This is an optional argument for the schurResolution routine. It specifies an upper bound for the number of syzygy modules in the equivariant resolution of an equivariant module M to be computed by the routine. If a SyzygyLimit is not specified, then all syzygy modules are computed.
The example below computes the 0-th to 3-rd syzygy modules of the 5-th Veronese embedding of P^2.
i1 : S = schurRing(s,3); |
i2 : rep = s_{5}; |
i3 : M = {1_S,s_{5},s_{10},s_{15},s_{20},s_{25},s_{30}}; |
i4 : schurResolution(rep,M,SyzygyLimit => 3) o4 = {{(0, s )}, {(2, s + s )}, {(3, s + s + s + s + s + s + s + 2s + s + s () 8,2 6,4 12,2,1 11,4 11,3,1 10,5 10,4,1 10,3,2 9,6 9,5,1 9,4,2 8,7 ---------------------------------------------------------------------------------------------------------------------------- + s + s + s + s + s + s )}, {(4, s + s + 2s + s + s + s + 8,6,1 8,5,2 8,4,3 7,6,2 7,5,3 6,5,4 15,4,1 15,3,2 14,5,1 14,4,2 14,3,3 13,7 ---------------------------------------------------------------------------------------------------------------------------- 3s + 3s + 2s + s + 3s + 4s + 4s + s + s + 3s + 5s + 5s + 13,6,1 13,5,2 13,4,3 12,8 12,7,1 12,6,2 12,5,3 12,4,4 11,9 11,8,1 11,7,2 11,6,3 ---------------------------------------------------------------------------------------------------------------------------- 3s + 2s + 3s + 5s + 4s + 3s + 2s + 3s + 4s + 3s + s + 2s + 11,5,4 10,9,1 10,8,2 10,7,3 10,6,4 10,5,5 9,9,2 9,8,3 9,7,4 9,6,5 8,8,4 8,7,5 ---------------------------------------------------------------------------------------------------------------------------- s )}} 7,7,6 o4 : List |