# semialgebraic

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semialgebraic
Describing any algebraic system in which only real roots are investigated.

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• Semialgebraic set — In mathematics, a semialgebraic set is a subset S of real n dimensional space defined by a finite sequence of polynomial equations and inequalities; or any finite union of such sets. Such sets are studied as an extension of real algebraic… …   Wikipedia

• Semialgebraic space — In mathematics, especially in real algebraic geometry, a semialgebraic space is a space which is locally isomorphic to a semialgebraic set.DefinitionLet U be an open subset of R n for some n . A semialgebraic function on U is defined to be a… …   Wikipedia

• Mnev's universality theorem — In algebraic geometry, Mnev s universality theorem is a result which can be used to represent algebraic (or semi algebraic) varieties as realizations of oriented matroids, a notion of combinatorics. Contents 1 Oriented matroids 2 Stable… …   Wikipedia

• Nash functions — In real algebraic geometry, a Nash function on an open semialgebraic subset U ⊂ Rn is an analytic function f: U → R satisfying a non trivial polynomial equation P(x,f(x)) = 0 for all x in U (A semialgebraic subset of Rn is a subset obtained from… …   Wikipedia

• Tarski–Seidenberg theorem — In mathematics, the Tarski–Seidenberg theorem states that a set in n +1 dimensional space defined by polynomial identities and inequalities can be projected down onto n dimensional space, and the resulting set is still definable in terms of… …   Wikipedia

• Sheaf (mathematics) — This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… …   Wikipedia

• Stengle's Positivstellensatz — In mathematics, Stengle s Positivstellensatz characterizes polynomials which are positive on a given semialgebraic set over the real numbers, or more generally, any real closed field. It can be thought of as an ordered analogue of Hilbert s… …   Wikipedia

• List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

• O-minimal theory — In mathematical logic, and more specifically in model theory, a totally ordered structure ( M , lt;,...) is o minimal if and only if every definable set X sub; M (with parameters) can be realized as a finite union of intervals and points.A theory …   Wikipedia

• o-minimal theory — In mathematical logic, and more specifically in model theory, an infinite structure (M,<,...) which is totally ordered by < is called an o minimal structure if and only if every definable subset X ⊂ M (with parameters taken from… …   Wikipedia