mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of...

them (in particular real polynomial mappings). Semialgebraic geometry is the study of semialgebraic sets, i.e. real-number solutions to algebraic inequalities...

of a semialgebraic set is a semialgebraic set, and that there is an algorithm that, given a quantifier-free formula defining a semialgebraic set, produces...

widely used in computational algebraic geometry. A semialgebraic set in Rn is a finite union of sets defined by a finite number of polynomial equations...

geometry, a semialgebraic space is a space which is locally isomorphic to a semialgebraic set. Let U be an open subset of Rn for some n. A semialgebraic function...

real dimension of a set of real points, typically a semialgebraic set, is the dimension of its Zariski closure. For a semialgebraic set S, the real dimension...

"positive-locus-theorem") characterizes polynomials that are positive on a semialgebraic set, which is defined by systems of inequalities of polynomials with real...

closed convex semialgebraic set in the plane can be written as a feasible region of a SOCP, it is known that there exist convex semialgebraic sets that are...

stable equivalence of semialgebraic sets is defined as follows. Let U {\displaystyle U} and V {\displaystyle V} be semialgebraic sets, obtained as a disconnected...

solution sets are called algebraic sets if there are no inequalities. Over the reals, and with inequalities, there are called semialgebraic sets. More generally...