Characterization and description of basic semialgebraic sets

2003 ◽  
pp. 1-12
Author(s):  
C. Andradas
Keyword(s):  
Semialgebraic Sets

ON THE IRREDUCIBLE COMPONENTS OF A SEMIALGEBRAIC SET

2012 ◽  
Vol 23 (04) ◽  
pp. 1250031 ◽  
Author(s):  
JOSÉ F. FERNANDO ◽  
J. M. GAMBOA
Keyword(s):  
Integral Domain ◽  
Hilbert Problem ◽  
Semialgebraic Sets ◽  
Semialgebraic Set ◽  
Irreducible Components ◽  
Real Geometry ◽  
Nash Manifold ◽  
Substitution Theorem ◽  
Satisfactory Theory ◽  
17Th Hilbert Problem

In this work we define a semialgebraic set S ⊂ ℝn to be irreducible if the noetherian ring [Formula: see text] of Nash functions on S is an integral domain. Keeping this notion we develop a satisfactory theory of irreducible components of semialgebraic sets, and we use it fruitfully to approach four classical problems in Real Geometry for the ring [Formula: see text]: Substitution Theorem, Positivstellensätze, 17th Hilbert Problem and real Nullstellensatz, whose solution was known just in case S = M is an affine Nash manifold. In fact, we give full characterizations of the families of semialgebraic sets for which these classical results are true.

A measure for semialgebraic sets related to Boolean complexity

1989 ◽  
Vol 283 (2) ◽  
pp. 203-209 ◽  
Author(s):  
Gilbert Stengle
Keyword(s):  
Semialgebraic Sets

When is a Distribution of Signs Locally Completable?

1994 ◽  
Vol 46 (3) ◽  
pp. 449-473 ◽  
Author(s):  
F. Acquistapace ◽  
F. Broglia ◽  
E. Fortuna
Keyword(s):  
Algebraic Curve ◽  
Algebraic Surface ◽  
Regular Function ◽  
Connected Components ◽  
Semialgebraic Sets ◽  
Sign Distribution

AbstractLet V be an irreducible nonsingular algebraic surface, Y ⊂ V be an algebraic curve and P a point of Y. Suppose a sign distribution is given locally in a neighbourhood of P on some connected components of V — Y. We give an algorithmic criterion to decide whether this sign distribution is induced by a regular function or not. As an application, this criterion enables one to decide whether two semialgebraic sets can be locally separated or not.

On the Structure of Semialgebraic Sets Over p-Adic Fields

1988 ◽  
Vol 53 (4) ◽  
pp. 1138 ◽  
Author(s):  
Philip Scowcroft ◽  
Lou van den Dries
Keyword(s):  
Semialgebraic Sets

scholarly journals How fast do polynomials grow on semialgebraic sets?

2014 ◽  
Vol 413 ◽  
pp. 320-344 ◽  
Author(s):  
Pinaki Mondal ◽  
Tim Netzer
Keyword(s):  
Semialgebraic Sets
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