71.19 SaveDecompositionMatrix

SaveDecompositionMatrix(d)
SaveDecompositionMatrix(d, filename)

The function SaveDecompositionMatrix saves the decomposition matrix d. After a decomposition matrix has been saved, the functions H.S, H.P, and H.D will automatically access it as needed. So, for example, before saving d in order to retrieve the indecomposable P(mu) from d it is necessary to type H.P(d, mu); once d has been saved, the command H.P(mu) suffices.

Since InducedDecompositionMatrix(d) consults the decomposition matrices for smaller n, if they are available, it is advantageous to save decomposition matrices as they are calculated. For example, over a field of characteristic~5, the decomposition matrices for the symmetric groups Sym_n with n le 20 can be calculated as follows:

gap> H:=Specht(5,5);;
gap> d:=DecompositionMatrix(H,9);; 
gap> for r in [10..20] do
>      d:=InducedDecompositionMatrix(d); 
>      SaveDecompositionMatrix(d); 
>    od; 

If your Hecke algebra record H is defined using a non--standard valuation map (see Specht) then it is also necessary to set the string ``H.HeckeRing'', or to supply the function with a filename before it will save your matrix. SaveDecompositionMatrix will also save adjustment matrices and the various other matrices that appear in Specht (they can be read back in using DecompositionMatrix). Each matrix has a default filename which you can over ride by supplying a filename. Using non--standard file names will stop Specht from automatically accessing these matrices in future.

See also DecompositionMatrix DecompositionMatrix DecompositionMatrix and CrystalDecompositionMatrix CrystalDecompositionMatrix. This function requires the package ``specht'' (see RequirePackage).

Previous Up Top Next
Index