Computing with semi-algebraic sets : Relaxation techniques and effective boundaries

Reference:

Chen, C., Davenport, J.H., Moreno Maza, M., Xia, B. and Xiao, R., 2012. Computing with semi-algebraic sets : Relaxation techniques and effective boundaries. Journal of Symbolic Computation, 52, pp. 72-96.

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Official URL:

http://dx.doi.org/10.1016/j.jsc.2012.05.013

Abstract

We discuss parametric polynomial systems, with algorithms for real root classification and triangular decomposition of semi-algebraic systems as our main applications. We exhibit new results in the theory of border polynomials of parametric semi-algebraic systems: in particular a geometric characterization of its "true boundary" (Definition 1). In order to optimize the corresponding decomposition algorithms, we also propose a technique, that we call relaxation, which can simplify the decomposition process and reduce the number of components in the output. This paper extends our earlier works ([Chen et al., 2010] and [Chen et al., 2011]).

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