#9555: Series expansions at singularities don't work
---------------------------------+------------------------------------------
Reporter: fredrik.johansson | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone:
Component: symbolics | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Changes (by kcrisman):
* cc: kcrisman (added)
Comment:
Maxima:
{{{
(%i1) taylor(sqrt(x),x,0,3);
(%o1)/T/ sqrt(x) + . . .
(%i3) taylor(%e^(-x)/x,x,0,5);
2 3 4 5
1 x x x x x
(%o3)/T/ - - 1 + - - -- + -- - --- + --- + . . .
x 2 6 24 120 720
}}}
The first one in particular seems odd. Maybe that should be considered a
bug? I've submitted
[https://sourceforge.net/tracker/?func=detail&aid=3341693&group_id=4933&atid=104933
this Maxima bug].
----
Anyway, perhaps that's not relevant. There's a pretty relevant followup
to the discussion referenced above:
{{{
> Actually, ginac cannot do a series on x^n or on sqrt(x^2). Here's the
> ginsh output:
>
> > series(x^n,x,1);
> (0^n)+Order(x)
> > series(x^n,x,2);
> power::eval(): division by zero
> > series(sqrt(x^2),x,3);
> power::eval(): division by zero
Oh, you're so right! Actually, that's because the result of
series(sqrt(x^2),x==0,3) is not necessarly x: it could just as well be
-x. The presence of the branch point makes it more tricky.
Sorry for not being able to help.
}}}
That doesn't resolve things here. My guess is that the current behavior
in Ginac could actually be considered correct, so that we should just add
some documentation saying so?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9555#comment:3>
Sage <http://www.sagemath.org>
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