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Mixed-volume computation by dynamic lifting applied to polynomial system solving
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/9781118033296.scardopenalex-snapshot
Wiley‐Interscience Series in Discrete Mathematics and Optimization
inferredcites →https://doi.org/10.1006/aama.1995.1005openalex-snapshot
Symmetrical Newton Polytopes for Solving Sparse Polynomial Systems
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/10.1007/3-540-55210-3_205openalex-snapshot
Four results on randomized incremental constructions
inferredcites →https://doi.org/10.1007/3-540-56686-4_36openalex-snapshot
An efficient algorithm for the sparse mixed resultant
inferredcites →https://doi.org/10.1007/978-0-8176-4771-1openalex-snapshot
Discriminants, Resultants, and Multidimensional Determinants
inferredcites →https://doi.org/10.1007/978-3-642-61568-9openalex-snapshot
Algorithms in Combinatorial Geometry
inferredcites →https://doi.org/10.1007/978-3-642-97881-4openalex-snapshot
Geometric Algorithms and Combinatorial Optimization
inferredcites →https://doi.org/10.1007/978-94-011-0924-6_13openalex-snapshot
Polytopes and Brunn-Minkowski Theory
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On the Complexity of Some Basic Problems in Computational Convexity
inferredcites →https://doi.org/10.1007/bf00054997openalex-snapshot
Motion from point matches: Multiplicity of solutions
inferredcites →https://doi.org/10.1007/bf01075534openalex-snapshot
Newton polytopes and the Bezout theorem
inferredcites →https://doi.org/10.1007/bf01075595openalex-snapshot
The number of roots of a system of equations
inferredcites →https://doi.org/10.1007/bf01077562openalex-snapshot
Newton polyhedra and the genus of complete intersections
inferredcites →https://doi.org/10.1007/bf01758770openalex-snapshot
Randomized incremental construction of Delaunay and Voronoi diagrams
inferredcites →https://doi.org/10.1007/bf02293050openalex-snapshot
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
inferredcites →https://doi.org/10.1016/0001-8708(90)90048-ropenalex-snapshot
Generalized Euler integrals and A-hypergeometric functions
inferredcites →https://doi.org/10.1016/0094-114x(91)90024-xopenalex-snapshot
Solving the 6R inverse position problem using a generic-case solution methodology
inferredcites →https://doi.org/10.1016/0096-3003(89)90099-4openalex-snapshot
Coefficient-parameter polynomial continuation
inferredcites →https://doi.org/10.1016/0096-3003(92)90070-hopenalex-snapshot
Bezout number calculations for multi-homogeneous polynomial systems
inferredcites →https://doi.org/10.1016/0167-8396(94)00018-nopenalex-snapshot
Implementation of a randomized algorithm for Delaunay and regular triangulations in three dimensions
inferredcites →https://doi.org/10.1016/0304-3975(93)00062-aopenalex-snapshot
A convex geometric approach to counting the roots of a polynomial system
inferredcites →https://doi.org/10.1016/0304-3975(94)00064-6openalex-snapshot
Homotopies for solving polynomial systems within a bounded domain
inferredcites →https://doi.org/10.1016/0304-3975(94)90122-8openalex-snapshot
Complexity of Bezout's theorem V: polynomial time
inferredcites →https://doi.org/10.1016/0377-0427(89)90025-3openalex-snapshot
Mathematical reduction of a heart dipole model
inferredcites →https://doi.org/10.1016/b978-0-444-89596-7.50023-7openalex-snapshot
Mathematical Programming and Convex Geometry
inferredcites →https://doi.org/10.1016/s0747-7171(08)80153-8openalex-snapshot
A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots
inferredcites →https://doi.org/10.1023/a:1022497624378openalex-snapshot
On the Newton Polytope of the Resultant
inferredcites →https://doi.org/10.1090/dimacs/004/35openalex-snapshot
Regular triangulations of convex polytopes
inferredcites →https://doi.org/10.1090/s0025-5718-1995-1297471-4openalex-snapshot
A Polyhedral Method for Solving Sparse Polynomial Systems
inferredcites →https://doi.org/10.1090/s0894-0347-1993-1175980-4openalex-snapshot
Complexity of Bézout’s theorem. I. Geometric aspects
inferredcites →https://doi.org/10.1108/ir.1999.04926fae.001openalex-snapshot
Lecture Notes in Computer Science 1205
inferredcites →https://doi.org/10.1109/tbme.1981.324681openalex-snapshot
Determination of Magnitudes, Directions, and Locations of Two Independent Dipoles in a Circular Conducting Region from Boundary Potential Measurements
inferredcites →https://doi.org/10.1112/blms/15.3.270openalex-snapshot
CONVEX SETS AND THEIR APPLICATIONS
inferredcites →https://doi.org/10.1112/blms/21.6.621openalex-snapshot
THEORY OF LINEAR AND INTEGER PROGRAMMING (Wiley-Interscience Series in Discrete Mathematics and Optimization)
inferredcites →https://doi.org/10.1115/1.2916909openalex-snapshot
Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages
inferredcites →https://doi.org/10.1137/0217060openalex-snapshot
On the Complexity of Computing the Volume of a Polyhedron
inferredcites →https://doi.org/10.1137/0406019openalex-snapshot
Minkowski Addition of Polytopes: Computational Complexity and Applications to Gröbner Bases
inferredcites →https://doi.org/10.1137/0731049openalex-snapshot
Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems
inferredcites →https://doi.org/10.1137/0732061openalex-snapshot
A Product-Decomposition Bound for Bezout Numbers
inferredcites →https://doi.org/10.1137/1.9780898719031openalex-snapshot
Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems
inferredcites →https://doi.org/10.1137/s0097539794278384openalex-snapshot
On The Complexity of Computing Mixed Volumes
inferredcites →https://doi.org/10.1145/109648.109659openalex-snapshot
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
inferredcites →https://doi.org/10.1145/120694.120707openalex-snapshot
An optimal condition for determining the exact number of roots of a polynomial system
inferredcites →https://doi.org/10.1145/120694.120708openalex-snapshot
How we proved that there are exactly 924 cyclic 7-roots
inferredcites →https://doi.org/10.1145/142675.142688openalex-snapshot
Incremental topological flipping works for regular triangulations
inferredcites →https://doi.org/10.1145/328512.328521openalex-snapshot
Box-bisection for solving second-degree systems and the problem of clustering
inferredcites →https://doi.org/10.1215/s0012-7094-92-06707-xopenalex-snapshot
Chow polytopes and general resultants
inferredcites →https://doi.org/10.2307/2008200openalex-snapshot
Computational Geometry--An Introduction.
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Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems.
inferredcites →https://doi.org/10.2307/2325168openalex-snapshot
Algorithms in Combinatorial Geometry.
inferredcites →https://doi.org/10.2307/253980openalex-snapshot
Theory of Linear and Integer Programming
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Counting Affine Roots of Polynomial Systems via Pointed Newton Polytopes
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Matrices in Elimination Theory
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Finding All Isolated Zeros of Polynomial Systems inCnvia Stable Mixed Volumes
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Toric Newton Method for Polynomial Homotopies
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A Systematic Framework for Solving Geometric Constraints Analytically
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Enumerating Regular Mixed-Cell Configurations
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Decomposing the Secondary Cayley Polytope
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Mixed Volume Computation for Semi-Mixed Systems
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Elimination for Generic Sparse Polynomial Systems
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Unmixing the Mixed Volume Computation
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The Cayley Trick, lifting subdivisions and the Bohne–Dress theorem on zonotopal tilings
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Deformation Techniques for Sparse Systems
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Computing Mixed Volume and All Mixed Cells in Quermassintegral Time
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Mixed cell computation in Hom4PS-3
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Parallel degree computation for binomial systems
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Computing isolated roots of sparse polynomial systems in affine space
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Toric intersection theory for affine root counting
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Heuristic methods for computing the minimal multi-homogeneous Bézout number
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Polyhedral methods in numerical algebraic geometry
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