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 <i>F</i> ⊂ [<i>y<sub>1</sub></i>,...,<i>y<sub>n</sub></i>] we apply comprehensive triangular decomposition in order to obtain an <i>F</i>-invariant cylindrical decomposition of the <i>n</i>-dimensional complex space, from which we extract an <i>F</i>-invariant cylindrical algebraic decomposition of the <i>n</i>-dimensional real space. We report on an implementation of this new approach for constructing cylindrical algebraic decompositions.

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