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: 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
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