How to count efficiently all affine roots of a polynomial system
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Publication:1289017
DOI10.1016/S0166-218X(99)00003-7zbMath1034.68715OpenAlexW1987964348MaRDI QIDQ1289017
Jan Verschelde, Ioannis Z. Emiris
Publication date: 1999
Published in: Discrete Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0166-218x(99)00003-7
Related Items (8)
Singular bifurcations in higher index differential-algebraic equations ⋮ Computing isolated roots of sparse polynomial systems in affine space ⋮ Global optimality conditions and optimization methods for polynomial programming problems ⋮ Elimination for generic sparse polynomial systems ⋮ Matrices in elimination theory ⋮ Mixed volume techniques for embeddings of Laman graphs ⋮ On the multiplicity of isolated roots of sparse polynomial systems ⋮ Numerical homotopies to compute generic points on positive dimensional algebraic sets
Cites Work
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- Bernstein's theorem in affine space
- Fiber polytopes
- Mixed volumes of polytopes
- Toric intersection theory for affine root counting
- On the Newton polytope of the resultant
- A convex geometric approach to counting the roots of a polynomial system
- Efficient incremental algorithms for the sparse resultant and the mixed volume
- Mixed-volume computation by dynamic lifting applied to polynomial system solving
- Counting affine roots of polynomial systems via pointed Newton polytopes
- On the complexity of sparse elimination
- Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems
- On The Complexity of Computing Mixed Volumes
- The BKK root count in $\mathbf {C}^n$
- A Polyhedral Method for Solving Sparse Polynomial Systems
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