24.02.2011 17:51, Alexander Eberspächer пишет:
Thank you for reminding about algebraic structures...
I want to add one more keyword to the discussion: Google just taught me
about Puiseux series (http://en.wikipedia.org/wiki/Puiseux_series),
which seem to be series with rational exponents on the base functions.
I think that in Ronan's wiki page must be a sections with description of
various kinds of Series.
(I am sorry, but it is hard to me in this week to edit this page with LaTeX)
Also, as number of terms with positive powers in "Laurent series" can
be infinitely too with the same time as negative ones, it's
interesting in this case what to do with O() when consider some
asymptotic expansion from this series or does sense of it exists, and
what sort of if it does. I do not know exactly the answer now.
>
> Alex
>
I have seen just now (I can't read and translate all messages quickly
now) that Ondrej yesterday have bring up almost similar question what to
do with the series like "1 + 1/x + 1/x**2 and so on".
> Me neither. If this is unclear it is possibly the best options not to
> provide the order of the remainder terms.
I should to bring you up to date about providing. At the last week or
two it was discussed about it, if we saying about "asymptotic expansion"
(by implication) then O() must be present. Ronan protested against
omitting O() in this case, there is one reason among others why he was
inspired to write wiki page we talk about in this thread.
So we distinguish now the Series and "asymptotic expansion".
And (as I understand Ronan's tendency) if we can't provide O(x) then we
can't provide "asymptotic expansion" upon the whole. (only some terms,
that generally speaking is neither "asymptotic expansion", nor Series,
just truncated terms of Series).
In other world the task of obtaining "asymptotic expansion" is
considered to be solved only if appropriate O(x) is provided.
And if we provide only truncated terms then it is truncated Series only,
nothing else.
--
You received this message because you are subscribed to the Google Groups
"sympy" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sympy?hl=en.
