<< File name = 3cycP/readme3cycP>> 

1. This directory 3cycP contains the following files: 

	readme3cycP(this file)
	para3cycP.dat
	solve_3cycP.m
	3cycP.coef
	3cycP1, 3cycP2

In addition to these files, MATLAB, CMPSm2.m and traceOneCurve2.m are necessary 
to execute solve_3cycP.m.

2. 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.

3. The file 3cycP.coef, 3cycP1 and 3cycP2 provide data for two polyhedral 
homotopies of an auxiliary  cyclic polynomial 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. 

Here r11, . . . , r33 denote randomly generated complex numbers. 
 
4. To trace the solution curves of the polyhedral homotopies, 

(1) copy CMPSm2.m and traceOneCurve2.m to this directory 3cycP,
(2) run MATLAB, 
(3) execute 
>>solve_3cycP
in the MATLAB environment. 

This will give the set of solutions of the auxiliary cyclic polynomial with 
random coefficients described in 3 above. To obtain the solutions of 
the target cyclic polynomial described in 1, we need to apply CMPSm again to 
the linear homotopy beteen the auxiliary cyclic polynomial and the target 
cyclic polynomial with data in 3cycPL. See readme3cycPL/3cycPL. 

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

April 14, 2003
 
