Excess intersections and numerical irreducible decompositions



A fundamental problem in algebraic geometry is to decompose the solution set of a given polynomial system. A numerical description of this solution set is called a numerical irreducible decomposition and currently all standard algorithms use a sequence of homotopies forming a dimension-by-dimension approach. In this article, we pair a classical result to compute a smooth point on every irreducible component in every dimension using a single homotopy together with the theory of isosingular sets. Examples are presented to compare this approach with current algorithms for computing a numerical irreducible decomposition.


Attribute NameValues
  • Dan Bates

  • David Eklund

  • Jonathan Hauenstein

  • Chris Peterson

  • Jonathan Hauenstein

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  • All rights reserved

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