Computing cylindrical algebraic decomposition via triangular decomposition

Cylindrical algebraic decomposition is one of the most important tools for computing with semi-algebraic sets, while triangular decomposition is among the most important approaches for manipulating constructible sets. In this paper, for an arbitrary finite set F ⊂ R[y1, . . . , yn] we apply comprehensive triangular decomposition in order to obtain an F-invariant cylindrical decomposition of the n-dimensional complex space, from which we extract an F-invariant cylindrical algebraic decomposition of the n-dimensional real space. We report on an implementation of this new approach for constructing cylindrical algebraic decompositions. Categories and Subject Descriptors G.4 [Mathematics of Computing]: Mathematical Software—Algorithm design and analysis General Terms Algorithms, Theory Keywords CAD, regular chain, triangular decomposition

• Type: Conference
• Year: 2009
• Where: ISSAC
• Authors: Changbo Chen, Marc Moreno Maza, Bican Xia, Lu Yang
• Keywords: Cylindrical Algebraic Decompositions, F-invariant Cylindrical Decomposition, ISSAC 2009, Mathematics, Triangular Decomposition