# Singular Book 2.1.7 -- maps induced by Hom

 i1 : A = QQ[x,y,z] o1 = A o1 : PolynomialRing i2 : M = matrix(A, {{1,2,3},{4,5,6},{7,8,9}}) o2 = | 1 2 3 | | 4 5 6 | | 7 8 9 | 3 3 o2 : Matrix A <--- A i3 : Hom(M,A^2) o3 = | 1 0 4 0 7 0 | | 0 1 0 4 0 7 | | 2 0 5 0 8 0 | | 0 2 0 5 0 8 | | 3 0 6 0 9 0 | | 0 3 0 6 0 9 | 6 6 o3 : Matrix A <--- A i4 : Hom(A^2,M) o4 = | 1 2 3 0 0 0 | | 4 5 6 0 0 0 | | 7 8 9 0 0 0 | | 0 0 0 1 2 3 | | 0 0 0 4 5 6 | | 0 0 0 7 8 9 | 6 6 o4 : Matrix A <--- A
Notice that the basis that Macaulay2 uses for Hom(A^3,A^2) is different than the basis used by Singular.

The function contraHom of the Singular book in example 2.1.7 could be coded in the following way.

 i5 : contraHom = (M, s) -> ( (n,m) := (numgens target M, numgens source M); R := mutableMatrix(ring M, s*n, s*m); for b from 0 to m-1 do for a from 0 to s-1 do for c from 0 to n-1 do R_(a*n+c,a*m+b) = M_(b,c); matrix R ) o5 = contraHom o5 : FunctionClosure
Let's try an example.
 i6 : contraHom(M,2) o6 = | 1 4 7 0 0 0 | | 2 5 8 0 0 0 | | 3 6 9 0 0 0 | | 0 0 0 1 4 7 | | 0 0 0 2 5 8 | | 0 0 0 3 6 9 | 6 6 o6 : Matrix A <--- A