LIB "/home/galuis/graphical-models/singular/Markov.lib";

intvec d = 3,3,4; int n = size(d);
def pdR = probring(d);
intvec d2 = d[1..size(d)-1];
def H = probring(d2);
setring pdR;
int i,l;
string s;
poly form;
ideal phi;
for (i=1;i<=nvars(H);i++)
{
   s = "form = ";
   for (l=1; l<=d[n]; l++)
   {
     s = s , varstr(H,i) + string(l);
     if (l<d[n])
      {
        s = s , "+";
      }
   }
   execute(s);
   phi = phi,form;
}
phi = phi+0;
map Phi = H,phi;

/////////////////////////////////////////////////////////////////

setring pdR;
intvec v1 = 0,0,0; intmat m1 = bnet(n,v1); 
list g1 = globalMarkov(m1);
ideal G1 = MarkovIdeal(g1,d); 
ideal T1 = torideal(G1,d);
setring H;
ideal Q1 = preimage(pdR,Phi,T1);
Q1;


////////////////////////////////////////////////////////////////

setring pdR;
intvec v2 = 0,0,1; intmat m2 = bnet(n,v2); 
list g2 = globalMarkov(m2);
ideal G2 = MarkovIdeal(g2,d); 
ideal T2 = torideal(G2,d);
setring H;
ideal Q2 = preimage(pdR,Phi,T2);
Q2;

////////////////////////////////////////////////////////////////

setring pdR;
intvec v3 = 1,0,1; intmat m3 = bnet(n,v3); 
list g3 = globalMarkov(m3);
ideal G3 = MarkovIdeal(g3,d); 
ideal T3 = torideal(G3,d);
setring H;
ideal Q3 = preimage(pdR,Phi,T3);
Q3;

////////////////////////////////////////////////////////////////

setring pdR;
intvec v4 = 0,1,1; intmat m4 = bnet(n,v4); 
list g4 = globalMarkov(m4);
ideal G4 = MarkovIdeal(g4,d); 
ideal T4 = torideal(G4,d);
setring H;
ideal Q4 = preimage(pdR,Phi,T4);
Q4;

////////////////////////////////////////////////////////////////

setring pdR;
intvec v5 = 1,1,0; intmat m5 = bnet(n,v5); 
list g5 = globalMarkov(m5);
ideal G5 = MarkovIdeal(g5,d); 
ideal T5 = torideal(G5,d);
setring H;
ideal Q5 = preimage(pdR,Phi,T5);
Q5;