# [Maxima] ind and und

Richard Hennessy rich.hennessy at verizon.net
Sat Sep 26 22:17:23 CDT 2009

```I left out my conclusion.  If limit(x^3/3,x,inf) generated a message in this case and all other cases like it too then you would never have to worry about inf - inf or und*2 or inf + minf, etc...

Rich

----- Original Message -----
From: Richard Hennessy
To: Stavros Macrakis ; Maxima List
Sent: Saturday, September 26, 2009 10:56 PM
Subject: Re: [Maxima] ind and und

My thinking was that limits do not always exist so the answer should not always be a number but instead a message.  ind and und could be treated like stings but I would not be happy with that.  Maybe you could error out if there is no limit.  integrate(x^2,x,minf,inf) produces an error which could be grabbed by the errcatch() statement for programmers to check and can be read by users.  So could limit(x^3/3,x,inf) if it generated a error message instead of an inf.  You never should compute with messages so I think integrate handles this case better than limit().

Rich

----- Original Message -----
From: Stavros Macrakis
To: Maxima List
Sent: Friday, September 25, 2009 3:22 PM
Subject: [Maxima] ind and und

The ind and und documentation is a bit terse, so here is a longer explanation.

limit(...) -> ind means that the limit is not defined or that limit cannot determine it, but that limit can guarantee that the limit set is bounded.
limit(...) -> und means that the limit is not defined or that limit cannot determine it, and that limit cannot prove that the limit set is bounded.

In both cases, Maxima gives a "best effort" result.  For example, limit(sin(x)-sin(x+1/x),x,inf) gives ind, when the correct solution is 0: limit can determine that the limit set is bounded, but was unable to determine that it was actually the single number 0 (though a simple

I don't think there is a clear specification of when limit returns ind/und and when it returns a noun form.  For example:

limit(sin(x)-sin(x+1/x),x,inf) => ind
limit(sin(x)-sin(x+f(x)),x,inf) => noun form (even though the result must be bounded by [-2,2])
limit(sin(x)-sin(x+1/sin(x)),x,inf) => und (oops)

But this is a general problem with the "best effort" philosophy: und is always, in some sense, a correct answer. It would be better if und were reserved for "limit can prove that the limit set is not bounded".

-s

--------------------------------------------------------------------------------

_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima

--------------------------------------------------------------------------------

_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://www.math.utexas.edu/pipermail/maxima/attachments/20090926/999b79b5/attachment.htm
```