Results 1 to 10 of about 846,189 (343)
Noncommutative real algebraic geometry of Kazhdan's property (T) [PDF]
Journal of the Institute of Mathematics of Jussieu, 2015 It is well-known that a finitely generated group $\Gamma$ has Kazhdan's property (T) if and only if the Laplacian element $\Delta$ in ${\mathbb R}[\Gamma]$ has a spectral gap.
Ozawa, Narutaka
core +11 more sources
Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination [PDF]
Logical Methods in Computer Science, 2012 This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic properties.
Assia Mahboubi, Cyril Cohen
doaj +4 more sources
Enumerative real algebraic geometry [PDF]
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, 2003 Enumerative Geometry is concerned with the number of solutions to a structured system of polynomial equations, when the structure comes from geometry. Enumerative real algebraic geometry studies real solutions to such systems, particularly a priori information on their number. Recent results in this area have, often as not, uncovered new and unexpected
Frank Sottile
semanticscholar +8 more sources
Some Speed-Ups and Speed Limits for Real Algebraic Geometry [PDF]
Journal of Complexity, 2000 We give new positive and negative results (some conditional) on speeding up computational algebraic geometry over the reals: (1) A new and sharper upper bound on the number of connected components of a semialgebraic set.
Rojas, J. Maurice
core +8 more sources
Rational maps in real algebraic geometry [PDF]
advg, 2009 Abstract The paper deals with rational maps between real algebraic sets. We are interested in the rational maps which extend to continuous maps defined on the entire source space. In particular, we prove that every continuous map between unit spheres is homotopic to a rational map of such a type.
Wojciech Kucharz
semanticscholar +5 more sources
Formulating problems for real algebraic geometry [PDF]
, 2014 We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition.
England, Matthew
core +7 more sources
Extremal Real Algebraic Geometry and A-Discriminants [PDF]
Moscow Mathematical Journal, 2007 24 pages, 13 figures, final version with several improvements and small ...
Korben Rusek +3 more
+6 more sources
Algebraic cycles and approximation theorems in real algebraic geometry [PDF]
Transactions of the American Mathematical Society, 1993 Let Af be a compact C°° manifold. A theorem of Nash-Tognoli asserts that M has an algebraic model, that is, M is diffeomorphic to a nonsingular real algebraic set X. Let FV^AfX, Z/2) denote the subgroup of Hk(X, Z/2) of the cohomology classes determined by algebraic cycles of codi- mension k on X. Assuming that M is connected, orientable and dim M > 5 ,
Jacek Bochnak, Wojciech Kucharz
openaire +3 more sources
Geometrically rational real conic bundles and very transitive actions [PDF]
Compositio Math. 147 (2011) 161-187, 2009 In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups.
Biswas +8 more
core +8 more sources
Real enumerative geometry and effective algebraic equivalence [PDF]
Journal of Pure and Applied Algebra, 1996 We describe an approach to the question of finding real solutions to problems of enumerative geometry, in particular the question of whether a problem of enumerative geometry can have all of its solutions be real.
Sottile, Frank
core +5 more sources