Symbolic solution of large stationary chemical kinetics problems
IMPACT of Computing in Science and Engineering
Regular Article: Symmetrical Newton Polytopes for Solving Sparse Polynomial Systems
Advances in Applied Mathematics
A polyhedral method for solving sparse polynomial systems
Mathematics of Computation
Asymptotically fast computation of Hermite normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Near optimal algorithms for computing Smith normal forms of integer matrices
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Finding all isolated zeros of polynomial systems in Cn via stable mixed volumes
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Journal of Symbolic Computation
Journal of Symbolic Computation
Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems
Journal of Symbolic Computation
Computing hopf bifurcations in chemical reaction networks using reaction coordinates
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
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The positive steady states of chemical reaction systems modeled by mass action kinetics are investigated. This sparse polynomial system is given by a weighted directed graph and a weighted bipartite graph. In this application the number of real positive solutions within certain affine subspaces of RM is of particular interest. We show that the simplest cases are equivalent to binomial systems and are explained with the help of toric varieties. The argumentation is constructive and suggests algorithms. In general the solution structure is highly determined by the properties of the two graphs. We explain how the graphs determine the Newton polytopes of the system of sparse polynomials and thus determine the solution structure. Results on positive solutions from real algebraic geometry are applied to this particular situation. Examples illustrate the theoretical results. Copyright 2002 Elsevier Science Ltd.