QUESTION: Can Gap calculate kernel and image of module homomorphisms like
this one?

let T be a module homomorphism defined as follows:

Domain: K[x1,x2,w1,w2]/I (+) K[x1,x2,w1,w2]/I (+) K[x1,x2] (+) K[y1,y2]
Range: K[x1,x2,w1,w2]/I

T{h1(x1,x2,w1,w2),h2(x1,x2,w1,w2),f(x1,x2),g(y1,y2)}=
p1*h1+p2*h2-f(x1,x2)+g(r1(x1,x2,w1,w2),r2(x1,x2,w1,w2))

Where (+) denotes direct sum, I is an ideal in the polynomial ring
K[x1,x2,w1,w2], and p1, p2, r1 and r2 are fixed polynomials in K[x1,x2,w1,w2]

David.