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Semialgebraic Set


A semialgebraic set is a subset of R^n which is a finite Boolean combination of sets of the form {x^_=(x_1,...,x_n):f(x^_)>0} and {x^_:g(x^_)=0}, where f and g are polynomials in x_1, ..., x_n over the reals.

By Tarski's theorem, the solution set of a quantified system of real algebraic equations and inequalities is a semialgebraic set (Strzebonski 2000).


See also

Tarski's Theorem

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References

Bierstone, E. and Milman, P. "Semialgebraic and Subanalytic Sets." IHES Pub. Math. 67, 5-42, 1988.Marker, D. "Model Theory and Exponentiation." Not. Amer. Math. Soc. 43, 753-759, 1996.Strzebonski, A. "Solving Algebraic Inequalities." Mathematica J. 7, 525-541, 2000.

Referenced on Wolfram|Alpha

Semialgebraic Set

Cite this as:

Weisstein, Eric W. "Semialgebraic Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SemialgebraicSet.html

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