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Abstract: Regular chains and triangular decompositions are fundamental andwell-developed tools for describing the complex solutions of polynomialsystems. This paper proposes adaptations of these tools focusing on solutionsof the real analogue: semi-algebraic systems. We show that any such system canbe decomposed into finitely many {\em regular semi-algebraic systems}. Wepropose two specifications of such a decomposition and present correspondingalgorithms. Under some assumptions, one type of decomposition can be computedin singly exponential time w.r.t.\ the number of variables. We implement ouralgorithms and the experimental results illustrate their effectiveness.



Autor: Changbo Chen, James H. Davenport, John P. May, Marc Moreno Maza, Bican Xia, Rong Xiao

Fuente: https://arxiv.org/



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