BeginPackage["Gaussian`"]
(* Copyright: Erich Kaltofen, 4/27/1990.
   Permission to use provided the copyright notice is not removed. *)

Gaussian`Quotient::usage =
"Quotient[a_, b_] computes a Gaussian integral quotient of two Gaussian integers. "

Gaussian`Remainder::usage =
"Remainder[a_, b_] computes a Gaussian integral remainder of two Gaussian integers. "

Gaussian`Normalize::usage =
"Normalize[a_] returns b such that b/a = 1, -1, I, or -I and -Pi/4 < Arg[b] <= Pi/4"

Begin["`private`"]

Quotient[a_, b_]:=
(* Gaussian integer division *)
   Block[{ratq, rp, ip},
         ratq = a/b;
         rp = Floor[ Re[ratq] + 1/2 ];
         ip = Floor[ Im[ratq] + 1/2 ];
         Return[rp + I ip]
        ]

Remainder[a_, b_]:=
(* Gaussian integer remainder *)
   a - Gaussian`Quotient[a, b] * b;

Normalize[a_]:=
(* normalize a such that -Pi/4 < Arg <= Pi/4 *)
   Block[{rp = Re[a], ip = Im[a]},
         Which[rp < 0 && ip == rp, -a,
               rp < 0 && Abs[ip] < Abs[rp], -a,
               ip > 0 && rp == -ip, - a * I,
               ip > 0 && Abs[rp] < Abs[ip], - a * I,
               ip < 0 && rp == ip, a * I,
               ip < 0 && Abs[rp] < Abs[ip], a * I,
               True, a]
        ]

End[]
EndPackage[]
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