HOM4PS-2.0 (Linux system)

64-bit Linux operating system (x86-64/AMD-64/Intel-64)

(HOM4PS2_64-bit.tar.gz)

• Features:

1. Run on 64-bit Linux operating system (x86-64/AMD-64/Intel-64).

2. No library installation is needed.

3. No compiler is needed.

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

(HOM4PS2_64-bit_ifort.tar.gz)

• Features:

1. Run on 64-bit Linux operating system (x86-64/AMD-64/Intel-64).

2. No library installation is needed.

3. ifort (Intel fortran) is needed. But it takes less running time.

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

• The usage of the code:

Step1: Untar HOM4PS2_xx-bit_xx.tar.gz. i.e. tar –zxf HOM4PS2_xx-bit_xx.tar.gz

Step2: Change directory to HOM4PS2. i.e. cd HOM4PS2

Step3: Create/Copy input file (symbolic format) in the directory HOM4PS2.

Step4: Execute ./hom4ps2 filename.

Ex: ./hom4ps2 barry.sym

Ex: ./hom4ps2 cyclic5.sym

Note: The solutions are listed in file HOM4PS2/data.roots.

• 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.

Sample 1: barry.sym

{

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

5*y^4-3;

-20*x+y-z;

}

Sample 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