Triangular decomposition of semi-algebraic systems
Chen, C., Davenport, J. H., May, J. P., Maza, M. M., Xia, B. and Xiao, R., 2010. Triangular decomposition of semi-algebraic systems. In: ISSAC '10 Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation , 2010. New York, U. S. A.: ACM, pp. 187-194.
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Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue: semi-algebraic systems. We show that any such system can be decomposed into finitely many regular semi-algebraic systems. We propose two specifications of such a decomposition and present corresponding algorithms. Under some assumptions, one type of decomposition can be computed in singly exponential time w.r.t. the number of variables. We implement our algorithms and the experimental results illustrate their effectiveness.
|Item Type||Book Sections|
|Creators||Chen, C., Davenport, J. H., May, J. P., Maza, M. M., Xia, B. and Xiao, R.|
|Departments||Faculty of Science > Computer Science|
|Additional Information||2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010. 25-28 July 2010. Munich, Germany.|
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