJG,
>
> >> Exactly, the function log base 2 of x is not defined at 0.
> >> So, why won't sage return some sort of domain error?
>
> > We call numpy for the numerical roots and I guess this might be a bug
> > there, but we will check. Somebody please open a ticket for this.
>
> >> I noticed something similar when I plotted (x^2-1)/(x-1) and got the
> >> graph of x+1.
> >> I was hoping for a removeable discontinuity to show in the graph!
> >> IE a hole in y=x+1 at x=1.
>
> > Ouch, I think this might explain the problem:
>
> > ----------------------------------------------------------------------
> > | Sage Version 3.2.3.final, Release Date: 2009-01-02 |
> > | Type notebook() for the GUI, and license() for information. |
> > ----------------------------------------------------------------------
> > sage: f=(x^2-1)/(x-1); f
> > (x^2 - 1)/(x - 1)
> > sage: f.simplify()
> > (x^2 - 1)/(x - 1)
> > sage: f.simplify_full()
> > x + 1
> > sage:
>
> > Not sure is this is an issue with Maxima, but I would guess so.
> > simplify_full() shouldn't do this since it is clearly mathematically
> > not equivalent.
>
> It's documented in the Maxima documentation, where one finds
> "cancelling the greatest common divisor of the numerator and
> denominator..." in the docs for ratexpand, which is called in the
> course of the above. Who says simplify_full() shouldn't do the above?
Well, for me simplification implies equivalence operations. But Maxima
seems to be more careful here than MMA. But then I don't do symbolic
manipulation, but I must say I am very surprised.
> Mathematica also does the above simplification:
>
> sage: mathematica.eval('Simplify[(x^2-1)/(x-1)]')
> 1 + x
That looks plain wrong to me assuming equivalence operations, but
maybe the MMA documentation defines what Simplify does.
> I don't think there is any claim that simplify(expr) gives back a 100%
> mathematically equivalent expression. However, the types of changes
> that occur are well defined.
Ok. Maybe the Sage documentation ought to make this clearer then.
> > My suspicion is that we probably call simplify_full()
> > before plotting and/or feeding it into _fast_float(). Someone please
> > open another ticket for this one.
>
> I do not think fast_float calls simplify_full.
Ok, but I am curious how this bug happens then. But I am sure someone
more familiar with the plotting code will find out.
> William
Cheers,
Michael
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