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Cylindrical algebraic decomposition is one of the most important tools forcomputing with semi-algebraic sets, while triangular decomposition is among themost important approaches for manipulating constructible sets. In this paper,for an arbitrary finite set $F \subset {\R}[y_1, ..., y_n]$ we applycomprehensive triangular decomposition in order to obtain an $F$-invariantcylindrical decomposition of the $n$-dimensional complex space, from which weextract an $F$-invariant cylindrical algebraic decomposition of the$n$-dimensional real space. We report on an implementation of this new approachfor constructing cylindrical algebraic decompositions.

Computing Cylindrical Algebraic Decomposition via Triangular Decomposition