<< File name = 3cycPL/readme3cycPL>> 

1. This directory 3cycPL contains the following files: 

	readme3cycPL(this file)
	para3cycPL.dat
	solve_3cycPL.m
	3cycPL.coef
	3cycPL

In addition to these files, MATLAB, CMPSm2.m and traceOneCurve2.m are necessary 
to execute solve_3cycPL.m.

2. The file 3cycPL.coef and 3cycPL provide data for a linear 
homotopy between a starting cyclic polynomial system with 
random coefficients 

r11 + r12*x1*x2*x3                = 0,
r21*x1*x2 + r22*x2*x3 + r23*x3*x1 = 0,
r31*x1   + r32*x2     + r33*x3    = 0, 

where r11, . . . , r33 denote randomly generated complex numbers, 
and the target cyclic polynomial system 

Description of the cyclic polynomial system with the dimension 3. 

1 - x1*x2*x3          = 0,
x1*x2 + x2*x3 + x3*x1 = 0,
x1   + x2     + x3    = 0.

The solutions of the starting cyclic polynomial system were computed by 
cheater's homotopy applied to the starting cyclic polynomial system. 
See 3cycP/readme3cycP. 
 
3. To trace the solution curves of the linear homotopy to compute 
the solutions of the target system,  

(1) copy CMPSm2.m and traceOneCurve2.m to this directory 3cycPL,
(2) run MATLAB, 
(3) execute 
>>solve_3cycPL
in the MATLAB environment. 

Sunyoung Kim (skim@ewha.ac.kr) and Masakazu Kojima (kojima@is.titech.ac.jp)

April 14, 2003
 
