kernel(RingMap) -- kernel of a ringmap

• Function: kernel

• Usage:

  kernel f

• Inputs:
  • f, a ring map, $f: R \rightarrow S$
• Optional inputs:
  • SubringLimit => an integer, default value infinity, stop the computation after this many elements of the kernel have been found.
  • DegreeLimit => an integer, default value {}, stop the computation after generators for the kernel in this degree have been found
  • Strategy => a string, default value {}, Groebner basis computation strategy. See gb.
• Outputs:
  • an ideal, an ideal of $R$

i1 : R = QQ[a..d];

i2 : S = QQ[s,t];

i3 : F = map(S,R,{s^3, s^2*t, s*t^2, t^3})

                  3   2      2   3
o3 = map (S, R, {s , s t, s*t , t })

o3 : RingMap S <-- R

i4 : ker F

             2                    2
o4 = ideal (c  - b*d, b*c - a*d, b  - a*c)

o4 : Ideal of R

i5 : R = QQ[a..d];

i6 : S = QQ[s,t];

i7 : F = map(S,R,{s^3, s^2*t, s*t^2, t^3})

                  3   2      2   3
o7 = map (S, R, {s , s t, s*t , t })

o7 : RingMap S <-- R

i8 : K = ker(F, SubringLimit => 1)

            2
o8 = ideal(c  - b*d)

o8 : Ideal of R

i9 : assert(numgens K == 1)