Algorithms of intrinsic complexity for point searching in compact real singular hypersurfaces
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Publication:431820
DOI10.1007/s10208-011-9112-6zbMath1246.14071OpenAlexW2016419624MaRDI QIDQ431820
Luis Miguel Pardo, Marc Giusti, Lutz Lehmann, Joos Heintz, Bernd Bank
Publication date: 3 July 2012
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10208-011-9112-6
singularitiesdegree of varietiesintrinsic complexitypolar and bipolar varietiesreal polynomial solving
Symbolic computation and algebraic computation (68W30) Singularities in algebraic geometry (14B05) Real algebraic sets (14P05) Deformations of singularities (14B07)
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Uses Software
Cites Work
- Thom's lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets
- Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers
- Properness defects and projections and computation of at least one point in each connected component of a real algebraic set
- Definability and fast quantifier elimination in algebraically closed fields
- Lectures on results on Bezout's theorem. Notes by D. P. Patil
- On the intrinsic complexity of point finding in real singular hypersurfaces
- Evaluation techniques for zero-dimensional primary decomposition
- Solving systems of polynomial inequalities in subexponential time
- Variétés polaires locales et classes de Chern des variétés singulieres
- Effective Łojasiewicz inequalities in semialgebraic geometry
- On the computational complexity and geometry of the first-order theory of the reals. I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals
- Lower bounds for diophantine approximations
- Polar varieties, real equation solving, and data structures: the hypersurface case
- Straight-line programs in geometric elimination theory
- The hardness of polynomial equation solving
- Computing parametric geometric resolutions
- Quadratic Newton iteration for systems with multiplicity
- Real solving for positive dimensional systems.
- Deformation techniques for efficient polynomial equation solving.
- On the geometry of polar varieties
- Generalized polar varieties: geometry and algorithms
- A concise proof of the Kronecker polynomial system solver from scratch
- Polar classes of singular varieties
- On the combinatorial and algebraic complexity of quantifier elimination
- Le rôle des structures de données dans les problèmes d'élimination
- Polars of real singular curves
- The Geometrical Invariants of Algebraic Loci
- The Arithmetical Invariants of Algebraic Loci
- La serie canonica e la teoria delle serie principali di gruppi di punti sopra una superficie algebrica
- Algorithms in real algebraic geometry
- On the time-space complexity of geometric elimination procedures
- A Gröbner free alternative for polynomial system solving
- Polar varieties and efficient real elimination
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