Minkowski Sums of Newton Polyhedra in the Analysis of Nonlinear Algebraic Systems
Received: 2026-05-30
Published: 2026-06-06
Abstract
A geometric approach based on the Minkowski sums of Newton polyhedra has been presented for the analysis of nonlinear algebraic systems. By constructing the common Newton-Minkowski polyhedron of the system, it becomes possible to identify significant faces, determine the corresponding normal cones, and derive truncated systems that preserve the essential local properties of the original system. The use of the Motzkin-Burger algorithm further facilitates the computation of cone generators and the analysis of local solutions. The results confirm that Minkowski sums provide an effective framework for investigating the structure and local behavior of nonlinear algebraic systems. Future work may focus on extending this approach to higher-dimensional systems and developing efficient computer algebra implementations.
Keywords
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