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Critical Points and Gröbner Bases: the Unmixed Case

Jean-Charles Faugère , Mohab Safey El Din , Pierre-Jean Spaenlehauer
ISSAC 2012 - International Symposium on Symbolic and Algebraic Computation - 2012, Jul 2012, Grenoble, France. pp.162-169, ⟨10.1145/2442829.2442855⟩
Communication dans un congrès hal-00667494v1
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Computing Small Certificates of Inconsistency of Quadratic Fewnomial Systems

Jean-Charles Faugère , Pierre-Jean Spaenlehauer , Jules Svartz
International Symposium on Symbolic and Algebraic Computation (ISSAC 2016), Jul 2016, Waterloo, Canada. pp.223-230, ⟨10.1145/2930889.2930927⟩
Communication dans un congrès hal-01314651v1

A Quadratically Convergent Algorithm for Structured Low-Rank Approximation

Éric Schost , Pierre-Jean Spaenlehauer
Foundations of Computational Mathematics, 2016, 16 (2), pp.457-492. ⟨10.1007/s10208-015-9256-x⟩
Article dans une revue hal-00953684v1

Refined Analysis of the Asymptotic Complexity of the Number Field Sieve

Aude Le Gluher , Pierre-Jean Spaenlehauer , Emmanuel Thomé
Mathematical Cryptology, 2021, 1 (1), pp.71-88. ⟨10.48550/arXiv.2007.02730⟩
Article dans une revue hal-02934273v1

On the Complexity of Computing Critical Points with Gröbner Bases

Pierre-Jean Spaenlehauer
SIAM Journal on Optimization, 2014, 24 (3), pp.1382-1401. ⟨10.1137/130936294⟩
Article dans une revue hal-01017032v1

On the Complexity of the Generalized MinRank Problem

Jean-Charles Faugère , Mohab Safey El Din , Pierre-Jean Spaenlehauer
Journal of Symbolic Computation, 2013, 55, pp.30-58. ⟨10.1016/j.jsc.2013.03.004⟩
Article dans une revue hal-00654094v1
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Solving multi-homogeneous and determinantal systems: algorithms, complexity, applications.

Pierre-Jean Spaenlehauer
Symbolic Computation [cs.SC]. Université Pierre et Marie Curie (Univ. Paris 6), 2012. English. ⟨NNT : ⟩
Thèse tel-01110756v1

Algebraic-Differential Cryptanalysis of DES

Jean-Charles Faugère , Ludovic Perret , Pierre-Jean Spaenlehauer
Western European Workshop on Research in Cryptology - WEWoRC 2009, Jul 2009, Graz, Austria. pp.1--5
Communication dans un congrès hal-01298884v1
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Improved Complexity Bounds for Counting Points on Hyperelliptic Curves

Simon Abelard , Pierrick Gaudry , Pierre-Jean Spaenlehauer
Foundations of Computational Mathematics, 2019, 19 (3), pp.591-621. ⟨10.1007/s10208-018-9392-1⟩
Article dans une revue hal-01613530v2

A Fast Randomized Geometric Algorithm for Computing Riemann-Roch Spaces

Aude Le Gluher , Pierre-Jean Spaenlehauer
Mathematics of Computation, 2020, 89, pp.2399-2433. ⟨10.1090/mcom/3517⟩
Article dans une revue hal-01930573v1
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Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree (1,1): Algorithms and complexity

Jean-Charles Faugère , Mohab Safey El Din , Pierre-Jean Spaenlehauer
Journal of Symbolic Computation, 2011, 46 (4), pp.406-437. ⟨10.1016/j.jsc.2010.10.014⟩
Article dans une revue inria-00596631v1

Computing a Group Action from the Class Field Theory of Imaginary Hyperelliptic Function Fields

Pierre-Jean Spaenlehauer , Antoine Leudière
Journal of Symbolic Computation, 2024, 125, ⟨10.1016/j.jsc.2024.102311⟩
Article dans une revue hal-03633990v1
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Counting points on genus-3 hyperelliptic curves with explicit real multiplication

Simon Abelard , Pierrick Gaudry , Pierre-Jean Spaenlehauer
ANTS-XIII - Thirteenth Algorithmic Number Theory Symposium, Jul 2018, Madison, United States. pp.1--19
Communication dans un congrès hal-01816256v3

A Polyhedral Method for Sparse Systems with many Positive Solutions

Frederic Bihan , Francisco Santos , Pierre-Jean Spaenlehauer
SIAM Journal on Applied Algebra and Geometry, 2018, 2 (4), pp.620-645. ⟨10.1137/18M1181912⟩
Article dans une revue hal-01877602v1
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Critical Point Computations on Smooth Varieties: Degree and Complexity bounds

Mohab Safey El Din , Pierre-Jean Spaenlehauer
International Symposium on Symbolic and Algebraic Computation (ISSAC), Jul 2016, Waterloo, Canada. pp.183--190, ⟨10.1145/2930889.2930929⟩
Communication dans un congrès hal-01312750v1

Dimension results for extremal-generic polynomial systems over complete toric varieties

Matías R Bender , Pierre-Jean Spaenlehauer
Journal of Algebra, 2024, 646, pp.156-182. ⟨10.1016/j.jalgebra.2024.01.029⟩
Article dans une revue hal-04102564v1

Exact Solutions in Structured Low-Rank Approximation

Giorgio Ottaviani , Pierre-Jean Spaenlehauer , Bernd Sturmfels
SIAM Journal on Matrix Analysis and Applications, 2014, 35, 4, pp.1521-1542. ⟨10.1137/13094520X⟩
Article dans une revue hal-00953702v1
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Sparse Polynomial Systems with many Positive Solutions from Bipartite Simplicial Complexes

Frédéric Bihan , Pierre-Jean Spaenlehauer
2016
Pré-publication, Document de travail hal-01217547v2
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Sparse Gröbner Bases: the Unmixed Case

Jean-Charles Faugère , Pierre-Jean Spaenlehauer , Jules Svartz
ISSAC 2014, Jul 2014, Kobe, Japan. ⟨10.1145/2608628.2608663⟩
Communication dans un congrès hal-00953501v3

Algebraic Cryptanalysis of the PKC'09 Algebraic Surface Cryptosystem

Jean-Charles Faugère , Pierre-Jean Spaenlehauer
PKC 2010 - 13th International Conference on Practice and Theory in Public Key Cryptography, May 2010, Paris, France. pp.35-52, ⟨10.1007/978-3-642-13013-7_3⟩
Communication dans un congrès hal-01057831v1

Computing Loci of Rank Defects of Linear Matrices using Gröbner Bases and Applications to Cryptology

Jean-Charles Faugère , Mohab Safey El Din , Pierre-Jean Spaenlehauer
ISSAC 2010 - 35th International Symposium on Symbolic and Algebraic Computation, Jul 2010, Munich, Germany. pp.257-264, ⟨10.1145/1837934.1837984⟩
Communication dans un congrès hal-01057840v1

On the Complexity of Solving Quadratic Boolean Systems

Magali Bardet , Jean-Charles Faugère , Bruno Salvy , Pierre-Jean Spaenlehauer
Journal of Complexity, 2013, 29 (1), pp.53-75. ⟨10.1016/j.jco.2012.07.001⟩
Article dans une revue hal-00655745v1