ring S = 32003, x(0..4), dp;
module MI=maxideal(1);
attrib(MI,"isHomog",intvec(-1));  
resolution kos = nres(MI,0);
print(betti(kos),"betti");

matrix alpha0 = random(32002,10,3);
module pres = module(alpha0)+kos[3];

attrib(pres,"isHomog",intvec(1,1,1,1,1,1,1,1,1,1));
resolution fcokernel = mres(pres,0);
print(betti(fcokernel),"betti");

module dir = transpose(pres);
intvec w = -1,-1,-1,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2;
attrib(dir,"isHomog",w);
resolution fdir = mres(dir,2);
print(betti(fdir),"betti");

if (not(defined(flatten))){ LIB "matrix.lib"; }
ideal I = groebner(flatten(fdir[2]));
resolution FI = mres(I,0);
print(betti(FI),"betti");

int codimI = nvars(S)-dim(I);
codimI;
degree(I); 
nvars(S)-dim(groebner(minor(jacob(I),codimI) + I));