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arXiv · 0903.5221

Computing Cylindrical Algebraic Decomposition via Triangular Decomposition

Changbo Chen·Marc Moreno Maza·Bican Xia·Lu Yang
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Abstract

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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Changbo Chen, Marc Moreno Maza, Bican Xia, Lu Yang. 2009-03-30. Computing Cylindrical Algebraic Decomposition via Triangular Decomposition. https://arxiv.org/abs/0903.5221

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