Kurt Ewald wrote:

Many thanks for the procedure. But some actions, for instance IsNilPotent(GH), fail.

Permutation groups are the most efficient representation, and all commands work on them AFAIK. The group returned by FactorGroup should be converted to a permutation representation:

GH:= FactorGroup(G,H):
GH:= PermutationGroup(GH);

IsNilpotent(GH);

   true

Kurt Ewald wrote:

I had found another way, to create the FactorGroup.
R:=map(Representative,LeftCosets(H,G)) and then
M:=Group(R).
The results were the same as with your procedure. But I was not sure, weather my way is allright.

That was my first idea. I had posted it, and then I deleted it. That method can only work if G has a subgroup isomorphic to G/H. That is often true, but not always.

What do you want each frame of the animation to represent? For example, each frame could represent the intersection of the surface with a horizontal plane (also known as the level curves).

@Preben Alsholm You're right. I got stuck by a bug in Maple 16.0 (only) where the whole curve is not plotted if there is a single undefined point. Using other Maple, everything is fine.

@brian bovril You do have a point. Unfortunately, when you use is with a type, it's the same as using the type command. Unfortunately, integer is a type, not a property (in the Maple sense). (In contrast, real is a property, not a type.) See the eighth and ninth paragraphs at ?is .

@toandhsp Thank you for spotting the error in my Answer. I've fixed the original. The error was caused by my cutting-and-pasting from two separate runs, thus different random polynomials. I hope that you now understand the Answer.

Your equations are highly nonlinear---the exponents aren't even integers. There are 72 equations and 72 unknowns. It is reasonable to expect fsolve to take a long time with that. How long does it take?

@brian bovril Of course the tests fail. That Answer is just a floating-point approximation to the true answer. It isn't even an integer.

In the future, please use the upload arrow (green arrow---last item on the second row of the MaplePrimes toolbar) to upload your worksheet, or cut-and-paste your code in plaintext format, rather than pasting your code as an image. This will make it much easier for other people to work with your code.

@acer Good idea. But selectremove works just as well with functions as lists, and the Vector form makes the shuffling easier. So I reduced the code to this:

rearrangeCurves:= proc(
     v_items::specfunc(anything, PLOT),
     v_reorder::list([integer,integer]):= []
)
local p, curves, rest;
     (curves,rest):= selectremove(type, v_items, specfunc(anything, CURVES));
     curves:= < op(curves) >:         
     for p in v_reorder do
          curves[p]:= curves[p[[2,1]]]
     end do;
     PLOT(convert(curves,list)[], op(rest))
end proc:

@taro Note that op(a) and a[] are the same only for lists and sets.

@mehdi jafari Sorry, I meant imaginaryunit, not complexunit. I have corrected the original.

Regarding method= float: If you have a large Matrix of exact values (say, Gaussian integers as in this example), then it will be much faster to use method= float; for a 2x2 Matrix, it makes no significant difference.

@MuriloLobo Yes, I understand that extra values may need to be added after the trimming, if trimming is used.

I don't know how to account for the changing mean and standard deviation. Perhaps there is a standard distribution that is like a Normal but has finite bounds. I don't know enough about distributions to answer that. If you check ?Statistics,Distributions , you might find something.

Note that the mean and standard deviation of a random sample are unlikely to be exactly equal to the mean and standard deviation of the distribution from which the sample is drawn.

@MuriloLobo Your question is now well formed to me. Thank you.

To answer your question, would it be acceptable to generate a normal Normal sample with given mean and sd and then trim off the values that lie outside the 95% bounds? Do you want it trimmed on bottom end also?

I executed your worksheet twice using the menu command Edit -> Execute -> Worksheet and I cannot reproduce your problem. I get fully displayed matrices.

@Christopher2222 Are you referring to

kernelopts(limitjvmheap= true);
kernelopts(jvmheaplimit= 2000*Unit(mebibyte));

?