4.11 Kernel of module homomorphisms

Let A, B two matrices of size m x r and m x s over the ring R and consider the corresponding maps

   r   A     m
  R  -----> R
            ^
            |
            |
             s
            R  .

We want to compute the kernel of the map

   r   A     m         m
  R  -----> R  -----> R /Im(B) .

This can be done using the modulo command:

                   r   A     m
  modulo(A,B)=ker(R  -----> R /Im(B))  .
ring r=0,(x,y,z),(c,dp);
matrix A[2][2]=x,y,z,1;
matrix B[2][2]=x2,y2,z2,xz;
modulo(A,B);
==> _[1]=[yz2-x2,x2z-xz2]
==> _[2]=[xyz-y2,-x2z+y2z]
==> _[3]=[x2z-xy,xyz-yz2]
==> _[4]=[x3-y2z]