The program listed below is a TCL script. You need to run TCL to run the script. I assume you have TCL on the Math department computers. (TCL is used by Dr. W. Schelter's version of GCL.) You can also get a copy for free for a PC or Mac from http://dev.scriptics.com/software/tcltk/ .
On a Unix system you need to start the graphic version of TCL, usually by typing "wish" at the command prompt. Then type "source loops.tcl" to load the script. On an MS Windows system, just double click on the script file and TCL will start automatically.
Once the program has started, just click where you want to move z. The three values of w which will make the polynomial equal 0 will automatically be updated. A path will follow each point. Hit the reset button to start fresh.
The displays on the bottom will show the values of z and of each w. "Err=" shows sum of the absolute values of the polynomial at the given z and w's. The goal is to find the 0's of the polynomial, so err should be 0 or close to 0.
Source code: loops.tcl
Source, instructions, and samples: loops.zip
Written by Philip Smolen for a class at UT.