Speeding Up Cylindrical Algebraic Decomposition by Gröbner Bases

  • David J. Wilson
  • Russell J. Bradford
  • James H. Davenport
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7362)


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.


Time Cell Triangular Decomposition Decrease Factor Regular Chain Real Close Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • David J. Wilson
    • 1
  • Russell J. Bradford
    • 1
  • James H. Davenport
    • 1
  1. 1.Department of Computer ScienceUniversity of BathBathU.K.

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