#16202: implement the agm(x,y) function
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Reporter: rws | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: calculus | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by rws:
Old description:
> https://en.wikipedia.org/wiki/Arithmetic-geometric_mean
>
> Pari has a numeric implementation:
> {{{
> ? 1/agm(1,sqrt(2))
> %1 = 0.83462684167407318628142973279904680900
> }}}
> but Wikipedia provides a closed form integral expression, and if we had
> the "complete elliptic integral of the first kind" this would be even
> simpler.
New description:
https://en.wikipedia.org/wiki/Arithmetic-geometric_mean
Pari has a numeric implementation:
{{{
? 1/agm(1,sqrt(2))
%1 = 0.83462684167407318628142973279904680900
}}}
but Wikipedia provides a closed form integral expression, and if we had
the "complete elliptic integral of the first kind" this would be even
simpler.
Numerically there is `sage.rings.real_mpfr.RealNumber`.
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Ticket URL: <http://trac.sagemath.org/ticket/16202#comment:5>
Sage <http://www.sagemath.org>
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