Geometric Involutive Bases and Applications to Approximate Commutative Algebra

Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)


This article serves to give an introduction to some classical results on involutive bases for polynomial systems. Further, we survey recent developments, including a modification of the above: geometric projected involutive bases, for the treatment of approximate systems, and their application to ideal membership testing and Gröbner basis computation.


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Copyright information

© Springer-Verlag Vienna 2009

Authors and Affiliations

  • Robin Scott
    • 1
  • Greg Reid
    • 2
  • Wenyuan Wu
    • 3
  • Lihong Zhi
    • 4
  1. 1.Department of Mathematics and StatisticsCarleton UniversityOttawaCanada
  2. 2.Department of Applied MathematicsUniversity of Western OntarioLondonCanada
  3. 3.Department of MathematicsMichigan State UniversityEast LansingUSA
  4. 4.Key Lab of Mathematics MechanizationAMSS, Chinese Academy of SciencesBeijingChina

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