Singular

LIB "modules.lib";
ring R=0,(x,y),(lp,c);
Matrix M=id(2);
Module src=image(M);
matrix rules[2][2]=x,y,x2,y2;
Module tar=coker(M);
src;
==> R^2
==> 
==> 
tar;
==> cokernel | 1 0 |
==>          | 0 1 |
==> 
==> 
rules;
==> rules[1,1]=x
==> rules[1,2]=y
==> rules[2,1]=x2
==> rules[2,2]=y2
Homomorphism f=homomorphism(rules,src,tar);
f;
==> | x  y  |
==> | x2 y2 |
==> 
==> cokernel | 1 0 | <--- R^2
==>          | 0 1 |         
==> 
source(f);
==> R^2
==> 
==>