Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10693)


Given a polynomial system f, this article provides a general construction for homotopies that yield at least one point of each connected component on the set of solutions of \(f = 0\). This algorithmic approach is then used to compute a superset of the isolated points in the image of an algebraic set which arises in many applications, such as computing critical sets used in the decomposition of real algebraic sets. An example is presented which demonstrates the efficiency of this approach.


Numerical algebraic geometry Homotopy continuation Projections 

AMS Subject Classification

65H10 68W30 14P05 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsColorado State UniversityFort CollinsUSA
  2. 2.Department of MathematicsUniversity of Wisconsin - Eau ClaireEau ClaireUSA
  3. 3.Department of Applied and Computational Mathematics and StatisticsUniversity of Notre DameNotre DameUSA

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