Student:-Calculus1:-ShowSolution(int(ln(1+sqrt((1+x)/x)),x))

Thank you, my friends.

The fsolve and DirectSearch is most helpful for me.

I'm appreciated for the analysis by Kitonum.

That's very kind of you.

Thank you for your reply, my friends.

I got it. The author on the page http://12000.org/my_notes/rankTest/test.htm maybe show a discrepancy.

But I want to know is,

if The Intel MKL vesion in maple is newer, for example 2013 version(I don't know,I guess),

whether the speed will be faster? if so, why use a 6 year old version?

That's the point.

thank you, my friends.

here is some details

restart;
Digits,evalhf(Digits);
14, 14.
with(LinearAlgebra):
A:=Matrix([[1,3],[2,5]],datatype=float):
b:=Vector([1,1],datatype=float):
infolevel[LinearAlgebra]:=5:
LinearSolve(A,b,method=hybrid);
LinearSolve: using method hybrid
LinearSolve: using method hybrid
LinearSolve: calling external function
HybridLinearSolve: NAG hw_f07adf
HybridLinearSolve: NAG hw_f07aef
HybridLinearSolve: CLAPACK sw_dgerfs_
Error, (in SWcallhybrid[1]) param 4 should be an rtable

I don't know what's happening.

Maybe realroot or sturm is more appropriate for you

who can make this parameter estimation with DirectSearch package?

thank you very much.

I didn't heard a toolbox have the function link between zemax and maplesim.

But, I guess there is a way.

Both Zemax and Maple has a link with Matlab. Maybe you can get it through Matlab.

good luck!

commandline mode or classic worksheet mode

wish to help you

Thank you, Markiyan Hirnyk and acer.

Your methods are very useful.

To acer:

the NextZero command does resolve my problem.

but for the second method, commands is below:

(

restart:

F := Int(sqrt((2.138+0.3e-2*exp((4.2^2-z^2)/d^2))^2-2.141^2), z=0 .. 4.2,
         digits=15, epsilon=1e-12, method=_d01ajc) = .5:

fsolve(F,d=2..6);
)

there still exists problem.

Usually my worksheet is in Worksheet Mode.

Unless I set the commands above Join Execution Groups, I wouldn't get the result(3.957142936).

xp 32, maple 13, Celeron 2.53GHz.

still need help.

> p := convert(lhs(eq2), rational);
> p := p/lcoeff(p); lcoeff(p), tcoeff(p);
> CM := LinearAlgebra[CompanionMatrix](p);
> evalf[300](CM);
> LinearAlgebra[Eigenvalues](%);
> Student[NumericalAnalysis][SpectralRadius](`%%`);

Unfortunately,commands above can't solve this problem, and the results don't coincide with the results given by RootFinding:-Analytic under the default digits.

In fsolve command, one needn't provide the root range, and in RootFinding:-Analytic command, root range need to be estimated first. So I think that's why fsolve is more popular.

Thank you very much, Markiyan Hirnyk, acer and Axel Vogt.

With the command LinearAlgebra[CompanionMatrix], I got a matrix which has the eigenvalues same to the roots of eq2.

But the result is wrong absolutely, there are only two nonzero eigenvalues.

I also use the command Student[NumericalAnalysis][SpectralRadius] to estimate the range of roots on the complex plane, but with the answer given above, it's wrong.

With matlab or mathematica, the eq2 can be solved. So I guess maple doesn't ready for large scale numerical computation.

I'll try the methods given above.

Thank you very much, my friends.

Thank you for your replies, rlopez and Preben Alsholm.

These two methods can't resolve my problems.

First, I think the 1st figure which derived by fsolve command is absolutely right, but the deficiency is obvious that there exist the jumps between different branches, the method from rlopez also has this fault. This figure can be used to validate the result derived from dsolve command.

Secondly, the method use dsolve command is not a perfect idea although it does distinguish the different branches for l2 in the complex plane. The problem is that there are differences between figures plotted with different initial values. Maybe, I think,  from Preben Alsholm, the reason is singularities. After analyzing the compute procedure, I think diff(f(l2, v), l2) in the DE may be the source. It's on the divisor position. I plotted a figure after using cross multiply, but the problem still exists.

I still need help, eight functions, eight branches.

Any method will be appreciated.Thank you in advance.

Thank you very much for your reply, Adri vanderMeer van der Meer,

That's a good idea.

From this problem, it looks like that the symbolic-numeric hybrid computation in maple can be further improved.

because of (diff(f(x), x))^2, the eq1 have two solution.

you can get the square root by hand or manipulate the eq1, following equations can be found

(.6740221708*(diff(diff(diff(f(x), x), x), x))+f(x)*(diff(diff(f(x), x), x))+1)^(1/2) = diff(f(x), x),

(.6740221708*(diff(diff(diff(f(x), x), x), x))+f(x)*(diff(diff(f(x), x), x))+1)^(1/2) = -diff(f(x), x),

then use the dsolve to solve the problem.

BTW, what does b mean in (D(f))(b) = 1?

In my opinion, you can use the color as the fourth dimension.

Also, you can use the vector to describe it.

As far as I know, the colored vector can plot five variables, I think that's the most dimension can be plot on the display.