//SINGULAR Example7.2.9




proc isLocallyFree(matrix S, int r)
{
   ideal F=fitting(S,r);
   ideal G=fitting(S,r-1);
   if((deg(F[1])==0)&&(size(G)==0)){return(1);}
   return(0);
}

ring R=0,(x,y,z),dp;
matrix S[2][3];
S=x-1,y-1,z,y-1,x-2,x;
ideal I=fitting(S,0);

qring Q=I;
matrix S=fetch(R,S);
isLocallyFree(S,1);

isLocallyFree(S,0);