@Carl Love 

I don't know much about Maplels, but I found the following in the help page ?Maplets,Elements,TextField: The command Maplets:-Elements:-TextField has an option tooltip= "...".

@Alejandro Jakubi Thanks for spotting. Code corrected above.

@JohnS Pattern matching "any name except x" is possible like this:

define(
     L, orderless, multilinear,
     L(a::And(name,Not(identical(x)))*b::function, c::function) = a*L(b,c),
     L(
          a::And(name,Not(identical(x)))*b::function,
          c::And(name,Not(identical(x)))*d::function
     ) = a*c*L(b,d)
);

@JohnS Under your definitions for L, we have L(x*f(x)) = x*L(f(x)). If that makes sense for your application, fine; but it doesn't fit my usual conception of linearity.

@JohnS 

It will work if you first put them on the sequence of constants:

constants:= constants, c, d, e, f;

@acer 

It wasn't the extra function calls that worried me; indeed, my procedure above has only one call per dimension, which is trivial. But I was worried about the one-element-at-a-time list building; each tuple is created that way. There might be a recursive way using Vectors. For a Cartesian product we know the number of tuples and their size from the start.

@Chia Go to help page ?parameter_classes and read the ninth section "End-of-Parameters marker, $". This usage of $ has no relation whatsoever to the more-familiar usage of $ as a sequence-building operator.

What do you mean by "high powers, like 10^17 by 10^12"?

Your story seems strange: Raising a 250x250 Matrix of floats to the 10^17 power is nearly instantaneous. What exactly are you doing? Why is a loop needed to raise a Matrix to a power?

@Preben Alsholm 

To convert any procedure to an inert form, you can prepend % to the name. So your

df_dz[s][i,j]:=subs(D=DD,convert(df_dz[s][i,j],D));

could be

df_dz[s][i,j]:= subs(D= %D, convert(df_dz[s][i,j], D));

The benefit of doing it this way is that it can be converted back to active form with the value command.

@ger89

Here I'm only answering your question #4: <0,0,0,0> is a column vector of four zeros. So, in the line in question, Preben solves the homogenous system of linear equations whose coefficient matrix is A10, and he requests that the prefix p be used for the names of any free variables.

For more information on the angle-bracket notation for vectors and matrices, see ?LinearAlgebra,General,MVshortcut

@kevinmaple The arrow notation -> is an abbreviation allowed for procedures (usually one-liners) that contain only an expression, an expression sequence, or an if statement. So

CountUnique:= (L::list)-> nops({L[]}):

is essentially equivalent to

CountUnique:= proc(L::list) return nops({L[]}) end proc:

See ?operators,functional

It's possible to do what you want using the parse statement. However, there's almost always a better way. What's your ultimate goal? to generate a Cartesian product of sets or lists? or some other combinatorial object? These things can be done without using loops nested to arbitrary depth. Nonetheless, in the Answer below, I show how to do what you asked for.

@Preben Alsholm Yes, thanks, that's what I meant. I corrected the Answer.

@GPY You need to minimize the 2-norm, which is equivalent to minimizing its square. Try this:

Minimize(LinearAlgebra:-Norm(minmat, 2)^2);

This should resolve the absolute-value error.

@ger89 The second argument to pdsolve needs to be w(x,t), not w(u,t).