#16197: provide function expansions of power series (from Pari)
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Reporter: rws | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.2
Component: calculus | Resolution:
Keywords: function, series expansion | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by kcrisman):
Similarly to my other comment on this, I don't know if we want `n(pi/4)`
in here or not...
Also, the regular `SR` one works fine:
{{{
sage: ex.series(X,16)
(sin(1)) + (4*cos(1))*X^2 + (-8*sin(1))*X^4 + (-32/3*cos(1))*X^6 +
(32/3*sin(1))*X^8 + (128/15*cos(1))*X^10 + (-256/45*sin(1))*X^12 +
(-1024/315*cos(1))*X^14 + Order(X^16)
}}}
so I'm not sure why you referenced it, though I agree that the error you
get for power series rings is not ideal. Is there a way to either use SR
for this (perhaps not "correct" for power series rings though?) or to get
Pari to return a symbolic constant term?
{{{
sage: atan(4*X^2+1)
arctan(4*X^2 + 1)
sage: _.series(X,16)
(1/4*pi) + 2*X^2 + (-4)*X^4 + 16/3*X^6 + (-128/5)*X^10 + 256/3*X^12 +
(-1024/7)*X^14 + Order(X^16)
}}}
What if the coefficients weren't rationals? Or integers? Note that in
your example there is a 16/3 coefficient, which presumably isn't in the
power series ring over integers. These may be dumb questions, but I'm
just trying to explore what is really the desired behavior - certainly
wrapping more Pari stuff is not a bad idea!
--
Ticket URL: <http://trac.sagemath.org/ticket/16197#comment:1>
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