LIB "matrix.lib";
ring S = 32003, x(0..4), dp;
resolution kos = nres(maxideal(1),0);
betti(kos);
matrix kos5 = kos[5];
matrix tphi = transpose(dsum(kos5,kos5));
matrix kos3 = kos[3];
matrix psi = dsum(kos3,kos3);
matrix beta1 = random(32002,20,2);
matrix tbeta1tilde = transpose(psi*beta1);
matrix tbeta0 = lift(tphi,tbeta1tilde);
if (not(defined(Ext_R))){ LIB "homolog.lib"; }
def E = Ext_R(1,kos[4]);
matrix kos4 = kos[4];
matrix tkos4pluskos4 = transpose(dsum(kos4,kos4));
matrix tgammamin1 = random(32002,20,1);
matrix tgamma0 = tkos4pluskos4*tgammamin1;
matrix talpha0 = concat(tbeta0,tgamma0);
matrix zero[20][1];
matrix tpsi = transpose(psi);
matrix tpresg = concat(tpsi,zero);
matrix pres = module(transpose(talpha0)) 
                + module(transpose(tpresg));
module dir = transpose(pres);
dir = prune(dir);
homog(dir);  
intvec deg_dir = attrib(dir,"isHomog");
attrib(dir,"isHomog",deg_dir-2);        // set degrees
resolution fdir = mres(prune(dir),2);
print(betti(fdir),"betti");
ideal I = groebner(flatten(fdir[2]));
resolution FI = mres(I,0);
print(betti(FI),"betti");

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