#9555: Series expansions at singularities don't work
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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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Comment(by jlhsage):
This problem shows up in pure ginac-1.60, as you can check in their ginsh
shell. I posted about this error on the ginac-devel list, and their reply
is here:
http://www.cebix.net/pipermail/ginac-devel/2011-June/001946.html
Essentially, they don't claim to work with fractional power series.
Here's the reply:
GiNaC can only compute Taylor and Laurent series. Your's is a Puiseux
series: a series not in integer powers of x but in rational powers of x.
The Puiseux expansion of sqrt(x) is, well, x^(1/2).
You may try to set x=y^q and compute the Laurent expansion in y. Setting
q=2 in your case would give the desired result:
series(sqrt(x),x,0,3)
= series(sqrt(y^2),y,0,3*2)
= y
= x^(1/2).
Note that the member functions degree() and ldegree() currently return
int, so this would have to be generalized somehow, when implementing
Puiseux series directly in GiNaC.
Bye
-richy.
Note that Richy's suggestion about using 'x=y^2' doesn't work either in
ginsh. Does anybody know how maxima resolves this issue?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9555#comment:2>
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