WFactorTex:= function (n)
        if n eq 1 then return 1; end if;
	n:=Factorization(n);
	s:="";
	for i in [1..#n] do
		s:=s*IntegerToString(n[i][1]);
		if n[i][2] gt 1 then s:=s*"^{"*IntegerToString(n[i][2])*"}"; end if;
		if i lt #n then s:=s*"\\cdot"; end if;
	end for;
	return s;
end function;

Pri:=function(n)
  if IsPrime(n) eq true then return IntegerToString(n); end if;
  return IntegerToString(n)*" = "*WFactorTex(n);
end function;

ListToTex:=function(s: selected := [], factors := [])
  a:=Open(s,"r");
  b:=Open(Substring(s,1,#s-3)*"tex.res","w");
  s:=Gets(a);
  t:=#StringToIntegerSequence(s);
  if #selected eq 0 then selected := [1..t]; end if;
  inf:=selected[1];
  Remove(~selected,1);
  while IsEof(s) ne true do
    s:=StringToIntegerSequence(s);
    t:= inf in factors select Pri(s[inf]) else s[inf];
    for i in selected do
      t*:= " & ";
      t*:= i in factors select Pri(s[i]) else IntegerToString(s[i]);
    end for;
    t*:="\\\\\n";
    fprintf b, t;
    s:=Gets(a);
  end while;
  delete(a); delete(b);
  return true;
end function;

PrintMatrixFile:=function(s,A)
  b:=Open(s,"w");
  for i in [1..#A] do
    for j in [1..#A[i]] do
      fprintf b,"%o ",A[i][j];
    end for;
    fprintf b,"\n"; Flush(b);
  end for;
  delete b;
  return(true);
end function;

OpenAndRead:=function(s)
  a:=Open(s,"r");
  s:=Gets(a);
  A:=[];
  while IsEof(s) ne true do
    Append(~A,StringToIntegerSequence(s));
    s:=Gets(a);
  end while;
  delete(a);
  return(A);
end function;

Ordena:=function(s,n:invers:=false, sortida)
  if Type(s) eq MonStgElt then A:=OpenAndRead(s); 
  elif Type(s) eq SeqEnum then A:=s; 
  else return false;
  end if;

  for i in [1..#A] do
    Insert(~A[i],1,0,[A[i][n]]);
    Remove(~A[i],n+1);
  end for;
  Sort(~A);
  for i in [1..#A] do
    Insert(~A[i],n+1,n,[A[i][1]]);
    Remove(~A[i],1);
  end for;
  if invers then
    for i in [1..Floor(#A/2)] do
      aux:=A[i]; A[i]:=A[#A-i+1]; A[#A-i+1]:=aux;
    end for;
  end if;
  if Type(sortida) eq MonStgElt then
    return(PrintMatrixFile(sortida,A));
  elif Type(sortida) eq SeqEnum then
    return A;
  else
    return(PrintMatrixFile(Substring(s,1,#s-3)*"ord.res",A));
  end if;
  return(false);
end function;

OrderByBiggestExponent:=function(s:invers:=false)
  A:=OpenAndRead(s); 
  B:=[];
  for i in [1..#A] do
    f:=Factorization(A[i][8]);
    m:=0;
    for j in [1..#f] do
      if f[j][2] gt m then m:=f[j][2]; end if;
    end for;
    p:=1;
    for j in [1..#f] do
      if f[j][2] eq m then p:=f[j][1]*p; end if;
    end for;
    Append(~B, [A[i][1],A[i][2],A[i][3],A[i][4],A[i][8], p, m]);
  end for;
  aux:=Ordena(B,7:invers:=invers, sortida:= Substring(s,1,#s-3)*"max.ord.res");
  return(aux);
end function;


pPart:=function(N,p)
while Integers()!N mod p eq 0 do N:=N/p; end while;
return Integers()!N;
end function;

ProbablyIrred:= function(N,i,l);
  A:=Open("prob-red-primes.res","r");
  s:=Gets(A);
  while not IsEof(s) do
    s:=StringToIntegerSequence(s);
    if s[1] eq N and s[2] eq i then
      p:=Factorization(s[3]);
      for i in p do
        l:=pPart(l,i[1]);
      end for;
      return l;
    end if;
    s:=Gets(A);
  end while;
  return false;
end function;


NotRamified:= function(N,i,l);
  A:=Open("ramif-primes.res","r");
  s:=Gets(A);
  while not IsEof(s) do
    s:=StringToIntegerSequence(s);
    if s[1] eq N and s[2] eq i then
      p:=Factorization(s[3]);
      for i in p do
        l:=pPart(l,i[1]);
      end for;
      return l;
    end if;
    s:=Gets(A);
  end while;
  return false;
end function;


IsMinimal:=function(N, i, l)
  a:=Open("1-2000.txt","r");
  s:=Gets(a);
  while IsEof(s) ne true do
    s:=StringToIntegerSequence(s);
    if s[1] gt N then delete(a); return true; end if;
    if s[1] eq N and s[2] eq i and s[1] ne s[3] and s[5] mod l eq 0 then delete(a); return false; end if;
    s:=Gets(a);
  end while;
  delete(a);
  return true;
end function;