import java.applet.Applet;
import java.awt.*;
import java.awt.event.*;
import java.applet.*;
import java.awt.geom.*;
import java.math.*;
import java.io.*;


/*This class does basic real arithmetic in the ring Z[phi], where
  phi is the golden ratio.  The class has the form

       a[0]+ phi a[1]

*/


public class GoldenComplex {
    GoldenReal x,y;



    
    /**constructors*/

    public GoldenComplex() {
	x=new GoldenReal();
	y=new GoldenReal();
    } 

    public GoldenComplex(GoldenComplex z) {
	x=new GoldenReal(z.x);
	y=new GoldenReal(z.y);
    } 

    public GoldenComplex(GoldenReal x0,GoldenReal y0) {
	this.x=x0;
	this.y=y0;
    }

    public GoldenComplex(int[] X) {
	x=new GoldenReal(X[0],X[1]);
	y=new GoldenReal(X[2],X[3]);
    }

    public GoldenComplex(long[] X) {
	x=new GoldenReal(X[0],X[1]);
	y=new GoldenReal(X[2],X[3]);
    }

    public GoldenComplex(int x1,int x2,int x3,int x4) {
        x=new GoldenReal(x1,x2);
        y=new GoldenReal(x3,x4);
    }

    public GoldenComplex(Complex w,int depth) {
	this.x=new GoldenReal(w.x,depth);
	this.y=new GoldenReal(w.y,depth);
    }

    public GoldenComplex(Complex w,int depth,double tol) {
	this.x=new GoldenReal(w.x,depth,tol);
	this.y=new GoldenReal(w.y,depth,tol);
    }



    public void print() {  
	x.printNoLine();
	System.out.print("  ");
	y.printNoLine();
	System.out.print("          ");
	double xx=x.toDouble();
	double yy=y.toDouble();
	System.out.println(xx+"   "+yy);
    }


    public void print2() {  
	double xx=x.toDouble();
	double yy=y.toDouble();
	System.out.println(xx+" "+yy);
    }


    public Complex toComplex() {
	Complex z=new Complex(x.toDouble(),y.toDouble());
	return(z);
    }

    public static GoldenComplex random() {

	double d1=Math.random();
	double d2=Math.random();
	int[] t1=GoldenRatio.bestFit(d1,50);
	int[] t2=GoldenRatio.bestFit(d2,50);
	GoldenComplex z=new GoldenComplex(t1[0],t1[1],t2[0],t2[1]);
	return(z);
    }

    public static boolean equals(GoldenComplex z1,GoldenComplex z2) {
	if(GoldenReal.equals(z1.x,z2.x)==false) return(false);
	if(GoldenReal.equals(z1.y,z2.y)==false) return(false);
	return(true);
    }

    public static GoldenComplex plus(GoldenComplex z1,GoldenComplex z2) {
	GoldenComplex z3=new GoldenComplex(GoldenReal.plus(z1.x,z2.x),GoldenReal.plus(z1.y,z2.y));
	return(z3);
    }


    public static GoldenComplex minus(GoldenComplex z1,GoldenComplex z2) {
	GoldenComplex z3=new GoldenComplex(GoldenReal.minus(z1.x,z2.x),GoldenReal.minus(z1.y,z2.y));
	return(z3);
    }


    public static GoldenComplex times(GoldenComplex z1,GoldenComplex z2) {
	GoldenReal a11=GoldenReal.times(z1.x,z2.x);
	GoldenReal a22=GoldenReal.times(z1.y,z2.y);
	GoldenReal a12=GoldenReal.times(z1.x,z2.y);
	GoldenReal a21=GoldenReal.times(z1.y,z2.x);
	GoldenComplex w=new GoldenComplex(GoldenReal.minus(a11,a22),GoldenReal.plus(a12,a21));
	return(w);
    }


    public GoldenComplex conjugate() {
	long[] U={x.a[0],x.a[1],-y.a[0],-y.a[1]};
	GoldenComplex z=new GoldenComplex(U);
	return(z);
    }

    public GoldenComplex scale(GoldenReal t) {
	GoldenComplex V=new GoldenComplex();
	V.x=GoldenReal.times(x,t);
	V.y=GoldenReal.times(y,t);
	return(V);
    }

    public static GoldenComplex triple(GoldenComplex z1,GoldenComplex z2,GoldenComplex z3) {
        GoldenComplex[] z=new GoldenComplex[5];
        z[1]=GoldenComplex.minus(z2,z1);
        z[2]=GoldenComplex.minus(z3,z1);
        z[3]=z[2].conjugate();
        z[4]=GoldenComplex.times(z[1],z[3]);
	return(z[4]);
    }

    /**This checks if the triangle z1,z2,z3 is positively oriented**/

    public static boolean isPositivelyOriented(GoldenComplex z1,GoldenComplex z2,GoldenComplex z3) {
	GoldenComplex z=triple(z1,z2,z3);
	GoldenReal y=new GoldenReal(-z.y.a[0],-z.y.a[1]);
	if(y.isPositive()==true) return(true);
	return(false);
    }

    /**This checks if z1 is on the line segment joining z2 to z2*/

    public static boolean isBetween(GoldenComplex z1,GoldenComplex z2,GoldenComplex z3) {
	GoldenComplex z=triple(z1,z2,z3);
	if((z.y.a[0]!=0)||(z.y.a[1]!=0)) return(false);
	GoldenReal x=new GoldenReal(-z.x.a[0],-z.x.a[1]);
	if(x.isPositive()==true) return(true);
	return(false);
    }

    public static boolean weakBetween(GoldenComplex z1,GoldenComplex z2,GoldenComplex z3) {
	if(equals(z1,z2)==true) return(true);
	if(equals(z1,z3)==true) return(true);
	GoldenComplex z=triple(z1,z2,z3);
	if((z.y.a[0]!=0)||(z.y.a[1]!=0)) return(false);
	GoldenReal x=new GoldenReal(-z.x.a[0],-z.x.a[1]);
	if(x.isPositive()==true) return(true);
	return(false);
    }

    /**This checks if the vectors z2-z1 and z3-z1 are positive multiples of each other.**/

    public static boolean isFolded(GoldenComplex z1,GoldenComplex z2,GoldenComplex z3) {
	GoldenComplex z=triple(z1,z2,z3);
	if((z.y.a[0]!=0)||(z.y.a[1]!=0)) return(false);
	GoldenReal x=new GoldenReal(z.x.a[0],z.x.a[1]);
	if(x.isPositive()==true) return(true);
	return(false);
    }

    /**This checks if the 3 points are collinear**/

    public static boolean collinear(GoldenComplex z1,GoldenComplex z2,GoldenComplex z3) {
	if(equals(z1,z2)==true) return(true);
	if(equals(z2,z3)==true) return(true);
	if(equals(z3,z1)==true) return(true);
	if(isBetween(z1,z2,z3)==true) return(true);
	if(isBetween(z2,z3,z1)==true) return(true);
	if(isBetween(z3,z1,z2)==true) return(true);
	return(false);
    }



    public static boolean collinear(GoldenComplex z1,GoldenComplex z2,GoldenComplex z3,GoldenComplex z4) {
	if(collinear(z1,z2,z3)==false) return(false);
	if(collinear(z2,z3,z4)==false) return(false);
	if(collinear(z3,z4,z1)==false) return(false);
	if(collinear(z4,z1,z2)==false) return(false);
	return(true);
    }


    /**This checks if the triangle z1,z2,z3 is positively oriented OR if the points 
       are collinear*/

    public static boolean weakPositivelyOriented(GoldenComplex z1,GoldenComplex z2,GoldenComplex z3) {
	if(isPositivelyOriented(z1,z2,z3)==true) return(true);
	if(collinear(z1,z2,z3)==true) return(true);
	return(false);
    }

    public static GoldenComplex random(int N) {
	return(new GoldenComplex(GoldenReal.random(N),GoldenReal.random(N)));
    }

    public static GoldenComplex interpolate(GoldenComplex z1,GoldenComplex z2) {
	GoldenReal x=GoldenReal.interpolate(z1.x,z2.x);
	GoldenReal y=GoldenReal.interpolate(z1.y,z2.y);
	GoldenComplex z=new GoldenComplex(x,y);
	return(z);
    }


}