Polynomial systems arise naturally in many areas of human endeavor. These include the modeling of tumor growth; the design of robotic devices; chemical systems arising in areas ranging from combustion to blood clotting; assorted problems in physics; plus many areas with mathematics. The solution of the polynomial systems answers questions critical to these endeavors. This research will be devoted to developing the next generation of Bertini, an open source software package, which has been used successfully by many researchers on many problems, which include all those mentioned above.
Bertini will be rewritten in C++ to be scriptable and modular, which will allow it to be interfaced transparently with symbolic software. The new Bertini will include tools allowing the user to construct and manipulate homotopies based on the output of Bertini. A major focus of the research will be given to systems of polynomials arising from the discretization of systems of differential equations. The great challenge of these very large systems of polynomials is balanced by the great potential impact new efficient and robust methods of solution will have.
