Remove files of the previous version

Diagram/Diagram.java

@@ -1,644 +0,0 @@
-import javax.swing.*;
-import java.awt.*;
-import java.awt.event.*;
-import java.awt.geom.*;
-import java.net.*;
-import java.io.*;
-import java.applet.*;
-
-
-class Node {
-    //*********************************************
-    //*                                           *
-    //* This class is needed for the class list.  *
-    //* A Node looks like an element of the list. *
-    //*                                           *
-    //*********************************************
-    
-    private int value;      //Value of the Node 
-    private Node next;      //The next Node in the list
-    private Node previous;  //The previous Node in the list
-    
-    public Node(){
-	value=0;
-    }
-    
-    public Node(int _value){
-	value=_value;
-    }
-    
-    public void setValue(int _value){
-	value=_value;
-    }
-
-    public void setPrevious(Node _previous){
-	previous=_previous;
-    }
-    
-    public void setNext(Node _next){
-	next=_next;
-    }
-
-    public int getValue(){
-	return value;
-    }
-    
-    public Node getPrevious(){
-	return previous;
-    }
-    
-    public Node getNext(){
-	return next;
-    }
-}
-
-class List {
-    //******************************************
-    //*                                        *
-    //* This class decribe a bichained list.   *
-    //* I don't use the linkedList of java     *
-    //* because it need use of complex Object. *
-    //*                                        *
-    //******************************************
-
-    private Node first;   //The first Node of the list
-    private Node last;    //The last Node of the list
-    public Node current;  //A Node we play the game of an iterator
-    public int length;    //The length of the list
-    
-    public List(){
-	length=0;
-    }
-    
-    public Node getFirst(){
-	return first;
-    }	
-    
-    public Node getLast(){
-	return last;
-    }
-
-    public void initCurrent(){
-	current=first;
-    }
-    
-    public void setCurrent(Node _current){
-	current=_current;
-    }
-    
-    public Node getCurrent(){
-	return current;
-    }
-    
-    public int isEnd(){
-	if(current==last){
-	    return 1;
-	}
-	else{
-	    return 0;
-	}
-    }
-
-    public void shift(){
-	// ---------------------------------------
-	//| Change the current node with the next |
-	// ---------------------------------------
-	current=current.getNext();
-    }
-
-    public void addLast(int value){
-	// ----------------------------------------------------
-	//| Add a Node of value 'value' at the end of the list |
-	// ----------------------------------------------------
-	Node node=new Node(value);
-	if(length==0){
-	    first=node;
-	    last=node;
-	}
-	else{
-	    last.setNext(node);
-	    node.setPrevious(last);
-	    last=node;
-	}
-	length++;
-    }
-    
-    public Node addBefore(int value){
-	// -----------------------------------------------------------------
-	//| Add a Node of value 'value' before the current Node of the list | 
-	//| and return the new Node                                         |
-	// -----------------------------------------------------------------
-	Node node=new Node(value);
-	if(current==first){
-	    first=node;
-	    node.setNext(current);
-	    current.setPrevious(node);
-	}
-	else {
-	    Node temp=current.getPrevious();
-	    temp.setNext(node);
-	    node.setPrevious(temp);
-	    current.setPrevious(node);
-	    node.setNext(current);
-	}
-	length++;
-	return node;
-    }
-    
-    public Node addAfter(int value){
-	// ----------------------------------------------------------------
-	//| Add a Node of value 'value' after the current Node of the list | 
-	//| and return the new Node                                        |
-	// ----------------------------------------------------------------
-	Node node=new Node(value);
-	if(current==last){
-	    last=node;
-	    node.setPrevious(current);
-	    current.setNext(node);
-	}
-	else{
-	    Node temp=current.getNext();
-	    temp.setPrevious(node);
-	    node.setNext(temp);
-	    current.setNext(node);
-	    node.setPrevious(current);
-	}
-	length++;
-	return node;
-    }
-	       
-    public void remove(Node node){
-	// ----------------------------------
-	//| Remove the Node node of the list |
-	// ----------------------------------
-	if(length!=0){
-	    if(length==1){
-		length=0;
-	    }
-	    else{
-		if(node==first){
-		    first=node.getNext();
-		    node=first;
-		}
-		else if(node==last){
-		    last=node.getPrevious();
-		    current=last;
-		}
-		else{
-		    (node.getPrevious()).setNext(node.getNext());
-		    (node.getNext()).setPrevious(node.getPrevious());
-		}
-		length--;
-	    }
-	}
-    }
-    
-    public int value(){
-	return current.getValue();
-    }
-
-    public int length(){
-	return length;
-    }
-}	  
- 
-public class Diagram extends JApplet implements ActionListener{
-    //*******************************************************
-    //*                                                     *
-    //* This class represent the window of the application. *
-    //*                                                     *
-    //*******************************************************
-
-
-    public static final long serialVersionUID = 0;
-    private Panel panel;           //Will draw graphics on the panel
-    private JTextField textField;  //An area in which will enter a braid word
-	    
-    public void init(){
-	JLabel label=new JLabel("Enter a word :");
-	label.setBounds(0,0,100,20);
-	add(label);
-	textField=new JTextField(10);
-	textField.addActionListener(this);  //Active the action listener of
-	textField.setBounds(100,0,380,20);
-	add(textField);
-	panel=new Panel();
-	panel.setBackground(Color.darkGray);
-	panel.setBounds(0,20,480,600);
-	add(panel);
-	add(new JLabel(""));
-    }
-
-    public void actionPerformed (ActionEvent event){
-	// ----------------------------------------------------------
-	//| Specify what the action on the element of the windows do |
-	// ----------------------------------------------------------
-	if(event.getSource()==textField){
-	    StringBuffer word=new StringBuffer(event.getActionCommand());
-	    panel.writeBraidWord(word);
-	}
-    }
-	
-    public String getAppletInfo() {
-        return "Handle reduction algorithm.";
-    }
-}
-    
-
-class Panel extends JPanel{
-    //************************************************
-    //*                                              *
-    //* This class is the key class of this program. *
-    //* It contains algoritms and drawing tools.     *
-    //*                                              *
-    //************************************************
-    
-    public static final long serialVersionUID = 0;
-
-    //=====> Braid variable
-    private StringBuffer braidWord;         //The initial braid word
-    private int braidWordSet=0;
-    private List braid;                     //The braid word as a list
-    
-    //=====> Strand variable
-    private int strandNumber=5;             //The number of strand
-    private float strandStep;               //The distance between two strand
-    private float strandWidth;              //The width of a strand
-    private float strandLeft;               //The x position of the leftmost strand
-    private float[] xPos;                   //The x postion of strands
-    private float[] xPosNext;               //The next x position of strands 
-    private float yUp;                      //The y position of the first element of the braid
-    
-    //======> Color variable
-    private Color[] strandColor;             //The color of different strand
-    private Color handleColor=Color.black;   //The color of the handle
-    private Color originalHandleStrandColor; //The original color of the handle strand
-      
-    //======> Way variable 
-    private GeneralPath[] continuousWay;     //The currant continuous way of strands
-    
-    //======> Double Buffering variable   
-    private Image offScreenBuffer;           //A buffer in wich we draw and after drawing we will show this buffer
-    private int isDraw;                      //For not repeat drawing
-
-    // =================
-    //I                 I
-    //I Braid functions I
-    //I                 I
-    // =================
-
-    private void initBraid(){
-	// -----------------------------------------------------
-	//| Iniliasition of braid as a list and of strandNumber |
-	// -----------------------------------------------------
-	int length;
-	int value;
-	char letter;
-	strandNumber=2;
-	value=0;
-	braid=new List();
-	length=braidWord.length();                 //get the length of the braid word 
-	braid.addLast(0);                          //add a trivial at the begin
-	for(int i=0;i<length;i++){
-	    letter=braidWord.charAt(i);
-	    if(letter>='a' && letter<='z'){        //if we have a lower case letter
-		value=(int)(letter-'a')+1;         //value is 1 for 'a', 2 for 'b', ...
-		if(value+1>strandNumber){          //update the strand number        
-		    strandNumber=value+1;     
-		}
-	    }
-	    else if(letter>='A' && letter<='Z'){   //if we have an upper case letter
-		value=-(int)(letter-'A')-1;        //value is -1 for 'A', -2 for 'B', ... 
-		if(-value+1>strandNumber){         //update the strand number
-		    strandNumber=-value+1;
-		}
-	    }
-	    else{
-		value=0;
-	    }
-	    braid.addLast(value);                  //add the value at the list of the braid
-	}
-	braid.addLast(0);                          //add a trivial at th end
-    }
-
-
-    public void writeBraidWord(StringBuffer buffer){
-	// -----------------------------------------------------
-	//| Initialise the braid word and some other parameters |
-	//------------------------------------------------------
-	braidWord=buffer;
-	initBraid();                              //initialise the braid list
-	isDraw=0;                                 //we draw a new image
-	braidWordSet=1;
-	update(super.getGraphics());              //update draw
-    }
-
-    
-    // =================
-    //I                 I
-    //I Color functions I
-    //I                 I
-    // =================
-    
-    public void initStrandColor(){
-	// ---------------------------
-	//| Init the color of strands |
-	// ---------------------------
-	strandColor=new Color[strandNumber];                         //Make the table of strand color
-	for(int strand=1;strand<strandNumber+1;strand++){
-	    if(strandNumber<10){
-		strandColor[strand-1]=Color.getHSBColor((float)1-(float)strand/(float)10,(float)0.8,1);     
-	    }
-	    else {
-		strandColor[strand-1]=Color.getHSBColor((float)1-(float)strand/(float)strandNumber,(float)0.8,1);     
-	    }	
-	}
-    }
-
- 
-    // ==========================
-    //I                          I
-    //I Continuous way functions I
-    //I                          I
-    // ==========================
-
-    public void initContinuousWay(){
-	// -----------------------------------------
-	//| Start the continuous way for all strand |
-	// -----------------------------------------
-	continuousWay=new GeneralPath[strandNumber];             //Make the table of continuous way
-	xPos=new float[strandNumber];                            //Make the table of x position of strands
-	xPosNext=new float[strandNumber];                        //Make the table of next x position of strands
-	for(int strand=1;strand<strandNumber+1;strand++){
-	    continuousWay[strand-1]=new GeneralPath();           
-	    xPos[strand-1]=strandLeft+strand*strandStep;         //The xPos of n is strandLeft+n*strandStep
-	    continuousWay[strand-1].moveTo(xPos[strand-1],yUp);  //Start the continuous way at the y position yUp
-	}
-    }
-
-    public void closeContinuousWay(Graphics2D g,int strand){
-	// -------------------------------------------
-	//| Stop and draw the continous way of strand |
-	// -------------------------------------------
-	GeneralPath gp;
-	gp=continuousWay[strand-1];
-	g.setColor(strandColor[strand-1]);                                                            //Apply the color of strand
-	g.draw(gp);
-	gp=new GeneralPath();                                                                         //Make a new general path                                   
-	continuousWay[strand-1]=gp;                                                                   //Start the new continuous way
-    }
-   
-    public void permuteContinuousWay(int strand){
-	// ----------------------------------------------------------------- 
-	//| Echange the continuous way and the color of strand and strand+1 |
-	// -----------------------------------------------------------------
-	GeneralPath gp;
-	Color color;
-	//Echange continuous way 
-	gp=continuousWay[strand-1];
-	continuousWay[strand-1]=continuousWay[strand];
-	continuousWay[strand]=gp;
-	//Echange color
-	color=strandColor[strand-1];
-	strandColor[strand-1]=strandColor[strand];
-	strandColor[strand]=color;
-    }
-
-    // ================
-    //I                I
-    //I Math functions I
-    //I                I
-    // ================
-   
-    public double min(double a,double b){
-	if(a<b){
-	    return a;
-	}
-	else{
-	    return b;
-	}
-    }
-
-    public double max(double a,double b){
-	if(a>b){
-	    return a;
-	}
-	else{
-	    return b;
-	}
-    }
-
-    public double square(double a){
-	return a*a;
-    }
-
-    // ===================
-    //I                   I
-    //I Position function I
-    //I                   I
-    // ===================
-
-    public void calcXPosNext(){
-	// ----------------------------------------
-	//| Compute the nex x position of strands. |
-	//| It's a key function for animation.     |
-	// ----------------------------------------
-	for(int strand=0;strand<strandNumber;strand++){
-	    xPosNext[strand]=strandLeft+(strand+1)*strandStep;                                             //The general case
-	}
-    }
-
-    public void updateXPos(){
-	// ------------------------------------------------------------------
-	//| Update the x postion of strand with the nex x position of strand | 
-	// ------------------------------------------------------------------
-	for(int strand=0;strand<strandNumber;strand++){
-	    xPos[strand]=xPosNext[strand];
-	}	
-    }
-
-    public float[] calculIntersection(int strand,float yPos,int type){
-	// -----------------------------------------------------------------------
-	//| Compute the two key point for draw the generator strand |
-	// -----------------------------------------------------------------------
-	float []res=new float[4]; 
-	//res[0]<=res[1] is the x position of this points
-	//res[2]<=res[3] is the y position of this points
-	double decale=1.5*strandWidth;                                                      //Is distance of a strand with the other in the crossing
-	double distance;                         
-	if(type==1){                                                                        //If the crossing is positive 
-	    //We compute the distance between the left-up point and then right-down  
-	    distance=Math.sqrt(square(xPosNext[strand]-xPos[strand-1])+square(strandStep));
-	}
-	else {                                                                              //If the crossing is negative
-	    //We compute the distance between the right-up and the left-down 
-	    distance=Math.sqrt(square(xPos[strand]-xPosNext[strand-1])+square(strandStep));
-	}
-	double alpha=Math.acos(strandStep/distance);                                        //The angle of the crossing
-	double decalX=Math.sin(alpha)*decale;                                               //The x coords of decale
-	double decalY=Math.cos(alpha)*decale;                                               //The y coords of decale
-	
-	//The straight line D1 of equation x=m1*y+p1 contains the left-up and the right-down point
-	double m1=((double)strandStep)/((double)(xPosNext[strand]-xPos[strand-1]));
-	double p1=yPos-m1*((double)xPos[strand-1]);
-	//The straight line D2 of equation x=m2*y+p2 contains the right-up and the left-down point
-	double m2=((double)strandStep)/((double)(xPosNext[strand-1]-xPos[strand]));
-	double p2=yPos-m2*((double)xPos[strand]);
-	
-	double xInter=(p2-p1)/(m1-m2);                                                      //x coord of D1 inter D2               
-	double yInter=m1*xInter+p1;                                                         //y coord of D1 inter D2
-	
-	//Computaion of values of res, the min and max fonction are usefull for a good drawing
-	res[0]=(float)max(xInter-decalX,xPosNext[strand-1]);
-	res[1]=(float)min(xInter+decalX,xPosNext[strand]);
-	res[2]=(float)max(yInter-decalY,yPos);
-	res[3]=(float)min(yInter+decalY,yPos+strandStep);
-	return res;
-    }
-
-    // ===================
-    //I                   I
-    //I Drawing functions I
-    //I                   I
-    // ===================
-
-   
-    public void drawTrivial(float yPos){
-	// -------------------------------------
-	//| Draw a not extrem trivial generator |
-	// -------------------------------------
-	for(int strand=0;strand<strandNumber;strand++){
-	    continuousWay[strand].lineTo(xPosNext[strand],yPos+strandStep);
-	}
-    }
-    
-    public void drawNoCrossing(Graphics2D g,int strand,float yPos){
-	// ----------------------
-	//| Draw straight strand |
-	// ----------------------
-	continuousWay[strand-1].lineTo(xPosNext[strand-1],yPos+strandStep);
-    }
-
-    public void drawPositiveCrossing(Graphics2D g,int strand,float yPos){
-	// --------------------------
-	//| Draw a positive crossing |
-	// --------------------------
-	float inter[]=calculIntersection(strand,yPos,1);
-	continuousWay[strand-1].lineTo(inter[0],inter[2]);
-	closeContinuousWay(g,strand);	
-	continuousWay[strand-1].moveTo(inter[1],inter[3]);
-	continuousWay[strand-1].lineTo(xPosNext[strand],yPos+strandStep);
-	continuousWay[strand].lineTo(xPosNext[strand-1],yPos+strandStep);
-	permuteContinuousWay(strand);
-    }
-   
-    public void drawNegativeCrossing(Graphics2D g,int strand,float yPos){
-	// --------------------------
-	//| Draw a negative crossing |
-	// --------------------------
-	float inter[]=calculIntersection(strand,yPos,-1);
-	continuousWay[strand].lineTo(inter[1],inter[2]);
-	closeContinuousWay(g,strand+1);	
-	continuousWay[strand].moveTo(inter[0],inter[3]);
-	continuousWay[strand].lineTo(xPosNext[strand-1],yPos+strandStep);
-	continuousWay[strand-1].lineTo(xPosNext[strand],yPos+strandStep);
-	permuteContinuousWay(strand);
-    }
-
-    public void draw(Graphics g){
-	// --------------------------------------------
-	//| The main and first called drawing function |
-	// --------------------------------------------
-	Graphics2D g2=(Graphics2D) g;                                                            //A Graphics2D context is needed
-       	Rectangle r;                         
-	int generator;                                                                           //The absolute value of generator
-	int exponent;                                                                            //The sign of generator 1 or -1
-	float yPos;
-	//The current y position
-	r=getBounds();                                                                           //The dimension of the graphics window
-	g.setColor(Color.darkGray);                                                              //Background color       
-        g.clearRect(0,0,r.width,r.height);                                                       //Clear the drawing window 
-        g.drawRect(0,0,r.width-1,r.height-1);                                                    //Aply background color
-	
-	//Defintion of some strand parameter
-	strandStep=(float)min((double)r.width/(double)(strandNumber+1),(double)r.height/((double)(braid.length())));
-	strandWidth=strandStep/(float)5;
-	strandLeft=((float)r.width-((float)(strandNumber+1)*(float)strandStep+strandWidth))/(float)2;
-	yUp=(float)max((double)0,(double)((double)r.height-(double)strandStep*((double)(braid.length())))/(double)2);
-	
-	braid.initCurrent();                                                                     //Set current as braid.first  
-	initStrandColor();                                                                       //Init the strand color
-	initContinuousWay();                                                                     //Init then continuous way
-	g2.setStroke(new BasicStroke(strandWidth,BasicStroke.CAP_ROUND,BasicStroke.JOIN_BEVEL)); //Type of general path
-	yPos=yUp;                                                                                //Init current y position
-	int stop=0;                                                                              //stop is a flag for break the main while
-	while(stop==0){
-	    generator=braid.value();                                                             //Get braid value
-	    exponent=1;
-	    if(generator<0){                                                                     // \
-		exponent=-1;                                                                     //  Computation of generator and exponent
-		generator=-generator;                                                            // /
-	    }
-	    calcXPosNext();
-	    for(int strand=1;strand<strandNumber+1;strand++){
-		if(strand==generator && exponent==1){                                        //If the generator is positive        
-		    drawPositiveCrossing(g2,strand,yPos);
-		    strand++;
-		}
-		else if(strand==generator && exponent==-1){                                  //If the generato is negative 
-		    drawNegativeCrossing(g2,strand,yPos);
-		    strand++;
-		}
-		else{
-		    drawNoCrossing(g2,strand,yPos);
-		}
-	    }
-	    yPos+=strandStep;                                                                //Update yPos
-	    if(braid.isEnd()==1){                                                                //Are we at the end of the braid ?
-		stop=1;
-	    }
-	    else{
-		braid.shift();
-	    }
-	    updateXPos();                                                                        //Update xPos
-	}                                                                                        //Restart with the new generator
-	for(int strand=1;strand<strandNumber+1;strand++){                                         
-	    closeContinuousWay(g2,strand);                                                       //Close the continuous way
-	}
-    }
-
-    // ===================
-    //I                   I
-    //I Graphics function I
-    //I                   I
-    // ===================
-
-    public void paint(Graphics g){
-	if(isDraw==0){
-	    update(g);
-	    isDraw=1;
-	}
-	else{
-	    g.drawImage(offScreenBuffer,0,0,this);
-	}
-    }
-   
-    public void update(Graphics g) {
-	// -----------------------------------------------
-	//| Graphic update function with double-buffering |
-	// -----------------------------------------------
-	if(braidWordSet==1){
-	    Graphics gr; 
-	    if (offScreenBuffer==null||(!(offScreenBuffer.getWidth(this)==getBounds().width && offScreenBuffer.getHeight(this)==getBounds().height))){
-		offScreenBuffer=this.createImage(getBounds().width,getBounds().height);
-	    }
-	    gr=offScreenBuffer.getGraphics();
-	    draw(gr); 
-	    g.drawImage(offScreenBuffer,0,0,this);
-	}
-   }
-}
-
-
-
-

Diagram/diagram.html

@@ -1,14 +0,0 @@
-<html><head>
-<title>Braid applet, diagram page</title>   
-<script language="javascript"> </script> 
-</head>
-
-<body style="background-color: rgb(220, 220, 220);"> 
-<center><h1>Braid diagram applet</h1></center>
-
-<p><center>
-<applet code="Diagram.class" height="640" width="480">
-</applet>
-</p></center>
-
-</body>

HandleReduction.java

@@ -1,1519 +0,0 @@
-import javax.swing.*;
-import java.awt.*;
-import java.awt.event.*;
-import java.awt.geom.*;
-import java.net.*;
-import java.io.*;
-import java.applet.*;
-
-
-class Node {
-    //*********************************************
-    //*                                           *
-    //* This class is needed for the class list.  *
-    //* A Node looks like an element of the list. *
-    //*                                           *
-    //*********************************************
-    
-    private int value;      //Value of the Node 
-    private Node next;      //The next Node in the list
-    private Node previous;  //The previous Node in the list
-    
-    public Node(){
-	value=0;
-    }
-    
-    public Node(int _value){
-	value=_value;
-    }
-    
-    public void setValue(int _value){
-	value=_value;
-    }
-
-    public void setPrevious(Node _previous){
-	previous=_previous;
-    }
-    
-    public void setNext(Node _next){
-	next=_next;
-    }
-
-    public int getValue(){
-	return value;
-    }
-    
-    public Node getPrevious(){
-	return previous;
-    }
-    
-    public Node getNext(){
-	return next;
-    }
-}
-
-class List {
-    //******************************************
-    //*                                        *
-    //* This class decribe a bichained list.   *
-    //* I don't use the linkedList of java     *
-    //* because it need use of complex Object. *
-    //*                                        *
-    //******************************************
-
-    private Node first;   //The first Node of the list
-    private Node last;    //The last Node of the list
-    public Node current;  //A Node we play the game of an iterator
-    public int length;    //The length of the list
-    
-    public List(){
-	length=0;
-    }
-    
-    public Node getFirst(){
-	return first;
-    }	
-    
-    public Node getLast(){
-	return last;
-    }
-
-    public void initCurrent(){
-	current=first;
-    }
-    
-    public void setCurrent(Node _current){
-	current=_current;
-    }
-    
-    public Node getCurrent(){
-	return current;
-    }
-    
-    public boolean isEnd(){
-	return current==last;
-    }
-
-    public void shift(){
-	// ---------------------------------------
-	//| Change the current node with the next |
-	// ---------------------------------------
-	current=current.getNext();
-    }
-
-    public void addFirst(int value){
-	// ----------------------------------------------------
-	//| Add a Node of value 'value' at the end of the list |
-	// ----------------------------------------------------
-	Node node=new Node(value);
-	if(length==0){
-	    first=node;
-	    last=node;
-	}
-	else{
-	    first.setPrevious(node);
-	    node.setNext(first);
-	    first=node;
-	}
-	length++;
-    }
-
-    public void addLast(int value){
-	// ----------------------------------------------------
-	//| Add a Node of value 'value' at the end of the list |
-	// ----------------------------------------------------
-	Node node=new Node(value);
-	if(length==0){
-	    first=node;
-	    last=node;
-	}
-	else{
-	    last.setNext(node);
-	    node.setPrevious(last);
-	    last=node;
-	}
-	length++;
-    }
-    
-    public Node addBefore(int value){
-	// -----------------------------------------------------------------
-	//| Add a Node of value 'value' before the current Node of the list | 
-	//| and return the new Node                                         |
-	// -----------------------------------------------------------------
-	Node node=new Node(value);
-	if(current==first){
-	    first=node;
-	    node.setNext(current);
-	    current.setPrevious(node);
-	}
-	else {
-	    Node temp=current.getPrevious();
-	    temp.setNext(node);
-	    node.setPrevious(temp);
-	    current.setPrevious(node);
-	    node.setNext(current);
-	}
-	length++;
-	return node;
-    }
-    
-    public Node addAfter(int value){
-	// ----------------------------------------------------------------
-	//| Add a Node of value 'value' after the current Node of the list | 
-	//| and return the new Node                                        |
-	// ----------------------------------------------------------------
-	Node node=new Node(value);
-	if(current==last){
-	    last=node;
-	    node.setPrevious(current);
-	    current.setNext(node);
-	}
-	else{
-	    Node temp=current.getNext();
-	    temp.setPrevious(node);
-	    node.setNext(temp);
-	    current.setNext(node);
-	    node.setPrevious(current);
-	}
-	length++;
-	return node;
-    }
-	       
-    public void remove(Node node){
-	// ----------------------------------
-	//| Remove the Node node of the list |
-	// ----------------------------------
-	if(length!=0){
-	    if(length==1){
-		length=0;
-	    }
-	    else{
-		if(node==first){
-		    first=node.getNext();
-		    node=first;
-		}
-		else if(node==last){
-		    last=node.getPrevious();
-		    current=last;
-		}
-		else{
-		    (node.getPrevious()).setNext(node.getNext());
-		    (node.getNext()).setPrevious(node.getPrevious());
-		}
-		length--;
-	    }
-	}
-    }
-    
-    public int value(){
-	return current.getValue();
-    }
-
-    public int length(){
-	return length;
-    }
-}	  
- 
-public class HandleReduction extends JApplet implements ActionListener{
-    //*******************************************************
-    //*                                                     *
-    //* This class represent the window of the application. *
-    //*                                                     *
-    //*******************************************************
-
-
-    public static final long serialVersionUID = 0;
-    private Panel panel;           //Will draw graphics on the panel
-    private JTextField textFieldDraw;
-    private JTextField textFieldReduce;
-    private JTextField textFieldCompare1;
-    private JTextField textFieldCompare2; 
-    private JButton draw; 
-    private JButton reduce;
-    private JButton compare;       
-    private JButton option;
-    private JButton startDraw;
-    private JButton startReduce;    
-    private JButton startCompare;
-    private JButton applyOption;
-    private JButton cancelDraw;
-    private JButton cancelReduce;
-    private JButton cancelCompare;
-    private JButton cancelOption;
-    private JFrame drawFrame;
-    private JFrame reduceFrame;
-    private JFrame compareFrame;
-    private JFrame optionFrame;
-    private JScrollBar delay;
-    private JLabel speed;
-    private JRadioButton continuous;
-    private JRadioButton stepbystep;
-    public JLabel currentWord;
-    public int speedValue=100;
-    public boolean continuousAnimation=true;
-    public int speedValue2;
-    public boolean continuousAnimation2;
-
-	    
-    public void init(){
-	panel=new Panel();
-	panel.setBackground(Color.darkGray);
-	panel.setBounds(0,20,480,600);
-	add(panel);
-	currentWord=new JLabel("No braid word");
-	currentWord.setBounds(0,0,480,20);
-	add(currentWord);
-	draw=new JButton("Draw");
-	draw.addActionListener(this);
-	draw.setBounds(0,620,120,20);
-	add(draw);
-	reduce=new JButton("Reduce");       
-	reduce.addActionListener(this);     
-	reduce.setBounds(120,620,120,20);
-	add(reduce);            
-	compare=new JButton("Compare");
-	compare.addActionListener(this);
-	compare.setBounds(240,620,120,20);
-	add(compare);
-	option=new JButton("Controls");
-	option.addActionListener(this);
-	option.setBounds(360,620,120,20);
-	add(option);
-	add(new JLabel(""));
-    }
-
-    public void start(){
-	update(getGraphics());
-	validate();
-    }
-	
-    public void lock(){
-	draw.setEnabled(false);
-	reduce.setEnabled(false);
-	compare.setEnabled(false);
-	option.setEnabled(false);
-    }
-
-    public void unlock(){
-	draw.setEnabled(true);
-	reduce.setEnabled(true);
-	compare.setEnabled(true);
-	option.setEnabled(true);
-    }
-
-
-    public void actionPerformed(ActionEvent event){
-	// ----------------------------------------------------------
-	//| Specify what the action on the element of the windows do |
-	// ----------------------------------------------------------
-
-	//===> Draw
-	If(event.getSource()==draw){
-	    drawFrame=new JFrame("Draw");
-	    drawFrame.setSize(300,105);
-	    drawFrame.setLocationRelativeTo(null);
-	    drawFrame.setDefaultCloseOperation(JFrame.DO_NOTHING_ON_CLOSE);	    
-	    drawFrame.setResizable(false);
-	    lock();	
-	    JLabel message=new JLabel("Enter a braid word : ");
-	    message.setBounds(5,5,290,20);
-	    textFieldDraw=new JTextField(10);
-	    textFieldDraw.setBounds(5,25,290,20);
-	    textFieldDraw.addActionListener(this);
-	    startDraw=new JButton("Draw");
-	    startDraw.addActionListener(this);
-	    startDraw.setBounds(20,55,120,20);
-	    cancelDraw=new JButton("Cancel");
-	    cancelDraw.addActionListener(this);
-	    cancelDraw.setBounds(160,55,120,20);
-	    drawFrame.add(message);
-	    drawFrame.add(textFieldDraw);
-	    drawFrame.add(startDraw);
-	    drawFrame.add(cancelDraw);
-	    drawFrame.add(new JLabel(""));
-	    drawFrame.setVisible(true);
-        }
-	else if(event.getSource()==startDraw){
-	    panel.init(this,speedValue,continuousAnimation);
-	    panel.writeBraidWord(textFieldDraw.getText());
-	    unlock();
-	    drawFrame.dispose();
-	}
-	else if(event.getSource()==cancelDraw){
-	    unlock();
-	    drawFrame.dispose();	    
-	}
-
-	//===> Reduce
-	else if(event.getSource()==reduce){
-	   	reduceFrame=new JFrame("Reduce");
-		reduceFrame.setSize(300,105);
-		reduceFrame.setLocationRelativeTo(null);
-		reduceFrame.setDefaultCloseOperation(JFrame.DO_NOTHING_ON_CLOSE);
-		reduceFrame.setResizable(false);	    
-		lock();
-		JLabel message=new JLabel("Enter a braid word : ");
-		message.setBounds(5,5,290,20);
-		textFieldReduce=new JTextField(10);
-		textFieldReduce.setBounds(5,25,290,20);
-		textFieldReduce.addActionListener(this);
-		startReduce=new JButton("Reduce");
-		startReduce.addActionListener(this);
-		startReduce.setBounds(20,55,120,20);
-		cancelReduce=new JButton("Cancel");
-		cancelReduce.addActionListener(this);
-		cancelReduce.setBounds(160,55,120,20);
-		reduceFrame.add(message);
-		reduceFrame.add(textFieldReduce);
-		reduceFrame.add(startReduce);
-		reduceFrame.add(cancelReduce);
-		reduceFrame.add(new JLabel(""));
-		reduceFrame.setVisible(true);
-	}
-	else if(event.getSource()==startReduce){
-	    textFieldReduce.setEnabled(false);
-	    if(!panel.working){
-		panel.init(this,speedValue,continuousAnimation);
-		panel.writeBraidWord(textFieldReduce.getText());
-		panel.working=true;
-		startReduce.setText("Continue");
-		startReduce.updateUI();
-	    }
-	    startReduce.setEnabled(false);
-	    boolean red=panel.reduce();
-	    String message;
-	    int ind=panel.indice();
-	    if(red){
-		if(ind==0){
-		    message="The final word is empty, so your initial braid word \n"+textFieldReduce.getText()+" is trivial.";
-		}
-		else{
-		    message="There is no more handle and the final word is nonempty, so your initial braid word\n "+textFieldReduce.getText()+" is not trivial.";
-		}
-		JOptionPane.showMessageDialog(null,message);
-		unlock();
-		panel.working=false;
-		reduceFrame.dispose();
-	    }
-	    else{
-		startReduce.setEnabled(true);
-	    }
-	}
-	else if(event.getSource()==cancelReduce){
-	    reduceFrame.dispose();
-	    unlock();
-	    panel.working=false;
-	}
-	
-	//===> Compare
-	else if(event.getSource()==compare){
-	    compareFrame=new JFrame("Compare");
-	    compareFrame.setSize(300,145);
-	    compareFrame.setLocationRelativeTo(null);
-	    compareFrame.setDefaultCloseOperation(JFrame.DO_NOTHING_ON_CLOSE);
-	    compareFrame.setResizable(false);
-	    lock();
-	    JLabel message1=new JLabel("Enter a first braid word : ");
-	    message1.setBounds(5,5,290,20);
-	    textFieldCompare1=new JTextField(10);
-	    textFieldCompare1.setBounds(5,25,290,20);
-	    JLabel message2=new JLabel("Enter a second braid word : ");
-	    message2.setBounds(5,45,290,20);
-	    textFieldCompare2=new JTextField(10);
-	    textFieldCompare2.setBounds(5,65,290,20);
-	    startCompare=new JButton("Compare");
-	    startCompare.addActionListener(this);
-	    startCompare.setBounds(20,95,120,20);
-	    cancelCompare=new JButton("Cancel");
-	    cancelCompare.addActionListener(this);
-	    cancelCompare.setBounds(160,95,120,20);
-	    compareFrame.add(message1);
-	    compareFrame.add(textFieldCompare1);
-	    compareFrame.add(message2);
-	    compareFrame.add(textFieldCompare2);
-	    compareFrame.add(startCompare);	    
-	    compareFrame.add(cancelCompare);
-	    compareFrame.add(new JLabel(""));
-	    compareFrame.setVisible(true);
-	}
-	else if(event.getSource()==startCompare){
-	    if(!panel.working){
-		String word1,word2;	    
-		word1=textFieldCompare1.getText();
-		word2=textFieldCompare2.getText();
-		textFieldCompare1.setEnabled(false);
-		textFieldCompare2.setEnabled(false);
-		panel.init(this,speedValue,continuousAnimation);
-		panel.compare(word1,word2);
-		startCompare.setText("Continue");
-		startCompare.updateUI();
-	    }
-	    boolean red;
-	    startCompare.setEnabled(false);
-	    red=panel.reduce();
-	    if(red){
-		String message;
-		int ind=panel.indice();
-		if(ind==0){
-		    message="The final word is empty,\nso your initial braid words "+textFieldCompare1.getText()+" and "+textFieldCompare2.getText()+" are equivalent.";
-		}
-		else if(ind>0){
-		    //smaller
-		    message="There is no more handle and the final word is nonempty,\nso your initial braid words "+textFieldCompare1.getText()+" and "+textFieldCompare2.getText()+" are not equivalent.";
-		}
-		else{
-		    //larger
-		    message="There is no more handle and the final word is nonempty,\nso your initial braid words "+textFieldCompare1.getText()+" and "+textFieldCompare2.getText()+" are not equivalent.";
-		}
-		JOptionPane.showMessageDialog(null,message);
-		compareFrame.dispose();
-		panel.working=false;
-		unlock();
-	    }
-	    else{
-		startCompare.setEnabled(true);
-	    }	
-	}
-	else if(event.getSource()==cancelCompare){
-	    compareFrame.dispose();
-	    unlock();
-	    panel.working=false;
-	}
-
-	//===> Option
-	else if(event.getSource()==option){
-	    optionFrame=new JFrame("Controls");
-	    optionFrame.setSize(300,110);
-	    optionFrame.setLocationRelativeTo(null);
-	    optionFrame.setDefaultCloseOperation(JFrame.DO_NOTHING_ON_CLOSE);
-	    optionFrame.setResizable(false);
-	    lock();
-	    continuous=new JRadioButton();
-	    stepbystep=new JRadioButton();
-	    ButtonGroup group = new ButtonGroup();
-	    continuous.setText("Continuous");
-	    stepbystep.setText("Step-by-step");
-	    continuous.addActionListener(this);
-	    stepbystep.addActionListener(this);
-	    continuousAnimation2=continuousAnimation;
-	    speedValue2=speedValue;
-	    if(continuousAnimation){
-		continuous.setSelected(true);
-	    }
-	    else{
-		stepbystep.setSelected(true);
-	    }
-	    group.add(continuous);
-	    group.add(stepbystep);
-	    JLabel label1=new JLabel("Mode :");
-	    delay=new JScrollBar(JScrollBar.HORIZONTAL,speedValue,0,0,100);
-	    delay.addAdjustmentListener(new java.awt.event.AdjustmentListener(){
-		    public void adjustmentValueChanged(AdjustmentEvent event){
-			scrollBarValueChanged(event);
-		    }
-		});
-	    speed=new JLabel("Speed : "+speedValue);
-  	    label1.setBounds(5,5,60,20);
-	    continuous.setBounds(65,5,100,20);
-	    stepbystep.setBounds(165,5,120,20);
-	    speed.setBounds(5,30,80,20);
-	    delay.setBounds(85,30,200,20);
-	    applyOption=new JButton("Apply");
-	    applyOption.addActionListener(this);
-	    applyOption.setBounds(20,60,120,20);
-	    cancelOption=new JButton("Cancel");
-	    cancelOption.addActionListener(this);
-	    cancelOption.setBounds(160,60,120,20);
-	    optionFrame.add(label1);
-	    optionFrame.add(continuous);
-	    optionFrame.add(stepbystep);
-	    optionFrame.add(speed);	  
-	    optionFrame.add(delay);
-	    optionFrame.add(applyOption);
-	    optionFrame.add(cancelOption);
-	    optionFrame.add(new JLabel(""));
-	    optionFrame.setVisible(true);
-	}
-	else if(event.getSource()==continuous){
-	    if(continuous.isSelected()){
-		continuousAnimation2=true;
-	    }
-	}
-	else if(event.getSource()==stepbystep){
-	    if(stepbystep.isSelected()){
-		continuousAnimation2=false;
-	    }
-	}
-	else if(event.getSource()==applyOption){
-	    continuousAnimation=continuousAnimation2;
-	    speedValue=speedValue2;
-	    unlock();
-	    optionFrame.dispose();
-	}
-	else if(event.getSource()==cancelOption){
-	    optionFrame.dispose();
-	    unlock();
-	}
-    }
-
-    public void scrollBarValueChanged(AdjustmentEvent event){
-	if(event.getSource()==delay){
-	    speedValue2=delay.getValue();
-	    speed.setText("Speed : "+speedValue2);
-	}
-    }
-    
-    public String getAppletInfo() {
-        return "Handle reduction algorithm.";
-    }
-}
-    
-
-class Pause extends Thread{
-    //*********************************
-    //*                               *
-    //* This class pause the program. *
-    //*                               *
-    //*********************************
-
-    public void pause(int delayValue){
-	try {
-	    sleep(delayValue);
-	}
-	catch (InterruptedException ex) {}
-    }
-}
-
-class Panel extends JPanel{
-    //************************************************
-    //*                                              *
-    //* This class is the key class of this program. *
-    //* It contains algoritms and drawing tools.     *
-    //*                                              *
-    //************************************************
-    
-    public static final long serialVersionUID = 0;
-
-    //Word variable
-    private HandleReduction myWindow;
-    private JLabel currentBraidWord;
-
-    //=====> Braid variable
-    private String braidWord;         //The initial braid word
-    private boolean braidWordSet=false;
-    private List braid;                     //The braid word as a list
-    public String currentWord="";
-    public boolean working=false;
-    private String compareWord1;
-    private String compareWord2;
-    
-
-    //=====> Strand variable
-    private int strandNumber=5;             //The number of strand
-    private float strandStep;               //The distance between two strand
-    private float strandWidth;              //The width of a strand
-    private float strandLeft;               //The x position of the leftmost strand
-    private float[] xPos;                   //The x postion of strands
-    private float[] xPosNext;               //The next x position of strands 
-    private float yUp;                      //The y position of the first element of the braid
-    
-    //=====> Handle variable
-    private Node handleBegin;                //The first node of the handle
-    private Node handleEnd;                  //The last node of the handle
-    private int handleStrand;                //The current strand of the handle
-    private int handleType;                  //The type of the handle, is 1 if the handle start with a positive element
-    private boolean handleNormalDraw;        //This variable is true if we draw the handle with the classic metod
-    private boolean onHandle;                //This variable is true if we are in between the handleBegin Node and the handleEnd node
-    private float handleBeginYPos;           //The y position of the begin of the handle
-    private float handleEndYPos;             //The y position of the end of the handle
-    
-    //======> Trivial variable
-    private int trivialNumber;               //The number of trivial element without the extremity
-    private float trivialHeight;             //The height of a trivial element
-    
-    //======> Animation variable
-    private int animationStep;               //The current animation step
-    private float parameterAnimationStep2;   // \
-    private float parameterAnimationStep4;   //  | Parameters for the animation 
-    private float parameterAnimationStep5;   // /
-    private boolean continuousAnimation;
-    private int delayValue; 
-    private Pause pause=new Pause();         //For make pause during animation   
-
-    //======> Color variable
-    private Color[] strandColor;             //The color of different strand
-    private Color handleColor=Color.black;   //The color of the handle
-    private Color originalHandleStrandColor; //The original color of the handle strand
-      
-    //======> Way variable 
-    private GeneralPath[] continuousWay;     //The currant continuous way of strands
-    
-    //======> Double Buffering variable   
-    private Image offScreenBuffer;           //A buffer in wich we draw and after drawing we will show this buffer
-    private boolean isDraw;                  //For not repeat drawing
- 
-
-    // =================
-    //I                 I
-    //I Braid functions I
-    //I                 I
-    // =================
-
-    private void initBraid(){
-	// -----------------------------------------------------
-	//| Iniliasition of braid as a list and of strandNumber |
-	// -----------------------------------------------------
-	int length;
-	int value;
-	char letter;
-	strandNumber=2;
-	value=0;
-	braid=new List();
-	length=braidWord.length();                 //get the length of the braid word 
-	braid.addLast(0);                          //add a trivial at the begin
-	for(int i=0;i<length;i++){
-	    letter=braidWord.charAt(i);
-	    if(letter>='a' && letter<='z'){        //if we have a lower case letter
-		value=(int)(letter-'a')+1;         //value is 1 for 'a', 2 for 'b', ...
-		if(value+1>strandNumber){          //update the strand number        
-		    strandNumber=value+1;     
-		}
-	    }
-	    else if(letter>='A' && letter<='Z'){   //if we have an upper case letter
-		value=-(int)(letter-'A')-1;        //value is -1 for 'A', -2 for 'B', ... 
-		if(-value+1>strandNumber){         //update the strand number
-		    strandNumber=-value+1;
-		}
-	    }
-	    else{
-		value=0;
-	    }
-	    braid.addLast(value);                  //add the value at the list of the braid
-	}
-	braid.addLast(0);                          //add a trivial at th end
-    }
-    
-    public void init(HandleReduction _myWindow,int _delayValue,boolean _continuousAnimation){
-	myWindow=_myWindow;
-	delayValue=100-_delayValue;
-	continuousAnimation=_continuousAnimation;
-    }
-
-    public void writeBraidWord(String buffer){
-	// -----------------------------------------------------
-	//| Initialise the braid word and some other parameters |
-	//------------------------------------------------------
-	braidWord=buffer;
-	initBraid();                              //initialise the braid list
-	animationStep=0;                          //initialise the animation step
-	trivialNumber=0;                          // \
-	trivialHeight=0;                          //  Initilise the trivial parameters
-	handleNormalDraw=true;                    //we draw the handle with the classic method for the moment
-	updateCurrentBraidWord();
-	braidWordSet=true;
-	isDraw=false;                             //we draw a new image
-	update(super.getGraphics());              //update draw
-    }
-
-    public void compare(String word1, String word2){
-	int length;
-	int value;
-	char letter;
-	compareWord1=word1;
-	compareWord2=word2;
-	strandNumber=2;
-	value=0;
-	braid=new List();
-	length=word2.length();                 //get the length of the braid word          
-	for(int i=0;i<length;i++){
-	    letter=word2.charAt(i);
-	    if(letter>='a' && letter<='z'){        //if we have a lower case letter
-		value=(int)(letter-'a')+1;         //value is 1 for 'a', 2 for 'b', ...
-		if(value+1>strandNumber){          //update the strand number        
-		    strandNumber=value+1;     
-		}
-	    }
-	    else if(letter>='A' && letter<='Z'){   //if we have an upper case letter
-		value=-(int)(letter-'A')-1;        //value is -1 for 'A', -2 for 'B', ... 
-		if(-value+1>strandNumber){         //update the strand number
-		    strandNumber=-value+1;
-		}
-	    }
-	    else{
-		value=24;
-	    }
-	    braid.addLast(value);                  //add the value at the list of the braid
-	}
-	braid.addLast(0);
-	length=word1.length();                  
-	for(int i=0;i<length;i++){
-	    letter=word1.charAt(i);
-	    if(letter>='a' && letter<='z'){       
-		value=-(int)(letter-'a')-1;        
-		if(-value+1>strandNumber){        
-		    strandNumber=-value+1;     
-		}
-	    }
-	    else if(letter>='A' && letter<='Z'){ 
-		value=(int)(letter-'A')+1;         
-		if(value+1>strandNumber){       
-		    strandNumber=value+1;
-		}
-	    }
-	    else{
-		value=24;
-	    }
-	    braid.addFirst(value);                  
-	}
-	braid.addFirst(0);
-	animationStep=0;                          
-	trivialNumber=0;                          
-	trivialHeight=0;                         
-	handleNormalDraw=true;                      
-	updateCurrentBraidWord();
-	braidWordSet=true;
-	isDraw=false;                             //we draw a new image
-	working=true;
-	update(super.getGraphics());              //update draw
-    }                          
-
-    public void updateCurrentBraidWord(){
-	boolean stop;
-	int value;
-	String res="";
-	braid.initCurrent();
-	stop=false;
-	while(!stop){
-	    value=braid.value();
-	    if(value>0){
-		res+=(char)((value-1)+'a');
-	    }
-	    else if(value<0){
-		res+=(char)((-value-1)+'A');
-	    }
-	    if(braid.isEnd()){
-		stop=true;
-	    }
-	    if(!stop){
-		braid.shift();
-	    }
-	}
-	if(res==""){
-	    res="1";
-	}
-	currentWord=res;
-	(myWindow.currentWord).setText("Current braid word: "+res);
-	myWindow.update(myWindow.getGraphics());
-	myWindow.validate();
-    }
-
-
-    // ===============================
-    //I                               I
-    //I  Handle reduction algorithms  I
-    //I                               I
-    // ===============================
-
-    public void findHandle(){
-	// -----------------------------------
-	//| Search a handle in the braid word | 
-	//| with no intricated handle         |
-	// -----------------------------------
-	Node handles[]=new Node[strandNumber];     //We stock information of potential handle
-	int signs[]=new int[strandNumber];         //We stock the sign of the last n generato in signs[n];
-	int sign,value;
-	boolean stop;                                  //A flag for stop the main while
-	for(int i=0;i<strandNumber;i++){
-	    signs[i]=0;
-	}
-	stop=false;
-	value=0;
-	sign=0;
-	braid.initCurrent();                       //Initiliastion of braid current
-	while(!stop){
-	    value=braid.value();
-	    sign=1;
-	    if(value<0){                           //We compte the sign
-		value=-value;
-		sign=-1;
-	    }
-	    else if(value==0){                
-		sign=0;
-	    }
-	    if(signs[value]*sign<0){               //We have found the first handle with no imbricated handle
-		stop=true;
-	    }
-	    else{
-		signs[value]=sign;                 //Update signs
-		handles[value]=braid.getCurrent(); //Update value
-		for(int j=1;j<value;j++){          //Clear the potentialy imbricated handle
-		    signs[j]=0;
-		}
-	    }
-	    if(braid.isEnd()){                  //End of the braid ?
-		stop=true;
-	    }
-	    if(!stop){                           //Restart with the ext generator 
-		braid.shift(); 
-	    }
-	}
-	if(signs[value]*sign<0){                   //If we have found a handle
-	    handleBegin=handles[value];
-	    handleEnd=braid.getCurrent();
-	    handleStrand=value;
-	    handleType=-sign;
-	}
-	else{
-	    handleStrand=0;                        //If we haven't found handle
-	}
-    }
-
-    private void insertTrivials(){
-	// -----------------------------------------------------
-	//| This fonction insert trivials generato in the braid |
-        //| in order to make some space for the animation.      |
-	// -----------------------------------------------------
-	int value;
-	boolean stop;
-	stop=false;
-	braid.setCurrent(handleBegin);               //We start at the begin of the handle
-	trivialNumber=0;
-	while(!stop){
-	    value=braid.value();
-	    if(Math.abs(value)==handleStrand-1){     //If the generator is handleStrand-1 or -(handleStrand-1)
-		braid.addBefore(0);                  //We add a trivial before 
-		braid.setCurrent(braid.addAfter(0)); //We add a trivial after
-		trivialNumber+=2;                    //Update the number of trivials
-	    }
-	    braid.shift();
-	    if(braid.getCurrent()==handleEnd){       //If we are at the end of the handlee
-		stop=true;                           //we stop the main while
-	    }
-	}
-    }
-
-    public void removeHandle(){
-	// -------------------------------------------
-	//| This function remove the handle was found |
-	// -------------------------------------------
-	int sign;
-	int value;
-	boolean stop;
-	sign=-handleType;                                              //sign is a variable for alternating sign of new handleStrand generator
-	stop=false;
-	braid.setCurrent(handleBegin);                                 //We strat at the begin of the handle
-	while(!stop){
-	    value=braid.value();
-	    if(Math.abs(value)==handleStrand){                         //If the generator is handleStrand or -handleStrand
-		(braid.getCurrent()).setValue(0);                      //we replace it with a trivial generator
-	    }
-	    if(value==0){
-		(braid.getCurrent()).setValue((handleStrand-1)*sign);  //If the generator is a trivial we replace it
-		sign=-sign;                                            //with (handleStrand-1)*sign
-	    }
-	    if(value==handleStrand-1){                                 //If the genertaor is handleStrand-1
-		(braid.getCurrent()).setValue(value+1);                //we replace it with handleStrand
-	    }
-	    if(value==-(handleStrand-1)){                             //If the generator is -(handleStand-1)
-		(braid.getCurrent()).setValue(value-1);               //we replace it with -handleStrand
-	    }
-	    if(braid.getCurrent()==handleEnd){                        //If we are at he end of te endle
-		stop=true;                                               //we stop the main while
-	    }
-	    else{
-		braid.shift();                                        //else we restart with the next generator
-	    }
-	}
-	trivialNumber=2;                                              //At the end trivial numbers must be 2
-    }
-
-    private void removeTrivials(){
-	// -------------------------------------------
-	//| Remove the not extreme trivials generator | 
-	// -------------------------------------------
-	braid.remove(handleBegin);
-	braid.remove(handleEnd);
-	trivialNumber=0;
-    }
-
-    public int indice(){
-	int value;
-	int indice=0;
-	boolean stop=false;
-	braid.initCurrent();
-	while(!stop){
-	    value=braid.value();
-	    if(Math.abs(value)>Math.abs(indice)){
-		indice=value;
-	    }
-	    if(braid.isEnd()){
-		stop=true;  
-	    }
-	    else{        
-		braid.shift(); 
-	    }
-	}
-	return indice;
-    }
-    
-    // =================
-    //I                 I
-    //I Color functions I
-    //I                 I
-    // =================
-    
-    public void initStrandColor(){
-	// ---------------------------
-	//| Init the color of strands |
-	// ---------------------------
-	strandColor=new Color[strandNumber];                         //Make the table of strand color
-	for(int strand=1;strand<strandNumber+1;strand++){
-	    if(strandNumber<10){
-		strandColor[strand-1]=Color.getHSBColor((float)1-(float)strand/(float)10,(float)0.8,1);     
-	    }
-	    else {
-		strandColor[strand-1]=Color.getHSBColor((float)1-(float)strand/(float)strandNumber,(float)0.8,1);     
-	    }	
-	}
-    }
-
-    // ==================
-    //I                  I
-    //I Handle functions I
-    //I                  I
-    // ==================
-
-    public void colorizeHandle(Graphics2D g,float yPos){
-	// --------------------------------------
-	//| Colorize the handle if we are on her | 
-	// --------------------------------------
-	if(handleStrand!=0){                                                     //We verify we have found a handle
-	    if(braid.getCurrent()==handleBegin){                                 //If we are at the begin of the handle
-		handleBeginYPos=yPos;                                            //Initialize the y position of the begin of the handle
-		onHandle=true;                                                      //We are on the handle
-		closeContinuousWay(g,handleStrand);                              //Close the conitnuous way of handleStrand
-		originalHandleStrandColor=strandColor[handleStrand-1];           //Save the original color of the strand handleStrand
-		strandColor[handleStrand-1]=handleColor;                         //Change color of the strand handleStrand
-		continuousWay[handleStrand-1].moveTo(xPos[handleStrand-1],yPos); //Start position of the new continuous way of handleStrand
-	    }
-	    else if(braid.getCurrent()==handleEnd.getNext()){                    //If we are at the end of the handle
-		handleEndYPos=yPos;                                              //Initailaize the y position of the end of the handle
-		closeContinuousWay(g,handleStrand);                              //Close the continuous way of handleStrand
-		strandColor[handleStrand-1]=originalHandleStrandColor;           //The original color of strand handleStrand
-		continuousWay[handleStrand-1].moveTo(xPos[handleStrand-1],yPos); //Start position of the new continuous way
-		onHandle=false;                                                  //We are no longer in the handle
-	    }
-	}
-    }
-
-    public void changeHandleStrand(int generator){
-	// ------------------------------------------------------
-	//| Update the value of the strand on wich the handle is |
-	// ------------------------------------------------------
-	if(handleStrand!=0 && onHandle){
-	    if(generator==handleStrand){
-		handleStrand++;
-	    }
-	    else if(generator+1==handleStrand){
-		handleStrand--;
-	    }
-	}
-    }
-
-    // ==========================
-    //I                          I
-    //I Continuous way functions I
-    //I                          I
-    // ==========================
-
-    public void initContinuousWay(){
-	// -----------------------------------------
-	//| Start the continuous way for all strand |
-	// -----------------------------------------
-	continuousWay=new GeneralPath[strandNumber];             //Make the table of continuous way
-	xPos=new float[strandNumber];                            //Make the table of x position of strands
-	xPosNext=new float[strandNumber];                        //Make the table of next x position of strands
-	for(int strand=1;strand<strandNumber+1;strand++){
-	    continuousWay[strand-1]=new GeneralPath();           
-	    xPos[strand-1]=strandLeft+strand*strandStep;         //The xPos of n is strandLeft+n*strandStep
-	    continuousWay[strand-1].moveTo(xPos[strand-1],yUp);  //Start the continuous way at the y position yUp
-	}
-    }
-
-    public void closeContinuousWay(Graphics2D g,int strand){
-	// -------------------------------------------
-	//| Stop and draw the continous way of strand |
-	// -------------------------------------------
-	GeneralPath gp;
-	gp=continuousWay[strand-1];
-	g.setColor(strandColor[strand-1]);                                                            //Apply the color of strand
-	if(strand!=handleStrand || handleNormalDraw || strandColor[handleStrand-1]!=handleColor){ 
-	    //We verify we must draw the continuous way or not
-	    //We don't draw this way if we are on the handle and the value of handleNormalDraw is 0
-	    g.draw(gp);
-	}
-	gp=new GeneralPath();                                                                         //Make a new general path                                   
-	continuousWay[strand-1]=gp;                                                                   //Start the new continuous way
-    }
-   
-    public void permuteContinuousWay(int strand){
-	// ----------------------------------------------------------------- 
-	//| Echange the continuous way and the color of strand and strand+1 |
-	// -----------------------------------------------------------------
-	GeneralPath gp;
-	Color color;
-	//Echange continuous way 
-	gp=continuousWay[strand-1];
-	continuousWay[strand-1]=continuousWay[strand];
-	continuousWay[strand]=gp;
-	//Echange color
-	color=strandColor[strand-1];
-	strandColor[strand-1]=strandColor[strand];
-	strandColor[strand]=color;
-    }
-
-    // ================
-    //I                I
-    //I Math functions I
-    //I                I
-    // ================
-   
-    public double min(double a,double b){
-	if(a<b){
-	    return a;
-	}
-	else{
-	    return b;
-	}
-    }
-
-    public double max(double a,double b){
-	if(a>b){
-	    return a;
-	}
-	else{
-	    return b;
-	}
-    }
-
-    public double square(double a){
-	return a*a;
-    }
-
-    // ===================
-    //I                   I
-    //I Position function I
-    //I                   I
-    // ===================
-
-    public void calcXPosNext(){
-	// ----------------------------------------
-	//| Compute the nex x position of strands. |
-	//| It's a key function for animation.     |
-	// ----------------------------------------
-	for(int strand=0;strand<strandNumber;strand++){
-	    xPosNext[strand]=strandLeft+(strand+1)*strandStep;                                             //The general case
-	}
-	if(braid.getCurrent()==handleBegin){                                                               //If we have at the begin of the handle
-	    if(animationStep==2){                                                                          //If the step of animation is 2 
-		xPosNext[handleStrand]=(strandLeft+(handleStrand+parameterAnimationStep2)*strandStep);
-	    }
-	    else if(animationStep==4){                                                                     //If the step ofanimation is 4
-		xPosNext[handleStrand-1]+=parameterAnimationStep4*(float)strandStep;
-	    }
-	}
-	else if(braid.getCurrent()==handleEnd){                                                            //If we are at the end of the handle
-	}
-	else if(onHandle){                                                                              //If we are on the interior of the handle
-	    if(animationStep==2){                                                                          //If the step of animation is 2
-		xPosNext[handleStrand-1]=(strandLeft+(handleStrand+parameterAnimationStep2-1)*strandStep);
-	    }
-	    else if(animationStep==4){                                                                     //If the step of animation is 4
-		xPosNext[handleStrand-2]+=parameterAnimationStep4*(float)strandStep;
-		if(Math.abs(((braid.getCurrent()).getNext()).getValue())==handleStrand-2 ||
-		   Math.abs((braid.getCurrent()).getValue())==handleStrand-2){
-		    xPosNext[handleStrand-3]+=parameterAnimationStep4*(float)strandStep;
-		}
-	    }
-	    else if(animationStep==5){                                                                    //If the step of animation is 5
-		if(Math.abs((braid.getCurrent()).getValue())==handleStrand-1){		  
-		    xPosNext[handleStrand-2]+=parameterAnimationStep5*(float)strandStep;
-		}
-		else if(Math.abs((braid.getCurrent()).getValue())==handleStrand+1){
-		    xPosNext[handleStrand-1]+=parameterAnimationStep5*(float)strandStep;
-		}   
-	    }
-	}
-    }
-
-    public void updateXPos(){
-	// ------------------------------------------------------------------
-	//| Update the x postion of strand with the nex x position of strand | 
-	// ------------------------------------------------------------------
-	for(int strand=0;strand<strandNumber;strand++){
-	    xPos[strand]=xPosNext[strand];
-	}	
-    }
-    
-    public float[] calculIntersection(int strand,float yPos,int type){
-	// -----------------------------------------------------------------------
-	//| Compute the two key point for draw the generator strand |
-	// -----------------------------------------------------------------------
-	float []res=new float[4]; 
-	//res[0]<=res[1] is the x position of this points
-	//res[2]<=res[3] is the y position of this points
-	if(!handleNormalDraw && braid.getCurrent()==handleBegin){
-	    //If we are at the begin of handle and then handleNormal draw is 0 we send special values
-	    res[0]=xPosNext[strand-1];
-	    res[1]=xPosNext[strand-1];
-	    res[2]=yPos+strandStep;
-	    res[3]=yPos+strandStep;
-	    return res;
-	}
-	else if(!handleNormalDraw && braid.getCurrent()==handleEnd){
-	    //If we are at the end of handle and then handleNormal draw is 0 we send special value
-	    res[0]=xPosNext[strand];
-	    res[1]=xPosNext[strand];
-	    res[2]=yPos+strandStep;
-	    res[3]=yPos+strandStep;
-	    return res;
-	}
-	else{
-	    double decale=1.5*strandWidth;                                                      //Is distance of a strand with the other in the crossing
-	    double distance;                         
-	    if(type==1){                                                                        //If the crossing is positive 
-		//We compute the distance between the left-up point and then right-down  
-		distance=Math.sqrt(square(xPosNext[strand]-xPos[strand-1])+square(strandStep));
-	    }
-	    else {                                                                              //If the crossing is negative
-		//We compute the distance between the right-up and the left-down 
-		distance=Math.sqrt(square(xPos[strand]-xPosNext[strand-1])+square(strandStep));
-	    }
-	    double alpha=Math.acos(strandStep/distance);                                        //The angle of the crossing
-	    double decalX=Math.sin(alpha)*decale;                                               //The x coords of decale
-	    double decalY=Math.cos(alpha)*decale;                                               //The y coords of decale
-	    
-	    //The straight line D1 of equation x=m1*y+p1 contains the left-up and the right-down point
-	    double m1=((double)strandStep)/((double)(xPosNext[strand]-xPos[strand-1]));
-	    double p1=yPos-m1*((double)xPos[strand-1]);
-	    //The straight line D2 of equation x=m2*y+p2 contains the right-up and the left-down point
-	    double m2=((double)strandStep)/((double)(xPosNext[strand-1]-xPos[strand]));
-	    double p2=yPos-m2*((double)xPos[strand]);
-	    
-	    double xInter=(p2-p1)/(m1-m2);                                                      //x coord of D1 inter D2               
-	    double yInter=m1*xInter+p1;                                                         //y coord of D1 inter D2
-	
-	    //Computaion of values of res, the min and max fonction are usefull for a good drawing
-	    res[0]=(float)max(xInter-decalX,xPosNext[strand-1]);
-	    res[1]=(float)min(xInter+decalX,xPosNext[strand]);
-	    res[2]=(float)max(yInter-decalY,yPos);
-	    res[3]=(float)min(yInter+decalY,yPos+strandStep);
-	    return res;
-	}
-    }
-
-    // ===================
-    //I                   I
-    //I Drawing functions I
-    //I                   I
-    // ===================
-
-    public void drawHandle(Graphics2D g){
-	// -------------------------------------------
-	//| Draw the handle if handleNormal draw is 0 |
-	// -------------------------------------------
-	GeneralPath gp=new GeneralPath();
-	gp.moveTo(strandLeft+handleStrand*strandStep,handleBeginYPos); 
-	gp.lineTo(strandLeft+handleStrand*strandStep,handleEndYPos);
-	g.setColor(handleColor);                                         //Apply the color of the handle
-	g.draw(gp);
-    }
-    
-    public void drawTrivial(float yPos){
-	// -------------------------------------
-	//| Draw a not extrem trivial generator |
-	// -------------------------------------
-	for(int strand=0;strand<strandNumber;strand++){
-	    continuousWay[strand].lineTo(xPosNext[strand],yPos+trivialHeight*strandStep);
-	}
-    }
-    
-    public void drawNoCrossing(Graphics2D g,int strand,float yPos){
-	// ----------------------
-	//| Draw straight strand |
-	// ----------------------
-	continuousWay[strand-1].lineTo(xPosNext[strand-1],yPos+strandStep);
-    }
-
-    public void drawPositiveCrossing(Graphics2D g,int strand,float yPos){
-	// --------------------------
-	//| Draw a positive crossing |
-	// --------------------------
-	float inter[]=calculIntersection(strand,yPos,1);
-	continuousWay[strand-1].lineTo(inter[0],inter[2]);
-	closeContinuousWay(g,strand);	
-	continuousWay[strand-1].moveTo(inter[1],inter[3]);
-	continuousWay[strand-1].lineTo(xPosNext[strand],yPos+strandStep);
-	continuousWay[strand].lineTo(xPosNext[strand-1],yPos+strandStep);
-	permuteContinuousWay(strand);
-    }
-   
-    public void drawNegativeCrossing(Graphics2D g,int strand,float yPos){
-	// --------------------------
-	//| Draw a negative crossing |
-	// --------------------------
-	float inter[]=calculIntersection(strand,yPos,-1);
-	continuousWay[strand].lineTo(inter[1],inter[2]);
-	closeContinuousWay(g,strand+1);	
-	continuousWay[strand].moveTo(inter[0],inter[3]);
-	continuousWay[strand].lineTo(xPosNext[strand-1],yPos+strandStep);
-	continuousWay[strand-1].lineTo(xPosNext[strand],yPos+strandStep);
-	permuteContinuousWay(strand);
-    }
-
-    public void draw(Graphics g){
-	// --------------------------------------------
-	//| The main and first called drawing function |
-	// --------------------------------------------
-	Graphics2D g2=(Graphics2D) g;                                                            //A Graphics2D context is needed
-       	Rectangle r;                         
-	int generator;                                                                           //The absolute value of generator
-	int exponent;                                                                            //The sign of generator 1 or -1
-	float yPos;                                                                              //The current y position
-	r=getBounds();                                                                           //The dimension of the graphics window
-	g.setColor(Color.darkGray);                                                              //Background color       
-        g.clearRect(0,0,r.width,r.height);                                                       //Clear the drawing window 
-        g.drawRect(0,0,r.width-1,r.height-1);                                                    //Aply background color
-	
-	//Defintion of some strand parameter
-	strandStep=(float)min((double)r.width/(double)(strandNumber+1),(double)r.height/((double)(braid.length())-((double)1-(double)trivialHeight)*(double)trivialNumber));
-	strandWidth=strandStep/(float)5;
-	strandLeft=((float)r.width-((float)(strandNumber+1)*(float)strandStep+strandWidth))/(float)2;
-	yUp=(float)max((double)0,(double)((double)r.height-(double)strandStep*((double)(braid.length())-((double)1-(double)trivialHeight)*(double)trivialNumber))/(double)2);
-	
-	braid.initCurrent();                                                                     //Set current as braid.first  
-	initStrandColor();                                                                       //Init the strand color
-	initContinuousWay();                                                                     //Init then continuous way
-	g2.setStroke(new BasicStroke(strandWidth,BasicStroke.CAP_ROUND,BasicStroke.JOIN_BEVEL)); //Type of general path
-	yPos=yUp;                                                                                //Init current y position
-	int stop=0;                                                                              //stop is a flag for break the main while
-	if(!handleNormalDraw && handleType==1){
-	    //If handleNormalDraw is 0 and hande type is 1 we draw the handle first
-	    drawHandle(g2);
-	}
-	while(stop==0){
-	    generator=braid.value();                                                             //Get braid value
-	    exponent=1;
-	    if(generator<0){                                                                     // \
-		exponent=-1;                                                                     //  Computation of generato and exponent
-		generator=-generator;                                                            // /
-	    }
-	    colorizeHandle(g2,yPos);
-	    calcXPosNext();
-	    if(onHandle && generator==0){                                                     //If the generator is trivial and we are on the handle
-		drawTrivial(yPos);
-		yPos+=trivialHeight*strandStep;                                                  //Update yPos
-	    }
-	    else{
-		for(int strand=1;strand<strandNumber+1;strand++){
-		    if(strand==generator && exponent==1){                                        //If the generator is positive        
-			drawPositiveCrossing(g2,strand,yPos);
-			strand++;
-		    }
-		    else if(strand==generator && exponent==-1){                                  //If the generato is negative 
-			drawNegativeCrossing(g2,strand,yPos);
-			strand++;
-		    }
-		    else{
-			drawNoCrossing(g2,strand,yPos);
-		    }
-		}
-		changeHandleStrand(generator);                                                   //Update handle strand
-		yPos+=strandStep;                                                                //Update yPos
-	    }
-	    if(braid.isEnd()){                                                                //Are we at the end of the braid ?
-		stop=1;
-	    }
-	    else{
-		braid.shift();
-	    }
-	    updateXPos();                                                                        //Update xPos
-	}                                                                                        //Restart with the new generator
-	for(int strand=1;strand<strandNumber+1;strand++){                                         
-	    closeContinuousWay(g2,strand);                                                       //Close the continuous way
-	}
-	if(!handleNormalDraw && handleType==-1){
-	    //If handleNormalDraw is 0 and hande type is 1 we draw the handle last
-	    drawHandle(g2);
-	}
-    }
-
-    // ===================
-    //I                   I
-    //I Graphics function I
-    //I                   I
-    // ===================
-
-    public void paint(Graphics g){
-	if(!isDraw){
-	    update(g);
-	    isDraw=true;
-	}
-	else{
-	    g.drawImage(offScreenBuffer,0,0,this);
-	}
-    }
-   
-    public void update(Graphics g) {
-	// -----------------------------------------------
-	//| Graphic update function with double-buffering |
-	// -----------------------------------------------
-	if(braidWordSet){
-	    Graphics gr; 
-	    if (offScreenBuffer==null||(!(offScreenBuffer.getWidth(this)==getBounds().width && offScreenBuffer.getHeight(this)==getBounds().height))){
-		offScreenBuffer=this.createImage(getBounds().width,getBounds().height);
-	    }
-	    gr=offScreenBuffer.getGraphics();
-	    draw(gr); 
-	    g.drawImage(offScreenBuffer,0,0,this);
-	}
-   }
-
-    // ====================
-    //I                    I
-    //I Animation function I
-    //I                    I
-    // ====================
-
-    public boolean reduce(){
-	if(!braidWordSet){
-	    JOptionPane.showMessageDialog(null,"You must enter a braid word first ! ","Error",JOptionPane.ERROR_MESSAGE);
-	    return true;
-	}
-	else if(animationStep==0){
-	    findHandle();
-	    update(getGraphics());
-	    if(handleStrand==0){
-		//update(getGraphics());
-		return true;
-	    }
-	    else{
-		update(getGraphics());
-		insertTrivials();
-		trivialHeight=0;
-		animationStep=1;
-		handleNormalDraw=true;
-		if(continuousAnimation){
-		    return reduce();
-		}
-		else{
-		    return false;
-		}
-	    }
-	}
-	else if(animationStep==1){
-	    if(trivialHeight>=1){
-		trivialHeight=1;
-		parameterAnimationStep2=1;	    
-		animationStep=2;
-		pause.pause(delayValue);
-		return reduce();
-	    }
-	    else{
-		trivialHeight+=0.1;
-		update(getGraphics());
-		pause.pause(delayValue);
-		return reduce();
-	    }
-	}
-	else if(animationStep==2){
-	    if(handleStrand==0){
-		return true;
-	    }
-	    else if(parameterAnimationStep2<(float)(1.25)*((float)strandWidth/strandStep)){
-		handleNormalDraw=false;
-		animationStep=3;
-		pause.pause(delayValue);
-		return reduce();
-	    }
-	    else{
-		parameterAnimationStep2-=(float)0.05;
-		update(getGraphics());	
-		pause.pause(delayValue);
-		return reduce();
-	    }
-	}
-	else if(animationStep==3){
-	    parameterAnimationStep4=0;
-	    animationStep=4;
-	    update(getGraphics());
-	    pause.pause(delayValue);
-	    return reduce();
-	}
-	else if(animationStep==4){
-	    if(parameterAnimationStep4>=1){
-		removeHandle();
-		handleNormalDraw=true;
-		parameterAnimationStep5=1-(float)(1.25)*((float)strandWidth/strandStep);
-		animationStep=5;
-		pause.pause(delayValue);
-		return reduce();
-	    }
-	    else{
-		parameterAnimationStep4+=(float)0.05;
-		update(getGraphics());	
-		pause.pause(delayValue);
-		return reduce();
-	    }
-	}
-	else if(animationStep==5){
-	    if(parameterAnimationStep5<=(float)0.05){
-		parameterAnimationStep5=0;
-		animationStep=6;
-		pause.pause(delayValue);
-		return reduce();
-	    }
-	    else{
-		parameterAnimationStep5-=(float)0.05;
-		update(getGraphics());	
-		pause.pause(delayValue);
-		return reduce();
-	    }
-	}
-	else if(animationStep==6){
-	    if(trivialHeight<=0){
-		trivialHeight=0;
-		animationStep=7;
-		pause.pause(delayValue);
-		update(getGraphics());
-		return reduce();
-	    }
-	    else{
-		trivialHeight-=0.1;
-		update(getGraphics());	
-		pause.pause(delayValue);
-		return reduce();
-	    }
-	}
-	else if(animationStep==7){
-	    removeTrivials();
-	    handleStrand=0;
-	    update(getGraphics());	
-	    animationStep=0;
-	    updateCurrentBraidWord();
-	    update(getGraphics());	
-	    pause.pause(delayValue);
-	    if(continuousAnimation){
-		return reduce();
-	    }
-	    else{
-		return false;
-	    }
-	}
-	return false;
-    }
-}
-
-
-
-

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