Subset of n-space defined by a finite sequence of polynomial equations and inequalities
In mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of basic semialgebraic sets. A semialgebraic function is a function with a semialgebraic graph. Such sets and functions are mainly studied in real algebraic geometry which is the appropriate framework for algebraic geometry over the real numbers.
mathematics, a basic semialgebraicset is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraicset is a finite union of...
them (in particular real polynomial mappings). Semialgebraic geometry is the study of semialgebraicsets, i.e. real-number solutions to algebraic inequalities...
of a semialgebraicset is a semialgebraicset, and that there is an algorithm that, given a quantifier-free formula defining a semialgebraicset, produces...
real dimension of a set of real points, typically a semialgebraicset, is the dimension of its Zariski closure. For a semialgebraicset S, the real dimension...
geometry, a semialgebraic space is a space which is locally isomorphic to a semialgebraicset. Let U be an open subset of Rn for some n. A semialgebraic function...
solution sets are called algebraic sets if there are no inequalities. Over the reals, and with inequalities, there are called semialgebraicsets. More generally...
and hence is not subanalytic. Semialgebraicset Edward Bierstone and Pierre D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ...
mathematics, a piecewise algebraic space is a generalization of a semialgebraicset, introduced by Maxim Kontsevich and Yan Soibelman. The motivation...
graphs. Nikolai E. Mnev for Mnev's universality theorem, that every semialgebraicset is equivalent to the space of realizations of an oriented matroid...
geometry. Given a set S of polynomials in Rn, a cylindrical algebraic decomposition is a decomposition of Rn into connected semialgebraicsets called cells...
false. Equivalently, it is the problem of testing whether a given semialgebraicset is non-empty. This decision problem is NP-hard and lies in PSPACE...
Polynomials positive on semialgebraicsets. The most general result is Stengle's Positivstellensatz. For compact semialgebraicsets we have Schmüdgen's positivstellensatz...
varieties and of the definable relations on real-closed fields as semialgebraicsets In the 1960s, the introduction of the ultraproduct construction led...
can be given Whitney stratifications, such as semialgebraicsets (due to René Thom) and subanalytic sets (due to Heisuke Hironaka). This has led to their...
Didier; Lagoa, Constantino M. (2017). "Simple approximations of semialgebraicsets and their applications to control". Automatica. 78: 110–118. arXiv:1509...
in this area is the use of the number of connected components of a semialgebraicset to provide a lower bound on the time complexity of an associated computational...
calculus Semialgebraic geometry a part of algebraic geometry; more specifically a branch of real algebraic geometry that studies semialgebraicsets. Set-theoretic...
spaces, including algebraic varieties, analytic varieties, semialgebraicsets, and subanalytic sets. CW-complexes A CW complex is a topological space formed...
2001 (with Claus Scheiderer) "The moment problem for non-compact semialgebraicsets.", Adv. Geom, vol.1, 71-88 2001 (with Bruce Reznick) "A new bound...
l_{p}}^{d}(G,\delta _{G})} is the projection of the Cayley-Menger semialgebraicset, with fixed ( G , δ ) {\displaystyle (G,\delta )} or ( G , [ δ G l...
spectrahedral shadows. Every spectrahedral shadow is a convex set that is also semialgebraic, but the converse (conjectured to be true until 2017) is false...
surfaces it lies (with polynomial surfaces, the cells are also known as semialgebraicsets). 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. Some authors consider an o-minimal structure to be a candidate...