fsolve finds solution, solve doesn't -- eq. simply too nasty?
Hi. I have a function F as follows:
F := 1/16*sin(Pi*cos(h))^2*sin(Pi*sin(h))^2/cos(1/2*Pi*cos(h))^2/cos(1/2*Pi*sin(h))^2;
It has a maximum in the interval 0..Pi/2 at Pi/4. If I do:
Fder := diff(F, h);
solve(Fder, h);
> (1/2)*Pi, -(1/2)*Pi, 0, Pi
the solution Pi/4 is missing from the set returned by solve, and solve does not even issue a warning about the incomplete solution set. Surely Pi/4 is a solution, as you can find it visually:
plot(F, 0..Pi/2);
and also numerically:
fsolve(Fder, h=Pi/4+0.1);
> (1/4)*Pi
I tried AllSolutions, but the warning is not terribly informative:
solve(Fder, h, AllSolutions=true);
> Warning, solutions may have been lost
Tried even tge RealDomain package, but it never finishes evaluation:
use RealDomain in solve(Fder, h, AllSolutions=true) end use;
Is this function F simply too nasty or can I try something else?
Your help is appreciated.
Thanks,
-Felipe.
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