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

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

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 BasisGa := 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});noticeG2a == G1aG2a -> G1a -> Ga -> K2 -> K1 -> K0 -> Kfinal ideal K2 = r - v^4/w^3, u - v^3/w^2`
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