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Macaulay2Doc > basic commutative algebra > M2SingularBook > Singular Book 1.3.3

Singular Book 1.3.3 -- properties of ring maps

i1 : S = QQ[a,b,c];
i2 : R = QQ[x,y,z];
i3 : phi = map(R,S,{x,y,x^2-y^3})

                          3    2
o3 = map (R, S, {x, y, - y  + x })

o3 : RingMap R <--- S
i4 : isInjective phi

o4 = false
i5 : ker phi

            3    2
o5 = ideal(b  - a  + c)

o5 : Ideal of S
Packaged code for computing preimage is missing, but it's easy to do, as follows.
i6 : psi = map(R,S,{x,x+y,z-x^2+y^3})

                            3    2
o6 = map (R, S, {x, x + y, y  - x  + z})

o6 : RingMap R <--- S
i7 : isInjective psi

o7 = true
i8 : ker psi

o8 = ideal ()

o8 : Ideal of S