@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.

@Preben Alsholm 

How do you explain the fact that even if f is declared global, the remember table is not removed 
when f is redefined. (Now f should be the same.)
This does not happen when f is redefined at top level.

@Mariusz Iwaniuk 

interface(version);
  Standard Worksheet Interface, Maple 2016.1, Windows 7, April 22 2016 Build ID 1133417

kernelopts(version);
  Maple 2016.1, X86 64 WINDOWS, Apr 22 2016, Build ID 1133417

@Carl Love 

I obtain correct results without forget. (Maple 2016.1, 64 bit, Win7).

@Carl Love 

Unfortunately in maths the pathological objects are in "majority". For example, most real numbers are transcendental and most continuous functions are nowhere differentiable.

@Carl Love 

I understood that the two examples were aimed to illustrate two different situations, but they are actually the same.

And the usual situation is that there are not as many linearly independent eigenvectors as the multiplicity of the corresponding eigenvalue (for multiplicities >1 of course).

@Carl Love 

The 2x2 identity matrix and the 2x2 zero matrix are both non-defective.
You should consider e.g. [[0,0],[0,0]] and [[0,1],[0,0]].

Edit: We may say that among the matrices with a single eigenvalue, the "majority" are defective.

I have included both stats.

@Christopher2222 

EurosimGrxxxkn1.mw

@Christopher2222 

This was really easy.
The delicate problem is to find a solid generator for scores X versus Y, knowing the rankings x and y.
I am not a statistician, but probably such problems are treated somewhere.

EurosimGrxxxkn.mw

@Christopher2222 

I have uploaded a corrected version.

Here is a simulation including qualifications from groups.
The qualification part is a bit un-orthodox because the points are chosen randomly around 1 and 3.
Maybe this should be fine-tuned -- the procedure myscor(i,j) -- using a nonuniform distribution
["Continuous" points have the advantage of avoiding the ties]

Also instead of using the "17.03" table to determines the third place matches,
a simple search was used, but respecting the "17.02" directive.

EurosimGrxxx.mw

edit: corrected

@Christopher2222 

The code does not update the ELOs. It is not difficult to include this.

It is also easy to include the group rounds (at least without graphics, unless it's done by someone knowing Maplets), but I do not know exaclty the qualification algorithm. AFAIK the first 2 teams in each group are automatically qualified.

In order to have a more realistic simulation one must decide when a draw occurs; probably something like outcome(X_versus_Y) in [0.5-e,0.5+e] for some e>0, e.g. e=0.1 or 0.2.