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Semialgebraic geometry is the study of inequalities expressible in algebraic functions in one or several variables, usually over the real numbers or some field with similar properties.

Semialgebraic geometry is the study of semialgebraic sets, i.e. sets cut out by finitely many inequalities expressible in algebraic functions in one or several variables, usually over the real numbers or some field with similar properties. Semialgebraic sets are invariant under linear projection and under complements and finite unions and intersections.

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