Please post your points as plaintext so that I can cut and paste them.

@Kurt Ewald:

It is an important issue that I don't know the answer to. I am hoping that someone who is expert in the GroupTheory package will see this and respond. In this case, the group F returned by FactorGroup is reported to be isomorphic to G!

You have 16 equations and 12 unknowns. Do you expect some of the equations to be redundant?

@Markiyan Hirnyk 

The code can be corrected simply by adding with(stats) and removing the extraneous {}* from before the plot command. The is command and the change of the form of the inequalities are unnecessary.

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.