Koszul-Type Determinantal Formulas for Families of Mixed Multilinear Systems
DOI10.1137/20M1332190zbMath1477.13053arXiv2105.13188OpenAlexW3168856416MaRDI QIDQ5157586
Matías R. Bender, Jean-Charles Faugère, Elias P. Tsigaridas, Angelos Mantzaflaris
Publication date: 19 October 2021
Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2105.13188
determinantal formulamultiparameter eigenvalue problemmultilinear polynomialsresultant matrixKoszul-type matrixWeyman complex
Eigenvalues, singular values, and eigenvectors (15A18) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Solving polynomial systems; resultants (13P15)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Spectral collocation solutions to multiparameter Mathieu's system
- Vector bundles on complex projective spaces. With an appendix by S. I. Gelfand
- Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree \((1,1)\): algorithms and complexity
- Multiparameter eigenvalue problems. Volume I: Matrices and compact operators
- The resultant as the determinant of a Koszul complex
- On the quadratic two-parameter eigenvalue problem and its linearization
- Multiparameter eigenvalue problems and expansion theorems
- Multigraded resultants of Sylvester type
- Inertia forms and resultant: A formulary
- Matrices in elimination theory
- Multihomogeneous resultant formulae by means of complexes
- Multilinear polynomial systems: root isolation and bit complexity
- Fiber product homotopy method for multiparameter eigenvalue problems
- Numerical root finding via Cox rings
- Matrix formulæ for resultants and discriminants of bivariate tensor-product polynomials
- Discriminants, resultants, and multidimensional determinants
- On the complexity of sparse elimination
- Constructing Sylvester-type resultant matrices using the Dixon formulation
- Macaulay style formulas for sparse resultants
- A Homotopy Method for Finding All Solutions of a Multiparameter Eigenvalue Problem
- Heights of varieties in multiprojective spaces and arithmetic Nullstellensatze
- A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic
- On the Bit Complexity of Solving Bilinear Polynomial Systems
- Conditions for exact resultants using the Dixon formulation
- Cryptanalysis of MinRank
- Calculating Discriminants by Higher Direct Images
- A Jacobi--Davidson Type Method for the Two-Parameter Eigenvalue Problem
- Resultants and Discriminants for Bivariate Tensor-Product Polynomials
- Bilinear Systems with Two Supports
- Towards Mixed Gröbner Basis Algorithms
- Gröbner Basis over Semigroup Algebras
- A Poisson formula for the sparse resultant
- Basic Algebraic Geometry 1
- Expressing a fraction of two determinants as a determinant
- The Expected Number of Nash Equilibria of a Normal Form Game
- Multihomogeneous resultant formulae for systems with scaled support
- Introduction to algebraic independence theory. With contributions from F. Amoroso, D. Bertrand, W. D. Brownawell, G. Diaz, M. Laurent, Yu. V. Nesterenko, K. Nishioka, P. Philippon, G. Rémond, D. Roy, M. Waldschmidt
- Explicit formulas for the multivariate resultant.
This page was built for publication: Koszul-Type Determinantal Formulas for Families of Mixed Multilinear Systems
