Uses a free resolution and takes the maximum degree of a term minus the homological position in each component. Then adjusts so that the sum of the degrees is at least the ordinary regularity.
i1 : (S,E) = productOfProjectiveSpaces{1,1,2}
o1 = (S, E)
o1 : Sequence
|
i2 : I = ideal(x_(0,0)^2,x_(1,0)^3,x_(2,0)^4)
2 3 4
o2 = ideal (x , x , x )
0,0 1,0 2,0
o2 : Ideal of S
|
i3 : R = coarseMultigradedRegularity(S^1/I)
o3 = {2, 3, 4}
o3 : List
|
i4 : N = truncate(R,S^1/I); |
i5 : betti res N
0 1 2 3 4
o5 = total: 84 312 432 264 60
9: 84 312 432 264 60
o5 : BettiTally
|
i6 : netList toList tallyDegrees res N
+-----------------------+
o6 = |Tally{{2, 3, 4} => 84} |
+-----------------------+
|Tally{{2, 3, 5} => 144}|
| {2, 4, 4} => 84 |
| {3, 3, 4} => 84 |
+-----------------------+
|Tally{{2, 3, 6} => 60 }|
| {2, 4, 5} => 144 |
| {3, 3, 5} => 144 |
| {3, 4, 4} => 84 |
+-----------------------+
|Tally{{2, 4, 6} => 60 }|
| {3, 3, 6} => 60 |
| {3, 4, 5} => 144 |
+-----------------------+
|Tally{{3, 4, 6} => 60} |
+-----------------------+
|Tally{} |
+-----------------------+
|
We haven’t yet proven that this is right.