import java.applet.*;import java.awt.*;import java.awt.event.*;import java.math.*;/* Clebsch-Gordan coefficient calculator */public class Cleblet extends Applet implements ActionListener, Runnable {        Thread playing;        // declare our A.M values out here        BigRational j1,j2,j,m1,m2,m;    // Let's allow the user to input the numbers as reals.     // a double will be just fine here.    double hj1,hj2,hj,hm1,hm2,hm;        // the approximate answer as a 'double'    double approxanswer;        // panels for the rows of GUI items:        Panel row1 = new Panel();    Label j1label = new Label("<j1=",Label.RIGHT);    TextField j1field = new TextField(4);    Label m1label = new Label("m1=",Label.RIGHT);    TextField m1field = new TextField(4);    Label j2label = new Label("j2=",Label.RIGHT);    TextField j2field = new TextField(4);    Label m2label = new Label("m2=",Label.RIGHT);    TextField m2field = new TextField(4);    Label jlabel = new Label("| j=",Label.RIGHT);    TextField jfield = new TextField(4);    Label mlabel = new Label("m=",Label.RIGHT);    TextField mfield = new TextField(4);    Label endket = new Label(">",Label.LEFT);    Button go = new Button("Go!");    Button clear = new Button("Clear");    Panel row3 = new Panel();    Panel row4 = new Panel();    TextField outfield = new TextField(70);    Label approxlabel = new Label("approx:",Label.RIGHT);    TextField approxfield = new TextField(40);            // initialization routine: set up the GUI    // this gets called by the Java Virtual Machine when we start up    public void init() {		Font myfont = new Font("SansSerif", Font.PLAIN, 12);	setFont(myfont);		// set up the layout of the GUI		GridLayout mylayout = new GridLayout(3,1,1,1);	setLayout(mylayout);			FlowLayout layout2 = new FlowLayout(FlowLayout.CENTER, 1, 1);	row1.setLayout(layout2);	row1.add(j1label);	row1.add(j1field);	row1.add(m1label);	row1.add(m1field);	row1.add(j2label);	row1.add(j2field);	row1.add(m2label);	row1.add(m2field);	row1.add(jlabel);	row1.add(jfield);	row1.add(mlabel);	row1.add(mfield);	row1.add(endket);	row1.add(go);	row1.add(clear);	add(row1);		FlowLayout layout3 = new FlowLayout(FlowLayout.CENTER, 1, 1);	row3.setLayout(layout3);	outfield.setEditable(false);	row3.add(outfield);	add(row3);		FlowLayout layout4 = new FlowLayout(FlowLayout.CENTER, 1, 1);	row4.setLayout(layout4);	approxfield.setEditable(false);	row4.add(approxlabel);	row4.add(approxfield);	add(row4);	// done setting up the layout. Now add some listeners (to the buttons)	go.addActionListener(this);	clear.addActionListener(this);    }            // Set up button listener    public void actionPerformed(ActionEvent event) {	String command = event.getActionCommand();	if(command == "Go!") { 	    playing = new Thread(this);	    playing.start();	    go.setEnabled(false);	    clear.setEnabled(false);	    outfield.setText(null);	    approxfield.setText(null);	}	if(command == "Clear") 	    clearAllFields();    }        void clearAllFields(){	j1field.setText(null);	m1field.setText(null);	j2field.setText(null);	m2field.setText(null);	jfield.setText(null);	mfield.setText(null);	outfield.setText(null);	approxfield.setText(null);    }        // This is where the thread starts when the user hits 'go'.    public void run() {		final BigRational ONE_R = new BigRational(1);			// We get the input from the input boxes and convert to the 	// BigInteger type.	// This can throw an exception if bad input is given, so let's catch	// it.		try {	    hj1 = (new java.lang.Double(j1field.getText())).doubleValue();	    hm1 = (new java.lang.Double(m1field.getText())).doubleValue();	    hj2 = (new java.lang.Double(j2field.getText())).doubleValue();	    hm2 = (new java.lang.Double(m2field.getText())).doubleValue();	    hj = (new java.lang.Double(jfield.getText())).doubleValue();	    hm = (new java.lang.Double(mfield.getText())).doubleValue();	}	catch (java.lang.NumberFormatException e) {	    outfield.setText("All input must be numerical");	    go.setEnabled(true);	    clear.setEnabled(true);	    return;	}	// convert decimal input to BigRational.	j1 = new BigRational(new BigInteger(Long.toString(Math.round(2.*hj1))),			     new BigInteger("2"));	m1 = new BigRational(new BigInteger(Long.toString(Math.round(2.*hm1))),			     new BigInteger("2"));	j2 = new BigRational(new BigInteger(Long.toString(Math.round(2.*hj2))),			     new BigInteger("2"));	m2 = new BigRational(new BigInteger(Long.toString(Math.round(2.*hm2))),			     new BigInteger("2"));	j = new BigRational(new BigInteger(Long.toString(Math.round(2.*hj))),			     new BigInteger("2"));	m = new BigRational(new BigInteger(Long.toString(Math.round(2.*hm))),			     new BigInteger("2"));		// There is a kronecker delta on the m-values - so we catch this one	// early on:		if ( ! ((m1.add(m2)).equals(m)) ) {	    outfield.setText("0 (m1+m2 not equal to m)");	    approxfield.setText("0.0");	    go.setEnabled(true);	    clear.setEnabled(true);	    return;	}		// Another problem with the input would be if any of the m's have a	// bigger magnitude than their j.		if ( Math.abs(hm1) > hj1) {	    outfield.setText("0  (|m1| is greater than j1)");	    approxfield.setText("0.0");	    go.setEnabled(true);	    clear.setEnabled(true);      	    return;	}	if ( Math.abs(hm2) > hj2 ) {	    outfield.setText("0  (|m2| is greater than j2)");	    approxfield.setText("0.0");	    go.setEnabled(true);	    clear.setEnabled(true);      	    return;	}	if ( Math.abs(hm) > hj ) {	    outfield.setText("0  (|m| is greater than j)");	    approxfield.setText("0.0");	    go.setEnabled(true);	    clear.setEnabled(true);      	    return;	}		// also, each of the values 2m must have the same parity as their	// corresponding 2j.		if (Math.abs(Math.abs(hm1-hj1)-Math.round(Math.abs(hm1-hj1)))>0.0001 ){	    outfield.setText("0 (m1="+m1field.getText()+			     " is not consistent with j1="+			     j1field.getText()+")");	    approxfield.setText("0.0");	    go.setEnabled(true);	    clear.setEnabled(true);      	    return;	}	if (Math.abs(Math.abs(hm2-hj2)-Math.round(Math.abs(hm2-hj2)))>0.0001){	    outfield.setText("0 (m2="+m2field.getText()+			     " is not consistent with j2="+			     j2field.getText()+")");	    approxfield.setText("0.0");	    go.setEnabled(true);	    clear.setEnabled(true);      	    return;	}	if (Math.abs(Math.abs(hm-hj)-Math.round(Math.abs(hm-hj)))>0.0001 ) {	    outfield.setText("0 (m="+mfield.getText()+			     " is not consistent with j="			     +jfield.getText()+")");	    approxfield.setText("0.0");	    go.setEnabled(true);	    clear.setEnabled(true);      	    return;	}		// and finally, the j's must satisfy the triangle relations..		if(Math.abs(hj1-hj2) > hj || Math.abs(hj1+hj2) < hj) {	    outfield.setText("0 (j1, j2 and j do not satisfy the triangle"+			     " relation)");	    approxfield.setText("0.0");	    go.setEnabled(true);	    clear.setEnabled(true);      	    return;	}		//	// Now all trivial zeros have been accounted for, so we proceed	// with calculation	//			// First we calculate the fraction delta(j1,j2,j)^2	BigRational delta = new 	    BigRational(factorial( (j1.add(j2)).subtract(j).toBigInteger() ),			factorial( (((j1.add(j2)).add(j)).add(ONE_R)				    ).toBigInteger() ) );	delta=delta.multiply(factorial(j1.add(j).subtract(j2).toBigInteger()));	delta=delta.multiply(factorial(j2.add(j).subtract(j1).toBigInteger()));		// There are also some other factors sitting outside the 	// sum which must be calculated.	BigInteger outfactors = 	    factorial(j1.add(m1).toBigInteger())	    .multiply( factorial(j1.subtract(m1).toBigInteger()) )	    .multiply( factorial(j2.add(m2).toBigInteger()))	    .multiply( factorial(j2.subtract(m2).toBigInteger()) )	    .multiply( factorial(j.add(m).toBigInteger()) )	    .multiply( factorial(j.subtract(m).toBigInteger()))	    .multiply( (j.add(j)).add(ONE_R) .toBigInteger() );	// Now we can do the sum.  Pre-calculate the constant terms inside the	// factorials:	BigInteger t1 = j1.subtract(m1).toBigInteger();	BigInteger t2 = j.add(m1).subtract(j2).toBigInteger();	BigInteger t3 = j2.add(m2).toBigInteger();	BigInteger t4 = (j.subtract(j1)).subtract(m2).toBigInteger();	BigInteger t5 = j1.add(j2).subtract(j).toBigInteger();	// Work out the limits of the sum:	BigInteger nulo = new BigInteger("0");	if(nulo.compareTo(t2.negate()) < 0) nulo = t2.negate();	if(nulo.compareTo(t4.negate()) < 0) nulo = t4.negate();	BigInteger nuhi = t1;	if(nuhi.compareTo(t3) > 0) nuhi = t3;	if(nuhi.compareTo(t5) > 0) nuhi = t5;	// now we are ready to perform the sum.		BigRational sumvar = new BigRational(0);	float pcdone = 0.0f;	int range = (nuhi.subtract(nulo)).intValue();	float pcpernu = 100.0f/(float) range;			for (BigInteger nu = nulo; nu.compareTo(nuhi)<=0;	     nu=nu.add(new BigInteger("1"))) {	    	    if(range >=10) {		outfield.setText("Thinking.."+				 java.lang.Integer.toString((int)pcdone)+				 "% done.");		pcdone += pcpernu;	    }	    	    if(nu.mod(new BigInteger("2")).compareTo(new BigInteger("0")						     ) == 0) {		sumvar=sumvar.		    add(new BigRational(new 					BigInteger("1"),					factorial(t1.subtract(nu)						  ).multiply(factorial(t2.								       add(nu))							     ).					multiply(factorial(t3.subtract(nu))						 ).					multiply(factorial(t4.add(nu))						 ).					multiply(factorial(t5.subtract(nu))						 ).multiply(factorial(nu))));	    }	    else		sumvar=sumvar.		    subtract( new BigRational(new BigInteger("1"),					      factorial(t1.subtract(nu)							).					      multiply(factorial(t2.add(nu))						       ).					      multiply(factorial(t3.								 subtract(nu))						       ).					      multiply(factorial(t4.add(nu))						       ).					      multiply(factorial(t5.								 subtract(nu))						       ).					      multiply(factorial(nu))));	}			// Now we have everything and we just need to do a little 	// manipulation for output.	boolean isneg=false;	if(sumvar.numerator.compareTo(new BigInteger("0"))<0) isneg=true;	BigRational inside = delta.multiply(outfactors);	outfield.setText("Simplifying Expression");	BigInteger denomfactors = squarefactor(inside.denominator);	BigInteger numerfactors = squarefactor(inside.numerator);	inside = (inside.divide(numerfactors.multiply(numerfactors))).	    multiply(denomfactors.multiply(denomfactors));	BigRational outside = sumvar;	outside = (outside.multiply(numerfactors)).divide(denomfactors);		// get an approximate (decimal) expression for an answer:	BigDecimal bigapprox = (new BigDecimal(inside.numerator)).	    setScale(200);	bigapprox = bigapprox.divide((new BigDecimal(inside.denominator)).				     setScale(200),BigDecimal.ROUND_HALF_DOWN);	approxanswer = java.lang.Math.sqrt(bigapprox.doubleValue());		   	bigapprox = (new BigDecimal(outside.numerator)).setScale(200);	bigapprox = bigapprox.divide((new BigDecimal(outside.denominator)).				     setScale(200),BigDecimal.ROUND_HALF_DOWN);	approxanswer = approxanswer * bigapprox.doubleValue();	approxfield.setText("");	approxfield.setText(approxfield.getText()+			    java.lang.Double.toString(approxanswer));	// print out the analytic answer	outfield.setText("");		if(isneg==true) outfield.setText("-");	if(inside.numerator.compareTo(new BigInteger("0"))==0) {	    outfield.setText("0");} 	else if(outside.numerator.compareTo(new BigInteger("0"))==0) {	    outfield.setText("0");} 	else { 	    if(outside.equals(ONE_R) == false) {		outfield.setText(outfield.getText()+"("+				 outside.abs().toString()+")*"); }	    if (inside.equals(ONE_R)==false) {		outfield.setText(outfield.getText()+"sqrt("+				 inside.toString()+")");}}	go.setEnabled(true);	clear.setEnabled(true);    }        //    // Here follows the factorial method (function) for BigIntegers.     // It is a class method, so must be static.    //    public static BigInteger factorial(BigInteger a) {	if (a.compareTo(new BigInteger("0"))<0) 	    return new BigInteger("0"); 	if (a.compareTo(new BigInteger("0"))==0 ||	    a.compareTo(new BigInteger("1"))==0) {	    return new BigInteger("1");	}	else {	    return a.multiply(factorial(a.subtract(new BigInteger("1"))));	}    }    // end of factorial method    //     // A method to simplify sqrt(I) where I is a BigInteger, by checking    // I for factors which are perfect squares.    //        public static BigInteger squarefactor(BigInteger a) {	BigInteger i = new BigInteger("2");	BigInteger result = new BigInteger("1");	while(i.multiply(i).compareTo(a.min(new BigInteger("10000000")))<=0) {	    if ( a.mod(i.multiply(i)).compareTo(new BigInteger("0"))==0) {		return (i.multiply(squarefactor(a.divide(i.multiply(i))))); }	    i = i.add(new BigInteger("1"));	}	return result;    }}