Whats the best way to express this...?

[NotLKH]

I'm at a loss here.

I'm trying to describe the following, but I'll use an example to illustrate.

Given variables X, Y, and Z.

You have an equation, E1, such that

E1 = X²Y + X²Z + Y²X + Y²Z + Z²X + Z²Y

As you can see, the right hand side is the summation of all combinations of 2 elements taken from the group (X,Y,Z) Where one element is raised to the 2nd power, while the second element is to the first.

So, I'd like to ascribe a symbolic description to this, something along the lines of

E1 = Sum{X,Y,Z}^2,1,0
Of course, the 0 is superfluous, so this could also be said to be identical to:
E1 = Sum{X,Y,Z}^2,1

However, is this the best way? How would you do it?


Next:

lets say you had the following:

E1 = Sum{X₁,X₂,X₃}^1,1

and E2 = E1, thus
E1 x E2 = Sum{X₁,X₂,X₃}^2,2 + 2*Sum{X₁,X₂,X₃}^2,1,1

How would you approach developing a program to input E1 and E2, and outputing their product?