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Solving a polynomial system, or computing an associated Gr\"obner basis, has been a fundamental task in computational algebra.
On the structure of the special linear group over polynomial rings
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The construction of multivariate polynomials with preassigned zeros
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Algebraic solution of systems of polynomial equations using Groebner bases
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Gröbner Bases: A Computational Approach to Commutative Algebra
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Efficient computation of zero-dimensional Gröbner bases by change of ordering
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Introduction To Commutative Algebra
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Algebraic algorithms for sampling from conditional distributions
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A new efficient algorithm for computing Gröbner bases (F4)
Faugère, J.-C. (1999) · 1999
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A modular method to compute the rational univariate representation of zero-dimensional ideals
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Étude du résultant sur une variété algébrique
Busé, L. (2001) · 2001
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Resultant over the residual of a complete intersection
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A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
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Solving systems of polynomial equations
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Modular algorithms for computing Gröbner bases
Arnold, E. (2003) · 2003
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A computational algebra approach to the reverse engineering of gene regulatory networks
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Computing zero-dimensional schemes
Abbott, J., Kreuzer, M., and Robbiano, L. (2005) · 2005
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Solving equations via algebras
Cox, D. A. (2005) · 2005
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Suslin’s algorithms for reduction of unimodular rows
Lombardi, H. and Yengui, I. (2005) · 2005
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Gröbner Basis Methods for Minimal Problems in Computer Vision
Stewenius, H. (2005) · 2005
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Analytic manifold learning: Unifying and evaluating representations for continuous control
Antonova, R., Maydanskiy, M., Kragic, D., Devlin, S., and Hofmann, K. (2020) · 2006
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Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal (An Algorithm for Finding the Basis Elements in the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal)
Buchberger, B. (1965) · 2006
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Computing border bases
Kehrein, A. and Kreuzer, M. (2006) · 2006
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Gröbner Bases in Control Theory and Signal Processing
Park, H. and Regensburger, G., editors (2007) · 2007
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Stable border bases for ideals of points
Abbott, J., Fassino, C., and Torrente, M.-L. (2008) · 2008
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A Singular Introduction to Commutative Algebra, 2nd Edition
Gruel, G.-M. and Pfister, G. (2008) · 2008
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Algorithms for Solving Polynomial Systems
Bard, G. V. (2009) · 2009
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Approximate computation of zero-dimensional polynomial ideals
Heldt, D., Kreuzer, M., Pokutta, S., and Poulisse, H. (2009) · 2009
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Computer algebra in systems biology
Laubenbacher, R. and Sturmfels, B. (2009) · 2009
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Slimgb: Gröbner bases with slim polynomials
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Almost vanishing polynomials for sets of limited precision points
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New Techniques for Polynomial System Solving
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Hibi, T. (2014) · 2014
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Dual-to-kernel learning with ideals
Király, F. J., Kreuzer, M., and Theran, L. (2014) · 2014
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On the complexity of the F5 Gröbner basis algorithm
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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
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Border basis computation with gradient-weighted normalization
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