############## ####################################################### # this is example 3.2.25 in the book ###################################################################### ###################################################################### t := CharacterTable("Suz");; irr := Irr(t){[1]};; ind := InducedCyclic( t, "all");; red := Reduced( t, irr, ind );; l := LLL( t, red.remainders );; r := l.remainders;; List( r , Norm ); ###################################################################### for i in [2,3,4] do Append(r , Symmetrizations(t,r,i) ); r := Reduced(t,irr,r).remainders; r := LLL(t,r).remainders; od; List(r , Norm); M := MatScalarProducts( t, r, r );; oe := OrthogonalEmbeddings( M, 42 );; Length( oe.solutions ); C := oe.vectors;; ###################################################################### Xli := List( oe.solutions , x -> C{x} );; irrli := List( Xli , x -> ( TransposedMat( x ) )^-1 * r );; for i in [1..Length( irrli )] do for j in [1..Length( irrli[i] )] do if irrli[i][j][1] < 0 then irrli[i][j] := - irrli[i][j]; fi; od; od; ###################################################################### irrli := Filtered(irrli, x -> not 0 in List( x, x_i -> x_i[1] ) );; Length(irrli); for i in [1..8] do red:= Reduced( t, irrli[i], Tensored(irrli[i], irrli[i] ) ); if red.remainders = [] then Print(i,","); fi; od; irrli := irrli{[5,6,7,8]};; ###################################################################### for i in [1..4] do red:= Reduced( t, irrli[i], Symmetrizations (t, irrli[i], 3) ); if red.remainders = [] then Print(i,","); fi; od; Append( irr, irrli[3] );