Applets...

Note for Internet Explorer: To use this you need Sun's Java Runtime environment which may be downloaded

from their website http://www.sun.com.

Diophantine equation solver (Michael Leeming)

This applet is designed to find zeroes of multivariable polynomials over a prime-order field by the power method, developed by N J Wildberger and described in N J Wildberger, Row-reduction and invariants of Diophantine equations, Proc. Indian Academy of Sciences, Vol 104, No. 3 1994 549-555. It does not find solutions all the time, but you can experiment and see that it is quite succesful in general. It works best with `random' equations containing many terms and variables.

The applet is the work of Michael Leeming, a student of computer science and mathematics at UNSW in 2005.

How to use it:

First, choose how many terms are in the polynomial, the number of variables, and the order of the field. Then click the "New Equation Class" button.

If you followed step 1 correctly, then boxes should appear for you to enter the coefficients and exponents. If a variable does not appear in a term, then enter "0" as the exponent. When you have filled in all the boxes, click the "Solve Equation Instance" button.

The applet will try to make a substitution to solve the system of equations. If it can make a substitution which makes one variable appear linearly wherever it appears, then it will present a parameterized set of solutions. If not, it will display an error message which includes the text "could not find solution".

If a set of solutions are found, then substitutions of integers for the parameters can be made by entering the values into each of the boxes, then clicking the "Perform Substitution" button.

Backtracking can be performed at any time by editing the earlier text and then clicking the corresponding button.

NOTE: Just changing the prime field will have no effect until the "New Equation Class" button is clicked.