On Jan 23, 3:55 am, "ma...@mendelu.cz" <ma...@mendelu.cz> wrote:
> On 23 led, 12:39, "ma...@mendelu.cz" <ma...@mendelu.cz> wrote:
>
> > Hello, I have a partial answer and perhaps you found a bug in
> > elliptic_e in Sage (read below).
>
> > To evaluate the integral do something like this (note replacing A by
> > lowercase letter)
>
> > T,r,a,b=var('T r a b')
> > F(x)=integrate(sqrt(1+r*sin(x)^2),x, algorithm='mathematica_free')
> > eq = T==F(b)-F(a)
> > eq
>
> > the answer is
>
> > T == -elliptice(a, -r) + elliptice(b, -r)
>
> So you have to solve
> T == -elliptic_e(a, -r) + elliptic_e(b, -r)
>
> in Sage. Sorry for the chaos in my first answer.
>
> Robert
Thanks, that's helpful, I didn't think to try 'mathematica_free', and
I don't know anything about elliptic integrals. But now I don't know
how to proceed. I have some other constants, so my integral ends up
being defined as follows:
sage: var('a')
sage: D=5280
sage: F(x) = integrate(sqrt(1 + 4*pi^2*a^2/D^2 * (sin(2*pi*x/D))^2),
x, algorithm='mathematica_free')
sage: F
x |--> 2640*elliptice(1/2640*pi*x, -1/6969600*pi^2*a^2)/pi
and I want to solve
sage: find_root(5281 == F(D/2) - F(-D/2), 20, 30)
...
TypeError: unable to simplify to float approximation
In fact:
sage: F(2640).subs(a=23)
2640*elliptice(pi, -529/6969600*pi^2)/pi
sage: n(_)
...
TypeError: cannot evaluate symbolic expresssion numerically
Maybe I should stick with Taylor polynomials?
--
John
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