Results 21 to 30 of about 341,235 (326)
Weak normalization and seminormalization in real algebraic geometry
, 2021 We define the weak-normalization and the seminormalization of a real algebraic variety relative to its central locus. The study is related to the properties of the rings of continuous rational functions and hereditarily rational functions on real ...
Goulwen Fichou +2 more
openalex +3 more sources
Computing the Dimension of Real Algebraic Sets [PDF]
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
semanticscholar +1 more source
Some open questions in real algebraic geometry
Proyecciones (Antofagasta), 2022 Many interesting problems arise on the borderline between real algebraic geometry and topology. We focus on 12 open questions. Some of them come from regulous geometry, which emerged as a subfield of real algebraic geometry less than 15 years ago.
W. Kucharz
semanticscholar +1 more source
Functional norms, condition numbers and numerical algorithms in algebraic geometry [PDF]
Forum of Mathematics, Sigma, 2021 In numerical linear algebra, a well-established practice is to choose a norm that exploits the structure of the problem at hand to optimise accuracy or computational complexity.
F. Cucker +2 more
semanticscholar +1 more source
Central algebraic geometry and seminormality [PDF]
Rendiconti del Seminario Matematico della Universita di Padova, 2021 We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.
J. Monnier
semanticscholar +1 more source
Mathematics, 2021 Recently developed GeoGebra tools for the automated deduction and discovery of geometric statements combine in a unique way computational (real and complex) algebraic geometry algorithms and graphic features for the introduction and visualization of ...
Tomás Recio +3 more
doaj +1 more source
Non-commutative Real Algebraic Geometry - Some Basic Concepts and First Ideas [PDF]
, 2007 We propose and discuss how basic notions (quadratic modules, positive elements, semialgebraic sets, Archimedean orderings) and results (Positivstellensatze) from real algebraic geometry can be generalized to noncommutative *-algebras.
Konrad Schmuedgen
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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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Point-free Construction of Real Exponentiation [PDF]
Logical Methods in Computer Science, 2022 We define a point-free construction of real exponentiation and logarithms, i.e.\ we construct the maps $\exp\colon (0, \infty)\times \mathbb{R} \rightarrow \!(0,\infty),\, (x, \zeta) \mapsto x^\zeta$ and $\log\colon (1,\infty)\times (0, \infty ...
Ming Ng, Steven Vickers
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Open string theory and planar algebras [PDF]
, 2009 In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions ...
Alling N L +12 more
core +9 more sources