Question: How to calculate the image of ideal in maple?

below code is calculate basis of kernel and kernel

i guess basis of image is 

remove(has, Ga, [r,u,v,w]); if this correct, i eliminate this, i can get the image

however it include variable 'a'

is it correct? if not, how to calculate? 

my final goal is to make unexact sequence into exact sequence

restart;
with(Groebner):
K := {r-x^4,u-(x^3)*y,v-x*y^3,w-y^4};
G := Basis(K, 'tord', degrevlex(r,u,v,w));
R1 := eliminate(G, {r,u,v,w}); # eliminate is the reverse of Basis
Ga := Basis({a*G[1],a*G[2],a*G[3],a*G[4],a*G[5],a*G[6],a*G[7],a*G[8],a*G[9],a*G[10],a*G[11],a*G[12],a*G[13],a*G[14], (1-a)*K[1], (1-a)*K[2], (1-a)*K[3], (1-a)*K[4]}, 'tord', deglex(a,r,u,v,w));
Ga := remove(has, Ga, [x,y,a]);
K0 := eliminate(Ga, {r,u,v,w});

G1 := Ga;
K1 := eliminate(G1, {r,u,v,w});
K1 := {r - (u*w^2)^(1/3)*u/w, v - u*w^2/(u*w^2)^(2/3)};
G1a := Basis({a*G1[1],a*G1[2],a*G1[3],a*G1[4], (1-a)*K1[1], (1-a)*K1[2]}, 'tord', deglex(a,r,u,v,w));
G1a := remove(has, G1a, [x,y,a]);
K1 := eliminate(G1a, {r,u,v,w});

G2 := G1a;
K2 := eliminate(G2, {r,u,v,w});
K2 := {r - v^4/w^3, u - v^3/w^2};
G2a := Basis({a*G2[1],a*G2[2], (1-a)*K1[1], (1-a)*K1[2]}, 'tord', deglex(a,r,u,v,w));
G2a := remove(has, G2a, [x,y,a]);
K2 := eliminate(G2a, {r,u,v,w});

notice
G2a == G1a

G2a -> G1a -> Ga -> 

K2 -> K1 -> K0 -> K

final ideal K2 = r - v^4/w^3, u - v^3/w^2