How I can evaluate the limit superior of a sequence?

limit

asked 2016-10-31 10:40:24 +0200

Masacroso
264 ●4 ●14 ●22

updated 2020-04-27 22:20:58 +0200

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.

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.

edit retag flag offensive close merge delete

add a comment

1 Answer

Sort by » oldest newest most voted

answered 2016-11-01 01:34:08 +0200

Sha
264 ●10 ●20 ●34

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.

edit flag offensive delete link

Comments

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 ( 2016-11-01 01:54:34 +0200 )edit

add a comment

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2016-10-31 10:40:24 +0200

Seen: 837 times

Last updated: Apr 27 '20

How I can evaluate the limit superior of a sequence? edit