# coarseMultigradedRegularity -- A truncation that has linear resolution

## Synopsis

• Usage:
• Inputs:
• Optional inputs:
• Strategy => , default value MinimalResolution
• Outputs:
• R, a list, degree such that truncate(R,M) has linear resolution

## Description

Uses a free resolution and takes the maximum degree of the terms.

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

See the proof of Proposition 2.7 in Tate Resolutions on Products of Projective Spaces.