Solve a system of polynomial equations using homotopy continuation methods. (See
track for more optional arguments.)
The system is assumed to be square (number of equations = number of variables) and to have finitely many solutions.
i1 : R = CC[x,y];
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i2 : F = {x^2+y^2-1, x*y};
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i3 : solveSystem F
o3 = {{1, -7.70372e-34-3.08149e-33*ii}, {-1, 7.70372e-34+3.08149e-33*ii},
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{5.91646e-31-8.87469e-31*ii, 1}, {-4.93038e-31+8.38165e-31*ii, -1}}
o3 : List
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The output (produced by
track with default options) contains all
points obtained at the end of homotopy paths when tracking starting at the
totalDegreeStartSystem. In particular, this means that solving a system that has fewer than Bezout bound many solutions will produce points that are not marked as regular. See
track for detailed examples.