@Christopher2222 

You can simply re-define the ranking of the loser(s) to 0.

@asa12 

I simply don't understand your maths and don't know about what solutiion you are talking.

The problem is very simple. GL(2,3) is (isomprphic to) a subgroup of S_8 generated by two permutations (those given by Generators(GL23)). So, it is also isomorphic to a group of permutation matrices. That's all.

@asa12 

Of course you can convert to matrices, but apriori there is none!

GL23 := GeneralLinearGroup(2, 3):
g:=Generators(GL23):
J:=LinearAlgebra:-IdentityMatrix(8):
J[convert(g[1],permlist,8)];  # this should be your aa;  

What solution? Having the generators, any element of the group is a product of them.
The sum of two matrices in GL is not generally in GL.

@asa12 

You were told that matrix representation is not implemented.
Actually, for GL(n,q) such a representation is obvious by definition and you may generate easily the matrices (al least when q is prime).

Representations as permutation groups are available only for GeneralLinearGroup and GeneralOrthogonalGroup, but for small parameters only (see the documentation).

@systemcode 

I do not know the algorithm in detail, the code is not simple, see:
showstat(fsolve);

@gkokovidis 

No, I have changed a bit the example such that Digits=400 is not enough.

@gkokovidis 

fsolve({(2*x+y+1)*exp(-(x-y-2)^4),   (3*x+2*y-1)*exp(-(x-y-1)^4)});

Sorry, but I don't know the meaning.

@samira moradi

In this case, you could try Microsoft Paint for the drawing.

Edit (for PS). The inequality appears implicitely in the definition of the disk.

@Markiyan Hirnyk 

I'd suggest to convert your code into a procedure (or module) and document it.

@one man 

@Al86 

Actually I have applied the Poisson formula for the Dirichlet problem for the unit disk in R^2(considered for u - x^2/2, which is harmonic).

See

Salsa S. et al - A Primer on PDEs, Springer, 2013

or

https://en.wikipedia.org/wiki/Dirichlet_problem

@Carl Love 

I knew that, but I wanted a simple wording.
Anyway in the help appears: "You should not assume that sets will be maintained in any particular order".

@John Fredsted 

I know, that is why I have provided alternatives (just in case the elements of f are really wanted).

Maple cannot find the general solution. But the provided analytic solution is not the general one neither (it depends only of a few constants).

In order to find such particular solutions, one can eliminate one of the unknown functions (using e.g. dsolve, or by hand) and then use pdsolve  with options HINT and build; in our case HINT=f(x)/(f(x)+g(t)) will work.

@Carl Love 

Yes, you are right.
It seems that the remember table is removed only at top level when f is redefined.