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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