i1 : pieri({3,1}, {1}, QQ[a,b,c]) -- removes the last box from row 1 of the partition {3,1} o1 = | 3a 0 b 0 c 0 0 0 0 0 0 0 0 0 0 | | 0 3a 0 b 0 c 0 0 0 0 0 0 0 0 0 | | 0 0 2a 0 0 0 2b 0 c 0 0 0 0 0 0 | | 0 0 0 2a 0 0 0 2b 0 c 0 0 0 0 0 | | 0 0 0 0 2a 0 0 0 b 0 2c 0 0 0 0 | | 0 0 0 0 0 2a 0 0 0 b 0 2c 0 0 0 | | 0 0 0 0 0 0 0 a -1/2a 0 0 0 3b c 0 | | 0 0 0 0 0 0 0 0 0 a -2a 0 0 2b 2c | 8 15 o1 : Matrix (QQ[a..c]) <--- (QQ[a..c]) |
i2 : res coker oo -- resolve this map 8 15 10 3 o2 = (QQ[a..c]) <-- (QQ[a..c]) <-- (QQ[a..c]) <-- (QQ[a..c]) <-- 0 0 1 2 3 4 o2 : ChainComplex |
i3 : betti oo -- check that the resolution is pure 0 1 2 3 o3 = total: 8 15 10 3 0: 8 15 . . 1: . . 10 . 2: . . . 3 o3 : BettiTally |
The object pieri is a method function.