Given a module M over the ring of operators $k[x_1..x_c]$, the call $N = moduleAsExt(M,R)$ produces a module N over the ring R whose ext module is the exterior algebra on n=numgensR generators tensored with M. This script computes numValues values of the Hilbert function of $$ M \otimes \wedge k^n, $$ which should be equal to the total betti numbers of N.
i1 : kk = ZZ/101; |
i2 : S = kk[a,b,c]; |
i3 : ff = matrix{{a^4, b^4,c^4}};
1 3
o3 : Matrix S <--- S
|
i4 : R = S/ideal ff; |
i5 : Ops = kk[x_1,x_2,x_3]; |
i6 : MM = Ops^1/(x_1*ideal(x_2^2,x_3)); |
i7 : N = moduleAsExt(MM,R); |
i8 : betti res( N, LengthLimit => 10)
0 1 2 3 4 5 6 7 8 9 10
o8 = total: 36 27 29 31 33 35 37 39 41 43 45
-6: 18 6 . . . . . . . . .
-5: . . . . . . . . . . .
-4: 18 21 21 7 . . . . . . .
-3: . . . . . . . . . . .
-2: . . 8 24 24 8 . . . . .
-1: . . . . . . . . . . .
0: . . . . 9 27 27 9 . . .
1: . . . . . . . . . . .
2: . . . . . . 10 30 30 10 .
3: . . . . . . . . . . .
4: . . . . . . . . 11 33 33
5: . . . . . . . . . . .
6: . . . . . . . . . . 12
o8 : BettiTally
|
i9 : hfModuleAsExt(12,MM,3) o9 = (23, 25, 27, 29, 31, 33, 35, 37, 39, 41) o9 : Sequence |
The object hfModuleAsExt is a method function.