Effective Łojasiewicz inequalities in semialgebraic geometry

DOI10.1007/BF01810850zbMath0754.14035OpenAlexW1999746037MaRDI QIDQ1177863

Pablo Solernó

Publication date: 26 June 1992

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01810850

zbMATH Keywords

basic open semi-algebraic setseffective version of Łojasiewicz inequalityeffective version of the finiteness theoremprenex formula

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Semialgebraic sets and related spaces (14P10) Effectivity, complexity and computational aspects of algebraic geometry (14Q20)

Related Items (15)

Łojasiewicz inequalities with explicit exponents for smallest singular value functions ⋮ Hamiltonian stability and subanalytic geometry ⋮ Metric properties of semialgebraic mappings ⋮ An effective version of Pólya's theorem on positive definite forms ⋮ On the complexity of Schmüdgen's Positivstellensatz ⋮ Topological triviality of deformations of regular mappings ⋮ Algorithms of intrinsic complexity for point searching in compact real singular hypersurfaces ⋮ Łojasiewicz inequality for a pair of semialgebraic functions ⋮ The reduced Bautin index of planar vector fields ⋮ Effective Lojasiewicz gradient inequality for Nash functions with application to finite determinacy of germs ⋮ Global Łojasiewicz-type inequality for non-degenerate polynomial maps ⋮ On the minimum of a positive polynomial over the standard simplex ⋮ Two-sided error proximity oblivious testing ⋮ Łojasiewicz-type inequalities with explicit exponents for the largest eigenvalue function of real symmetric polynomial matrices ⋮ A real Nullstellensatz and Positivstellensatz for the semipolynomials over an ordered field

Cites Work

• Complexity of deciding Tarski algebra
• Nullstellensatz effectif et Conjecture de Serre (Théorème de Quillen-Suslin) pour le Calcul Formel
• On the Worst-Case Arithmetic Complexity of Approximating Zeros of Systems of Polynomials
• A Global Lojasiewicz Inequality for Algebraic Varieties
• Sur la complexité du principe de Tarski-Seidenberg
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