### Numerically validating the completeness of the real solution set of a system of polynomial equations

**2016-02-01**

1602.00700 | math.NA

Computing the real solutions to a system of polynomial equations is a
challenging problem, particularly verifying that all solutions have been
computed. We describe an approach that combines numerical algebraic geometry
and sums of squares programming to test whether a given set is "complete" with
respect to the real solution set. Specifically, we test whether the Zariski
closure of that given set is indeed equal to the solution set of the real
radical of the ideal generated by the given polynomials. Examples with finitely
and infinitely many real solutions are provided, along with an example having
polynomial inequalities.

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