# LogTo("/home/wdj/gapfiles/comp_forms1.log");

composition:=function(F1,F2)
#buell's thrm 7.8
  local d1,d2,m,D,a1,b1,c1,a2,b2,c2,n1,n2,L1,L2,exps1,exps2,sqrfreed1,sqrfreed2,B,eqn1,eqn2,eqn3;
  a1:=F1[1];b1:=F1[2];c1:=F1[3];
  a2:=F2[1];b2:=F2[2];c2:=F2[3];
  d1:=b1^2-4*a1*c1;
  d2:=b2^2-4*a2*c2;
  L1:=PrimePowersInt(d1);
  exps1:=List([1..(Length(L1)/2)],i->L1[2*i]);
  sqrfreed1:=Product(List([1..Length(exps1)],i->L1[2*i-1]^(exps1[i] mod 2)));
  n1:=Int(Sqrt(d1/sqrfreed1));
  L2:=PrimePowersInt(d2);
  exps2:=List([1..(Length(L2)/2)],i->L2[2*i]);
  sqrfreed2:=Product(List([1..Length(exps2)],i->L2[2*i-1]^(exps2[i] mod 2)));
  n2:=Int(Sqrt(d2/sqrfreed2));
  if d1/n1^2 <> d2/n2^2 then Print("discrimants must be same mod squares\n"); return; fi;
  D:=d1/n1^2;
  m:=Gcd(a1*n2,a2*n1,(b1*n2+b2*n1)/2);
  for B in [1..AbsoluteValue(4*a1*a2)] do
    eqn1:=(m*n1*B mod (2*a1)=m*b1 mod (2*a1));
    eqn2:=(m*n2*B mod (2*a2)=m*b2 mod (2*a2));
    eqn3:=(m*(b1*n2+b2*n1)*B mod (4*a1*a2)=m*(b1*b2+D*n1*n2) mod (4*a1*a2));
#Print(eqn1,eqn2,eqn3,B,"\n");
    if (eqn1 and eqn2 and eqn3) then return [a1*a2/m^2,B,(B^2-D)*m^2/(4*a1*a2)]; fi;
  od;
Print("no soln\n");
end;