(no subject)

Consider the following polynomial

G := (y-(a*u+b*v))*(y-(a*v+b*u))

It is symmetric both in (a,b) and (u,v). I would like to espress it as a 
polynomial in Z[s,t,u,v,y]
where s=a+b and t=ab are the  symmetric elementary funcitions on a and b

Is it possible in axiom?

In other words, I am looking for a command which having G as input, 
returns

y^2 - s*(u+v)*y + (s^2-2*t)u*v + t*(u^2+v^2)

Thanks

Fabio