I've posted some software which I've written to do various algebraic computations in Java. You can learn more on my Java Algebra page.
A Tip on compiling applets
In the interest of producing an applet that can be run on most computers,
it is best to compile the applet for relatively old java versions. The list of release
dates for the various versions may be found on
Sun's website.
Compilation with the "-target" option will ensure that it runs on an older java version.
For example compiling with "
javac -target 1.3 yourapplet.java" will produce an applet that runs
on systems as old as java version 1.3.