[Maxima] Limit is wrong

Richard Hennessy rich.hennessy at verizon.net
Mon Aug 10 16:03:49 CDT 2009

Sorry, I meant

limit(signum(a*x^2),x,inf) = signum(a)


----- Original Message ----- 
From: "Richard Hennessy" <rich.hennessy at verizon.net>
To: "Richard Fateman" <fateman at cs.berkeley.edu>
Cc: "Maxima List" <maxima at math.utexas.edu>
Sent: Monday, August 10, 2009 4:42 PM
Subject: Re: [Maxima] Limit is wrong

The subst() call is unnecessary I agree.  I copied it from a program I wrote.  I would like my pwlimit() program to give
limit(a*x^2,x,inf) = signum(a) but this bug makes it harder to write pwlimit() because limit does not report the sign.


----- Original Message ----- 
From: "Richard Fateman" <fateman at cs.berkeley.edu>
To: "Richard Hennessy" <rich.hennessy at verizon.net>
Cc: "Maxima List" <maxima at math.utexas.edu>
Sent: Monday, August 10, 2009 4:36 PM
Subject: Re: [Maxima] Limit is wrong

Richard Hennessy wrote:
> try,
> (%i1) signum(limit(subst(inf,x, a*x^2)));
> sign: sign of infinity is undefined.
>  -- an error.  To debug this try debugmode(true);
> (%i2)
> This is another bug, present in 5.18.1 and 5.19.0.  In the limit the sign does matter.  I think it is incorrect for limit to give
> an
> answer of "unsigned" infinity.

That's not the error, or at least not the first error.

The  expression that makes sense is    signum(limit(a*x^2,x,inf));

Maxima should ask about the sign of "a", because it affects the answer
as follows:
if "a" is positive, the limit is inf     (positive).
if "a" is zero, the limit is 0
if "a" is negative, the limit is -inf .

Thus signum() depends on the sign of "a" which is (apparently) not known
since you start with line %i1.

subst(inf,x, .....)  is generally bogus, since inf is not a proper value.


> Rich
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