 ring r=32003,(a,b,c,d),dp;
ideal j=bcad,b3a2c,c3bd2,ac2b2d;
list T=mres(j,0); // 0 forces a full resolution
// a minimal set of generators for j:
print(T[1]);
==> bcad,
==> c3bd2,
==> ac2b2d,
==> b3a2c
// second syzygy module of r/j which is the first
// syzygy module of j (minimal generating set):
print(T[2]);
==> bd,c2,ac,b2,
==> a,b,0, 0,
==> c, d, b,a,
==> 0, 0, d,c
// the second syzygy module (minimal generating set):
print(T[3]);
==> b,
==> a,
==> c,
==> d
print(T[4]);
==> 0
betti(T);
==> 1,0,0,0,
==> 0,1,0,0,
==> 0,3,4,1
// most useful for reading off the graded Betti numbers:
print(betti(T),"betti");
==> 0 1 2 3
==> 
==> 0: 1   
==> 1:  1  
==> 2:  3 4 1
==> 
==> total: 1 4 4 1
==>
