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Jan 13, 2021 at 10:37 comment added Emil Jeřábek This computational problem is known as the existential theory of the reals. It sits somewhere between NP and PSPACE, but not much more is known; it’s important enough that it’s been given a complexity class of its own ($\exists\mathbb R$). (The official definition as in the Wikipedia article allows the arbitrary existential sentences, but this easily reduces to the case of satisfiability of a single polynomial equation by introduction of a few extension variables.)
Jan 13, 2021 at 10:30 history asked Arnold Neumaier CC BY-SA 4.0