# 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