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NumericalAlgebraicGeometry :: solveSystem(List)

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

Synopsis

Description

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];
i2 : F = {x^2+y^2-1, x*y};
i3 : solveSystem F 

o3 = {{1, 2.95823e-31+9.86076e-31*ii}, {-1, -2.95823e-31-9.86076e-31*ii},
     ------------------------------------------------------------------------
     {-1.18329e-30-4.93038e-31*ii, 1}, {1.18329e-30+4.93038e-31*ii, -1}}

o3 : List

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.