|Title||Speeding up cylindrical algebraic decomposition by Gr\"obner bases.|
|Author(s)|| Russell J. Bradford, James H. Davenport, David J. Wilson|
|Type||Book, Chapter in Book, Conference Proceeding|
|Abstract||Gröbner Bases [Buc70] and Cylindrical Algebraic Decomposition [Col75,CMMXY09] are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a mixed system of equalities and inequalities, it is possible to apply Gröbner bases to the (conjoined) equalities before invoking CAD. We see that this is, quite often but not always, a beneficial preconditioning of the CAD problem.|
It is also possible to precondition the (conjoined) inequalities with respect to the equalities, and this can also be useful in many cases.