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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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SDP representation of ideal polynomials for positivstellensatz refutations

If we want to certify the nonexistence of real solutions to a polynomial system of equations, i.e. $$ S = \{ x\in \mathbb{R}^n \ | \ h_i (x) = 0, \ i=1,\dots,t \} = \emptyset, $$ we can produce a Po …
Andrea Olivo's user avatar
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SDP representation of ideal polynomials for positivstellensatz refutations

As I guessed, I was missing a fairly trivial piece (and most of my question is not even relevant to the answer). Free decision variables $a_i$ can be represented in SDPs by the difference of two posi …
Andrea Olivo's user avatar