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Preliminary Version of StartSystem

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### When we solve a polynomial system by the polyhedral homotopy continuation method, the following four phases are necessary:

(1) Compute the mixed cells and construct a family of polyhedral homotopy equation systems.

(2) Solve the starting binomial equation system of each polyhedral system.

(3) Balance the lifting power constants of the family of homotopy equation systems.

(4) Trace the homotopy solution curves from the solutions of the binomial systems computed in (2).

The software package StartSystem provides steps (1) - (3), while either of the MATLAB
software packages CMPSm and the C++ software package
CMPSc provide step (4).
That is, the package StartSystem reads a data file which describes a polynomial system
to be solved and output data files which are necessary for the packages CMPSm and CMPSc
as their input files.

### The software package StartSystem is still under development. Please report any trouble
and bug that you may encounter to

Tomohiko MIZUTANI

mizutan8@is.titech.ac.jp

#### Yang Dai

Dept. of Bioengineering, University of Illinois at Chicago

Katsuki Fujisawa

Dept. of Architecture and Architectural Systems, Kyoto University

Takayuki Gunji, Masakazu Kojima and Tomohiko Mizutani

Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology

Akiko Takeda

Corporate Research & Development Center, Toshiba Corporation

#### May 12, 2002