Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Dissemination
Bibliography
XML PDF e-pub
PDF e-Pub


Bibliography

Major publications by the team in recent years
[1]
Y. Bouzidi, S. Lazard, G. Moroz, M. Pouget, F. Rouillier, M. Sagraloff.
Solving bivariate systems using Rational Univariate Representations, in: Journal of Complexity, 2016, vol. 37, pp. 34–75. [ DOI : 10.1016/j.jco.2016.07.002 ]
https://hal.inria.fr/hal-01342211
[2]
E. Brugallé, P.-V. Koseleff, D. Pecker.
On the lexicographic degree of two-bridge knots, in: Journal Of Knot Theory And Its Ramifications (JKTR), June 2016, vol. 25, no 7, 14p., 21 figs. [ DOI : 10.1142/S0218216516500449 ]
https://hal.archives-ouvertes.fr/hal-01084472
[3]
E. Brugallé, P.-V. Koseleff, D. Pecker.
Untangling trigonal diagrams, in: Journal Of Knot Theory And Its Ramifications (JKTR), June 2016, vol. 25, no 7, 10p., 24 figs. [ DOI : 10.1142/S0218216516500437 ]
https://hal.archives-ouvertes.fr/hal-01084463
[4]
F. Chyzak, A. Quadrat, D. Robertz.
Effective algorithms for parametrizing linear control systems over Ore algebras, in: Applicable Algebra in Engineering, Communications and Computing, 2005, vol. 16, pp. 319–376.
[5]
T. Cluzeau, A. Quadrat.
Factoring and decomposing a class of linear functional systems, in: Linear Algebra and Its Applications, 2008, vol. 428, pp. 324–381.
[6]
E. Falbel, A. Guilloux.
Dimension of character varieties for 3-manifolds, in: Proceedings of the American Mathematical Society, 2016. [ DOI : 10.1090/proc/13394 ]
https://hal.archives-ouvertes.fr/hal-01370284
[7]
E. Falbel, A. Guilloux, P.-V. Koseleff, F. Rouillier, M. Thistlethwaite.
Character Varieties For SL(3,C): The Figure Eight Knot, in: Experimental Mathematics, 2016, vol. 25, no 2, 17 p. [ DOI : 10.1080/10586458.2015.1068249 ]
https://hal.inria.fr/hal-01362208
[8]
E. Falbel, J. Wang.
Branched spherical CR structures on the complement of the figure-eight knot, in: Michigan Mathematical Journal, 2014, vol. 63, pp. 635-667.
https://hal.archives-ouvertes.fr/hal-01374789
[9]
A. Joux.
A one round protocol for tripartite Diffie-Hellman, in: J. Cryptology, 2004, vol. 17, no 4, pp. 263–276.
[10]
A. Joux, R. Lercier.
Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method, in: Math. Comput., 2003, vol. 72, no 242, pp. 953-967.
[11]
D. Lazard, F. Rouillier.
Solving Parametric Polynomial Systems, in: Journal of Symbolic Computation, June 2007, vol. 42, pp. 636-667.
[12]
A. Quadrat, D. Robertz.
Computation of bases of free modules over the Weyl algebras, in: Journal of Symbolic Computation, 2007, vol. 42, pp. 1113–1141.
[13]
F. Rouillier.
Solving zero-dimensional systems through the rational univariate representation, in: Journal of Applicable Algebra in Engineering, Communication and Computing, 1999, vol. 9, no 5, pp. 433–461.
[14]
F. Rouillier, P. Zimmermann.
Efficient Isolation of Polynomial Real Roots, in: Journal of Computational and Applied Mathematics, 2003, vol. 162, no 1, pp. 33–50.
Publications of the year

Articles in International Peer-Reviewed Journals

[15]
R. Barbulescu, S. Duquesne.
Updating key size estimations for pairings, in: Journal of Cryptology, 2019, vol. 32, no 4, pp. 1298–1336. [ DOI : 10.1007/s00145-018-9280-5 ]
https://hal.archives-ouvertes.fr/hal-01534101
[16]
R. Barbulescu, J. Ray.
Numerical verification of the Cohen-Lenstra-Martinet heuristics and of Greenberg's p-rationality conjecture, in: Journal de Théorie des Nombres de Bordeaux, 2019, forthcoming.
https://hal.archives-ouvertes.fr/hal-01534050
[17]
E. Bartzos, I. Z. Emiris, J. Legerský, E. Tsigaridas.
On the maximal number of real embeddings of minimally rigid graphs in 2, 3 and S2, in: Journal of Symbolic Computation, 2019, https://arxiv.org/abs/1811.12800, forthcoming. [ DOI : 10.1016/j.jsc.2019.10.015 ]
https://hal.archives-ouvertes.fr/hal-02271782
[18]
Y. M. Bouzidi, A. Quadrat, F. Rouillier.
Certified Non-conservative Tests for the Structural Stability of Discrete Multidimensional Systems, in: Multidimensional Systems and Signal Processing, July 2019, vol. 30, no 3, 31 p. [ DOI : 10.1007/s11045-018-0596-y ]
https://hal.inria.fr/hal-01951765
[19]
L. Busé, A. Mantzaflaris, E. Tsigaridas.
Matrix formulae for Resultants and Discriminants of Bivariate Tensor-product Polynomials, in: Journal of Symbolic Computation, June 2020, vol. 98, pp. 65-83. [ DOI : 10.1016/j.jsc.2019.07.007 ]
https://hal.inria.fr/hal-01654263
[20]
I. Z. Emiris, A. Mantzaflaris, E. Tsigaridas.
Multilinear Polynomial Systems: Root Isolation and Bit Complexity, in: Journal of Symbolic Computation, 2019, Special Issue of the Journal of Symbolic Computation on Milestones in Computer Algebra (MICA 2016), forthcoming.
https://hal.inria.fr/hal-02099556
[21]
I. Z. Emiris, B. Mourrain, E. Tsigaridas.
Separation bounds for polynomial systems, in: Journal of Symbolic Computation, 2019. [ DOI : 10.1016/j.jsc.2019.07.001 ]
https://hal.inria.fr/hal-01105276
[22]
T. Espitau, A. Joux.
Certified lattice reduction, in: Advances in Mathematics of Communications, February 2020, vol. 14, no 1, pp. 137-159. [ DOI : 10.3934/amc.2020011 ]
https://hal.archives-ouvertes.fr/hal-02383752
[23]
F. Göloğlu, A. Joux.
A simplified approach to rigorous degree 2 elimination in discrete logarithm algorithms, in: Mathematics of Computation, 2019, 1 p.
https://hal.archives-ouvertes.fr/hal-01960765
[24]
P. Molin, C. Neurohr.
Computing period matrices and the Abel-Jacobi map of superelliptic curves, in: Mathematics of Computation, 2019.
https://hal.inria.fr/hal-02416012

International Conferences with Proceedings

[25]
Y. Bouzidi, T. Cluzeau, A. Quadrat.
On the computation of stabilizing controllers of multidimensional systems, in: SSSC 2019 - 7th IFAC Symposium on Systems Structure and Control, Sinai, Romania, September 2019. [ DOI : 10.1016/j.ifacol.2019.11.032 ]
https://hal.inria.fr/hal-02419696
[26]
Y. Bouzidi, T. Cluzeau, A. Quadrat, F. Rouillier.
On the effective computation of stabilizing controllers of 2D systems, in: Maple Conference, Waterloo, Canada, October 2019.
https://hal.inria.fr/hal-02419719
[27]
D. Chablat, G. Moroz, F. Rouillier, P. Wenger.
Using Maple to analyse parallel robots, in: Maple Conference 2019, Waterloo, Canada, October 2019.
https://hal.inria.fr/hal-02406703
[28]
I. Z. Emiris, C. Katsamaki.
Voronoi diagram of orthogonal polyhedra in two and three dimensions, in: SEA 2019 - Symposium on Experimental Algorithms, Kalamata, Greece, I. Kotsireas, P. Pardalos, K. E. Parsopoulos, D. Souravlias, A. Tsokas (editors), LNCS - Lecture Notes in Computer Science, Springer, June 2019, vol. 11544. [ DOI : 10.1007/978-3-030-34029-2_1 ]
https://hal.inria.fr/hal-02398736
[29]
E. Hubert, Y. Bouzidi, R. Dagher, A. Barrau, A. Quadrat.
Algebraic aspects of the exact signal demodulation problem, in: SSSC 2019 - 7th IFAC Symposium on Systems Structure and Control, Sinaia, Romania, September 2019. [ DOI : 10.1016/j.ifacol.2019.11.031 ]
https://hal.inria.fr/hal-02419824

Scientific Books (or Scientific Book chapters)

[30]
Y. Bouzidi, A. Poteaux, A. Quadrat.
A symbolic computation approach to the asymptotic stability analysis of differential systems with commensurate delays, in: Delays and Interconnections: Methodology, Algorithms and Applications, Advances in Delays and Dynamics, G. Valmorbida, A. Seuret, I. Boussaada, R. Sipahi (editors), Springer, October 2019, vol. 10, 16 p. [ DOI : 10.1007/978-3-030-11554-8_11 ]
https://hal.inria.fr/hal-01485536
[31]
T. Cluzeau, C. Koutschan, A. Quadrat, M. Tõnso.
Effective algebraic analysis approach to linear systems over Ore algebras, in: Algebraic and Symbolic Computation Methods in Dynamical Systems, Advances in Delays and Dynamics, Springer, 2020.
https://hal.archives-ouvertes.fr/hal-02436985
[32]
T. Cluzeau, A. Quadrat.
Equivalence of Linear Functional Systems, in: Algebraic and Symbolic Computation Methods in Dynamical Systems, Advances in Delays and Dynamics, Springer, 2020.
https://hal.archives-ouvertes.fr/hal-02436978

Other Publications

[33]
J. G. Alcázar, J. Caravantes, G. M. Diaz-Toca, E. Tsigaridas.
Computing the topology of a planar or space hyperelliptic curve, January 2019, working paper or preprint.
https://hal.inria.fr/hal-01968776
[34]
R. Barbulescu, N. El Mrabet, L. Ghammam.
A taxonomy of pairings, their security, their complexity, May 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02129868
[35]
R. Barbulescu, S. Shinde.
A classification of ECM-friendly families using modular curves, February 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01822144
[36]
R. Dagher, G. Zheng, A. Quadrat.
General closed-form solutions of the position self-calibration problem, October 2019, Paper under submission.
https://hal.inria.fr/hal-02419854
[37]
G. Ivanyos, A. Joux, M. Santha.
Discrete logarithm and Diffie-Hellman problems in identity black-box groups, November 2019, https://arxiv.org/abs/1911.01662 - working paper or preprint.
https://hal.sorbonne-universite.fr/hal-02350271
[38]
A. Joux, C. Pierrot.
Algorithmic aspects of elliptic bases in finite field discrete logarithm algorithms, July 2019, https://arxiv.org/abs/1907.02689 - working paper or preprint.
https://hal.sorbonne-universite.fr/hal-02173688
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Tetrahedra of flags, volume and homology of SL(3), in: Geometry & Topology Monographs, 2014, vol. 18. [ DOI : 10.2140/gt.2014.18.1911 ]
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Computing generator in cyclotomic integer rings, in: 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2017), Paris, France, Lecture Notes in Computer Science, April 2017, vol. 10210, pp. 60-88. [ DOI : 10.1007/978-3-319-56620-7_3 ]
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Computing effectively stabilizing controllers for a class of nD systems, in: The 20th World Congress of the International Federation of Automatic Control, Toulouse, France, July 2017, vol. 50, no 1, pp. 1847 – 1852. [ DOI : 10.1016/j.ifacol.2017.08.200 ]
https://hal.archives-ouvertes.fr/hal-01667161
[49]
Y. Bouzidi, S. Lazard, G. Moroz, M. Pouget, F. Rouillier.
Improved algorithm for computing separating linear forms for bivariate systems, in: ISSAC - 39th International Symposium on Symbolic and Algebraic Computation, Kobe, Japan, July 2014.
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Solving bivariate systems using Rational Univariate Representations, in: Journal of Complexity, 2016, vol. 37, pp. 34–75. [ DOI : 10.1016/j.jco.2016.07.002 ]
https://hal.inria.fr/hal-01342211
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Y. Bouzidi, S. Lazard, M. Pouget, F. Rouillier.
Separating linear forms and Rational Univariate Representations of bivariate systems, in: Journal of Symbolic Computation, May 2015, vol. 68, no 0, pp. 84-119. [ DOI : 10.1016/j.jsc.2014.08.009 ]
https://hal.inria.fr/hal-00977671
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Y. Bouzidi, A. Poteaux, A. Quadrat.
A symbolic computation approach to the asymptotic stability analysis of differential systems with commensurate delays, in: Delays and Interconnections: Methodology, Algorithms and Applications, Advances on Delays and Dynamics at Springer, Springer Verlag, March 2017.
https://hal.inria.fr/hal-01485536
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Y. Bouzidi, A. Quadrat, F. Rouillier.
Computer algebra methods for testing the structural stability of multidimensional systems, in: IEEE 9th International Workshop on Multidimensional (nD) Systems (IEEE nDS 2015), Vila Real, Portugal, Proceedings of the IEEE 9th International Workshop on Multidimensional (nD) Systems (IEEE nDS 2015), September 2015.
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[54]
Y. Bouzidi, A. Quadrat, F. Rouillier.
Certified Non-conservative Tests for the Structural Stability of Multidimensional Systems, August 2017, 31 p, To appear in Multidimensional Systems and Signal Processing, https://link.springer.com/article/10.1007/s11045-018-0596-y.
https://hal.inria.fr/hal-01571230
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Y. Bouzidi, F. Rouillier.
Certified Algorithms for proving the structural stability of two dimensional systems possibly with parameters, in: MNTS 2016 - 22nd International Symposium on Mathematical Theory of Networks and Systems, Minneapolis, United States, Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems, July 2016.
https://hal.inria.fr/hal-01366202
[56]
E. Brugallé, P.-V. Koseleff, D. Pecker.
On the lexicographic degree of two-bridge knots, in: Journal Of Knot Theory And Its Ramifications (JKTR), June 2016, vol. 25, no 7, 14p., 21 figs. [ DOI : 10.1142/S0218216516500449 ]
https://hal.archives-ouvertes.fr/hal-01084472
[57]
E. Brugallé, P.-V. Koseleff, D. Pecker.
Untangling trigonal diagrams, in: Journal Of Knot Theory And Its Ramifications (JKTR), June 2016, vol. 25, no 7, 10p., 24 figs. [ DOI : 10.1142/S0218216516500437 ]
https://hal.archives-ouvertes.fr/hal-01084463
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E. Brugallé, P.-V. Koseleff, D. Pecker.
The lexicographic degree of the first two-bridge knots, September 2018, 30 p., 58 fig., 6 tables, submitted.
https://hal.archives-ouvertes.fr/hal-01108678
[59]
D. Chablat, R. Jha, F. Rouillier, G. Moroz.
Non-singular assembly mode changing trajectories in the workspace for the 3-RPS parallel robot, in: 14th International Symposium on Advances in Robot Kinematics, Ljubljana, Slovenia, June 2014, pp. 149 – 159.
https://hal.archives-ouvertes.fr/hal-00956325
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D. Chablat, R. Jha, F. Rouillier, G. Moroz.
Workspace and joint space analysis of the 3-RPS parallel robot, in: ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Buffalo, United States, August 2014, vol. Volume 5A, pp. 1-10.
https://hal.archives-ouvertes.fr/hal-01006614
[61]
F. Chyzak, A. Quadrat, D. Robertz.
Effective algorithms for parametrizing linear control systems over Ore algebras, in: Applicable Algebra in Engineering, Communications and Computing, 2005, vol. 16, pp. 319–376.
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Bounds for polynomials on algebraic numbers and application to curve topology, October 2018, working paper or preprint.
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Hilbert metric, beyond convexity, 2018, working paper or preprint.
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Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity, in: Geometriae Dedicata, August 2015, vol. 177, no 1, 52 p. [ DOI : 10.1007/s10711-014-9987-x ]
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Flag structures on real 3-manifolds, April 2018, working paper or preprint.
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Deformation space of discrete groups of SU(2,1) in quaternionic hyperbolic plane, March 2018, working paper or preprint.
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Volume function and Mahler measure of exact polynomials, April 2018, working paper or preprint.
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Workspace, Joint space and Singularities of a family of Delta-Like Robot, in: Mechanism and Machine Theory, September 2018, vol. 127, pp. 73-95. [ DOI : 10.1016/j.mechmachtheory.2018.05.004 ]
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An algebraic method to check the singularity-free paths for parallel robots, in: International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Boston, United States, ASME, August 2015.
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Workspace and Singularity analysis of a Delta like family robot, in: 4th IFTOMM International Symposium on Robotics and Mechatronics, Poitiers, France, June 2015.
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