Computing Cylindrical Algebraic Decomposition via Triangular Decomposition

Details Computing Cylindrical Algebraic Decomposition via Triangular Decomposition Computing Cylindrical Algebraic Decomposition via Triangular Decomposition

2009-03-30

arxiv.org/abs/0903.5221v1

Computer Science

Symbolic Computation

10 pages

Scientific paper

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 $F \subset {\R}[y_1, ..., y_n]$ 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.

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