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How I can evaluate the limit superior of a sequence?

asked 2016-10-31 04:40:24 -0500

Masacroso gravatar image

updated 2016-11-02 00:08:59 -0500

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.

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.

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answered 2016-10-31 19:34:08 -0500

Sha gravatar image

Are 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.

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Not 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.)

Masacroso gravatar imageMasacroso ( 2016-10-31 19:54:34 -0500 )edit

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Asked: 2016-10-31 04:40:24 -0500

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Last updated: Nov 02 '16