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Macaulay2Doc :: kernel(RingMap)

kernel(RingMap) -- kernel of a ringmap

Synopsis

Description

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 : G = map(S,R,{s^5, s^3*t^2-t, s*t-s, t^5})

               5   3 2                5
o5 = map(S,R,{s , s t  - t, s*t - s, t })

o5 : RingMap S <--- R
i6 : ker(G, SubringLimit=>1)

            2 10      2   7     2 7      2 2 4     3 5         6       3 3  
o6 = ideal(a c   + 10a b*c  - 5a c  + 25a b c  + 2a c  - 5a*b*c  - 5a*b c  +
     ------------------------------------------------------------------------
         6      5      2 3       3   2       2 3       4      2 2      3 2  
     5a*c  - a*b  + 10a b c - 15a b*c  - 5a*b c  - 5a*b  + 25a b c - 5a c  -
     ------------------------------------------------------------------------
      5    4        3      2           2     2
     c  + a  - 10a*b  + 20a b*c - 10a*b  + 5a c - 5a*b - a)

o6 : Ideal of R
In the case when everything is homogeneous, Hilbert functions are used to speed up the computations.

Caveat

It should be possible to interrupt the computation and restart it, but this has not yet been implemented.

See also