import java.applet.*;
import java.awt.*;
import java.util.*;
// A drill on completing the square

public class Csq extends Applet { 
	int a,b,c;		//Coefficients of sample problem
	int LastError[]={0,0,0,0,0,0,0,0,0,0};
	int NumberErrorsInARow[]={0,0,0,0,0,0,0,0,0,0};
	TextField banswer;
	
	Random r;
	int numerator, denominator; 
	int rightnumerator, rightdenominator;
	int n1, d1;
	
	int state;
	String usercomm;

	private Font f;

	public void setnumbers(){
		// Select coefficients randomly.
	   	a = 0;
		while(Math.abs(a) < 2){
			a = Math.abs(r.nextInt()) % 20 - 10;
		}
		b = 0;
		while(Math.abs(b) == 0){
			b = Math.abs(r.nextInt()) % 10;
		}
		c = 0;
		while(Math.abs(c) == 0){
			c = Math.abs(r.nextInt()) % 10;
		}
		// Expected answer in state 1 is b/a
		rightnumerator = b;
		rightdenominator = a;
		if(rightdenominator < 0){
			rightdenominator = - rightdenominator;
			rightnumerator = - rightnumerator;
		}
		int g = gcd(rightdenominator, rightnumerator);
		rightnumerator /= g;
		rightdenominator /= g;
	}

	int gcd(int x, int y){
		int remainder;
		x = Math.abs(x);
		y = Math.abs(y);
		remainder = x % y;
		while( remainder != 0){
			x = y;
			y = remainder;
			remainder = x % y;
		}
		return y;
	}

	public void init() {
		f = new Font("TimesRoman", Font.PLAIN, 14);
		setBackground(Color.cyan);
		r = new Random();
		setnumbers();

		banswer = new TextField(20);
		banswer.setBackground(Color.yellow);
		add(banswer);


		state = 1;
		usercomm = "Enter the value after factoring.";

		banswer.requestFocus();

	}

	public void paint(Graphics g){
		if(state == 1 || state == 2){			
			paintstate1(g);
		}
		else if(state == 3 || state == 4){
			paintstate3(g);
		}
		else if(state == 5 || state == 6){
			paintstate5(g);
		}
		else if(state == 7 || state == 8){
			paintstate7(g);
		}
		else if(state == 9 || state == 10){
			paintstate9(g);
		}
	
	}

    public void paintstate3(Graphics g){
			String part1 = a + "x";
			String part2;
			g.setFont( f );
     			g.drawString(part1, 10, 28);
        		FontMetrics fm = g.getFontMetrics();
        		int newPosition = fm.stringWidth(part1) + 10;
        		g.drawString("2", newPosition, 20);
        		newPosition += fm.stringWidth("2");
			if(b > 0){
				part2 = " + " + b + "x";
			}
			else {
				part2 = " - " + Math.abs(b) + "x";
			}
			if(c > 0){
				part2 = part2 + " + " + c;
			}
			else {
				part2 = part2 + " - " + Math.abs(c);
			}
			part2 = part2 + " = " + a + " ( x";

	
		        g.drawString(part2, newPosition, 28);
        		newPosition += fm.stringWidth(part2);
      			g.drawString("2", newPosition, 20);
			newPosition += fm.stringWidth("2");
			String part3 = " + ";
			if(rightnumerator > 0){
				part3 = " + " + rightnumerator;
			}
			else {
				part3 = " - " + Math.abs(rightnumerator);
			}
			if(rightdenominator != 1){
				part3 = part3 + "/" + rightdenominator;
			}
				part3 = part3 + " x + ";
			g.drawString(part3, newPosition, 28) ;
	  		newPosition += fm.stringWidth(part3);
      
			banswer.reshape(newPosition, 12, 48 ,26);
			newPosition += 48 + 4;
			String part4;
			part4 = "  ) ";
			
			if(c > 0){
				part4 = part4 + " + " + c;
			}
			else {
				part4 = part4 + " - " + Math.abs(c);
			}
			part4 = part4 + " - [a number to be entered later]";

			
			g.drawString(part4, newPosition, 28) ;
	
		g.drawString(usercomm, 10, 58);
 		if(state == 3){
			switch(LastError[3]){
			case 0: break;
			case 1: g.drawString("Last time through you got the sign wrong.", 10, 88);
				break;
			case 2: g.drawString("On the previous problem, you were off by a factor of 4.", 10, 88);
				break;
			case 3: g.drawString("On the previous problem, you were off by a factor of 4 and the sign was wrong.", 10, 88);
				break;
			case 4: g.drawString("On the previous problem, you were off by a factor of 2.", 10, 88);
				break;
			case 5: g.drawString("On the previous problem, you were off by a factor of 2 and the sign was wrong.", 10, 88);
				break;

			case 6: g.drawString("Last time through you did something wrong, but I couldn't figure out what.", 10, 88);
				break;
			}
		}
		if(state == 4 && NumberErrorsInARow[3] > 1){
			String should = "You should take half of the coefficient of x, which is b/(2a) = " +
			   n1;
			if(d1 != 1)
					should = should + "/" + d1;
			should = should + ", and square it, to get " + n1*n1;
			if(d1 != 1)
					should = should + "/" + d1*d1;
			should = should + ".";
			g.drawString(should, 10, 118);
			
		}


	}
    public void paintstate1(Graphics g){
			String part1 = a + "x";
			String part2;
			g.setFont( f );
     			g.drawString(part1, 10, 28);
        		FontMetrics fm = g.getFontMetrics();
        		int newPosition = fm.stringWidth(part1) + 10;
        		g.drawString("2", newPosition, 20);
        		newPosition += fm.stringWidth("2");
			if(b > 0){
				part2 = " + " + b + "x";
			}
			else {
				part2 = " - " + Math.abs(b) + "x";
			}
			if(c > 0){
				part2 = part2 + " + " + c;
			}
			else {
				part2 = part2 + " - " + Math.abs(c);
			}
			part2 = part2 + " = " + a + " ( x";

	
		        g.drawString(part2, newPosition, 28);
        		newPosition += fm.stringWidth(part2);
      			g.drawString("2", newPosition, 20);
			newPosition += fm.stringWidth("2");
			String part3 = " + ";
			g.drawString(part3, newPosition, 28) ;
	  		newPosition += fm.stringWidth(part3);
      
			banswer.reshape(newPosition, 12, 48 ,26);
			newPosition += 48 + 4;
			String part4;
			part4 = " x ) ";
			
			if(c > 0){
				part4 = part4 + " + " + c;
			}
			else {
				part4 = part4 + " - " + Math.abs(c);
			}
			
			g.drawString(part4, newPosition, 28) ;
	
		g.drawString(usercomm, 10, 58);
		if(state == 1){
			switch(LastError[1]){
			case 0: break;
			case 1: g.drawString("Last time through you got the sign wrong.", 10, 88);
				break;
			case 2: g.drawString("Last time through you forgot to divide by a", 10, 88);
				break;
			case 3: g.drawString("Last time through your answer was upside down.", 10, 88);
				break;
			case 4: g.drawString("Last time through you did something wrong, but I couldn't figure out what.", 10, 88);
				break;
			}
		}
		if(state == 2 && NumberErrorsInARow[1] > 1){
			g.drawString("When you factor " + a + " out, the coefficient " + b +
				" of x has to be divided by " + a + ", so you should get " + b + "/" + a + ".",
				10, 118);
			
		}

	}

    public void paintstate5(Graphics g){
			String part1 = a + "x";
			String part2;
			g.setFont( f );
     			g.drawString(part1, 10, 28);
        		FontMetrics fm = g.getFontMetrics();
        		int newPosition = fm.stringWidth(part1) + 10;
        		g.drawString("2", newPosition, 20);
        		newPosition += fm.stringWidth("2");
			if(b > 0){
				part2 = " + " + b + "x";
			}
			else {
				part2 = " - " + Math.abs(b) + "x";
			}
			if(c > 0){
				part2 = part2 + " + " + c;
			}
			else {
				part2 = part2 + " - " + Math.abs(c);
			}
			part2 = part2 + " = " + a + " ( x";

	
		        g.drawString(part2, newPosition, 28);
        		newPosition += fm.stringWidth(part2);
      			g.drawString("2", newPosition, 20);
			newPosition += fm.stringWidth("2");
			String part3 = " + ";
			if(rightnumerator > 0){
				part3 = " + " + rightnumerator;
			}
			else {
				part3 = " - " + Math.abs(rightnumerator);
			}
			if(rightdenominator != 1){
				part3 = part3 + "/" + rightdenominator;
			}
				part3 = part3 + " x + " + n1*n1 +"/" + d1*d1 + " ) ";
			if(c > 0){
				part3 = part3 + " + " + c + " + ";
			}
			else {
				part3 = part3 + " - " + Math.abs(c) + " + ";
			}

			g.drawString(part3, newPosition, 28) ;
	  		newPosition += fm.stringWidth(part3);
      
			banswer.reshape(newPosition, 12, 48 ,26);
			newPosition += 48 + 4;
	
    		g.drawString(usercomm, 10, 58);
			if(state == 5){
			switch(LastError[5]){
			case 0: break;
			case 1: g.drawString("Last time through you got the sign wrong.", 10, 88);
				break;
			case 2: g.drawString("On the previous problem, you were off by a factor of 4.", 10, 88);
				break;
			case 3: g.drawString("On the previous problem, you were off by a factor of 4 and the sign was wrong.", 10, 88);
				break;
			case 4: g.drawString("On the previous problem, you were off by a factor of 2.", 10, 88);
				break;
			case 5: g.drawString("On the previous problem, you were off by a factor of 2 and the sign was wrong.", 10, 88);
				break;
			case 6: g.drawString("Last time through, you forgot the factor a.", 10, 88);
				break;
			case 7: g.drawString("Last time through, you forgot the factor a and the sign was wrong.", 10, 88);
				break;
			case 8: g.drawString("Last time through you did something wrong, but I couldn't figure out what.", 10, 88);
				break;
			}
		}
 		if(state == 6 && NumberErrorsInARow[5] > 1){
			String should = "Within the parentheses you added " + n1*n1;
			if(d1*d1 != 1)
				should = should + "/" + d1*d1;
			should = should + ". Since the expression in parentheses is multiplied by " + a +",";
			g.drawString(should, 10, 118);
	 		  int rnum = a * n1 * n1; 
			  int rdenom = d1 * d1; 
			int  g1 = gcd(rnum, rdenom);
			  rnum = rnum/g1;
			  rdenom = rdenom / g1;
			  if(rdenom < 0){
				  rnum = -rnum;
				  rdenom = -rdenom;
			  }

			should = "what was really added was " + rnum;
			if(rdenom != 1)
				should = should + "/" + rdenom;
			should = should + ", so now you should subtract that.";
			g.drawString(should, 10, 148);
		}


	}

	public void paintstate7(Graphics g){
			String part1 = a + "x";
			String part2;
			g.setFont( f );
     			g.drawString(part1, 10, 28);
        		FontMetrics fm = g.getFontMetrics();
        		int newPosition = fm.stringWidth(part1) + 10;
        		g.drawString("2", newPosition, 20);
        		newPosition += fm.stringWidth("2");
			if(b > 0){
				part2 = " + " + b + "x";
			}
			else {
				part2 = " - " + Math.abs(b) + "x";
			}
			if(c > 0){
				part2 = part2 + " + " + c;
			}
			else {
				part2 = part2 + " - " + Math.abs(c);
			}
			part2 = part2 + " = " + a + " ( x";

	
		        g.drawString(part2, newPosition, 28);
        		newPosition += fm.stringWidth(part2);
      			g.drawString("2", newPosition, 20);
			newPosition += fm.stringWidth("2");
			String part3 = " + ";
			if(rightnumerator > 0){
				part3 = " + " + rightnumerator;
			}
			else {
				part3 = " - " + Math.abs(rightnumerator);
			}
			if(rightdenominator != 1){
				part3 = part3 + "/" + rightdenominator;
			}
				part3 = part3 + " x + " + n1*n1;
			if(d1*d1 != 1) part3 = part3 +"/" + d1*d1;
			part3 = part3 + " ) ";
			if(c > 0){
				part3 = part3 + " + " + c ;
			}
			else {
				part3 = part3 + " - " + Math.abs(c) ;
			}
			int gc1 = gcd(b*b, 4*a);
			int rnum = -b*b/gc1;
			int rdenom =  4*a/gc1;
			if(rdenom < 0){
				rdenom = -rdenom;
				rnum = -rnum;
			}
			if(rnum > 0){
				part3 = part3 + " + " + rnum;
			}
			else {
				part3 = part3 + " - " + (-rnum);
			}
			part3 = part3;
			if(rdenom != 1) part3 = part3 + "/" + rdenom;
			part3 = part3 + " = " + a + "(x";

			g.drawString(part3, newPosition, 28) ;
	  		newPosition += fm.stringWidth(part3);
      	
			String part4 = " + ";
			g.drawString(part4, newPosition, 28);
			newPosition += fm.stringWidth(part4);
			banswer.reshape(newPosition, 12, 48 ,26);
			newPosition += 48 + 4;
			String part5 = " )";
			g.drawString(part5,newPosition, 28);
			newPosition += fm.stringWidth(part5);
			g.drawString("2", newPosition, 20);
			newPosition += fm.stringWidth("2");
			String part6 = "";
			if(c > 0){
				part6 = part6 + " + " + c ;
			}
			else {
				part6 = part6 + " - " + Math.abs(c) ;
			}
			if(rnum > 0){
				part6 = part6 + " + " + rnum;
			}
			else {
				part6 = part6 + " - " + (-rnum);
			}
			if(rdenom != 1) part6 = part6 + "/" + rdenom;
			g.drawString(part6, newPosition, 28);
			
    		g.drawString(usercomm, 10, 58);
			if(state == 7){
				switch(LastError[7]){
				case 0: break;
			case 1: g.drawString("Last time through you got the sign wrong.", 10, 88);
				break;
			case 2: g.drawString("On the previous problem, you were off by a factor of 2.", 10, 88);
				break;
			case 3: g.drawString("On the previous problem, you were off by a factor of 2 and the sign was wrong.", 10, 88);
				break;
			case 4: g.drawString("The last time through, you should have had b/(2a) but instead you squared it.", 10, 88);
				break;
			case 5: g.drawString("Last time through you did something wrong, but I couldn't figure out what.", 10, 88);
				break;
				}
			}
 		if(state == 8 && NumberErrorsInARow[7] > 1){
			String should = "This should be the number you squared previously to complete the square, b/(2a) = " + n1;
			if(d1 != 1)
				should = should + "/" + d1;
			should = should + ".";
			g.drawString(should, 10, 148);
		}
	}

 //
		public void paintstate9(Graphics g){
			String part1 = a + "x";
			String part2;
			g.setFont( f );
     			g.drawString(part1, 10, 28);
        		FontMetrics fm = g.getFontMetrics();
        		int newPosition = fm.stringWidth(part1) + 10;
        		g.drawString("2", newPosition, 20);
        		newPosition += fm.stringWidth("2");
			if(b > 0){
				part2 = " + " + b + "x";
			}
			else {
				part2 = " - " + Math.abs(b) + "x";
			}
			if(c > 0){
				part2 = part2 + " + " + c;
			}
			else {
				part2 = part2 + " - " + Math.abs(c);
			}
			part2 = part2 + " = " + a + " ( x";

	
		        g.drawString(part2, newPosition, 28);
        		newPosition += fm.stringWidth(part2);
      			g.drawString("2", newPosition, 20);
			newPosition += fm.stringWidth("2");
			String part3 = " + ";
			if(rightnumerator > 0){
				part3 = " + " + rightnumerator;
			}
			else {
				part3 = " - " + Math.abs(rightnumerator);
			}
			if(rightdenominator != 1){
				part3 = part3 + "/" + rightdenominator;
			}
				part3 = part3 + " x + " + n1*n1;
			if(d1*d1 != 1) part3 = part3 +"/" + d1*d1;
			part3 = part3 + " ) ";
			if(c > 0){
				part3 = part3 + " + " + c ;
			}
			else {
				part3 = part3 + " - " + Math.abs(c) ;
			}
			int gc1 = gcd(b*b, 4*a);
			int rnum = -b*b/gc1;
			int rdenom =  4*a/gc1;
			if(rdenom < 0){
				rdenom = -rdenom;
				rnum = -rnum;
			}
			if(rnum > 0){
				part3 = part3 + " + " + rnum;
			}
			else {
				part3 = part3 + " - " + (-rnum);
			}
			part3 = part3;
			if(rdenom != 1) part3 = part3 + "/" + rdenom;
			part3 = part3 + " = " + a + "(x";

			g.drawString(part3, newPosition, 28) ;
	  		newPosition += fm.stringWidth(part3);
      	
			String part4 = " + "  ;
			if(n1 > 0){
				part4 = part4 + " + " + n1;
			}
			else {
				part4 = part4 + " - " + Math.abs(n1);
			}
			if(d1 != 1) part4 = part4 + "/" + d1;
			part4 = part4 + " )";
			g.drawString(part4, newPosition, 28);
			newPosition += fm.stringWidth(part4);
			g.drawString("2", newPosition, 20);
			newPosition += fm.stringWidth("2");
			String part5 = " + ";
			g.drawString(part5, newPosition, 28);
			newPosition += fm.stringWidth(part5);

			banswer.reshape(newPosition, 12, 48 ,26);
   		g.drawString(usercomm, 10, 58);
			if(state == 9){
				switch(LastError[9]){
				case 0: break;
			case 1: g.drawString("Last time through you got the sign wrong.", 10, 88);
				break;
			case 2: g.drawString("On the previous problem, it looked like you didn't multiply c by the common denominator.", 10, 88);
				break;
			case 3: g.drawString("On the previous problem, it appears that you didn't use the correct sign on the second term.",10,88);
				break;

			case 4: g.drawString("Last time through you did something wrong, but I couldn't figure out what.", 10, 88);
				break;
				}
			}
 		if(state == 10 && NumberErrorsInARow[9] > 1){
			 int pnum = -b*b;
			 int pdenom = 4 * a;
			 int g1 = gcd(pnum, pdenom);
			 pnum = pnum/g1;
			 pdenom = pdenom/g1;
			 if(pdenom < 0){
				 pdenom = - pdenom;
				 pnum = -pnum;
			 }

		    String should;
			if(pdenom == 1){
				should = "Just add " + c;
				if(pnum > 0)
					should = should + " + " + pnum;
				else
					should = should + " - " + Math.abs(pnum);
				g.drawString(should, 10, 118);
			}
			else{
				should = "To add " + c;
				if(pnum > 0)
					should = should + " + " + pnum;
				else
					should = should + " - " + Math.abs(pnum);
				should = should + "/" + pdenom + ", note that the common denominator is " + pdenom + ".";
				g.drawString(should, 10, 118);
				should = "So you should get (" + c + " times " + pdenom;
				if(pnum > 0)
					should = should + ") + " + pnum;
				else
					should = should + ") - " + Math.abs(pnum);
				should = should	+ ", and divide that by " + pdenom + ".";
				g.drawString(should, 10, 148);
			}
		}
 
	}


     int intParse(String s){
                // If s represents an integer, return the integer; otherwise, throw an exception.
                Integer val;
                s = s.trim();
                if(s.indexOf('+') == 0)
                        s = s.substring(1, s.length());
                if(s.equals("-"))
                        throw new NumberFormatException();
                try{
                        val = new Integer(s);
                }
                catch(NumberFormatException nef){
                        throw nef;
                }
                return val.intValue();
        }

        void getRationalFrom( String s){
                // If s represents a rational number, break out the numerator and denominator
                int where;
                s = s.trim();
                if((where = s.indexOf('/')) < 0){
                        denominator = 1;
                        try{
                                numerator = intParse(s);
                        }
                        catch(NumberFormatException nef){
                                throw nef;
                        }
                        
                }
                else{
                        try{
                                numerator = intParse(s.substring(0,where));
                                denominator = intParse(s.substring(where + 1, s.length()));
                        }
                        catch(NumberFormatException nef){
                                throw nef;
                        }
                }
        }

		// State descriptions
		// In state 1, we have just posed a problem, and we are waiting
		// for input for factoring the coefficient of a x-squared out of 
		// the x terms.If that input produces a number
		// format exception, we stay in state 1. Otherwise we analyze
		// the input and go to state 2.
		//
		// In state 2, we give the student the good or bad news on the first
		// field, and then wait for a mouse click. This gives the student
		// time to read our analysis. On the mouse click, we move to state 3.
		//
		// In state 3, we wait for the input that completes the square
		// on x squared + (b/a)x. On a number format exception, stay in
		// state 3; otherwise move to state 4.
		//
		// In state 4, we wait for the student to read our analysis of
		// the state 3 input and click the mouse, whereupon we move to
		// state 5.
		//
		// States 5 and 6 are paired like the above states, and handle
		// the subtraction of what was added in state 3.
		//
		// States 7 and 8 are paired, and handle the factoring of the perfect
		// square term.
		//
		// States 9 and 10 are paired, to handle the finishing of the
		// arithmetic from the state 5 subtraction. On the click in
		// state 10, we pose a new problem and return to state 1.
		//

		public boolean action(Event e, Object o){
			if( (e.target == banswer) && (state == 1 )){
				try{
					getRationalFrom(e.arg.toString());
				}
				catch(NumberFormatException nef){
					usercomm = "Your answer isn't correctly typed. Enter the first field again.";
					repaint();
					return(true);
				}
				usercomm = "You entered " + e.arg.toString() + " . ";
				analyzeState1();
			
				repaint();
			
				return(true);
			}
			else if( (e.target == banswer) && (state == 3)){
				try{
					getRationalFrom(e.arg.toString());
				}
				catch(NumberFormatException nef){
					usercomm = "Your answer isn't correctly typed. Enter the first field again.";
					repaint();
					return(true);
				}
				usercomm = "You entered " + e.arg.toString() + " . ";
				analyzeState3();
			
				repaint();
			
				return(true);
			}
			else if( (e.target == banswer) && (state == 5)){
				try{
					getRationalFrom(e.arg.toString());
				}
				catch(NumberFormatException nef){
					usercomm = "Your answer isn't correctly typed. Enter the first field again.";
					repaint();
					return(true);
				}
				usercomm = "You entered " + e.arg.toString() + " . ";
				analyzeState5();
			
				repaint();
			
				return(true);
			}
			else if( (e.target == banswer) && (state == 7)){
				try{
					getRationalFrom(e.arg.toString());
				}
				catch(NumberFormatException nef){
					usercomm = "Your answer isn't correctly typed. Enter the first field again.";
					repaint();
					return(true);
				}
				usercomm = "You entered " + e.arg.toString() + " . ";
				analyzeState7();
			
				repaint();
			
				return(true);
			}
 			else if( (e.target == banswer) && (state == 9)){
				try{
					getRationalFrom(e.arg.toString());
				}
				catch(NumberFormatException nef){
					usercomm = "Your answer isn't correctly typed. Enter the first field again.";
					repaint();
					return(true);
				}
				usercomm = "You entered " + e.arg.toString() + " . ";
				analyzeState9();
			
				repaint();
			
				return(true);
			}

		
			
					
			return(false);
		}

		public boolean mouseUp(Event e, int x, int y){
			if(state == 2){
				state = 3;
				banswer.setText("");
				banswer.requestFocus();
				usercomm = "Enter a value to make the factor a perfect square.";
				repaint();
				
			}
			else if (state == 4){
				state = 5;
				banswer.setText("");
				banswer.requestFocus();
				usercomm = "Enter the number that makes the equality correct." ;
				repaint();
			}

			else if (state == 6){
				state = 7;
				banswer.setText("");
				banswer.requestFocus();
				usercomm = "Enter the number that makes the equality correct.";
				repaint();
			}
			else if (state == 8){
				state = 9;
				banswer.setText("");
				banswer.requestFocus();
				usercomm = "Enter the number that makes the equality correct.";
				repaint();
			}
			else if (state == 10){
				setnumbers();
				state = 1;
				usercomm = "Enter the value after factoring.";
				banswer.setText("");
				banswer.requestFocus();
				repaint();
			}

			return true;

		}


		void analyzeState1(){
			if(numerator * a == denominator * b){
				usercomm = usercomm + "That's right. ";
				LastError[1] = 0;
			}
			else if(numerator * a == - denominator * b){
				usercomm =  usercomm + "The sign is incorrect. ";
				LastError[1] = 1;
			}
			else if(numerator  == denominator * b) {
				usercomm =  usercomm + "You forgot to divide by " + a + ". ";
				LastError[1] = 2;
			}
			else if(denominator * a == numerator * b){
				usercomm =  usercomm + "Your answer is upside down. ";
				LastError[1] = 3;
			}
			else {
				usercomm =  usercomm + "I can't figure out what you did. ";
				LastError[1] = 4;
			}
			if(LastError[1] > 0)
				NumberErrorsInARow[1]++;
			else
				NumberErrorsInARow[1] = 0;
			usercomm = usercomm + "Click to go on.";
			String rightanswer = "" + rightnumerator;
			if(rightdenominator != 1) rightanswer = rightanswer + "/" + rightdenominator;
			banswer.setText(rightanswer); 
			state = 2;
		}

		void analyzeState3(){
			  int g = gcd(b, 2*a);
			  n1 = b / g;
			  d1 = (2 * a) / g;
			  if(d1 < 0){
				  d1 = -d1;
				  n1 = -n1;
			  }
			  int rdenom = d1 * d1;;
			  int rnum = n1 * n1;
			  
			  if(numerator * rdenom == denominator * rnum){
				  usercomm = usercomm + "That's right. Click for next part.";
				  LastError[3] = 0;
			  }
			  else if(numerator * rdenom == - denominator * rnum){
				  usercomm = usercomm + "Ok, except the sign should be positive. Click.";
				  LastError[3] = 1;
			  }
			  else if(numerator * rdenom == 4 * denominator * rnum){
				  usercomm = usercomm + "You're off by a factor of 4. Square half the coefficient of x, " + n1 + "/" + d1 + ". Click.";
				  LastError[3] = 2;
			  }
			  else if(numerator * rdenom == -4 * denominator * rnum){
				  usercomm = usercomm + "The sign is wrong, and you should square half the coefficient of x, " + n1 + "/" + d1 + ". Click.";
				  LastError[3] = 3;
			  }
			  else if(numerator * rdenom == 2 * denominator * rnum){
				  usercomm = usercomm + "You're off by a factor of 2. Square half the coefficient of x, " + n1 + "/" + d1 + ". Click.";
				  LastError[3] = 4;
			  }
			  else if(numerator * rdenom == -2 * denominator * rnum){
				  usercomm = usercomm + "The sign is wrong, and you should square half the coefficient of x, " + n1 + "/" + d1 + ". Click.";
				  LastError[3] = 5;
			  }
			  else {
				  usercomm = usercomm + "I don't know what you did. Square half the coefficient of x, " + n1 + "/" + d1 + ". Click for next part.";
			      LastError[3] = 6;
			  }
			if(LastError[3] > 0)
				NumberErrorsInARow[3]++;
			else
				NumberErrorsInARow[3] = 0;

			  state = 4;
 			  String rightanswer = "" + rnum;
			  if(rdenom!=1) rightanswer = rightanswer + "/" + rdenom;
			  banswer.setText(rightanswer);

			 
		}

		 void analyzeState5(){
			  // Yes, the state 3 analyzer did this already, but better safe
			  // than sorry.
			  int g = gcd(b, 2*a);
			  n1 = b / g;
			  d1 = (2 * a) / g;
			  if(d1 < 0){
				  d1 = -d1;
				  n1 = -n1;
			  }
			  // Compute the right answer, which is -a times what
			  // we added within the parentheses.
	 		  int rnum = -a * n1 * n1; 
			  int rdenom = d1 * d1; 
			  g = gcd(rnum, rdenom);
			  rnum = rnum/g;
			  rdenom = rdenom / g;
			  if(rdenom < 0){
				  rnum = -rnum;
				  rdenom = -rdenom;
			  }
			  if(numerator * rdenom == denominator * rnum){
				  usercomm = usercomm + "That's right. Click for next part.";
				  LastError[5] = 0;
			  }
			  else if(numerator * rdenom == - denominator * rnum){
				  usercomm = usercomm + "Ok, except for sign. You added " + a + " times " + n1*n1 + "/" + d1*d1 + " so subtract it. Click to go on.";
				  LastError[5] = 1;
			  }
			  else if(numerator * rdenom == 4 * denominator * rnum){
				  usercomm = usercomm + "You're off by  4. You added " + a + " times " + n1*n1 + "/" + d1*d1 + " so subtract it. Click to go on.";
				  LastError[5] = 2;
			  }
			  else if(numerator * rdenom == -4 * denominator * rnum){
				  usercomm = usercomm + "The sign is wrong, and you added " + a + " times " + n1*n1 + "/" + d1*d1 + " so subtract it. Click for next.";
			      LastError[5] = 3;
			  }
			  else if(numerator * rdenom == 2 * denominator * rnum){
				  usercomm = usercomm + "You're off by  2. You added " + a + " times " + n1*n1 + "/" + d1*d1 + " so subtract it. Click for next part.";
			      LastError[5] = 4;
			  }
			  else if(numerator * rdenom == -2 * denominator * rnum){
				  usercomm = usercomm + "The sign is wrong, and you added " + a + " times " + n1*n1 + "/" + d1*d1 + " so subtract it. Click for next.";
			      LastError[5] = 5;
			  }
			  else if(a * numerator * rdenom == denominator * rnum){
				  usercomm = usercomm + "You forgot the factor " + a + ". Click to go on."	;
			      LastError[5] = 6;
			  }
			  else if(a * numerator * rdenom == -denominator * rnum){
				  usercomm = usercomm + "You forgot the factor " + a + ", and you may have sign problems. Click to go on."	;
			      LastError[5] = 7;
			  }
			  else {
				  usercomm = "I don't know how you got that. You added " + a + " times " + n1*n1 + "/" + d1*d1 + " so subtract it. Click for next part.";
			      LastError[5] = 8;
			  }
			if(LastError[5] > 0)
				NumberErrorsInARow[5]++;
			else
				NumberErrorsInARow[5] = 0;

			  state = 6;
			  String rightanswer = "" + rnum;
			  if(rdenom !=1) rightanswer = rightanswer + "/" + rdenom;
			  banswer.setText(rightanswer);
		 }

		 void analyzeState7(){
			  int g = gcd(b, 2*a);
			  n1 = b / g;
			  d1 = (2 * a) / g;
			  if(d1 < 0){
				  d1 = -d1;
				  n1 = -n1;
			  }
			  if(numerator * d1 == denominator * n1){
				  usercomm = usercomm + "That's right. Click for next part.";
				  LastError[7] = 0;
			  }
			  else if(numerator * d1 == - denominator * n1){
			      usercomm =  usercomm + "The sign is incorrect. Click for next part ";
			      LastError[7] = 1;
			  }
			  else if(numerator * d1 == 2 * denominator * n1){
				  usercomm = usercomm + "You're off by 2. This should be " + b + "/(2 times " + a +"), which you squared before."	;
				  LastError[7] = 2;
			  }
			  else if(numerator * d1 == -2 * denominator * n1){
				  usercomm = usercomm + "You're off by 2 and a sign. This should be " + b + "/(2 times " + a +"), which you squared before."  ;
				  LastError[7] = 3;
			  }
			  else if(numerator * d1 * d1 == denominator * n1 * n1){
				  usercomm = usercomm + "You should have just " + 	b + "/(2 times " + a +"), not its square.Click for next part.";
				  LastError[7] = 4;
			  }
			  else {
				  usercomm = "I don't know how you got that. You added " + a + " times " + n1*n1 + "/" + d1*d1 + " so subtract it. Click for next part.";
				  LastError[7] = 5;
			  }
			if(LastError[7] > 0)
				NumberErrorsInARow[7]++;
			else
				NumberErrorsInARow[7] = 0;

			state = 8;
			String rightanswer = "" + n1;
			if(d1 != 1) rightanswer = rightanswer + "/" + d1;
			banswer.setText(rightanswer);
			
		 }

		 void analyzeState9(){
			 // Compute the right answer for c - b*b/(4*a)
			 int rnum = 4*a*c - b*b;
			 int rdenom = 4 * a;
			 int g = gcd(rnum,rdenom);
			 rnum = rnum/g;
			 rdenom = rdenom/g;
			 if(rdenom < 0){
				 rdenom = -rdenom;
				 rnum = -rnum;
			 }
			 int pnum = b*b;
			 int pdenom = 4 * a;
			 g = gcd(pnum, pdenom);
			 pnum = pnum/g;
			 pdenom = pdenom/g;
			 if(pdenom < 0){
				 pdenom = - pdenom;
				 pnum = -pnum;
			 }
			 if(numerator * rdenom == denominator * rnum){
				  usercomm = usercomm + "That's right. Click for another problem.";
				  LastError[9] = 0;
			  }
			  else if(numerator * rdenom == - denominator * rnum){
			      usercomm =  usercomm + "The sign is incorrect. Click for another problem.";
				  LastError[9] = 1;
			  }
			  else if(numerator * pdenom == denominator * (c - pnum)){
				  usercomm = usercomm + "It looks like you didn't multiply " + c + " by the common denominator " + pdenom;
			      LastError[9] = 2;
			  }
			  else if(numerator * pdenom == denominator * (c*pdenom + pnum)){
				  usercomm = usercomm + "It looks like you added the second term instead of subtracting.";
			      LastError[9] = 3;
			  }
			  else {
				  usercomm = usercomm + "I don't know what you did. Click for another problem.";
				  LastError[9] = 4;
			  }
			if(LastError[9] > 0)
				NumberErrorsInARow[9]++;
			else
				NumberErrorsInARow[9] = 0;

			state = 10;
			String rightanswer = "" + rnum;
			if(rdenom != 1) rightanswer = rightanswer + "/" + rdenom;
			banswer.setText(rightanswer);

		 }
}