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...

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...

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...

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

and hence is not subanalytic. Semialgebraic set Edward Bierstone and Pierre D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ...

in place of polynomials.) In the case of RCF, the definable sets are the semialgebraic sets. Thus the study of o-minimal structures and theories generalises...

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

false. Equivalently, it is the problem of testing whether a given semialgebraic set is non-empty. This decision problem is NP-hard and lies in PSPACE...

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

geometry. Given a set S of polynomials in Rn, a cylindrical algebraic decomposition is a decomposition of Rn into connected semialgebraic sets called cells...

combinatorics and algebraic geometry used to represent algebraic (or semialgebraic) varieties as realization spaces of oriented matroids. Informally it...

Polynomials positive on semialgebraic sets. The most general result is Stengle's Positivstellensatz. For compact semialgebraic sets we have Schmüdgen's positivstellensatz...

can be given Whitney stratifications, such as semialgebraic sets (due to René Thom) and subanalytic sets (due to Heisuke Hironaka). This has led to their...

mathematics, a piecewise algebraic space is a generalization of a semialgebraic set, introduced by Maxim Kontsevich and Yan Soibelman. The motivation...

calculus Semialgebraic geometry a part of algebraic geometry; more specifically a branch of real algebraic geometry that studies semialgebraic sets. Set-theoretic...

2001 (with Claus Scheiderer) "The moment problem for non-compact semialgebraic sets.", Adv. Geom, vol.1, 71-88 2001 (with Bruce Reznick) "A new bound...

Didier; Lagoa, Constantino M. (2017). "Simple approximations of semialgebraic sets and their applications to control". Automatica. 78: 110–118. arXiv:1509...

graphs. Nikolai E. Mnev for Mnev's universality theorem, that every semialgebraic set is equivalent to the space of realizations of an oriented matroid...

spaces, including algebraic varieties, analytic varieties, semialgebraic sets, and subanalytic sets. CW-complexes A CW complex is a topological space formed...

in this area is the use of the number of connected components of a semialgebraic set to provide a lower bound on the time complexity of an associated computational...

varieties and of the definable relations on real-closed fields as semialgebraic sets In the 1960s, the introduction of the ultraproduct construction led...

spectrahedral shadows. Every spectrahedral shadow is a convex set that is also semialgebraic, but the converse (conjectured to be true until 2017) is false...

Arijit; Jartoux, Bruno; Mustafa, Nabil (2019). "Shallow Packings, Semialgebraic Set Systems, Macbeath Regions, and Polynomial Partitioning". Discrete...

l_{p}}^{d}(G,\delta _{G})} is the projection of the Cayley-Menger semialgebraic set, with fixed ( G , δ ) {\displaystyle (G,\delta )} or ( G , [ δ G l...

surfaces it lies (with polynomial surfaces, the cells are also known as semialgebraic sets). For each cell, we either find a market-clearing price-vector (i...

algebra is the part of algebra which is relevant to real algebraic (and semialgebraic) geometry. It is mostly concerned with the study of ordered fields and...

dévissage can be applied to stratified structures such as semialgebraic or semianalytic sets, and which excludes some pathological spaces that do not correspond...