Simple CAD construction and its applications (Q5938543)

The method of quantifier elimination by cylindrical algebraic decomposition (CAD) takes a formula from the theory of real closed fields as input, and constructs a CAD of the space of unquantified variables. CAD \(B\) is ``simpler'' than CAD \(A\), if each cell in \(B\) is the union of some cells of \(A\). The author presents two algorithms for simplifying the so called truth-invariant CAD algorithm introduced by \textit{G. E. Collins} and \textit{H. Hong} [ibid. 12, No. 3, 299-328 (1991; Zbl 0754.68063)]. Examples are presented which show the performance of this new very fast method.