coarseMultigradedRegularity -- A truncation that has linear resolution

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{}                |
     +-----------------------+