TY - JOUR
T1 - Computing with semi-algebraic sets
T2 - Relaxation techniques and effective boundaries
AU - Chen, C.
AU - Davenport, J.H.
AU - Moreno Maza, M.
AU - Xia, B.
AU - Xiao, R.
PY - 2012/5
Y1 - 2012/5
N2 - 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]).
AB - 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]).
UR - http://www.scopus.com/inward/record.url?scp=84873570182&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1016/j.jsc.2012.05.013
U2 - 10.1016/j.jsc.2012.05.013
DO - 10.1016/j.jsc.2012.05.013
M3 - Article
AN - SCOPUS:84873570182
SN - 0747-7171
VL - 52
SP - 72
EP - 96
JO - Journal of Symbolic Computation
JF - Journal of Symbolic Computation
ER -