## Experimental results for the Poincaré center problem

Hans-Christian Graf v. Bothmer, Martin Cremer

Here we provide some C++ source code and a Macaulay scripts to supplement our article math.AG/0505547 .

### C++ Source Code

zahl.cpp, zahl.h. Class representing elements of F_q and F_q[epsilon].

koerper.cpp, korper.h. Here the operations of the finite field F_q and the ring F_q[epsilon] are defined.

polynom.cpp, polynom.h. Helper classes that store polynomials in one and two varibles.

KoeffListe.cpp, KoeffListe.h. A helper class used to store the coefficients of P and Q.

frommer.cpp, frommer.h. These files contains Frommers algorithm. For the implementation we followed Kay Moritzen and André Höhn .

Parameterliste.cpp, Parameterliste.h. This class handles the imput parameters from the imput file.

Statistik.cpp, Statistik.h. Class that counts how often a given number of equations are satisfied.

stdafx.cpp, stdafx.h. Contains compiler instructions for Windows clients.

zahlen.cpp, Main program including workflow and random number generation. For random number generation we use an algorithm from numerical recipies.

strudel/source.tgz All strudel/source files as gziped tar file. Unfold with tar xvzf strudel/source.tgz

### Precompiled Programms

FrommerLinux.out The compilation of the above strudel/source code under Linux.

FrommerMac.out The compilation of the above strudel/source code under Mac OS X 10.2.

Usage: FrommerLinux.out inputfile outputfile

The outputfile will be executable in Macaulay. The list L contains the coordinates of the points and the entries of the jacobi Matrix (if it was calculated). A sample inputfile is eingabe.m2.

### Macaulay-Scripts

sqlJacobi-files.m2 This script takes an output file from our C++ programm, calculated the rank of the Jacobi matrix and writes the information about the points as sql-code which can then be used to write this information into a mysql-database