Foundations of Computational Mathematics

, Volume 18, Issue 4, pp 867–890 | Cite as

Numerical Computation of Galois Groups

  • Jonathan D. Hauenstein
  • Jose Israel Rodriguez
  • Frank Sottile


The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. We give numerical methods to compute the Galois group and study it when it is not the full symmetric group. One algorithm computes generators, while the other studies its structure as a permutation group. We illustrate these algorithms with examples using a Macaulay2 package we are developing that relies upon Bertini to perform monodromy computations.


Galois group Monodromy Fiber product Homotopy continuation Numerical algebraic geometry Polynomial system 

Mathematics Subject Classification

65H10 65H20 14Q15 


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Copyright information

© SFoCM 2017

Authors and Affiliations

  • Jonathan D. Hauenstein
    • 1
  • Jose Israel Rodriguez
    • 2
  • Frank Sottile
    • 3
  1. 1.Department of Applied and Computational Mathematics and StatisticsUniversity of Notre DameNotre DameUSA
  2. 2.Department of StatisticsUniversity of ChicagoChicagoUSA
  3. 3.Department of MathematicsTexas A & M UniversityCollege StationUSA

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