An Improvement of the Projection Operator in Cylindrical Algebraic Decomposition

Abstract

The cylindrical algebraic decomposition (CAD) of Collins (1975) provides a potentially powerful method for solving many important mathematical problems, provided that the required amount of computation can be sufficiently reduced. An important component of the CAD method is the projection operation. Given a set A of r-variate polynomials, the projection operation produces a certain set P of (r − l)-variate polynomials such that a CAD of r-dimensional space for A can be constructed from a CAD of (r − 1)-dimensional space for P. The CAD algorithm begins by applying the projection operation repeatedly, beginning with the input polynomials, until univariate polynomials are obtained. This process is called the projection phase.

Reprinted with permission from Proceedings of the International Symposium on Symbolic & Algebraic Computation, edited by S. Watanabe and M. Nagata, ACM Press, 1990, pp. 261–264. Copyright 1990, Association for Computing Machinery, Inc.