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SchurRings :: schurResolution(..., SyzygyLimit => ...)

schurResolution(..., SyzygyLimit => ...) -- Specifies the number of syzygy modules to be computed

Description

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 P2.

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

Further information

See also