Complexity of Solving Systems with Few Independent Monomials and Applications to Mass-action Kinetics
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.
Keywords: 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.} }