@Nick : my solution found w[1] and w[2] in terms of w[3], assuming, as I said, that b and v are orthogonal.
Substitute those in to w[1]^2 + w[2]^2 + w[3]^2 = whatever, and solve for w[3].

@Nick : my solution found w[1] and w[2] in terms of w[3], assuming, as I said, that b and v are orthogonal.
Substitute those in to w[1]^2 + w[2]^2 + w[3]^2 = whatever, and solve for w[3].

In fact I think there will be convergence problems.  Note that for any positive integer k, one of the terms of the sum will have denominator ((k+1) alpha + alpha^2 + alpha^3 + (1 - alpha - alpha^2 - alpha^3) =  1 + k alpha, which means there is a singularity at alpha = -1/k.   This would mean that a series around alpha = 0 must have radius of convergence 0.  That doesn't mean that the approximation is bad, though: it may work as an asymptotic series.

In fact I think there will be convergence problems.  Note that for any positive integer k, one of the terms of the sum will have denominator ((k+1) alpha + alpha^2 + alpha^3 + (1 - alpha - alpha^2 - alpha^3) =  1 + k alpha, which means there is a singularity at alpha = -1/k.   This would mean that a series around alpha = 0 must have radius of convergence 0.  That doesn't mean that the approximation is bad, though: it may work as an asymptotic series.

> int((x+1)^(x+1), x);

                  x hypergeom([1, -x - 1], [2], -x)

It's certainly an incorrect antiderivative in this case.  I don't know if there is a closed-form antiderivative: integrals.com doesn't find one.  Interestingly enough, int(t^t, t) (which should be equivalent to this one by the change of variables t=x+1) returns unevaluated.

@pvrbik : I agree, exposition is important, but one aspect of good Maple exposition is to avoid "anti-patterns" such as building up a string one character at a time.

@pvrbik : I agree, exposition is important, but one aspect of good Maple exposition is to avoid "anti-patterns" such as building up a string one character at a time.

No worksheet was attached

Here's an improved version: I figured out how to change the images on labels in an existing Maplet rather than making a new Maplet for each run of the simulation.

fifasimulation2.mw

Here's how I got the flags.

I downloaded the flag gif files individually from the FIFA website, then used readbytes to get a list of integers corresponding to each file, putting the results in a table indexed by the countries.  I saved the table, then pasted the table into the code edit region.

An image can also be included in a document.  If it is in, say, a Label component, you can use DocumentTools[SetProperty] to change the image to a different one.

Here's an example, using Maplets to show the chart of a simulation.

fifasimulation.mw

The key point is to understand what display does.  Its inputs are plot structures that are already made.  While it can change some aspects of how those plot structures are viewed, e.g. it can "zoom in" by showing only part of a plot structure, it will never plot points that are not present in the original plot structure.

@acer : interesting, but the link to Doug's file 178_MakeMLA.zip doesn't work: I guess it didn't survive the move to the new MaplePrimes.

Yes, that's a pretty tall order. 

The graphics with the national flags would be hard to do in a document, I think, but it might be done in a Maplet.

Mathematica has the flags ready-made (except for England), but you can download individual gif files, e.g. from the FIFA web site, and they can be incorporated into a Maplet.  However, the user would then need to have those files:
I'd have to include code that produces the flag files on the user's system.  Then we have the annoyance that the default for currentdir is likely to be the Maple directory, where it's not a good idea to put files.

Downloading the ELO ratings data automatically is also not very simple, I think, although it should be possible using Sockets.

The simulation itself will be the easy part.

Jacques's link to JSTOR doesn't work any more: I'm not sure which document he was trying to link to, but it might have been either <http://www.jstor.org/stable/2307789> or <http://www.jstor.org/stable/330742>

Oh, I think I see what happened... Axel mentioned in another thread that he was adding "bug" tags to some of his postings.