A very simple question (by example):

Consider two polynomials g and h:

with(PolynomialTools):

g:=FromCoefficientList([1,2,3],x);

h:=FromCoefficientList([4,5,6,7],x);

What is the syntax for computing the composition of g with h? (As a polynomial.)

For instance, I would like to use CoefficientList on the result.

I know the @ operator and the subs command and have tried using them in various ways, but with no success.

(Of course, my question is general; the above is just an example.)

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Edit: Additional question (which is my real question):

I'm writing a procedure that takes two polynomials g and h, and in which I define an unknown polynomial f. I want to compute its coefficients so that

f "composition" g = h

I write:

fCoeff:=seq(a[i],i=0..t) (to define the unknown coefficients. I can compute t.)

f := FromCoefficientList([fCoeff],x);

Then I would like to do something like:

comCoeff:=CoefficientList(f "composition" g,x)

If I have this, then I know how to solve for the unkown coefficients in f.

Can Maple solve a (simple) nonlinear diophantine equation with restrictions on the variables?

For example, I would like to solve simple equations where all values of the variables are positive integers.

I have tried isolve. For example:

isolve({29 = x^2 + y^2, 1 <= x, 1 <= y})

and

{isolve}({29 = x^2 + y^2, 1 <= x, 1 <= y})

but they just give a warning (and no solutions):

Warning, solutions may have been lost