#18393: make Expression.series return an element of SR[[]]
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Reporter: rws | Owner:
Type: | Status: positive_review
enhancement | Milestone: sage-duplicate/invalid/wontfix
Priority: major | Resolution:
Component: calculus | Merged in:
Keywords: | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by nbruin):
Replying to [comment:13 rws]:
> Interesting. But that can be considered a bug and see the sage-devel
link for a bug report. I mean, what else do you expect as result when
dealing with a series? But I'll open a new ticket for that.
The problem is: there are SR allows expressions of such generality that
series expansions aren't always possible. Consider:
{{{
sage: function('f')
sage: s=series(sin(x))
sage: f(cos(x))+g
}}}
Should that be considered a series in x?
And then there are of course the cases with well-defined functions as
ingredients where you really can't make a series expansion:
{{{
sage: s=series(sin(x))
sage: exp(1/x)+s
}}}
The general problem is: an element of SR (and the fundamental data type in
maple) is just an expression tree. Mathematical meaning is only obtained
by *what* you do with the element (it's like an untyped programming
language). That means you can do algebra with objects in SR that represent
a series in such a way that you get another object that can't possibly be
interpreted as a series.
maple (and apparently pynac by default) solves that problem by not even
trying: they leave it to the user to do that, trusting that he/she will
take care to only do that in situations where it is possible to interpret
the result as a series.
--
Ticket URL: <http://trac.sagemath.org/ticket/18393#comment:14>
Sage <http://www.sagemath.org>
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