here is an example (I think, it looks quite nice, doesn't it?)
sage: RS = CartanType(['A',2,1]).root_system().root_space()
sage: X = iter(TransitiveIdealGraded(attrcall("pred"),RS.simple_roots()))
sage: i = 0
sage: while i < 25:^J x = X.next()^J print i,x^J i += 1
....:
0 alpha[0]
1 alpha[1]
2 alpha[2]
3 alpha[0] + alpha[1]
4 alpha[0] + alpha[2]
5 alpha[1] + alpha[2]
6 2*alpha[0] + alpha[1] + alpha[2]
7 alpha[0] + 2*alpha[1] + alpha[2]
8 alpha[0] + alpha[1] + 2*alpha[2]
9 2*alpha[0] + 2*alpha[1] + alpha[2]
10 alpha[0] + 2*alpha[1] + 2*alpha[2]
11 2*alpha[0] + alpha[1] + 2*alpha[2]
12 3*alpha[0] + 2*alpha[1] + 2*alpha[2]
13 2*alpha[0] + 2*alpha[1] + 3*alpha[2]
14 2*alpha[0] + 3*alpha[1] + 2*alpha[2]
15 2*alpha[0] + 3*alpha[1] + 3*alpha[2]
16 3*alpha[0] + 3*alpha[1] + 2*alpha[2]
17 3*alpha[0] + 2*alpha[1] + 3*alpha[2]
18 3*alpha[0] + 3*alpha[1] + 4*alpha[2]
19 4*alpha[0] + 3*alpha[1] + 3*alpha[2]
20 3*alpha[0] + 4*alpha[1] + 3*alpha[2]
21 4*alpha[0] + 4*alpha[1] + 3*alpha[2]
22 4*alpha[0] + 3*alpha[1] + 4*alpha[2]
23 3*alpha[0] + 4*alpha[1] + 4*alpha[2]
24 4*alpha[0] + 5*alpha[1] + 4*alpha[2]
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