ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 01 Nov 2016 01:54:34 +0100How I can evaluate the limit superior of a sequence?https://ask.sagemath.org/question/35309/how-i-can-evaluate-the-limit-superior-of-a-sequence/How I can evaluate the limit superior of a sequence? I don't found in the documentation something related to this tool.
**EDIT:** the limit superior of a sequence $(x_n)$ is defined as
$$\limsup x_n=\lim_{n\to\infty} \sup \\{x_k:k\ge n\\} =\inf\\{\sup \\{x_k:k\ge n\\}: n\in \mathbb N \\} $$
where the first definition is the more interesting computationally.
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It seems that, computationally, evaluating the limit superior is hard because it is done via "brute force". This doesn't happen only in sage, it happen also in other CAS. It seems that there is a long run in the developing of computer algebra systems.Mon, 31 Oct 2016 10:40:24 +0100https://ask.sagemath.org/question/35309/how-i-can-evaluate-the-limit-superior-of-a-sequence/Answer by Sha for <p>How I can evaluate the limit superior of a sequence? I don't found in the documentation something related to this tool.</p>
<p><strong>EDIT:</strong> the limit superior of a sequence $(x_n)$ is defined as</p>
<p>$$\limsup x_n=\lim_{n\to\infty} \sup \{x_k:k\ge n\} =\inf\{\sup \{x_k:k\ge n\}: n\in \mathbb N \} $$ </p>
<p>where the first definition is the more interesting computationally.</p>
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<p>It seems that, computationally, evaluating the limit superior is hard because it is done via "brute force". This doesn't happen only in sage, it happen also in other CAS. It seems that there is a long run in the developing of computer algebra systems.</p>
https://ask.sagemath.org/question/35309/how-i-can-evaluate-the-limit-superior-of-a-sequence/?answer=35320#post-id-35320Are you looking for something like this?
sage: f(x,y) = x^2 + y^2
sage: f.limit(x=0).limit(y=0)
(x, y) |--> 0
sage: f.limit(x=0).limit(y=2)
(x, y) |--> 4
Can you maybe give an example of questions.Tue, 01 Nov 2016 01:34:08 +0100https://ask.sagemath.org/question/35309/how-i-can-evaluate-the-limit-superior-of-a-sequence/?answer=35320#post-id-35320Comment by Masacroso for <p>Are you looking for something like this?</p>
<pre><code>sage: f(x,y) = x^2 + y^2
sage: f.limit(x=0).limit(y=0)
(x, y) |--> 0
sage: f.limit(x=0).limit(y=2)
(x, y) |--> 4
</code></pre>
<p>Can you maybe give an example of questions.</p>
https://ask.sagemath.org/question/35309/how-i-can-evaluate-the-limit-superior-of-a-sequence/?comment=35322#post-id-35322Not close. Well, I think that would be possible to construct it with two kinds of commands, but Im surprised this essential tool of mathematics is not implemented in any CAS (not only sage, maple, mathematica, maxima or sympy doesnt have a function for this!!! Or at least it doesnt appear in the documentation.)Tue, 01 Nov 2016 01:54:34 +0100https://ask.sagemath.org/question/35309/how-i-can-evaluate-the-limit-superior-of-a-sequence/?comment=35322#post-id-35322