//SINGULAR Example 2.8.6




ring R=0,(x,y,z),(c,dp);
module I=[xy,xz],[yz,xy];
module J=[y,z],[z,y];
ideal K=quotient(I,J);
K;

reduce(K*J,std(I));       //test if KJ is contained in I

qring A=std(K);
module Null;
module J=[xy,xyz-x2y2],[xy2,y2x];
ideal ann=quotient(Null,J);          //annihilator of J
ann;

module B1 = [x2,xy,y2],[xy,xz,yz];   //presentation of M1
module B  = [x,zx,zy],[y,zy,xy],[x+y,zx+zy,zy+xy];
module B2 = B[1],B[2],B1[1],B1[2];   //presentation of M2

reduce(B*B1,std(B2)); //test if im(B*B1) contained in im(B2)

quotient(B2+B,freemodule(3));        //the annihilator