Yes, 20 teams had perfect results and shared first place.  Trefethen was quite surprised that so many did well.  For a Maple worksheet of the problems and solutions, see www.math.ubc.ca/~israel/challenge/challenge.mws.

The default is to show whatever y values are computed.  If your expression goes to infinity at some points in the interval being plotted, you can expect some very large values.  If you don't like those large values, you can specify an interval for y.  I don't know what would be a "better heuristic".   What would you suggest?

Do you mean this?

> Sum(piecewise(n=6, f(6), g(n)), n=1..N);

Sum(PIECEWISE([f(6), n = 6],[g(n), otherwise]),n = 1 .. N)

Do you mean this?

> Sum(piecewise(n=6, f(6), g(n)), n=1..N);

Sum(PIECEWISE([f(6), n = 6],[g(n), otherwise]),n = 1 .. N)

It's because the 23rd column of ZZ is -25/26 times the 19th column

> convert(Column(ZZ,19), list);

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 26/25, 0]

> convert(Column(ZZ,23), list);

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25/26, 0, 0, 0, -1, 0]

It's because the 23rd column of ZZ is -25/26 times the 19th column

> convert(Column(ZZ,19), list);

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 26/25, 0]

> convert(Column(ZZ,23), list);

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25/26, 0, 0, 0, -1, 0]

Have you reported this as a bug?  Unless the developers know the problem exists, it's unlikely to be fixed.  There should be a handy "Submit Maple Software Change Request" link under "Navigation" in the left column of this page.  Maybe the bug  can be fixed  in time for Maple 13.

Perhaps if you uploaded your document we could figure out what's wrong.

Here's my document where it works.

View 4541_doc.mw on MapleNet or Download 4541_doc.mw
View file details

Perhaps if you uploaded your document we could figure out what's wrong.

Here's my document where it works.

View 4541_doc.mw on MapleNet or Download 4541_doc.mw
View file details

Just guessing, but I'd suspect there might still be cases, maybe several orders of magnitude larger, where this would give the wrong answer.  It would be nice to have a method that is provably correct.

It seems you can do it gradually, to avoid using too much stack at once.

(Maple 6)

>  with(combinat):
  for j from 1 to 22 do numbpart(j*500) od:
  numbpart(11269);

231139177231303975514411787649455628959060199360109972557851\
519105155176180318215891795874905318274163248033071850

This is one less than the result returned by Maple 9 to 12.

... also for the others.  It looks to me like the code for combinat[numbpart] has not changed recently.  The OEIS entry mentions that Maple 6 got these right.  I wonder
why the Maple 6 code was changed.

Maybe a simple example would help.

Consider the equations

x + y  + z = a

x - y + z = b

x + z = c

If you want to solve for x,y,z, there is no solution, because you can eliminate x,y,z from these equations to get an identity a+b=2*c.  If a + b is not 2*c, the system is inconsistent; only if a + b = 2*c do you get (non-unique) solutions.

Similarly, in your example you can eliminate the variables Lm, Lp, nsp, La, nlpa, npa and find

LEF1*LEF2*Rp^2+LEF1*LEF2*omega^2*LAB1^2-LEF1^2*LAB1*LAB2*omega^2
-LEF1^2*Rp^2+Rs^2*LAB1^2-LAB1*LAB2*Rs^2 = 0

If this is not the case, there is no solution.
If it is the case, then you do get solutions.

> solve(%, LAB2);

> subs(LAB2=%, eqns);

> solve(%, vars);

{Lm = LEF1, nlpa = nlpa, npa = RootOf((omega^2*LEF1^2*LAB1*LCD2+LAB1*LCD2*Rs^2)*_Z^2+omega^2*LEF1^2*LAB1^2-LEF1*LEF2*omega^2*LAB1^2+LEF1^2*Rp^2-LEF1*LEF2*Rp^2), La = (-LEF1*LEF2*Rp^2-LEF1*LEF2*omega^2*LAB1^2+LEF1^2*LCD2*nlpa^2*LAB1*omega^2+LCD2*nlpa^2*Rs^2*LAB1+LEF1^2*Rp^2)/LEF1^2/nlpa^2/LAB1/omega^2, Lp = 1/LEF1*(-LEF1*Rp^2+LEF2*omega^2*LAB1^2+LEF2*Rp^2)/LAB1/omega^2, nsp = RootOf((-LEF1*Rp^2-LEF1*omega^2*LAB1^2+LEF2*Rp^2+LEF2*omega^2*LAB1^2)*_Z^2+LAB1,label = _L2)*omega*LEF1}

Maybe a simple example would help.

Consider the equations

x + y  + z = a

x - y + z = b

x + z = c

If you want to solve for x,y,z, there is no solution, because you can eliminate x,y,z from these equations to get an identity a+b=2*c.  If a + b is not 2*c, the system is inconsistent; only if a + b = 2*c do you get (non-unique) solutions.

Similarly, in your example you can eliminate the variables Lm, Lp, nsp, La, nlpa, npa and find

LEF1*LEF2*Rp^2+LEF1*LEF2*omega^2*LAB1^2-LEF1^2*LAB1*LAB2*omega^2
-LEF1^2*Rp^2+Rs^2*LAB1^2-LAB1*LAB2*Rs^2 = 0

If this is not the case, there is no solution.
If it is the case, then you do get solutions.

> solve(%, LAB2);

> subs(LAB2=%, eqns);

> solve(%, vars);

{Lm = LEF1, nlpa = nlpa, npa = RootOf((omega^2*LEF1^2*LAB1*LCD2+LAB1*LCD2*Rs^2)*_Z^2+omega^2*LEF1^2*LAB1^2-LEF1*LEF2*omega^2*LAB1^2+LEF1^2*Rp^2-LEF1*LEF2*Rp^2), La = (-LEF1*LEF2*Rp^2-LEF1*LEF2*omega^2*LAB1^2+LEF1^2*LCD2*nlpa^2*LAB1*omega^2+LCD2*nlpa^2*Rs^2*LAB1+LEF1^2*Rp^2)/LEF1^2/nlpa^2/LAB1/omega^2, Lp = 1/LEF1*(-LEF1*Rp^2+LEF2*omega^2*LAB1^2+LEF2*Rp^2)/LAB1/omega^2, nsp = RootOf((-LEF1*Rp^2-LEF1*omega^2*LAB1^2+LEF2*Rp^2+LEF2*omega^2*LAB1^2)*_Z^2+LAB1,label = _L2)*omega*LEF1}

Why should that worry you?  The answer is clearly 0, because the integrand is an odd function of z and the interval for z is symmetric around 0.