hard code in this way is quite complex, how to do without hard code

after i get G which is an array for below, 

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));

the goal is to check kernel belong to image in Maple

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]);

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

after union ideal I and J, how to remove the intersection of I and J in order to do primedecomposition?

G1 := [v*y-w*x, r*y-u*x, -v*u+w*r, u*y^2-v*x^2, u^2*y-v*r*x, u*w*y-v^2*x, u^3-v*r^2, u^2*w-v^2*r, -v^3+u*w^2, x^4-r, x^3*y-u, x*y^3-v, y^4-w, w*y^2*x^2-v^2];

TypeTools[AddType](`w`,typefunc(string, symbol));
L:= `if`(G1::`w`, [op], '[]')(G1);

it seems above code incorrect.