ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 31 Oct 2016 19:54:34 -0500How I can evaluate the limit superior of a sequence?http://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 dont 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". Not only ths happen in sage, too in other CAS. It seems that there is a loooong run in the developing of computer algebra systems.Mon, 31 Oct 2016 04:40:24 -0500http://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 dont 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". Not only ths happen in sage, too in other CAS. It seems that there is a loooong run in the developing of computer algebra systems.</p>
http://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.Mon, 31 Oct 2016 19:34:08 -0500http://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>
http://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.)Mon, 31 Oct 2016 19:54:34 -0500http://ask.sagemath.org/question/35309/how-i-can-evaluate-the-limit-superior-of-a-sequence/?comment=35322#post-id-35322