D2DNumbers2D

The package D2DNumbers2D provides functions for special manipulations of real numbers.

Initialization

BeginPackage["D2DNumbers2D`", {"D2DExpressions2D`", "D2DMaster2D`"}];

D2DNumbers2D::usage=
   "D2DNumbers2D is a package that provides utilities for manipulating special numbers.";

ChopImaginary2D::usage=
   "ChopImaginary2D[expr,(tol)] removes tiny imaginary parts from complex numbers; the default tolerance, if omitted, is 10^(-10).";

PrimaryAngle2D::usage=
   "PrimaryAngle2D[theta,period] normalizes an angle to a period; the period must be Pi or 2Pi radians; if the period is omitted, it defaults to 2Pi.";

PrimaryAngleRange2D::usage=
   "PrimaryAngleRange2D[{t1,t2}] normalizes a range of angles to primary angles.";

Begin["`Private`"];

Chop Imaginary Part

Format: ChopImaginary2D[expr,(tol)]
Removes the tiny imaginary parts of complex numbers in the expression that are less than a given tolerance.  The default tolerance, if omitted, is .

ChopImaginary2D[expr_,tol_:(10^(-10))] :=
   MapAll[If[IsTinyImaginary2D[#],Re[#],#]&,expr] /;
TrueQ[N[tol]>=0];

Primary Angle

Format: PrimaryAngle2D[θ,2Pi|Pi]
Adjusts an angle to a primary angle in the range 0≤θ<period.  The period may be Pi or 2Pi radians.  The default period, if omitted, is 2Pi radians.

PrimaryAngle2D[theta_?IsScalar2D,period_:2Pi] :=
   Module[{theta1=theta},
      While[IsNegative2D[theta1],
            theta1+=period];
      While[IsZeroOrNegative2D[period-theta1],
            theta1-=period];
      If[Head[theta]===Real,N[theta1],theta1] ] /;
(period==Pi || period==2Pi);

Primary Angle Range

Format: PrimaryAngleRange2D[{,}]
Normalizes a list of two angles so that the first is in the range , and the second is in the range .

PrimaryAngleRange2D[{t1_?IsScalar2D,t2_?IsScalar2D}] :=
   Module[{T1,T2,twoPi},
      T1=PrimaryAngle2D[t1];
      T2=PrimaryAngle2D[t2];
      twoPi=If[Head[T2]===Real,N[2Pi],2Pi];
      If[IsZeroOrNegative2D[T2-T1],
         {T1,T2+twoPi},
         {T1,T2}] ];

Epilogue

End[ ]; (* end of "`Private" *)
EndPackage[ ]; (* end of "D2DNumbers2D`" *)