i1 : B = new MultigradedBettiTally from {(0, {0, 0}, 0) => 1, (1, {0, 2}, 2) => 1, (1, {1, 1}, 2) => 2, (1, {2, 0}, 2) => 1, (2, {1, 2}, 3) => 2, (2, {2, 1}, 3) => 2, (3, {2, 2}, 4) => 1} 0 1 2 3 o1 = 0: 1 . . . 2: . a2+2ab+b2 . . 3: . . 2a2b+2ab2 . 4: . . . a2b2 o1 : MultigradedBettiTally |
i2 : peek oo o2 = MultigradedBettiTally{(0, {0, 0}, 0) => 1} (1, {0, 2}, 2) => 1 (1, {1, 1}, 2) => 2 (1, {2, 0}, 2) => 1 (2, {1, 2}, 3) => 2 (2, {2, 1}, 3) => 2 (3, {2, 2}, 4) => 1 |
i3 : B({-1,-1}) 0 1 2 3 o3 = 0: ab . . . 2: . a3b+2a2b2+ab3 . . 3: . . 2a3b2+2a2b3 . 4: . . . a3b3 o3 : MultigradedBettiTally |
i4 : B[1] -1 0 1 2 o4 = 0: 1 . . . 2: . a2+2ab+b2 . . 3: . . 2a2b+2ab2 . 4: . . . a2b2 o4 : MultigradedBettiTally |
i5 : B[1] ++ B -1 0 1 2 3 o5 = 0: 1 1 . . . 2: . a2+2ab+b2 a2+2ab+b2 . . 3: . . 2a2b+2ab2 2a2b+2ab2 . 4: . . . a2b2 a2b2 o5 : MultigradedBettiTally |
i6 : B ** B 0 1 2 3 4 5 6 o6 = 0: 1 . . . . . . 2: . 2a2+4ab+2b2 . . . . . 3: . . 4a2b+4ab2 . . . . 4: . . a4+4a3b+6a2b2+4ab3+b4 2a2b2 . . . 5: . . . 4a4b+12a3b2+12a2b3+4ab4 . . . 6: . . . . 6a4b2+12a3b3+6a2b4 . . 7: . . . . . 4a4b3+4a3b4 . 8: . . . . . . a4b4 o6 : MultigradedBettiTally |
i7 : pdim B o7 = 3 |
i8 : compactMatrixForm = false o8 = false |
i9 : dual B -3 -2 -1 0 o9 = 1:{-2, -2} 2:{-1, -2} 2:{-1, -1} 1:{0, 0} 2:{-2, -1} 1:{0, -2} 1:{-2, 0} o9 : MultigradedBettiTally |
i10 : (1/2) * B 0 1 2 3 o10 = 1/2:{0, 0} 1/2:{2, 0} 1:{1, 2} 1/2:{2, 2} 1/2:{0, 2} 1:{2, 1} 1:{1, 1} o10 : MultigradedBettiTally |
i11 : 2 * oo 0 1 2 3 o11 = 1:{0, 0} 1:{0, 2} 2:{1, 2} 1:{2, 2} 1:{2, 0} 2:{2, 1} 2:{1, 1} o11 : MultigradedBettiTally |
i12 : lift(oo,ZZ) 0 1 2 3 o12 = 1:{0, 0} 1:{2, 0} 2:{1, 2} 1:{2, 2} 1:{0, 2} 2:{2, 1} 2:{1, 1} o12 : MultigradedBettiTally |
The object MultigradedBettiTally is a type, with ancestor classes BettiTally < VirtualTally < HashTable < Thing.