Results 1 to 10 of about 849,973 (204)
Computing the Dimension of Real Algebraic Sets [PDF]
Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation, 2021 Let V be the set of real common solutions to F = (f1, …, fs) in ℜ[x1, …;, xn] and D be the maximum total degree of the fi's. We design an algorithm which on input F computes the dimension of V. Letting L be the evaluation complexity of F and s=1, it runs
Pierre Lairez, M. S. E. Din
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Noncomputable functions in the Blum-Shub-Smale model [PDF]
Logical Methods in Computer Science, 2011 Working in the Blum-Shub-Smale model of computation on the real numbers, we answer several questions of Meer and Ziegler. First, we show that, for each natural number d, an oracle for the set of algebraic real numbers of degree at most d is insufficient ...
Wesley Calvert +2 more
doaj +3 more sources
Topology of injective endomorphisms of real algebraic sets [PDF]
Mathematische Annalen, 2002 Using only basic topological properties of real algebraic sets and regular morphisms we show that any injective regular self-mapping of a real algebraic set is surjective.
A. Parusiński
semanticscholar +6 more sources
An Upper Bound for the Size of $s$-Distance Sets in Real Algebraic Sets [PDF]
The Electronic Journal of Combinatorics, 2020 In a recent paper, Petrov and Pohoata developed a new algebraic method which combines the Croot-Lev-Pach Lemma from additive combinatorics and Sylvester’s Law of Inertia for real quadratic forms.
Gábor Hegedüs, Lajos R'onyai
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Homology classes of real algebraic sets [PDF]
Annales de l'Institut Fourier, 2008 There is a large research program focused on comparison between algebraic and topological categories, whose origins go back to 1952 and the celebrated work of J. Nash on real algebraic manifolds. The present paper is a contribution to this program. It investigates the homology and cohomology classes represented by real algebraic sets.
W. Kucharz
semanticscholar +4 more sources
On the partial algebraicity of holomorphic mappings between two real algebraic sets [PDF]
Bulletin de la Société mathématique de France, 2001 In this paper, we consider local holomorphic mappings f: M\to M' between real algebraic CR generic manifolds (or more generally, real algebraic sets with singularities) in the complex euclidean spaces of different dimensions and we search necessary and sufficient conditions for f to be algebraic.
J. Merker
semanticscholar +4 more sources
Moment functions on real algebraic sets
Arkiv för Matematik, 1992 Let \(X\) be a real algebraic subvariety of \(\mathbb{R}^ n\). The main problem treated in the paper under review is whether the power moment problem with support on \(X\) and virtual measure \(\mu\) has a solution in terms of the positivity of the associated representing functional: \(\varphi(p)= \int_ x p(x) d\mu(x)\), \(p\in \mathbb{R}[X_ 1,\dots ...
J. Stochel
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Algebraicity of holomorphic mappings between real algebraic sets inCn
Acta Mathematica, 1996 0. Introduction 1. Holomorphic nondegenera~y of real-analytic manifolds 1.1. Preliminaries on real submanifolds of C N 1.2. Holomorphic nondegeneracy and its propagation 1.3. The Levi number and essential finiteness 1.4. Holomorphic nondegeneracy of real algebraic sets 2. The Segre sets of a real~analytic CR submanifold 2.1.
M. S. Baouendi +2 more
semanticscholar +3 more sources
Logarithmic limit sets of real semi-algebraic sets [PDF]
advg, 2007 This paper is about the logarithmic limit sets of real semi-algebraic sets, and, more generally, about the logarithmic limit sets of sets definable in an o-minimal, polynomially bounded structure.
D. Alessandrini
semanticscholar +4 more sources
Numerically Computing Real Points on Algebraic Sets [PDF]
Acta Applicandae Mathematicae, 2011 Given a polynomial system f, a fundamental question is to determine if f has real roots. Many algorithms involving the use of infinitesimal deformations have been proposed to answer this question.
J. Hauenstein
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