Inserting such values for the functions into the system for l[0]=-1:

(`@`(simplify, eval))(sysl, 
[a[0](x, y, t) = -2*(diff(q(y, t), y))*(diff(p(x, t), x)), 
a[1](x, y, t) = 0, a[2](x, y, t) = 
2*(diff(q(y, t), y))*(diff(p(x, t), x)), 
b[0](x, y, t) = 
(diff(p(x, t), t)+diff(p(x, t), `$`(x, 3))-
2*(diff(p(x, t), x))^3)/(3*(diff(p(x, t), x))), 
b[1](x, y, t) = diff(p(x, t), `$`(x, 2)), 
b[2](x, y, t) = 2*(diff(p(x, t), x))^2, 
c[0](x, y, t) = 
(diff(q(y, t), t)+diff(q(y, t), `$`(y, 3))-
2*(diff(q(y, t), y))^3)/(3*(diff(q(y, t), y))), 
c[1](x, y, t) = diff(q(y, t), `$`(y, 2)), 
c[2](x, y, t) = 2*(diff(q(y, t), y))^2]);

some equations are satisfied (as 0=0) but other ones do not. Check whether their expressions and their translation from TeX notation are correct.

So, it appears like this new linear structure cannot become the default, but can only be created from the DAG structure after checking that it is the right type (names and integer coefficients, say), or by an explicit command called by a programmer who cares about inserting the right input.

Anyway, it is my opinion that expand should distribute products over sums, but not expand sin(2*x) (or other mathematical functions) unless explicitly requested.

As I have understood from your blog 1, the design of the current DAG structure for polynomials is generic in that it allows for objects like function calls, other sums, etc. 

Now, when you say "variables" for this new "linear" structure, you mean just names as in your example?

I have just observed here that constructs with the composition operator, may become interpreted as an email address and linked to mailto.

If you are using 2D input, this is problematic as your input may not be faithfully reproduced by cut and pasting on a post here. I think that your best chance to get some answer is by  uploading your worksheet.

If you are using 2D input, this is problematic as your input may not be faithfully reproduced by cut and pasting on a post here. I think that your best chance to get some answer is by  uploading your worksheet.

Analysis, by computer "algebra" systems seems a troublesome issue. See, e.g. this thread.

Analysis, by computer "algebra" systems seems a troublesome issue. See, e.g. this thread.

Note, by contrast:

int(x^(n), x);
                                (n + 1)
                               x
                               --------
                                n + 1

Note, by contrast:

int(x^(n), x);
                                (n + 1)
                               x
                               --------
                                n + 1

OK, each of the four products would use only (n/2)(m/2) memory. But by dividing the polynomials in three pieces even less memory would be used, and so on. Handling too many pieces involves an overhead, implying an optimum number of divisions?

What does "divide and conquer" approach mean here?

For output to a file it can be done on the cmd console, or a batch file, something like:

cmaple file.mpl > file.out

Indeed, there are ports of many unix utilities to Win32, including cat.

For output to a file it can be done on the cmd console, or a batch file, something like:

cmaple file.mpl > file.out

Indeed, there are ports of many unix utilities to Win32, including cat.

Note that each solution of the cubic has an interval of validity. E.g. compare the plot of s[1] with that of cos(theta/3).