//SINGULAR Example 2.7.14


ring A1=0,(a,b,c),dp;
ideal P=ab-c2;
qring A=std(P);                 // A=A1/P
poly p=abc;

ring B1=0,(x,y,z,a,b,c),dp;
ideal I=x2,y,ab-c2;
qring B=std(I);                 // B=B1/I
map ib=A,a,b,c;                 //the canonical map A---->B

ring C1=0,(u,v,a,b,c),lp;
ideal J=uv,ab-c2;
qring C=std(J);                 // C=C1/J
map ic=A,a,b,c;                 //the canonical map A---->C

ring T1=0,(x,y,z,u,v,a,b,c),dp; //B1 tensor C1 over A1
ideal K=imap(C1,J)+imap(B1,I);
qring T=std(K);                 //B tensor C over A
map jb=B,x,y,z,a,b,c;           //the canonical map B---->T
map jc=C,u,v,a,b,c;             //the canonical map C---->T

map psi=jc(ic);                 //the diagram is commutative
map phi=jb(ib);
psi(p);
phi(p);