# Singular Book 1.1.10 -- methods for creating ring maps

In Macaulay2, ring maps from a polynomial ring are defined and used as follows.
 i1 : A = QQ[a,b,c]; i2 : f = a+b+a*b+c^3; i3 : B = QQ[x,y,z]; i4 : F = map(B,A,{x+y, x-y, z}) o4 = map (B, A, {x + y, x - y, z}) o4 : RingMap B <--- A
Notice that ring maps are defined by first giving the target ring, then the source ring, and finally the data.

Parentheses for functions with one parameter are optional.

 i5 : g = F f 3 2 2 o5 = z + x - y + 2x o5 : B i6 : A1 = QQ[x,y,c,b,a,z]; i7 : substitute(f,A1) 3 o7 = c + b*a + b + a o7 : A1
To map the first variable of A to the first variable of A1, the second variable of A to the second variable of A1, and so on, create the list of the first generators of A1
 i8 : v = take(gens A1, numgens A) o8 = {x, y, c} o8 : List i9 : G = map(A1,A,v) o9 = map (A1, A, {x, y, c}) o9 : RingMap A1 <--- A i10 : G f 3 o10 = c + x*y + x + y o10 : A1