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, -3.9443e-31+2.71171e-31*ii}, {-1, 3.9443e-31-2.58845e-31*ii},
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{-2.66241e-30-2.36658e-30*ii, 1}, {2.66241e-30+2.36658e-30*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.