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.
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[*].
-- William
[*] Maple does this.
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