load "Markoff-Rosenberger_AP-K.mg";
load "Markoff-Rosenberger_AP-Z.mg";

D1:={-D : D in [1..400] | IsSquarefree(D) and (-D mod 4) eq 1}; // #D1 = 82
Dno1:={-D : D in [1..100] | IsSquarefree(D) and (-D mod 4) ne 1}; // #D3 = 20

a:=1;
b:=1;
c:=1;
DD:=D1 join Dno1;
for D in Sort(Setseq(DD)) do 
  LD:={};
  printf "====== %o ======\n",D;
  K:=NumberField(Polynomial([-D,0,1]));
  A1,A2:=Step4(K,1,1,1);
  for k1 in A1 do 
   for k2 in A2 do  
     boo,L6:=Step6(k1,k2,K,1,1,1); 
     if boo then 
     for us in L6 do
        u1:=us[1];  u2:=us[2];
        z:=((a+c+k1*u1)*((a+c)*(b+4*c)+4*c*k1*u1+k1^2*u1^2))/(u1*u2*k1*k2);
        if IsIntegral(Norm(z)) then 
	  if z eq 0 then  
            LD:=LD join {1,3}; 
          else 
            sss,R2:=SquarefreeFactorization(Integers()!Norm(z)); 
            LD:=LD join Seqset(Divisors(R2)); 
          end if;
        end if;
     end for;
     end if;
   end for;
  end for;
  for R in LD do 
    AP:=MarkoffRosenberger_AP(a,b,c,R,K);
    APZ:=MarkoffRosenberger_AP_Z(a,b,c,R);
    if #AP ne #APZ then	
      printf "%o -- %o --> %o \n",R,D,AP;
    end if;
  end for;	
end for;

/* OUTPUT

luna:cuentas enrique$ magma proof_theorem_quad_imaginary.txt 
Magma V2.18-3     Fri Feb 24 2012 11:45:01 on luna     [Seed = 2173281529]
Type ? for help.  Type <Ctrl>-D to quit.

Loading file "proof_theorem_quad_imaginary.txt"
Loading "Markoff-Rosenberger triplets in arithmetic progression-K.mg"
Loading "Markoff-Rosenberger triplets in arithmetic progression-Z.mg"
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1 -- -1 --> <<-K.1 + 2, K.1>, <2, 2*K.1>, <K.1 + 2, -K.1>, <-4*K.1 + 2, 2*K.1>, <2*K.1 - 1, -2*K.1>, <4*K.1 + 2, -2*K.1>, <3, 
-9>, <-2*K.1 - 1, 2*K.1>, <0, 0>, <-K.1 + 2, -K.1 - 3>, <3, 0>, <-15, 9>, <K.1 + 2, K.1 - 3>, <2, -2*K.1>, <3*K.1 - 4, -K.1 + 
3>, <-3*K.1 - 4, K.1 + 3>> 
2 -- -1 --> <<2*K.1 + 1, -K.1>, <-2*K.1 + 1, K.1>, <1, -K.1>, <1, K.1>, <0, 0>> 
> 
*/