Thank you for this clarification since I was really not able to follow this thread without knowing this and the documentation does not provide enough information to help me. Is limit the only function that returns ind or und, probably not since diff and integrate are defined as limits too basically. This really helps a lot.
Thanks,
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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