### A.3.11 Kernel of module homomorphisms

Let , be two matrices of size and over the ring and consider the corresponding maps

We want to compute the kernel of the map This can be done using the `modulo` command:

More precisely, the output of `modulo(A,B)` is a `module` such that the given generating `vector`s span the kernel on the right-hand side.

      ring r=0,(x,y,z),(c,dp);
      matrix A[2][2]=x,y,z,1;
      matrix B[2][2]=x2,y2,z2,xz;
      print(B);
    ==> x2,y2,
    ==> z2,xz
      def C=modulo(A,B);
      print(C);            // matrix of generators for the kernel
    ==> yz2-x2, xyz-y2,  x2z-xy, x3-y2z,
    ==> x2z-xz2,-x2z+y2z,xyz-yz2,0
      print(A*matrix(C));  // should be in Im(B)
    ==> x2yz-x3,y3z-xy2, x3z+xy2z-y2z2-x2y,x4-xy2z,
    ==> yz3-xz2,xyz2-x2z,x2z2-yz2,         x3z-y2z2

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