Solving Polynomial Systems Globally Invariant Under an
Action of the Symmetric Group and Application to the
Equilibria of N vortices in the Plane

Jean-Charles Faugère, Jules Svartz

Input systems:

• N=5 main component, other component
• N=6 main component, other component
• N=7 main component, other component
• N=8 main component, other component

Solutions:

• Equations and Numerical Solutions of the system for N=4,5,6 and 7 (html) or (pdf)

• Symbolic solutions (one Groebner Basis for each component) N=6
• Symbolic solutions (one Groebner Basis for each component) N=7
  • Univariate polynomial of degree 521 (component 1)
  • Factorization of the univariate polynomial of degree 521 (component 1)