Results 1 to 10 of about 4,854 (294)
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
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Hartogs-type theorems in real algebraic geometry, I [PDF]
Mathematische Annalen, 2022 AbstractLet $$f:X\rightarrow \mathbb {R}$$ f : X → R be a function defined on a connected nonsingular real algebraic set X in $$\mathbb {R}^n$$
Marcin Bilski +2 more
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Algebraic Cycles and Approximation Theorems in Real Algebraic Geometry [PDF]
Transactions of the American Mathematical Society, 1993 Let \(M\) be a compact orientable smooth manifold of dimension \(\geq 5\). This paper shows which subgroups \(G \subset H_ 2 (M, {\mathbf Z}/2)\) can possibly be the subgroup of two dimensional algebraic cycles in an algebraic model of \(M\). It shows that the possible \(G\)'s are exactly those containing the Poincaré dual of the second Stieffel ...
J. Bochnak, Wojciech Kucharz
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Algebraically special, real alpha-geometries [PDF]
Journal of Geometry and Physics, 2011 We exploit the spinor description of four-dimensional Walker geometry, and conformal rescalings of such, to describe the local geometry of four-dimensional neutral geometries with algebraically degenerate self-dual Weyl curvature and an integrable distribution of alpha-planes (algebraically special real alpha-geometry).
Peter R. Law, Yasuo Matsushita
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Integral closures in real algebraic geometry
Journal of Algebraic Geometry, 2020 We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety: the regular functions and the continuous rational functions.
Goulwen Fichou +2 more
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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
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, 2011 Cet ouvrage constitue les actes de la conférence de Géométrie Algébrique Réelle qui a eu lieu à Rennes du 20 au 24 Juin ...
Saugata Basu +4 more
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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. We recall how the variable ordering used can have a profound effect on both performance and output and summarise what may be done to assist with this choice.
Matthew England
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Real Numerical Algebraic Geometry
Notices of the American Mathematical SocietyJonathan D. Hauenstein +4 more
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Satisfiability of cross product terms is complete for real nondeterministic polytime Blum-Shub-Smale machines [PDF]
Electronic Proceedings in Theoretical Computer Science, 2013 Nondeterministic polynomial-time Blum-Shub-Smale Machines over the reals give rise to a discrete complexity class between NP and PSPACE. Several problems, mostly from real algebraic geometry / polynomial systems, have been shown complete (under many-one ...
Christian Herrmann +2 more
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