Cylindrical Algebraic Decomposition without Augmented Projection

Cylindrical Algebraic Decomposition without Augmented Projection

Cylindrical algebraic decomposition is a fundamental tool in computational real algebraic geometry. It takes a set of multivariate polynomials and decomposes the real space into cylindrically arranged cells which can be described by boolean expressions of polynomial equations and inequalities. It begins by repeated projection (elimination of variables) and follows by repeated lifting. During the lifting, the descriptions of cells are constructed using Thom's lemma. This necessitates the so-called augmented projection (the derivatives are also considered). It often makes the projection time-consuming and in turn increases the number of cells. In this talk, we show how to avoid augmented projection by describing cells using Sturm-Habicht theorem (instead of Thom's lemma).