Results 261 to 270 of about 850,072 (303)

Injective endomorphisms of real algebraic sets are surjective

Mathematische Annalen, 1999
It is proved that injective algebraic mappings from a real algebraic set \(X\) to itself are surjective. In the complex case (more generally over algebraically over algebraically closed field of characteristic 0) and for regular mappings this result was proved by \textit{J. Ax} [Ann. Math., II. Ser. 88, 239-271 (1968; Zbl 0195.05701)]. In the real case
K. Kurdyka
semanticscholar   +3 more sources

Topology of Real Algebraic Sets

, 1991
S. Akbulut, H. King
semanticscholar   +2 more sources

REAL ALGEBRAIC AND SEMI‐ALGEBRAIC SETS (Actualités Mathématiques 348)

Bulletin of the London Mathematical Society, 1991
C. Gibson
semanticscholar   +2 more sources

Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results

Journal of symbolic computation, 2022
Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical.
Rémi Prébet, M. S. E. Din, É. Schost
semanticscholar   +1 more source

Constructing strange real algebraic sets

, 1992
S. Akbulut, H. King
semanticscholar   +2 more sources

Formal verification of semi-algebraic sets and real analytic functions

Certified Programs and Proofs, 2021
Semi-algebraic sets and real analytic functions are fundamental concepts in Real Algebraic Geometry and Real Analysis, respectively. These concepts appear in the study of Differential Equations, where the real analytic solution to a differential equation
J. Slagel, Lauren M. White, Aaron Dutle
semanticscholar   +1 more source

THE TOPOLOGY OF REAL ALGEBRAIC SETS

1983
This paper is a survey of the author's work on the question: ''Which topological spaces are homeomorphic to real algebraic sets?''. In the non-singular case it is known [due to \textit{J. Nash}, Ann. Math. (2) 56, 405--421 (1952; Zbl 0048.38501) and \textit{A. Tognoli}, Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser.
Akbulut, Selman, King, Henry
openaire   +2 more sources

Effective Whitney stratification of real algebraic varieties

Mathematics of Computation, 2023
We describe new algorithms to compute Whitney stratifications of real algebraic varieties. Using either conormal or polar techniques, these algorithms stratify a complexification of a given real variety. We then show that the resulting stratification can
M. Helmer, Anton Leykin, Vidit Nanda
semanticscholar   +1 more source

Polynomial-time computing over quadratic maps i: sampling in real algebraic sets

Computational Complexity, 2004
.Given a quadratic map $$Q:\mathbb{K}^n \to \mathbb{K}^k $$ defined over a computable subring D of a real closed field $$\mathbb{K},$$ and p ∈D[Y1,...,Yk] of degree d, we consider the zero set $$Z = Z(p(Q(X)), \mathbb{K}^n) \subseteq \mathbb{K}^n$$ of p ...
D. Grigoriev, D. Pasechnik
semanticscholar   +1 more source

A Hybrid Procedure for Finding Real Points on a Real Algebraic Set

Journal of Systems Science and Complexity, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Yu, Xia, Bican
openaire   +2 more sources