Cylindrical algebraic decomposition by quantifier elimination

Abstract

Cylindrical algebraic decompositions were introduced as a major component of a new quantifier elimination algorithm for elementary algebra and geometry (G. Collins, 1973). In the present paper we turn the tables and show that one can use quantifier elimination for elementary algebra and geometry to obtain a new version of the cylindrical algebraic decomposition algorithm. A key part of our result is a theorem, of interest in its own right. that relates the multiplicities of the roots of a polynomial to their continuity.