On Thu, 27 Mar 2008 23:44:27 -0700
"William Stein" <[EMAIL PROTECTED]> wrote:
>
> On Thu, Mar 27, 2008 at 11:29 PM, Nils Bruin <[EMAIL PROTECTED]> wrote:
> >
> > I tried the first example below in sage. It failed , complaining that
> > maxima wanted to know whether x was positive, negative or 0. Hence, I
> > tried maxima via "sage -maxima". To my surprise, maxima computed the
> > limit without asking for extra information. Is the maxima that gets
> > called from sage put in a more inquisitive mode?
> >
> > I figure this might be a symptom of a sub-optimal interaction between
> > sage and maxima and hence might have some interest to developers.
>
> This is almost certainly related to us putting Maxima in "complex numbers"
> mode by default, since Maxima's non-complex mode is very stupid in numerous
> ways, as Paul Zimmerman has pointed out.
>
> >
> >
> > ///////////////////////////////////////////////////////////////////////////////////
> > %sage
> > var('p x')
> > limit((p+1)/pi*(1-x^2/4)/((sqrt(p)+sqrt(1/p))^2-x^2),p=oo)
> >
> > //complains that maxima wants extra information
> >
> >
> > ////////////////////////////////////////////////////////////////////////////////////
> > %maxima
> > f(p,x):=(p+1)/pi*(1-x^2/4)/((sqrt(p)+sqrt(1/p))^2-x^2);
> > limit(f(p,x),p, infinity);
> >
> > //works
>
> The issue is that you're passing in "infinity" which *not* what
> Sage converts oo to:
>
> sage: maxima(oo)
> inf
> sage: maxima('infinity')
> infinity
>
> Maxima has the "brilliant" design that inf = real infinity and
> infinity = complex infinity:
>
> (%i8) describe(infinity);
> -- Constant: infinity
> `infinity' represents complex infinity.
> (%o8) true
> (%i9) describe(inf);
> -- Constant: inf
> `inf' represents real positive infinity.
>
> I guess Maxima must not have a referee system for their code...
>
> Anyway, I'm not sure what to do about this. I don't even know what
> "complex infinity" means...
> But hopefully this sheds some light.
Complex infinity is the unsigned infinity. In Sage the "oo" in the default
namespace is signed infinity:
sage: oo
+Infinity
sage: -oo
-Infinity
sage: unsigned_infinity
Infinity
There is at least one bug in Sage here:
sage: maxima(unsigned_infinity)
inf
> By the way, if you ever design a computer algebra system, please don't
> make inf and infinity be
> two different kinds of infinity. Gees that's almost as confusing as
> making Matrix and matrix
> drastically different[*].
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