Arnold Mathematical Journal

, Volume 4, Issue 1, pp 113–125 | Cite as

Trace Test

  • Anton Leykin
  • Jose Israel Rodriguez
  • Frank Sottile
Research Contribution


The trace test in numerical algebraic geometry verifies the completeness of a witness set of an irreducible variety in affine or projective space. We give a brief derivation of the trace test and then consider it for subvarieties of products of projective spaces using multihomogeneous witness sets. We show how a dimension reduction leads to a practical trace test in this case involving a curve in a low-dimensional affine space.


Trace test Witness set Numerical algebraic geometry 

Mathematics Subject Classification



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Copyright information

© Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2018

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.George Herbert Jones LaboratoryThe University of ChicagoChicagoUSA
  3. 3.Department of MathematicsTexas A&M UniversityTXUSA

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