  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.
