Automating a formula

Hi all,
This is not homework.
This is a JAVA program but I need to get the math formula to a better format.
I am looking for an improvement in expanding the formula(s) for finding the roots of a polynomial.  The present setup is to use Horner's method and specifically show formulas that are for polynomials of degree 3  or 4.  I would like to express the formula using any number of degree. And for the moment, I do not see how to create a general formula using Horner's method.


import java.awt.*;
import java.awt.event.*;
import javax.swing.*;

// hornersMethodDemo attempts to find solutions to polynomial equations that are of degree 2 or 3.
// Any terms that are missing are given coefficients  0. Step size is variable.

/* Sample problems:
 p(x) = x^2-25 use coefficients 1,0,-25 separated by "," as shown; interval from -7 to 7
 p(x) = x^2-8x+15 use for coefficients 1,-8,15 separated by "," as shown; interval from 0 to 7
 p(x) = x^3-11x^2+14x+80 use for coefficients 1,-11,14,80 separated by "," as shown; interval from -10 to 10
 p(x) = 0.3x^2-3.8x+12 use coefficients 0.3,-3.8,+12 separated by "," as shown; interval from 5 to 7
 note:
 any x value that is at one point is above the line y = 0 and the next is below the line y=0, there exist a root.
 or similarly, any x value that is at one point is below the line y = 0 and the next is above the line y=0, there exist a root.
 */  
// This example demonstrates the use of JLabel, JTextField
// and JButton.

public class hornersMethodDemo
  implements ActionListener {
  JFrame HornerFrame;
  JPanel HornerPanel;
 
  JTextField FromTField;
  JTextField ToTField;
  JTextField IncTField;
  JTextField PolyCoefs;
  JLabel FromLabel, ToLabel, IncLabel, PolyCoefLabel, CalcValueLabel;
  JButton Calculate;
 
  // Constructor
  public hornersMethodDemo() {
    // Create the frame and container.
    HornerFrame = new JFrame("Looking For Roots");
    HornerPanel = new JPanel();
    HornerPanel.setLayout(new GridLayout(3, 2));
   
    // Add the widgets.
    addWidgets();
   
    // Add the panel to the frame.
    HornerFrame.getContentPane().add(HornerPanel, BorderLayout.CENTER);
   
    // Exit when the window is closed.
    HornerFrame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
   
    // Show the frame.
    HornerFrame.pack();
    HornerFrame.setVisible(true);
  }
 
  // Create and add the widgets for converter.
  private void addWidgets() {
    // Create widgets.
   
    FromTField = new JTextField();
    ToTField= new JTextField();  
    IncTField = new JTextField();
    PolyCoefs = new JTextField();
   
    FromLabel = new JLabel("Evaluate X From", SwingConstants.LEFT);
    ToLabel= new JLabel("Evaluate X To", SwingConstants.LEFT);
    IncLabel = new JLabel("Step Size", SwingConstants.LEFT);
    PolyCoefLabel = new JLabel("Enter Coefficients", SwingConstants.LEFT);
    CalcValueLabel = new JLabel("See System Out For Value", SwingConstants.LEFT);
    Calculate = new JButton("Calculate");
   
   
    // Listen to events from Calc button.
    Calculate.addActionListener(this);
   
    // Add widgets to container.
    HornerPanel.add(FromLabel);
    HornerPanel.add(FromTField);
    HornerPanel.add( ToLabel);
    HornerPanel.add(ToTField);
    HornerPanel.add(IncLabel);
    HornerPanel.add(IncTField);
    HornerPanel.add(PolyCoefLabel);
    HornerPanel.add(PolyCoefs);
   
   
    HornerPanel.add(Calculate);
    HornerPanel.add(CalcValueLabel);    
    //HornerPanel.add(CalcValue );  
   
    FromLabel.setBorder(BorderFactory.createEmptyBorder(5, 5, 5, 5));
    ToLabel.setBorder(BorderFactory.createEmptyBorder(5, 5, 5, 5));
    IncLabel.setBorder(BorderFactory.createEmptyBorder(5, 5, 5, 5));
    CalcValueLabel.setBorder(BorderFactory.createEmptyBorder(5, 5, 5, 5));
  }
 
  // Implementation of ActionListener interface.
  public void actionPerformed(ActionEvent event) {    
   
    try {      
      float gofrmX = Float.parseFloat(FromTField.getText());//from
      float gotoX = Float.parseFloat(ToTField.getText());//to
      float stp = Float.parseFloat(IncTField.getText());//step
      String in = new String(PolyCoefs.getText()); //coefficients in normal order  
     
     
      String[] atoms = in.split(",");      
      //P(x) = a0 + x *(a1 + x*(a2+x*(...x*an)...)): model
      float  y = 0;
      int atmlength = atoms.length;
      System.out.print(gofrmX + " ** is the first X point ** ");
      while (gofrmX <= gotoX )
      {
        if (atmlength == 3) // 2nd degree
        {        
          y = Float.parseFloat(atoms[atoms.length-1]) + gofrmX*(Float.parseFloat(atoms[atoms.length-2]) + gofrmX*Float.parseFloat(atoms[atoms.length-3]));
        }
        if (atmlength == 4) // 3rd degree
        {        
          y = Float.parseFloat(atoms[atoms.length-1]) + gofrmX*(Float.parseFloat(atoms[atoms.length-2]) + gofrmX*(Float.parseFloat(atoms[atoms.length-3]) + gofrmX*Float.parseFloat(atoms[atoms.length-4])));
        }
        System.out.print("Value for y is " + y);        
        if( y < 0 ){
          System.out.println(" and is below the line y = 0  ");
        }              
        if( y == 0 ){
          System.out.println(" and is on the line y = 0 and is a root ");
        }
        if( y > 0 ){
          System.out.println(" and is above the line y = 0 ");
        }
        gofrmX = gofrmX + stp;
        System.out.print(gofrmX + " ** is another step **  ");
      }  
    }
    catch (Exception e) {
      //e.printStackTrace();
    }
  }
  // main method
  public static void main(String[] args) {
    // Set the look and feel.
    try {
      UIManager.setLookAndFeel(
                               UIManager.getCrossPlatformLookAndFeelClassName());
    }
    catch (Exception e) {}
   
    hornersMethodDemo calculator = new hornersMethodDemo();
  }
}


Any help is appreciated.

Delphi3