HOM4PS-2.0 (Windows XP)

Executable version for Windows XP system

• Download: (HOM4PS2_xp.zip)

• Features:

1. Run on Windows XP.

2. No library installation is needed.

3. No compiler is needed.

4. One option (switch between Polyhedral homotopy and Linear homotopy).

• The usage of the code:

Step1: Unzip HOM4PS2_xp.zip.

Step2: Create/Copy input file (symbolic format) in the directory HOM4PS2.

Step3: Execute hom4ps2 filename.

Ex: hom4ps2 barry.sym

Ex: hom4ps2 cyclic5.sym

Note: The solutions are listed in file “data.roots” in the same directory.

• The symbolic format of input file:

1. The polynomial system should be in brackets { } .

2. Each equation should be separated by semicolon ; .

3. All comments should be outside the brackets and should have number sign # in the front.

Ex 1: barry.sym

{

-x^5+y^5-3*y-1;

5*y^4-3;

-20*x+y-z;

}

# barry from PoSSo

# Extended Mixed volume : 20

# Number of roots : 20

# Number of real roots : 2

Ex 2: cyclic5.sym

{

x1+x2+x3+x4+x5;

x1*x2+x2*x3+x3*x4+x4*x5+x1*x5;

x1*x2*x3+x2*x3*x4+x3*x4*x5+x4*x5*x1+x5*x1*x2;

x1*x2*x3*x4+x2*x3*x4*x5+x3*x4*x5*x1+x4*x5*x1*x2+x5*x1*x2*x3;

x1*x2*x3*x4*x5-1;

}

# cyclic 5-roots problem

# Mixed volume : 70

# Number of roots : 70

# Number of real roots : 10

Note: The input files of several well-known polynomial systems are available at equations.zip.

If you have any questions or comments, please contact

* Tsung-Lin Lee ( leetsung@math.nsysu.edu.tw )

Tien-Yien Li ( li@math.msu.edu )

Chih-Hsiung Tsai ( tsaichih@msu.edu )

* Corresponding author