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Communicated by J E Cremona.
Research of Hauenstein supported in part by NSF Grant ACI-1460032, Sloan Research Fellowship BR2014-110 TR14, and Army Young Investigator Program (YIP) W911NF-15-1-0219.
Research of Rodriguez supported in part by NSF Grant DMS-1402545.
Research of Sottile supported in part by NSF Grant DMS-1501370.
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.
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- Numerical Computation of Galois Groups
Jonathan D. Hauenstein
Jose Israel Rodriguez
- Publication date
- Springer US
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