An Improvement of the Projection Operator in Cylindrical Algebraic Decomposition
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.
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