// This script removes duplicate lattices
// from 1321out.txt. These are lattices
// that also appear in e4.txt or 1115red.txt.

load "e4.txt";
load "1115red.txt";
load "1321out.txt";

checking := e4 cat switch1red;

PrintFile("1321red.txt","switch2red := [");
newforms := 0;
for m in [1..#switch2] do
  found := false;
  for n in [1..#checking] do
    if Determinant(2*switch2[m]) eq Determinant(2*checking[n]) then
      L1 := LatticeWithGram(2*switch2[m]);
      L2 := LatticeWithGram(2*checking[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("1321red.txt",",");
    end if;
    printf "Lattice %o is new.\n",m;
    PrintFile("1321red.txt","Matrix(4,4,");
    PrintFile("1321red.txt",ElementToSequence(switch2[m]));
    PrintFile("1321red.txt",")");
  end if;
  if found eq true then
    printf "Lattice %o is old.\n",m;
  end if;
end for;
PrintFile("1321red.txt","];");
printf "There were %o new forms found.\n",newforms;