Re: Making a polynomial and evaluating it many times from C++

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Fri, Jul 23, 2021 at 10:00:24AM +0000, Neven Sajko wrote:
> FTR, your function for the perimeter of an ellipse is not accurate.
> 
> ? ellipse_perimeter(0.75, 0.25)
> %9 = 3.3412233051388145575
> ? ellperimeter(0.75, 0.25)
> %19 = 3.5553025205101225533
> 
> An independent implementation also agrees with my answer (3.34122...).

Ah sorry, ellperimeter was missing a sqrt when computing the
eccentricity.  Also my script is obsolete since PARI now includes the
function ellE, so now you can just write

ellperimeter(a,b)=4*a*ellE(sqrt(1-(b/a)^2))

which is correct:

? ellperimeter(.75, 0.25)
%7 = 3.3412233051388145575323755812650490598

Cheers,
Bill.