@toandhsp 

Here it is solve's fault:

solve([x2/(x2+x5) = a1, x3/(x2+x5) = a2, x5/(x2+x5) = a3], {x2, x3, x5});
                    {x2 = 0, x3 = 0, x5 = 0}

On the other side  the first n-1 parameters are supposed to be "independent"
which is not the case:  log[10](2) + log[10](5) = 1.
lnrel(log[10](2), log[10](3), log[10](150));  #works

The code looks to me as unnecessarily complicated, almost obfuscated.
Please compare with the similar general solution in the provided link.

@Preben Alsholm 

@J4James 

691-694

@taro 

Actually remove expects the result of the procedure to be Boolean-"evaluable", i.e. creates a Boolen context.
This is not a problem because evalb(evalb(u)) = evalb(u).

@J4James 

See e.g.

Burden R.L.,Faires J.D. - Numerical Analysis, 9th Ed., Brooks/Cole 2011
(pseudocode provided, Maple oriented).

(probably) if one asks for a function f : N ^2 -> Z, defined in Maple by an expression having at most 5 characters such that a[i+1] = f(a[i], i).

The answer for f(x,y) is  2*x-y.  Proof?
[f is probably still unique if more characters are allowed, e.g. 7].

@rlopez 

@Preben Alsholm 

restart;
with(VectorCalculus);
int(1,[x=0..1,y=0..1]);

produces an error because VectorCalculus wants us to use:
int(1,[x,y]=Rectangle(0..1,0..1));
or
int(1,[x,y]=Region(0..1,0..1));

@taro 

Right click on the plot, choose Export in the context menu then "Encapsulated postscript".
You can also use:
p:=plot3d(x^2+y^2, x=-1..1,y=-1..1);
plottools:-exportplot("d:/temp/fig.eps",p); # choose an existent directory

In this case the plot is different but also wrong.

Not sure whether it's a bug or just a "generic" result.
Note that if n,p are numeric, the result is correct.

@gkokovidis 

In Maple 2016.1 ==> error

Please set

infolevel[int]:=5;

run it again and post the results.

This is indeed interesting; if the method is general enough you deserve congratulations!
Maybe you will show us the code or the algorithm.

@one man 

For a good simulation you will probably need to use ELO ratings, see

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

and update the ratings after each game or competition.

See also http://www.mapleprimes.com/posts/204346-Eurocup-Simulation-In-Maple

@Mac Dude 

mseries works in your example, but as mentioned in the answer,  x=0  cannot be replaced with x.
In your example you must use:

map(vvmseries,TM,[x=0,xp=0,y=0,yp=0,dl=0,dp=0,dkQ1=0],3);

On the other side, iterated series does not always work;
An example:

restart;
(* Test case for mtaylor *)

vvmseries:=proc(f,X::list(name=anything),n::posint)
local t;
  eval( f, `=`~(lhs~(X), rhs~(X)+t*~(lhs~(X)-rhs~(X))) );
  eval(convert(series(%, t, n), polynom),t=1);
end proc:
mymseries:=proc(f,vars,norder)
      local i,fs:=f;
          for i from 1 to numelems(vars) do
              fs:=convert(series(fs,vars[-i],norder),polynom);
          end do;
          return fs;
end proc:

f:=(x+y)^x:
f1:=vvmseries(f,[x=0,y=0],5):
f2:=mymseries(f,[x,y],5):
eval([f,f1,f2],[x=0.0001, y=0.001]);

[.9993189875,  .9993189874,  .7786567398]

Best regards,

V.A.

[edited example]

@one man 

1. The only problem is that the thread is about parametrization of a surface and you insist in posting curves (animated or not).
Your curves are not bad, but their place is not here.

2. I do not have a general method. In your example:
(x1^2+x2^2-0.4)^2+(x3+sin(x1*x2+x3))^4-0.1=0;

a) start with a parametrization U(t), V(t) of the curve U^2 + V^4 - 0.1 = 0.
b) define g(v,w) as the unique root z of    z + sin(w + z) = v
     (In Maple it us a RootOf)
c) The parametrization is
     x := sqrt(U(t) + 0.4) * cos(u)
     y := sqrt(U(t) + 0.4) * sin(u)
     z := g(V(t), x*y).