// This script removes duplicate
// lattices from 1115out.txt
// Lattices that appear in 1115out.txt but not in
// e4.txt are written to 1115red.txt

load "e4.txt";
load "1115out.txt";

PrintFile("1115red.txt","switch1red := [");
newforms := 0;
for m in [1..#switch1] do
  found := false;
  for n in [1..#e4] do
    if Determinant(2*switch1[m]) eq Determinant(2*e4[n]) then
      L1 := LatticeWithGram(2*switch1[m]);
      L2 := LatticeWithGram(2*e4[n]);
      if IsIsometric(L1,L2) then
        found := true;
      end if;
    end if;
  end for;
  if found eq false then
    newforms := newforms + 1;
    if newforms gt 1 then
      PrintFile("1115red.txt",",");
    end if;
    printf "Lattice %o is new.\n",m;
    PrintFile("1115red.txt","Matrix(4,4,");
    PrintFile("1115red.txt",ElementToSequence(switch1[m]));
    PrintFile("1115red.txt",")");
  end if;
  if found eq true then
    printf "Lattice %o is old.\n",m;
  end if;
end for;
PrintFile("1115red.txt","];");
printf "A total of %o new forms were found.\n",newforms;