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02/16/2023
A Direttissimo Algorithm for Equidimensional Decomposition
We describe a recursive algorithm that decomposes an algebraic set into ...
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02/13/2023
Fast Algorithms for Discrete Differential Equations
Discrete Differential Equations (DDEs) are functional equations that rel...
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02/10/2023
Refined F_5 Algorithms for Ideals of Minors of Square Matrices
We consider the problem of computing a grevlex Gröbner basis for the set...
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03/18/2022
Gröbner bases and critical values: The asymptotic combinatorics of determinantal systems
We consider ideals involving the maximal minors of a polynomial matrix. ...
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03/09/2022
Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry
Cuspidal robots are robots with at least two inverse kinematic solutions...
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03/08/2022
Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results
Answering connectivity queries in real algebraic sets is a fundamental p...
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02/28/2022
A Signature-based Algorithm for Computing the Nondegenerate Locus of a Polynomial System
Polynomial system solving arises in many application areas to model non-...
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02/27/2022
New efficient algorithms for computing Gröbner bases of saturation ideals (F4SAT) and colon ideals (Sparse-FGLM-colon)
This paper is concerned with linear algebra based methods for solving ex...
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02/18/2022
Faster change of order algorithm for Gröbner bases under shape and stability assumptions
Solving zero-dimensional polynomial systems using Gröbner bases is usual...
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02/14/2022
Exact SOHS decompositions of trigonometric univariate polynomials with Gaussian coefficients
Certifying the positivity of trigonometric polynomials is of first impor...
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07/25/2021
Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients
Assessing non-negativity of multivariate polynomials over the reals, thr...
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05/21/2021
Computing the dimension of real algebraic sets
Let V be the set of real common solutions to F = (f_1, …, f_s) in ℝ[x_1,...
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04/08/2021
msolve: A Library for Solving Polynomial Systems
We present a new open source C library dedicated to solving multivariat...
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04/02/2021
On the computation of asymptotic critical values of polynomial maps and applications
Let 𝐟 = (f_1, …, f_p) be a polynomial tuple in ℚ[z_1, …, z_n] and let d ...
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03/25/2021
Faster One Block Quantifier Elimination for Regular Polynomial Systems of Equations
Quantifier elimination over the reals is a central problem in computatio...
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11/28/2020
Solving parametric systems of polynomial equations over the reals through Hermite matrices
We design a new algorithm for solving parametric systems having finitely...
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11/04/2020
Connectivity in Semi-Algebraic Sets I
A semi-algebraic set is a subset of the real space defined by polynomial...
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09/11/2020
Guessing Gröbner Bases of Structured Ideals of Relations of Sequences
Assuming sufficiently many terms of a n-dimensional table defined over a...
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09/02/2020
Computing critical points for invariant algebraic systems
Let 𝐊 be a field and ϕ, 𝐟 = (f_1, …, f_s) in 𝐊[x_1, …, x_n] be multivari...
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09/02/2020
Homotopy techniques for solving sparse column support determinantal polynomial systems
Let 𝐊 be a field of characteristic zero with 𝐊 its algebraic closure. Gi...
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08/31/2020
Robots, computer algebra and eight connected components
Answering connectivity queries in semi-algebraic sets is a long-standing...
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08/24/2020
Computing the Real Isolated Points of an Algebraic Hypersurface
Let ℝ be the field of real numbers. We consider the problem of computing...
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04/26/2019
Computing the volume of compact semi-algebraic sets
Let S⊂ R^n be a compact basic semi-algebraic set defined as the real sol...
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11/25/2018
On Exact Reznick, Hilbert-Artin and Putinar's Representations
We consider the problem of finding exact sums of squares (SOS) decomposi...
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11/25/2018
On Exact Polya, Hilbert-Artin and Putinar's Representations
We consider the problem of finding exact sums of squares (SOS) decomposi...
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06/21/2018
Real root finding for equivariant semi-algebraic systems
Let R be a real closed field. We consider basic semi-algebraic sets defi...
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05/06/2018
RealCertify: a Maple package for certifying non-negativity
Let Q (resp. R) be the field of rational (resp. real) numbers and X = (X...
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02/28/2018
Solving determinantal systems using homotopy techniques
Let be a field of characteristic zero and be an algebraic closure of ....
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02/28/2018
On Exact Polya and Putinar's Representations
We consider the problem of finding exact sums of squares (SOS) decomposi...
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02/08/2018
Exact algorithms for semidefinite programs with degenerate feasible set
Let A_0, ..., A_n be m × m symmetric matrices with entries in Q, and let...
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06/13/2017
Algorithms for Weighted Sums of Squares Decomposition of Non-negative Univariate Polynomials
It is well-known that every non-negative univariate real polynomial can ...
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05/19/2017
A lower bound on the positive semidefinite rank of convex bodies
The positive semidefinite rank of a convex body C is the size of its sma...
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11/07/2016
SPECTRA -a Maple library for solving linear matrix inequalities in exact arithmetic
This document describes our freely distributed Maple library spectra, f...
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05/24/2016
Bit complexity for multi-homogeneous polynomial system solving Application to polynomial minimization
Multi-homogeneous polynomial systems arise in many applications. We prov...
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05/09/2016
Critical Point Computations on Smooth Varieties: Degree and Complexity bounds
Let V ⊂ C n be an equidimensional algebraic set and g be an n-variate po...
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05/03/2016