Please show the commands that you entered into Maple. It should be something like

diff(ln(x^2+1), x);

diff(2*x, x);

@Kitonum 

It is possible with plot by using both the adaptive= false and sample options. It is not possible with implicitplot. The grid option defines the size of rectangles in the xy-plane, but neither x nor y can be individually specified within those rectangles.

@Kitonum I am not sure that I understand your question. Are you asking whether you can extract data from an existing plot structure using a specified step? No, not unless the step was specified or was inherent to the original plot command. All programmatically accessible plot structures contain specific numeric point data; they are not dynamic. There are a few dynamic plot features implemented in the Standard GUI, such as zooming and 3d fly through; however, these features are not programmatically accessible.

The data matrix extracted from a plot can be passed to CurveFitting:-ArrayInterpolation. (It may need to be sorted first.) Then evenly spaced ordinates can be specified. This is not exactly the same thing as points on the curve, but they are likely to very close to points on the plot itself, assuming that the graphics drivers use a similar interpolation algorithm.

I am currently working on a timewise and accuracywise comparison of the fsolve and implicitplot-plus-ArrayInterpolation approach. I have no doubt that fsolve will win for accuracy. But I think that the latter will win for time when then number of points is large.

I cannot duplicate your problem. I get realistic timings when I use large numbers. Also, for large numbers you'll need to reduce the number of iterations or not use the iterations parameter (equivalent to setting iterations= 1). Would you please post a worksheet that shows the phenomenon that you describe?

@jonlg I do not know much about the Gillespsie algorithm, but it strikes as odd the way that mu is computed in your code, and also that it is computed for every loop iteration. Certainly, the number of iterations of the algorithm is inversely (and stochastically) proportional to mu.

@wolfman29 

While Re itself is not a long computation, it is not differentiable. Since fsolve uses derivative-based methods (I believe), Re may lead to extra cases for fsolve to consider. I am not saying that this is the cause of the problem, but it is something to consider.

I've done a few experiments with your code, and it seems that the integration is not the cause of the hangup (although I am not sure of this). I put print statements surrounding the Int in your procedure RP1 so that I could see when integrations begin and end.

@jonlg 

The sequence of pseudorandom numbers always starts off the same after a restart. This leads to reproducibility of results, which is important for debugging. In order to get different pseudorandom numbers, include than command

randomize();

right after your restart.

@alljoyland 

Perhaps you could make use of one of the following:

sum('a||i'[m], i= 1..4);

sum(a[i][m], i= 1..4);

sum(a[i,m], i= 1..4);

In all of these cases, it is okay to iterate over i rather than m because the m is not being applied as a subscript directly to the i. Rather, the m is being applied to a name that the i is just a part of.

If you are trying to use Maple to do some fancy mathematical typesetting rather than trying to compute with these expressions, then you need to look for some other software. Typesetting is not what Maple is for. For example, you'll never make that summation sign that has n = 0 <> i below it. If you wanted to compute it, it would be easy; you just can't display it.

@alljoyland 

It would help if you could post a link to a picture of some mathematical text which has the features that you are trying to describe. Even a picture of some handwritten mathematical text would help.

@alljoyland 

No, your expression

sum(a[i[m]]*diff(f[m](x),x), i= 1..4)

is not "okay" or "natural" if you iterate over i. It would be okay if you iterate over m:

sum(a[i[m]]*diff(f[m](x),x), m= 1..4).

You should've mentioned that the combstruct package is a part of regular Maple. It does not need to downloaded separately.

@Axel Vogt Please post the steps to convert the integral to [0..1]^4.

@acer Thanks, that's really deep sleuthing, man. I suspected that the difference was in assigned but I couldn't see that code.

Could you please provide the source of the Maple code, its date of publication or posting, and a rough translation into mathematical English of any surrounding text?

What is your suggested value for "Zeigerlange vom Punkt (0,0) bis Pk in mm"?

The first problem is that there are some weird characters in the code and some inappropriate usage of unevaluation quotes (as in EE_:= 'E_ - P0_';). But even after correcting those I get errors.

@Thomas Richard The Cuba methods and all of Maple's numerical multiple integration methods are limited to regions of integration that are hyperrectangles. Perhaps there is a way to convert this integral thus.