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Macaulay2Doc > substitution and maps between rings > evaluation and composition of ring maps

evaluation and composition of ring maps

evaluating ring maps

Once a ring map F is defined, the image of an element m in the source ring can be found by applying the map as F(m).
i1 : R = ZZ[x,y,z];
i2 : S = ZZ/101[x,y,z,Degrees => {{1,2},{1,3},{1,3}}]/ideal(x+z^3);
i3 : F = map(S,R,{x,y^2,z^3})

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

o3 : RingMap S <--- R
i4 : use R; F(107*x+y+z)

      2
o5 = y  + 5x

o5 : S

composition of ring maps

The function RingMap * RingMap performs a composition of ring maps. Evaluation of elements in the source of a ring map G can also be done using F(G(m)).
i6 : T = ZZ/5[x,y];
i7 : G = map(T,S);

o7 : RingMap T <--- S
i8 : G*F

                     2
o8 = map (T, R, {x, y , -x})

o8 : RingMap T <--- R
i9 : use R; G(F(107*x+y+z))

       2
o10 = y

o10 : T