############################################################################
#
# this is the code of exercise 4.5.3
#
###########################################################################
subs := function( ct, basm, vec, irrB, p )
local nullv, x, y, v, cands, psing, preg, rest, relations;
cands := [];
psing := Filtered( [1..Length(Irr(ct))],
                  i->IsInt( OrdersClassRepresentatives(ct)[i]/p ) );
preg := Difference( [1..Length(Irr(ct))], psing );
nullv := List( [1..Length(psing)], x -> 0 );
rest := Difference( irrB, basm );
relations := List( rest, i -> SolutionMat( Irr(ct){basm}{preg},
                  Irr(ct)[i]{preg} ) );;
for x in Cartesian ( List( vec{List(basm, i -> Position(irrB,i) )} ,            
                              c -> [0..c] ) ) do
  v:= [] ; v{List( basm, i -> Position(irrB,i) )} := x;
  v{List( rest, i -> Position(irrB,i) )} := List([1..Length(rest)],
                                                    i-> x*relations[i]);
  y := v * Irr(ct){irrB};;
  if ForAll( v, c -> c >= 0 ) and  y{psing} = nullv
         and ForAll( [1..Length(v)] , i -> v[i] <= vec[i] ) and Sum(v) > 0
         then Add( cands, v );
  fi;
od;
return(cands);
end;;