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Polar varieties and efficient real elimination

https://doi.org/10.1007/pl00004896
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1006/jcom.1993.1002openalex-snapshot
Complexity of Bezout′s Theorem
inferredcites →https://doi.org/10.1006/jcom.1996.0010openalex-snapshot
On the Complexity of Sparse Elimination
inferredcites →https://doi.org/10.1006/jcom.1997.0432openalex-snapshot
Polar Varieties, Real Equation Solving, and Data Structures: The Hypersurface Case
inferredcites →https://doi.org/10.1006/jsco.1995.1041openalex-snapshot
Efficient Incremental Algorithms for the Sparse Resultant and the Mixed Volume
inferredcites →https://doi.org/10.1006/jsco.1996.0039openalex-snapshot
Polynomial-Time Computation of the Dimension of Algebraic Varieties in Zero-Characteristic
inferredcites →https://doi.org/10.1006/jsco.1997.0161openalex-snapshot
Estimations for the Separation Number of a Polynomial System
inferredcites →https://doi.org/10.1007/3-540-51083-4_54openalex-snapshot
Some new effectivity bounds in computational geometry
inferredcites →https://doi.org/10.1007/3-540-60114-7_16openalex-snapshot
When polynomial equation systems can be “solved” fast?
inferredcites →https://doi.org/10.1007/3-540-60114-7_4openalex-snapshot
How lower and upper complexity bounds meet in elimination theory
inferredcites →https://doi.org/10.1007/978-1-4612-0701-6openalex-snapshot
Complexity and Real Computation
inferredcites →https://doi.org/10.1007/978-1-4612-2752-6_19openalex-snapshot
Complexity of Bezout’s Theorem II Volumes and Probabilities
inferredcites →https://doi.org/10.1007/978-1-4615-7904-5openalex-snapshot
Stable Mappings and Their Singularities
inferredcites →https://doi.org/10.1007/978-3-0348-9104-2_11openalex-snapshot
A computational method for diophantine approximation
inferredcites →https://doi.org/10.1007/978-3-642-59932-3_9openalex-snapshot
On the Real Nullstellensatz
inferredcites →https://doi.org/10.1007/978-3-658-16241-2_8openalex-snapshot
Die Frage der endlich vielen Schritte in der Theorie der Polynomideale (1925)
inferredcites →https://doi.org/10.1007/bf01206635openalex-snapshot
Die Frage der endlich vielen Schritte in der Theorie der Polynomideale
inferredcites →https://doi.org/10.1007/bf01457454openalex-snapshot
Factoring polynomials with rational coefficients
inferredcites →https://doi.org/10.1007/bf01817776openalex-snapshot
Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
inferredcites →https://doi.org/10.1007/bf02573959openalex-snapshot
Feasibility testing for systems of real quadratic equations
inferredcites →https://doi.org/10.1007/bfb0016236openalex-snapshot
Parallel arithmetic computations: A survey
inferredcites →https://doi.org/10.1007/s002000000046openalex-snapshot
On the Time-Space Complexity of Geometric Elimination Procedures
inferredcites →https://doi.org/10.1007/s002000050115openalex-snapshot
Probabilistic Algorithms for Geometric Elimination
inferredcites →https://doi.org/10.1016/0022-0000(86)90029-2openalex-snapshot
The complexity of elementary algebra and geometry
inferredcites →https://doi.org/10.1016/0304-3975(81)90064-5openalex-snapshot
Resolution des systemes d'equations algebriques
inferredcites →https://doi.org/10.1016/0304-3975(83)90110-xopenalex-snapshot
The complexity of partial derivatives
inferredcites →https://doi.org/10.1016/0304-3975(94)90122-8openalex-snapshot
Complexity of Bezout's theorem V: polynomial time
inferredcites →https://doi.org/10.1016/0890-5401(91)90078-gopenalex-snapshot
Boolean circuits versus arithmetic circuits
inferredcites →https://doi.org/10.1016/s0022-4049(96)00099-0openalex-snapshot
Straight-line programs in geometric elimination theory
inferredcites →https://doi.org/10.1016/s0022-4049(96)00103-xopenalex-snapshot
Computation of real radicals of polynomial ideals — II
inferredcites →https://doi.org/10.1016/s0022-4049(97)00015-7openalex-snapshot
Lower bounds for diophantine approximations
inferredcites →https://doi.org/10.1016/s0747-7171(10)80003-3openalex-snapshot
On the computational complexity and geometry of the first-order theory of the reals. Part I: Introduction. Preliminaries. The geometry of semi-algebraic sets. The decision problem for the existential theory of the reals
inferredcites →https://doi.org/10.1016/s0747-7171(88)80005-1openalex-snapshot
Solving systems of polynomial inequalities in subexponential time
inferredcites →https://doi.org/10.1016/s0747-7171(88)80006-3openalex-snapshot
Complexity of deciding Tarski algebra
inferredcites →https://doi.org/10.1016/s0747-7171(88)80008-7openalex-snapshot
Thom's lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets
inferredcites →https://doi.org/10.1090/s0002-9947-1974-0349648-2openalex-snapshot
Constructions in Algebra
inferredcites →https://doi.org/10.1090/s0894-0347-1993-1175980-4openalex-snapshot
Complexity of Bézout’s theorem. I. Geometric aspects
inferredcites →https://doi.org/10.1093/oso/9780198534327.003.0004openalex-snapshot
Parallel Linear Algebra
inferredcites →https://doi.org/10.1137/0733008openalex-snapshot
Complexity of Bezout’s Theorem IV: Probability of Success; Extensions
inferredcites →https://doi.org/10.1142/9789812792839_0017openalex-snapshot
COMPLEXITY OF BEZOUT'S THEOREM II: VOLUMES AND PROBABILITIES
inferredcites →https://doi.org/10.1142/9789812792839_0018openalex-snapshot
Complexity of Bezout's Theorem: III. Condition Number and Packing
inferredcites →https://doi.org/10.1142/9789812792839_0019openalex-snapshot
COMPLEXITY OF BEZOUT'S THEOREM IV: PROBABILITY OF SUCCESS; EXTENSIONS
inferredcites →https://doi.org/10.1145/1088322.1088324openalex-snapshot
An efficient quantifier elimination algorithm for algebraically closed fields of any characteristic
inferredcites →https://doi.org/10.1145/129712.129725openalex-snapshot
Feasibility testing for systems of real quadratic equations
inferredcites →https://doi.org/10.1145/235809.235813openalex-snapshot
On the combinatorial and algebraic complexity of quantifier elimination
inferredcites →https://doi.org/10.1145/281508.281533openalex-snapshot
Complexity of computing semi-algebraic descriptions of the connected components of a semi-algebraic set
inferredcites →https://doi.org/10.1145/382242.382836openalex-snapshot
How to compute fast a function and all its derivatives
inferredcites →https://doi.org/10.1145/62212.62257openalex-snapshot
Some algebraic and geometric computations in PSPACE
inferredcites →https://doi.org/10.2307/1971299openalex-snapshot
Varietes Polaires Locales et Classes de Chern des Varietes Singulieres
inferredcites →https://doi.org/10.2307/2152805openalex-snapshot
Complexity of Bezout's Theorem I: Geometric Aspects
inferredcites →https://doi.org/10.24033/asens.1346openalex-snapshot
Polar classes of singular varieties
inferredcites →https://doi.org/10.24033/bsmf.1907openalex-snapshot
Minorations de nombres de Milnor
inferredcites →https://doi.org/10.24033/bsmf.2138openalex-snapshot
Sur la complexité du principe de Tarski-Seidenberg
inferredcites →https://doi.org/10.48550/arxiv.alg-geom/9609003openalex-snapshot
Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case
inferredcites →https://doi.org/10.5860/choice.35-6275copenalex-snapshot
Complexity and real computation

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1006/jsco.2002.0563openalex-snapshot
Real Solving for Positive Dimensional Systems
inferred← citeshttps://doi.org/10.1007/3-540-45410-1_3openalex-snapshot
Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study
inferred← citeshttps://doi.org/10.1007/978-0-387-75155-9_6openalex-snapshot
Polars of Real Singular Plane Curves
inferred← citeshttps://doi.org/10.1007/978-3-319-15081-9_8openalex-snapshot
Polar Varieties Revisited
inferred← citeshttps://doi.org/10.1007/978-3-540-25954-1_1openalex-snapshot
Constraint Databases, Data Structures and Efficient Query Evaluation
inferred← citeshttps://doi.org/10.1007/s00200-009-0117-1openalex-snapshot
On the geometry of polar varieties
inferred← citeshttps://doi.org/10.1007/s00200-019-00396-wopenalex-snapshot
Real root finding for low rank linear matrices
inferred← citeshttps://doi.org/10.1007/s002000000046openalex-snapshot
On the Time-Space Complexity of Geometric Elimination Procedures
inferred← citeshttps://doi.org/10.1007/s00454-004-1107-5openalex-snapshot
Properness Defects of Projections and Computation of at Least One Point in Each Connected Component of a Real Algebraic Set
inferred← citeshttps://doi.org/10.1007/s00454-009-9200-4openalex-snapshot
On Sign Conditions Over Real Multivariate Polynomials
inferred← citeshttps://doi.org/10.1007/s00454-009-9239-2openalex-snapshot
A Baby Steps/Giant Steps Probabilistic Algorithm for Computing Roadmaps in Smooth Bounded Real Hypersurface
inferred← citeshttps://doi.org/10.1007/s10208-002-0065-7openalex-snapshot
The Hardness of Polynomial Equation Solving
inferred← citeshttps://doi.org/10.1007/s10208-005-0175-0openalex-snapshot
The Complexity of Computing the Hilbert Polynomial of Smooth Equidimensional Complex Projective Varieties
inferred← citeshttps://doi.org/10.1007/s10208-011-9112-6openalex-snapshot
Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces
inferred← citeshttps://doi.org/10.1007/s10208-014-9214-zopenalex-snapshot
Degeneracy Loci and Polynomial Equation Solving
inferred← citeshttps://doi.org/10.1007/s10440-012-9782-3openalex-snapshot
Numerically Computing Real Points on Algebraic Sets
inferred← citeshttps://doi.org/10.1007/s11045-018-0596-yopenalex-snapshot
Certified non-conservative tests for the structural stability of discrete multidimensional systems
inferred← citeshttps://doi.org/10.1007/s11424-023-1406-7openalex-snapshot
VerifyRealRoots: A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities
inferred← citeshttps://doi.org/10.1007/s11424-023-2119-7openalex-snapshot
On Types of Isolated KKT Points in Polynomial Optimization
inferred← citeshttps://doi.org/10.1016/j.exmath.2007.07.001openalex-snapshot
A concise proof of the Kronecker polynomial system solver from scratch
inferred← citeshttps://doi.org/10.1016/j.ffa.2014.09.002openalex-snapshot
Polar varieties, Bertini's theorems and number of points of singular complete intersections over a finite field
inferred← citeshttps://doi.org/10.1016/j.ipl.2009.07.014openalex-snapshot
On the intrinsic complexity of point finding in real singular hypersurfaces
inferred← citeshttps://doi.org/10.1016/j.jco.2004.10.001openalex-snapshot
Generalized polar varieties: geometry and algorithms
inferred← citeshttps://doi.org/10.1016/j.jco.2014.02.005openalex-snapshot
Intrinsic complexity estimates in polynomial optimization
inferred← citeshttps://doi.org/10.1016/j.jsc.2014.12.002openalex-snapshot
A certificate for semidefinite relaxations in computing positive-dimensional real radical ideals
inferred← citeshttps://doi.org/10.1016/j.jsc.2015.06.010openalex-snapshot
Real root finding for determinants of linear matrices
inferred← citeshttps://doi.org/10.1016/j.jsc.2017.08.001openalex-snapshot
Bit complexity for multi-homogeneous polynomial system solving—Application to polynomial minimization
inferred← citeshttps://doi.org/10.1016/j.jsc.2020.09.008openalex-snapshot
Solving determinantal systems using homotopy techniques
inferred← citeshttps://doi.org/10.1016/j.jsc.2021.03.005openalex-snapshot
On exact Reznick, Hilbert-Artin and Putinar's representations
inferred← citeshttps://doi.org/10.1016/j.jsc.2021.12.002openalex-snapshot
Solving parametric systems of polynomial equations over the reals through Hermite matrices
inferred← citeshttps://doi.org/10.1016/j.jsc.2022.08.010openalex-snapshot
Bit complexity for computing one point in each connected component of a smooth real algebraic set
inferred← citeshttps://doi.org/10.1016/j.jsc.2025.102532openalex-snapshot
Computing roadmaps in unbounded smooth real algebraic sets II: Algorithm and complexity
inferred← citeshttps://doi.org/10.1016/s0885-064x(02)00028-6openalex-snapshot
Systems of rational polynomial equations have polynomial size approximate zeros on the average
inferred← citeshttps://doi.org/10.1090/conm/604/12068openalex-snapshot
Polar, bipolar and copolar varieties: Real solving of algebraic varieties with intrinsic complexity
inferred← citeshttps://doi.org/10.1090/s0025-5718-06-01878-3openalex-snapshot
Fast computation of a rational point of a variety over a finite field
inferred← citeshttps://doi.org/10.1090/s0025-5718-2013-02766-4openalex-snapshot
Point searching in real singularcomplete intersection varieties: algorithms of intrinsic complexity
inferred← citeshttps://doi.org/10.1109/nds.2015.7332633openalex-snapshot
Computer algebra methods for testing the structural stability of multidimensional systems
inferred← citeshttps://doi.org/10.1137/130931308openalex-snapshot
Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set
inferred← citeshttps://doi.org/10.1137/130936294openalex-snapshot
On the Complexity of Computing Critical Points with Gröbner Bases
inferred← citeshttps://doi.org/10.1137/15m1036543openalex-snapshot
Exact Algorithms for Linear Matrix Inequalities
inferred← citeshttps://doi.org/10.1137/19m1265776openalex-snapshot
The Bottleneck Degree of Algebraic Varieties
inferred← citeshttps://doi.org/10.1137/21m1436245openalex-snapshot
Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients
inferred← citeshttps://doi.org/10.1145/1390768.1390781openalex-snapshot
Computing the global optimum of a multivariate polynomial over the reals
inferred← citeshttps://doi.org/10.1145/2442829.2442855openalex-snapshot
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inferred← citeshttps://doi.org/10.1145/2442829.2442866openalex-snapshot
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inferred← citeshttps://doi.org/10.1145/2465506.2465951openalex-snapshot
Verified error bounds for real solutions of positive-dimensional polynomial systems
inferred← citeshttps://doi.org/10.1145/2755996.2756670openalex-snapshot
Probabilistic Algorithm for Computing the Dimension of Real Algebraic Sets
inferred← citeshttps://doi.org/10.1145/2930889.2930910openalex-snapshot
Validating the Completeness of the Real Solution Set of a System of Polynomial Equations
inferred← citeshttps://doi.org/10.1145/2996450openalex-snapshot
A Nearly Optimal Algorithm for Deciding Connectivity Queries in Smooth and Bounded Real Algebraic Sets
inferred← citeshttps://doi.org/10.1145/3208976.3208986openalex-snapshot
On Exact Polya and Putinar's Representations
inferred← citeshttps://doi.org/10.1145/3208976.3209023openalex-snapshot
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inferred← citeshttps://doi.org/10.1145/3373207.3404058openalex-snapshot
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inferred← citeshttps://doi.org/10.1145/3377006.3377014openalex-snapshot
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inferred← citeshttps://doi.org/10.1145/3476446.3536181openalex-snapshot
Computing Critical Points for Algebraic Systems Defined by Hyperoctahedral Invariant Polynomials
inferred← citeshttps://doi.org/10.1145/3476446.3536182openalex-snapshot
Finer Complexity Estimates for the Change of Ordering of Gröbner Bases for Generic Symmetric Determinantal Ideals
inferred← citeshttps://doi.org/10.1145/3597066.3597097openalex-snapshot
Faster real root decision algorithm for symmetric polynomials
inferred← citeshttps://doi.org/10.1145/860854.860901openalex-snapshot
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inferred← citeshttps://doi.org/10.18452/2801openalex-snapshot
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inferred← citeshttps://doi.org/10.48550/arxiv.1409.1534openalex-snapshot
Algorithms in Real Algebraic Geometry: A Survey
inferred← citeshttps://doi.org/10.48550/arxiv.cs/0610051openalex-snapshot
Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry
inferred← citeshttps://doi.org/10.5802/afst.1582openalex-snapshot
Local polar varieties in the geometric study of singularities
inferred← citeshttps://doi.org/10.70675/20c4db5az6bf5z4d03za9d9z5e6cd5011246openalex-snapshot
Certified Polynomial Optimization Based on Exact Sum of Squares Decompositions
inferred← citeshttps://doi.org/10.70675/2a76e51fz3424z4dd3zbed1z94f95e805983openalex-snapshot
Exact Algorithms for Polynomial Optimisation
inferred← citeshttps://doi.org/10.70675/2e9d6fe2z1705z4204zbbaezea86f5846d60openalex-snapshot
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inferred← citeshttps://doi.org/10.70675/d0b760d0z6de6z48cazb255zb7c4e16724ecopenalex-snapshot
Homotopy algorithms for solving structured determinantal systems
inferred← citeshttps://doi.org/10.7146/math.scand.a-101478openalex-snapshot
Nearest points on toric varieties
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