# kernel and coimage of a ring map

The kernel and coimage of a ring map can be computed using coimage and kernel . The output of ker is an ideal and the output of coimage is a ring or quotient ring.
 i1 : R = QQ[x,y,w]; U = QQ[s,t]/ideal(s^4+t^4); i3 : H = map(U,R,matrix{{s^2,s*t,t^2}}) 2 2 o3 = map (U, R, {s , s*t, t }) o3 : RingMap U <--- R i4 : ker H 2 2 2 o4 = ideal (y - x*w, x + w ) o4 : Ideal of R i5 : coimage H R o5 = ------------------- 2 2 2 (y - x*w, x + w ) o5 : QuotientRing