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solveSystem(List) -- solve a square system of polynomial equations

Synopsis

Description

Solve a system of polynomial equations using homotopy continuation methods.
i1 : R = CC[x,y];
i2 : F = {x^2+y^2-1, x*y};
i3 : solveSystem F / first                                

o3 = {{1.80186e-15-5.62014e-16*ii, -1}, {-1, -1.23685e-15-2.83811e-16*ii},
     ------------------------------------------------------------------------
     {1, 1.23685e-15+2.83811e-16*ii}, {-1.73681e-15+5.53341e-16*ii, 1}}

o3 : List

Caveat

The system is assumed to be square (#equations = #variables) and have finitely many solutions.