Bibliography

Major publications by the team in recent years

• 1Y. 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
• 2E. 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, n^o 7, 14p., 21 figs. [ DOI : 10.1142/S0218216516500449 ]
  
  https://hal.archives-ouvertes.fr/hal-01084472
• 3E. Brugallé, P.-V. Koseleff, D. Pecker.
  
  Untangling trigonal diagrams, in: Journal Of Knot Theory And Its Ramifications (JKTR), June 2016, vol. 25, n^o 7, 10p., 24 figs. [ DOI : 10.1142/S0218216516500437 ]
  
  https://hal.archives-ouvertes.fr/hal-01084463
• 4F. 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.
• 5T. Cluzeau, A. Quadrat.
  
  Factoring and decomposing a class of linear functional systems, in: Linear Algebra and Its Applications, 2008, vol. 428, pp. 324–381.
• 6E. 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
• 7E. 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, n^o 2, 17 p. [ DOI : 10.1080/10586458.2015.1068249 ]
  
  https://hal.inria.fr/hal-01362208
• 8E. 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
• 9A. Joux.
  
  A one round protocol for tripartite Diffie-Hellman, in: J. Cryptology, 2004, vol. 17, n^o 4, pp. 263–276.
• 10A. 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, n^o 242, pp. 953-967.
• 11D. Lazard, F. Rouillier.
  
  Solving Parametric Polynomial Systems, in: Journal of Symbolic Computation, June 2007, vol. 42, pp. 636-667.
• 12A. Quadrat, D. Robertz.
  
  Computation of bases of free modules over the Weyl algebras, in: Journal of Symbolic Computation, 2007, vol. 42, pp. 1113–1141.
• 13F. Rouillier.
  
  Solving zero-dimensional systems through the rational univariate representation, in: Journal of Applicable Algebra in Engineering, Communication and Computing, 1999, vol. 9, n^o 5, pp. 433–461.
• 14F. Rouillier, P. Zimmermann.
  
  Efficient Isolation of Polynomial Real Roots, in: Journal of Computational and Applied Mathematics, 2003, vol. 162, n^o 1, pp. 33–50.

Publications of the year

Articles in International Peer-Reviewed Journals

• 15R. Barbulescu, S. Duquesne.
  
  Updating key size estimations for pairings, in: Journal of Cryptology, 2019, vol. 32, n^o 4, pp. 1298–1336. [ DOI : 10.1007/s00145-018-9280-5 ]
  
  https://hal.archives-ouvertes.fr/hal-01534101
• 16R. 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
• 17E. Bartzos, I. Z. Emiris, J. Legerský, E. Tsigaridas.
  
  On the maximal number of real embeddings of minimally rigid graphs in ${ℝ}^2$, ${ℝ}^3$ and $S^2$, 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
• 18Y. 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, n^o 3, 31 p. [ DOI : 10.1007/s11045-018-0596-y ]
  
  https://hal.inria.fr/hal-01951765
• 19L. 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
• 20I. 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
• 21I. 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
• 22T. Espitau, A. Joux.
  
  Certified lattice reduction, in: Advances in Mathematics of Communications, February 2020, vol. 14, n^o 1, pp. 137-159. [ DOI : 10.3934/amc.2020011 ]
  
  https://hal.archives-ouvertes.fr/hal-02383752
• 23F. 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
• 24P. 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

• 25Y. 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
• 26Y. 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
• 27D. 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
• 28I. 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
• 29E. 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)

• 30Y. 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
• 31T. 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
• 32T. 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

• 33J. 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
• 34R. 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
• 35R. 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
• 36R. 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
• 37G. 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
• 38A. 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

References in notes

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• 44J.-F. Biasse, T. Espitau, P.-A. Fouque, A. Gélin, P. Kirchner.
  
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• 48Y. Bouzidi, T. Cluzeau, G. Moroz, A. Quadrat.
  
  Computing effectively stabilizing controllers for a class of $n$D systems, in: The 20th World Congress of the International Federation of Automatic Control, Toulouse, France, July 2017, vol. 50, n^o 1, pp. 1847 – 1852. [ DOI : 10.1016/j.ifacol.2017.08.200 ]
  
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• 49Y. Bouzidi, S. Lazard, G. Moroz, M. Pouget, F. Rouillier.
  
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• 50Y. 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 ]
  
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• 51Y. 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, n^o 0, pp. 84-119. [ DOI : 10.1016/j.jsc.2014.08.009 ]
  
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• 52Y. 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.
  
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• 53Y. 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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• 54Y. 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
• 55Y. 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
• 56E. 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, n^o 7, 14p., 21 figs. [ DOI : 10.1142/S0218216516500449 ]
  
  https://hal.archives-ouvertes.fr/hal-01084472
• 57E. Brugallé, P.-V. Koseleff, D. Pecker.
  
  Untangling trigonal diagrams, in: Journal Of Knot Theory And Its Ramifications (JKTR), June 2016, vol. 25, n^o 7, 10p., 24 figs. [ DOI : 10.1142/S0218216516500437 ]
  
  https://hal.archives-ouvertes.fr/hal-01084463
• 58E. 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
• 59D. 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
• 60D. 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
• 61F. 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.
• 62F. Chyzak, B. Salvy.
  
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• 63G. E. Collins.
  
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• 64D. A. Cox, J. Little, D. O'Shea.
  
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• 65M. Crocco, A. Del Bue, V. Murino.
  
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• 68R. Dagher, A. Quadrat, G. Zheng.
  
  Algebraic solutions to the metric multidimensional unfolding. Application to the position self-calibration problem, in: in preparation, 2019.
• 69M. Deraux, E. Falbel.
  
  Complex hyperbolic geometry of the figure eight knot, in: Geometry and Topology, February 2015, vol. 19, pp. 237–293. [ DOI : 10.2140/gt.2015.19.237 ]
  
  https://hal.archives-ouvertes.fr/hal-00805427
• 70D. N. Diatta, S. Diatta, F. Rouillier, M.-F. Roy, M. Sagraloff.
  
  Bounds for polynomials on algebraic numbers and application to curve topology, October 2018, working paper or preprint.
  
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• 71W. Diffie, M. E. Hellman.
  
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• 74J. Doliskani, A. K. Narayanan, É. Schost.
  
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• 75T. Espitau, A. Joux.
  
  Adaptive precision LLL and Potential-LLL reductions with Interval arithmetic, in: IACR Cryptology ePrint Archive, 2016, vol. 2016, 528 p.
  
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• 76H. Evelyne.
  
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• 77E. Falbel, A. Guilloux.
  
  Dimension of character varieties for 3-manifolds, in: Proceedings of the American Mathematical Society, 2016. [ DOI : 10.1090/proc/13394 ]
  
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• 78E. Falbel, A. Guilloux, P. Will.
  
  Hilbert metric, beyond convexity, 2018, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01768400
• 79E. Falbel, P.-V. Koseleff, F. Rouillier.
  
  Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity, in: Geometriae Dedicata, August 2015, vol. 177, n^o 1, 52 p. [ DOI : 10.1007/s10711-014-9987-x ]
  
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• 80E. Falbel, M. Maculan, G. Sarfatti.
  
  Configurations of flags in orbits of real forms, April 2018, working paper or preprint.
  
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• 81E. Falbel, R. Santos Thebaldi.
  
  A Flag structure on a cusped hyperbolic 3-manifold with unipotent holonomy, in: Pacific Journal of Mathematics, 2015, vol. 278, n^o 1, pp. 51-78.
  
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• 82E. Falbel, J. Veloso.
  
  Flag structures on real 3-manifolds, April 2018, working paper or preprint.
  
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  Volume of representations and birationality of peripheral holonomy, in: Experimental Mathematics, May 2017.
  
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• 87A. Guilloux, I. Kim.
  
  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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  On SL(3,C)-representations of the Whitehead link group, 2018, To appear in Geom. Ded.
  
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• 93M. L. Husty, H.-P. Schröcker.
  
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• 95R. Jha, D. Chablat, L. Baron, F. Rouillier, G. Moroz.
  
  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 ]
  
  https://hal.archives-ouvertes.fr/hal-01796066
• 96R. Jha, D. Chablat, F. Rouillier, G. Moroz.
  
  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.
  
  https://hal.archives-ouvertes.fr/hal-01142989
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