Complexity of Solving Systems with Few Independent Monomials and Applications to Mass-action Kinetics

Dima Grigoriev und Andreas Weber
In proceedings of Computer Algebra in Scientific Computing - 14th International Workshop (CASC 2012), Maribor, Slovenia, Springer, Sept. 2012
 

Abstract

We design an algorithm for nding solutions with nonzero coordinates of systems of polynomial equations which has a better complexity bound than for known algorithms when a system contains a few linearly independent monomials. For parametric binomial systems we construct an algorithm of polynomial complexity. We discuss the applications of these algorithms in the context of chemical reaction systems.

Stichwörter: chemical reaction networks, complexity of solving systems of polynomial equations, mass-action kinetics, Smith form, toric systems

Bibtex

@INPROCEEDINGS{GrigorievWeber2012a,
     author = {Grigoriev, Dima and Weber, Andreas},
      title = {Complexity of Solving Systems with Few Independent Monomials and Applications to Mass-action
               Kinetics},
  booktitle = {Computer Algebra in Scientific Computing - 14th International Workshop (CASC 2012)},
     series = {Lecture Notes in Computer Science},
       year = {2012},
      month = sep,
  publisher = {Springer},
   location = {Maribor, Slovenia},
   keywords = {chemical reaction networks, complexity of solving systems of polynomial equations, mass-action
               kinetics, Smith form, toric systems},
   abstract = {We design an algorithm for nding solutions with nonzero
               coordinates of systems of polynomial equations which has a better complexity
               bound than for known algorithms when a system contains a few
               linearly independent monomials. For parametric binomial systems we
               construct an algorithm of polynomial complexity. We discuss the applications
               of these algorithms in the context of chemical reaction systems.}
}