Some GAP routines

Some GAP routines

f5:= function(x,t,lcl,g,i)
     local hilf,hilf1,j;
     hilf:=Stabilizer(g,x[1]);
     hilf1:=ConjugacyClassSubgroups(g,hilf);
     j:=Position(lcl,hilf1);
     return t[i][j];
end;;

f4:= function(x,l,t,lcl,g)
     local hilf,i;
     i:=Position(lcl,x);
     hilf:=Product(l,x->f5(x,t,lcl,g,i));
     return (hilf/t[i][i]);
end;;

f3:= function(l,g)
     local t,ta,latt;
     t:=TableOfMarks(g);ta:=MatTom(t);
     latt:=Lattice(g);
     return Sum(latt.classes, x->f4(x,l,ta,latt.classes,g));
end;;

f2:= function(l,g)
     return Product(l,x->f3(x,g));
end;;

# Formula of White and Williamson to determine the number
# of g invariant partitions
f1:= function(l,g)
     return Sum(l,x->f2(x,g));
end;;

# dihedral group d12
d12:=Group((1,2,3,4,5,6,7,8,9,10,11,12),
(1,12)(2,11)(3,10)(4,9)(5,8)(6,7));;
d12.name:="D12";;
Print("Table of marks\n");
ta:=TableOfMarks(d12);
DisplayTom(ta);
Print("Subgroup lattice\n");
lat:=Lattice(d12);
Print("Number of U-invariant partitions\n");
for gtilde in lat.classes do
    g:=Representative(gtilde);
    if (IsCyclic(g)=false) then
       Print(g);Print("\n");
       o:=Orbits(g,[1..12]); # Print(o);Print("\n");
       po:=PartitionsSet(o);  # Print(po);Print("\n");
       erg:=f1(po,g);
       Print(erg);Print("\n");
    fi;
od;

Some GAP routines