Computing roadmaps in unbounded smooth real algebraic sets II: Algorithm and complexity.

Mohab Safey El Din LIP6, Paris http://www-polsys.lip6.fr/~safey/ https://zbmath.org/authors/?q=ai:safey-el-din.mohab https://orcid.org/0000-0001-9463-1257 https://www.wikidata.org/entity/Q130910293

Rémi Prébet Mohab Safey El Din Éric Schost Computing roadmaps in unbounded smooth real algebraic sets II: Algorithm and complexity. 102532 2026 135 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2025.102532 db/journals/jsc/jsc135.html#PrebetDS26 streams/journals/jsc

Mohab Safey El Din Georgy Scholten Emmanuel Trélat Probabilistic algorithm for computing all local minimizers of Morse functions on a compact domain. 2026 June 445-481 38 Math. Control. Signals Syst. 2 https://doi.org/10.1007/s00498-026-00441-3 db/journals/mcss/mcss38.html#DinST26 streams/journals/mcss

Elisabetta Rocchi Mohab Safey El Din Computing the Connected Components of Real Algebraic Curves. 344-353 2026 ISSAC https://doi.org/10.1145/3815436.3815466 conf/issac/2026 db/conf/issac/issac2026.html#RocchiD26

Elisabetta Rocchi Mohab Safey El Din Computing the connected components of real algebraic curves. 2026 March abs/2603.16283 CoRR https://doi.org/10.48550/arXiv.2603.16283 db/journals/corr/corr2603.html#abs-2603-16283 streams/journals/corr

Robin Kouba Vincent Neiger Mohab Safey El Din A complexity analysis of the F4 Gröbner basis algorithm with tracer data. 2026 March abs/2603.16378 CoRR https://doi.org/10.48550/arXiv.2603.16378 db/journals/corr/corr2603.html#abs-2603-16378 streams/journals/corr

Jérémy Berthomieu Edern Gillot Mohab Safey El Din Computing points in connected components defined by a real inequation: algorithms, complexity and implementations, Part I. 2026 May abs/2605.18110 CoRR https://doi.org/10.48550/arXiv.2605.18110 db/journals/corr/corr2605.html#abs-2605-18110 streams/journals/corr

Simone Naldi Mohab Safey El Din Adrien Taylor Weijia Wang Solving generic parametric linear matrix inequalities. 267-276 2025 ISSAC https://doi.org/10.1145/3747199.3747570 conf/issac/2025 db/conf/issac/issac2025.html#NaldiDTW25

Simone Naldi Mohab Safey El Din Adrien Taylor Weijia Wang Solving generic parametric linear matrix inequalities. 2025 March abs/2503.01487 CoRR https://doi.org/10.48550/arXiv.2503.01487 db/journals/corr/corr2503.html#abs-2503-01487 streams/journals/corr

Mohab Safey El Din Georgy Scholten Emmanuel Trélat Probabilistic algorithm for computing all local minimizers of Morse functions on a compact domain. 2025 July abs/2507.13071 CoRR https://doi.org/10.48550/arXiv.2507.13071 db/journals/corr/corr2507.html#abs-2507-13071 streams/journals/corr

Jesse Elliott Mark Giesbrecht Edern Gillot Mohab Safey El Din Éric Schost Refined bit complexity for the computation of at least onepoint per connected component of a smooth completeintersection real algebraic set. 2025 August abs/2508.20607 CoRR https://doi.org/10.48550/arXiv.2508.20607 db/journals/corr/corr2508.html#abs-2508-20607 streams/journals/corr

Rémi Prébet Mohab Safey El Din Éric Schost Computing roadmaps in unbounded smooth real algebraic sets I: Connectivity results. 102234 2024 120 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2023.102234 db/journals/jsc/jsc120.html#PrebetDS24

Alessandro Colotti Jorge García Fontán Alexandre Goldsztejn Sébastien Briot François Chaumette Olivier Kermorgant Mohab Safey El Din Determination of All Stable and Unstable Equilibria for Image-Point-Based Visual Servoing. 3406-3424 2024 40 IEEE Trans. Robotics https://doi.org/10.1109/TRO.2024.3422050 db/journals/trob/trob40.html#ColottiFGBCKD24 streams/journals/trob

Sriram Gopalakrishnan Vincent Neiger Mohab Safey El Din Optimized Gröbner basis algorithms for maximal determinantal ideals and critical point computations. 2024 ISSAC https://doi.org/10.1145/3666000.3669713 https://www.wikidata.org/entity/Q131122422 conf/issac/2024 db/conf/issac/issac2024.html#GopalakrishnanN24 400-409 Louis Gaillard Mohab Safey El Din Solving parameter-dependent semi-algebraic systems. 2024 ISSAC https://doi.org/10.1145/3666000.3669718 https://www.wikidata.org/entity/Q131122419 conf/issac/2024 db/conf/issac/issac2024.html#GaillardD24 447-456

Rémi Prébet Mohab Safey El Din Éric Schost Computing roadmaps in unbounded smooth real algebraic sets II: algorithm and complexity. 2024 abs/2402.03111 CoRR https://doi.org/10.48550/arXiv.2402.03111 db/journals/corr/corr2402.html#abs-2402-03111

Sriram Gopalakrishnan Vincent Neiger Mohab Safey El Din Optimized Gröbner basis algorithms for maximal determinantal ideals and critical point computations. 2024 abs/2402.07353 CoRR https://doi.org/10.48550/arXiv.2402.07353 db/journals/corr/corr2402.html#abs-2402-07353

Louis Gaillard Mohab Safey El Din Solving parameter-dependent semi-algebraic systems. 2024 abs/2402.07782 CoRR https://doi.org/10.48550/arXiv.2402.07782 db/journals/corr/corr2402.html#abs-2402-07782

Didier Henrion Jared Miller Mohab Safey El Din Algebraic Proofs of Path Disconnectedness using Time-Dependent Barrier Functions. 2024 abs/2404.06985 CoRR https://doi.org/10.48550/arXiv.2404.06985 db/journals/corr/corr2404.html#abs-2404-06985

Jose Capco Mohab Safey El Din Josef Schicho Positive dimensional parametric polynomial systems, connectivity queries and applications in robotics. 320-345 2023 115 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2022.08.008 db/journals/jsc/jsc115.html#CapcoDS23

Jean-Charles Faugère George Labahn Mohab Safey El Din Éric Schost Thi Xuan Vu Computing critical points for invariant algebraic systems. 365-399 2023 116 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2022.10.002 db/journals/jsc/jsc116.html#FaugereLDSV23

Christian Eder Pierre Lairez Rafael Mohr Mohab Safey El Din A signature-based algorithm for computing the nondegenerate locus of a polynomial system. 1-21 2023 119 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2023.02.001 db/journals/jsc/jsc119.html#EderLMD23

Victor Magron Mohab Safey El Din Trung Hieu Vu Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients. 63-88 2023 March 33 SIAM J. Optim. 1 https://doi.org/10.1137/21m1436245 db/journals/siamjo/siamjo33.html#MagronDV23

Alin Bostan Hadrien Notarantonio Mohab Safey El Din Fast Algorithms for Discrete Differential Equations. 80-89 2023 ISSAC https://doi.org/10.1145/3597066.3597103 conf/issac/2023 db/conf/issac/issac2023.html#BostanND23 Christian Eder Pierre Lairez Rafael Mohr Mohab Safey El Din A Direttissimo Algorithm for Equidimensional Decomposition. 260-269 2023 ISSAC https://doi.org/10.1145/3597066.3597069 https://www.wikidata.org/entity/Q130910294 conf/issac/2023 db/conf/issac/issac2023.html#EderLMD23 Sriram Gopalakrishnan Vincent Neiger Mohab Safey El Din Refined F5 Algorithms for Ideals of Minors of Square Matrices. 270-279 2023 ISSAC https://doi.org/10.1145/3597066.3597077 https://www.wikidata.org/entity/Q131124619 conf/issac/2023 db/conf/issac/issac2023.html#GopalakrishnanN23 George Labahn Cordian Riener Mohab Safey El Din Éric Schost Thi Xuan Vu Faster real root decision algorithm for symmetric polynomials. 452-460 2023 ISSAC https://doi.org/10.1145/3597066.3597097 https://www.wikidata.org/entity/Q131124591 conf/issac/2023 db/conf/issac/issac2023.html#LabahnRDSV23

Sriram Gopalakrishnan Vincent Neiger Mohab Safey El Din Refined $F_5$ Algorithms for Ideals of Minors of Square Matrices. 2023 abs/2302.05375 CoRR https://doi.org/10.48550/arXiv.2302.05375 db/journals/corr/corr2302.html#abs-2302-05375

Alin Bostan Hadrien Notarantonio Mohab Safey El Din Fast Algorithms for Discrete Differential Equations. 2023 abs/2302.06203 CoRR https://doi.org/10.48550/arXiv.2302.06203 db/journals/corr/corr2302.html#abs-2302-06203

Christian Eder Pierre Lairez Rafael Mohr Mohab Safey El Din A Direttissimo Algorithm for Equidimensional Decomposition. 2023 abs/2302.08174 CoRR https://doi.org/10.48550/arXiv.2302.08174 db/journals/corr/corr2302.html#abs-2302-08174

George Labahn Cordian Riener Mohab Safey El Din Éric Schost Thi Xuan Vu Faster real root decision algorithm for symmetric polynomials. 2023 abs/2306.03855 CoRR https://doi.org/10.48550/arXiv.2306.03855 db/journals/corr/corr2306.html#abs-2306-03855

Jorge García Fontán Alessandro Colotti Sébastien Briot Alexandre Goldsztejn Mohab Safey El Din Computer algebra methods for polynomial system solving at the service of image-based visual servoing. 36-40 2022 56 ACM Commun. Comput. Algebra 2 https://doi.org/10.1145/3572867.3572871 db/journals/cca/cca56.html#FontanCBGD22

Christian Eder Pierre Lairez Rafael Mohr Mohab Safey El Din Towards signature-based gröbner basis algorithms for computing the nondegenerate locus of a polynomial system. 41-45 2022 56 ACM Commun. Comput. Algebra 2 https://doi.org/10.1145/3572867.3572872 db/journals/cca/cca56.html#EderLMD22

Jorge García Fontán Abhilash Nayak Sébastien Briot Mohab Safey El Din Singularity Analysis for the Perspective-Four and Five-Line Problems. 909-932 2022 130 Int. J. Comput. Vis. 4 https://doi.org/10.1007/s11263-021-01567-4 db/journals/ijcv/ijcv130.html#FontanNBD22

Jérémy Berthomieu Mohab Safey El Din Guessing Gröbner bases of structured ideals of relations of sequences. 1-26 2022 111 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2021.11.001 db/journals/jsc/jsc111.html#BerthomieuD22

Huu Phuoc Le Mohab Safey El Din Solving parametric systems of polynomial equations over the reals through Hermite matrices. 25-61 2022 112 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2021.12.002 https://www.wikidata.org/entity/Q114154451 db/journals/jsc/jsc112.html#LeD22

Pavel Trutman Mohab Safey El Din Didier Henrion Tomás Pajdla Globally Optimal Solution to Inverse Kinematics of 7DOF Serial Manipulator. 6012-6019 2022 7 IEEE Robotics Autom. Lett. 3 https://doi.org/10.1109/LRA.2022.3163444 db/journals/ral/ral7.html#TrutmanDHP22

Alin Bostan Frédéric Chyzak Hadrien Notarantonio Mohab Safey El Din Algorithms for Discrete Differential Equations of Order 1. 101-110 2022 ISSAC https://doi.org/10.1145/3476446.3535471 https://www.wikidata.org/entity/Q131126906 conf/issac/2022 db/conf/issac/issac2022.html#BostanCND22 Victor Magron Mohab Safey El Din Markus Schweighofer Trung Hieu Vu Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients. 325-332 2022 ISSAC https://doi.org/10.1145/3476446.3535480 https://www.wikidata.org/entity/Q131120501 conf/issac/2022 db/conf/issac/issac2022.html#MagronDSV22 Jérémy Berthomieu Vincent Neiger Mohab Safey El Din Faster Change of Order Algorithm for Gröbner Bases under Shape and Stability Assumptions. 409-418 2022 ISSAC https://doi.org/10.1145/3476446.3535484 https://www.wikidata.org/entity/Q131126918 conf/issac/2022 db/conf/issac/issac2022.html#BerthomieuND22 Damien Chablat Rémi Prébet Mohab Safey El Din Durgesh Haribhau Salunkhe Philippe Wenger Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry. 439-448 2022 ISSAC https://doi.org/10.1145/3476446.3535477 https://www.wikidata.org/entity/Q131121815 conf/issac/2022 db/conf/issac/issac2022.html#ChablatPDSW22

Victor Magron Mohab Safey El Din Markus Schweighofer Trung Hieu Vu Exact SOHS decompositions of trigonometric univariate polynomials with Gaussian coefficients. 2022 abs/2202.06544 CoRR https://arxiv.org/abs/2202.06544 db/journals/corr/corr2202.html#abs-2202-06544

Jérémy Berthomieu Vincent Neiger Mohab Safey El Din Faster change of order algorithm for Gröbner bases under shape and stability assumptions. 2022 abs/2202.09226 CoRR https://arxiv.org/abs/2202.09226 db/journals/corr/corr2202.html#abs-2202-09226

Jérémy Berthomieu Christian Eder Mohab Safey El Din New efficient algorithms for computing Gröbner bases of saturation ideals (F4SAT) and colon ideals (Sparse-FGLM-colon). 2022 abs/2202.13387 CoRR https://arxiv.org/abs/2202.13387 db/journals/corr/corr2202.html#abs-2202-13387

Christian Eder Pierre Lairez Rafael Mohr Mohab Safey El Din A Signature-based Algorithm for Computing the Nondegenerate Locus of a Polynomial System. 2022 abs/2202.13784 CoRR https://arxiv.org/abs/2202.13784 db/journals/corr/corr2202.html#abs-2202-13784

Rémi Prébet Mohab Safey El Din Éric Schost Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results. 2022 abs/2203.03961 CoRR https://doi.org/10.48550/arXiv.2203.03961 db/journals/corr/corr2203.html#abs-2203-03961

Damien Chablat Rémi Prébet Mohab Safey El Din Durgesh Haribhau Salunkhe Philippe Wenger Deciding cuspidality of manipulators through computer algebra and algorithms in real algebraic geometry. 2022 abs/2203.04578 CoRR https://doi.org/10.48550/arXiv.2203.04578 db/journals/corr/corr2203.html#abs-2203-04578

Alin Bostan Jérémy Berthomieu Andrew Ferguson Mohab Safey El Din Gröbner bases and critical values: The asymptotic combinatorics of determinantal systems. 2022 abs/2203.10021 CoRR https://doi.org/10.48550/arXiv.2203.10021 db/journals/corr/corr2203.html#abs-2203-10021

Béatrice Bérard Serge Haddad Claudine Picaronny Mohab Safey El Din Mathieu Sassolas Polynomial interrupt timed automata: Verification and expressiveness. 104580 2021 277 Inf. Comput. https://doi.org/10.1016/j.ic.2020.104580 db/journals/iandc/iandc277.html#BerardHPDS21

Beatriz Pascual-Escudero Abhilash Nayak Sébastien Briot Olivier Kermorgant Philippe Martinet Mohab Safey El Din François Chaumette Complete Singularity Analysis for the Perspective-Four-Point Problem. 1217-1237 2021 129 Int. J. Comput. Vis. 4 https://doi.org/10.1007/s11263-020-01420-0 db/journals/ijcv/ijcv129.html#Pascual-Escudero21

George Labahn Mohab Safey El Din Éric Schost Thi Xuan Vu Homotopy techniques for solving sparse column support determinantal polynomial systems. 101557 2021 66 J. Complex. https://doi.org/10.1016/j.jco.2021.101557 db/journals/jc/jc66.html#LabahnDSV21

Mohab Safey El Din Zhi-Hong Yang Lihong Zhi Computing real radicals and <i>S</i>-radicals of polynomial systems. 259-278 2021 102 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2019.10.018 https://www.wikidata.org/entity/Q126840816 db/journals/jsc/jsc102.html#DinYZ21

Jonathan D. Hauenstein Mohab Safey El Din Éric Schost Thi Xuan Vu Solving determinantal systems using homotopy techniques. 754-804 2021 104 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2020.09.008 db/journals/jsc/jsc104.html#HauensteinDSV21

Didier Henrion Simone Naldi Mohab Safey El Din Exact algorithms for semidefinite programs with degenerate feasible set. 942-959 2021 104 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2020.11.001 db/journals/jsc/jsc104.html#HenrionND21

Victor Magron Mohab Safey El Din On exact Reznick, Hilbert-Artin and Putinar's representations. 221-250 2021 107 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2021.03.005 db/journals/jsc/jsc107.html#MagronD21

Jérémy Berthomieu Christian Eder Mohab Safey El Din msolve: A Library for Solving Polynomial Systems. 51-58 2021 ISSAC https://doi.org/10.1145/3452143.3465545 https://www.wikidata.org/entity/Q131128350 conf/issac/2021 db/conf/issac/issac2021.html#BerthomieuED21 Pierre Lairez Mohab Safey El Din Computing the Dimension of Real Algebraic Sets. 257-264 2021 ISSAC https://doi.org/10.1145/3452143.3465551 https://www.wikidata.org/entity/Q131128346 conf/issac/2021 db/conf/issac/issac2021.html#LairezD21 Huu Phuoc Le Mohab Safey El Din Faster One Block Quantifier Elimination for Regular Polynomial Systems of Equations. 265-272 2021 ISSAC https://doi.org/10.1145/3452143.3465546 conf/issac/2021 db/conf/issac/issac2021.html#LeD21

Huu Phuoc Le Mohab Safey El Din Faster one block quantifier elimination for regular polynomial systems of equations. 2021 abs/2103.13735 CoRR https://arxiv.org/abs/2103.13735 db/journals/corr/corr2103.html#abs-2103-13735

Jérémy Berthomieu Andrew Ferguson Mohab Safey El Din On the computation of asymptotic critical values of polynomial maps and applications. 2021 abs/2104.00913 CoRR https://arxiv.org/abs/2104.00913 db/journals/corr/corr2104.html#abs-2104-00913

Jérémy Berthomieu Christian Eder Mohab Safey El Din msolve: A Library for Solving Polynomial Systems. 2021 abs/2104.03572 CoRR https://arxiv.org/abs/2104.03572 db/journals/corr/corr2104.html#abs-2104-03572

Pierre Lairez Mohab Safey El Din Computing the dimension of a real algebraic set. 2021 abs/2105.10255 CoRR https://arxiv.org/abs/2105.10255 db/journals/corr/corr2105.html#abs-2105-10255

Victor Magron Mohab Safey El Din Trung Hieu Vu Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients. 2021 abs/2107.11825 CoRR https://arxiv.org/abs/2107.11825 db/journals/corr/corr2107.html#abs-2107-11825

Didier Henrion Simone Naldi Mohab Safey El Din Real root finding for low rank linear matrices. 101-133 2020 31 Appl. Algebra Eng. Commun. Comput. 2 https://doi.org/10.1007/s00200-019-00396-w https://www.wikidata.org/entity/Q114692906 db/journals/aaecc/aaecc31.html#HenrionND20

Jérémy Berthomieu Andrew Ferguson Mohab Safey El Din Towards fast one-block quantifier elimination through generalised critical values. 109-113 2020 54 ACM Commun. Comput. Algebra 3 https://doi.org/10.1145/3457341.3457348 db/journals/cca/cca54.html#BerthomieuFD20

Mohab Safey El Din Chee Yap Special Issue on Symbolic and Algebraic Computation: ISSAC 2017. 1-2 2020 98 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2019.07.003 https://www.wikidata.org/entity/Q127478724 db/journals/jsc/jsc98.html#DinY20

Jose Capco Mohab Safey El Din Josef Schicho Robots, computer algebra and eight connected components. 62-69 2020 ISSAC https://doi.org/10.1145/3373207.3404048 https://www.wikidata.org/entity/Q131127229 conf/issac/2020 db/conf/issac/issac2020.html#CapcoDS20 Huu Phuoc Le Mohab Safey El Din Timo de Wolff Computing the real isolated points of an algebraic hypersurface. 297-304 2020 ISSAC https://doi.org/10.1145/3373207.3404049 https://www.wikidata.org/entity/Q131130477 conf/issac/2020 db/conf/issac/issac2020.html#LeDW20

Pavel Trutman Mohab Safey El Din Didier Henrion Tomás Pajdla Globally Optimal Solution to Inverse Kinematics of 7DOF Serial Manipulator. 2020 abs/2007.12550 CoRR https://arxiv.org/abs/2007.12550 db/journals/corr/corr2007.html#abs-2007-12550

Huu Phuoc Le Mohab Safey El Din Timo de Wolff Computing the Real Isolated Points of an Algebraic Hypersurface. 2020 abs/2008.10331 CoRR https://arxiv.org/abs/2008.10331 db/journals/corr/corr2008.html#abs-2008-10331

Jose Capco Mohab Safey El Din Josef Schicho Robots, computer algebra and eight connected components. 2020 abs/2008.13392 CoRR https://arxiv.org/abs/2008.13392 db/journals/corr/corr2008.html#abs-2008-13392

George Labahn Mohab Safey El Din Éric Schost Thi Xuan Vu Homotopy techniques for solving sparse column support determinantal polynomial systems. 2020 abs/2009.00844 CoRR https://arxiv.org/abs/2009.00844 db/journals/corr/corr2009.html#abs-2009-00844

Jean-Charles Faugère George Labahn Mohab Safey El Din Éric Schost Thi Xuan Vu Computing critical points for invariant algebraic systems. 2020 abs/2009.00847 CoRR https://arxiv.org/abs/2009.00847 db/journals/corr/corr2009.html#abs-2009-00847

Jérémy Berthomieu Mohab Safey El Din Guessing Gr{ö}bner Bases of Structured Ideals of Relations of Sequences. 2020 abs/2009.05248 CoRR https://arxiv.org/abs/2009.05248 db/journals/corr/corr2009.html#abs-2009-05248

Hoon Hong James Rohal Mohab Safey El Din Éric Schost Connectivity in Semi-Algebraic Sets I. 2020 abs/2011.02162 CoRR https://arxiv.org/abs/2011.02162 db/journals/corr/corr2011.html#abs-2011-02162

Huu Phuoc Le Mohab Safey El Din Solving parametric systems of polynomial equations over the reals through Hermite matrices. 2020 abs/2011.14136 CoRR https://arxiv.org/abs/2011.14136 db/journals/corr/corr2011.html#abs-2011-14136

Victor Magron Mohab Safey El Din Markus Schweighofer Algorithms for weighted sum of squares decomposition of non-negative univariate polynomials. 200-220 2019 93 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2018.06.005 db/journals/jsc/jsc93.html#MagronDS19

Didier Henrion Simone Naldi Mohab Safey El Din SPECTRA - a Maple library for solving linear matrix inequalities in exact arithmetic. 62-78 2019 34 Optim. Methods Softw. 1 https://doi.org/10.1080/10556788.2017.1341505 db/journals/oms/oms34.html#HenrionND19

Pierre Lairez Marc Mezzarobba Mohab Safey El Din Computing the Volume of Compact Semi-Algebraic Sets. 259-266 2019 ISSAC https://doi.org/10.1145/3326229.3326262 conf/issac/2019 db/conf/issac/issac2019.html#LairezMD19

Pierre Lairez Marc Mezzarobba Mohab Safey El Din Computing the volume of compact semi-algebraic sets. 2019 abs/1904.11705 CoRR http://arxiv.org/abs/1904.11705 db/journals/corr/corr1904.html#abs-1904-11705

Victor Magron Mohab Safey El Din Realcertify: a maple package for certifying non-negativity. 34-37 2018 52 ACM Commun. Comput. Algebra 2 https://doi.org/10.1145/3282678.3282681 db/journals/cca/cca52.html#MagronD18

Mohab Safey El Din Éric Schost Bit complexity for multi-homogeneous polynomial system solving - Application to polynomial minimization. 176-206 2018 87 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2017.08.001 db/journals/jsc/jsc87.html#DinS18

Hamza Fawzi Mohab Safey El Din A Lower Bound on the Positive Semidefinite Rank of Convex Bodies. 126-139 2018 2 SIAM J. Appl. Algebra Geom. 1 https://doi.org/10.1137/17M1142570 https://www.wikidata.org/entity/Q130159436 db/journals/siaga/siaga2.html#FawziD18

Didier Henrion Simone Naldi Mohab Safey El Din Exact Algorithms for Semidefinite Programs with Degenerate Feasible Set. 191-198 2018 ISSAC https://doi.org/10.1145/3208976.3209022 https://www.wikidata.org/entity/Q131130148 conf/issac/2018 db/conf/issac/issac2018.html#HenrionND18 Victor Magron Mohab Safey El Din On Exact Polya and Putinar's Representations. 279-286 2018 ISSAC https://doi.org/10.1145/3208976.3208986 https://www.wikidata.org/entity/Q131125470 conf/issac/2018 db/conf/issac/issac2018.html#MagronD18 Cordian Riener Mohab Safey El Din Real Root Finding for Equivariant Semi-algebraic Systems. 335-342 2018 ISSAC https://doi.org/10.1145/3208976.3209023 https://www.wikidata.org/entity/Q131136635 conf/issac/2018 db/conf/issac/issac2018.html#RienerD18 Mohab Safey El Din Zhi-Hong Yang Lihong Zhi On the Complexity of Computing Real Radicals of Polynomial Systems. 351-358 2018 ISSAC https://doi.org/10.1145/3208976.3209002 https://www.wikidata.org/entity/Q131136611 conf/issac/2018 db/conf/issac/issac2018.html#DinYZ18

Didier Henrion Simone Naldi Mohab Safey El Din Exact algorithms for semidefinite programs with degenerate feasible set. 2018 abs/1802.02834 CoRR http://arxiv.org/abs/1802.02834 db/journals/corr/corr1802.html#abs-1802-02834

Victor Magron Mohab Safey El Din On Exact Polya and Putinar's Representations. 2018 abs/1802.10339 CoRR http://arxiv.org/abs/1802.10339 db/journals/corr/corr1802.html#abs-1802-10339

Jonathan D. Hauenstein Mohab Safey El Din Éric Schost Thi Xuan Vu Solving determinantal systems using homotopy techniques. 2018 abs/1802.10409 CoRR http://arxiv.org/abs/1802.10409 db/journals/corr/corr1802.html#abs-1802-10409

Victor Magron Mohab Safey El Din RealCertify: a Maple package for certifying non-negativity. 2018 abs/1805.02201 CoRR http://arxiv.org/abs/1805.02201 db/journals/corr/corr1805.html#abs-1805-02201

Cordian Riener Mohab Safey El Din Real root finding for equivariant semi-algebraic systems. 2018 abs/1806.08121 CoRR http://arxiv.org/abs/1806.08121 db/journals/corr/corr1806.html#abs-1806-08121

Victor Magron Mohab Safey El Din On Exact Polya, Hilbert-Artin and Putinar's Representations. 2018 abs/1811.10062 CoRR http://arxiv.org/abs/1811.10062 db/journals/corr/corr1811.html#abs-1811-10062

Mohab Safey El Din Éric Schost A Nearly Optimal Algorithm for Deciding Connectivity Queries in Smooth and Bounded Real Algebraic Sets. 48:1-48:37 2017 63 J. ACM 6 https://doi.org/10.1145/2996450 db/journals/jacm/jacm63.html#DinS17

Michael A. Burr Chee K. Yap Mohab Safey El Din Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC 2017, Kaiserslautern, Germany, July 25-28, 2017 ISSAC ACM 2017 978-1-4503-5064-8 https://doi.org/10.1145/3087604 db/conf/issac/issac2017.html

Hamza Fawzi Mohab Safey El Din A lower bound on the positive semidefinite rank of convex bodies. 2017 abs/1705.06996 CoRR http://arxiv.org/abs/1705.06996 db/journals/corr/corr1705.html#FawziD17

Victor Magron Mohab Safey El Din Markus Schweighofer Algorithms for Weighted Sums of Squares Decomposition of Non-negative Univariate Polynomials. 2017 abs/1706.03941 CoRR http://arxiv.org/abs/1706.03941 db/journals/corr/corr1706.html#MagronDS17

Didier Henrion Simone Naldi Mohab Safey El Din Real root finding for determinants of linear matrices. 205-238 2016 74 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2015.06.010 db/journals/jsc/jsc74.html#HenrionND16

Jean-Charles Faugère Mohab Safey El Din Thibaut Verron On the complexity of computing Gröbner bases for weighted homogeneous systems. 107-141 2016 76 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2015.12.001 db/journals/jsc/jsc76.html#FaugereDV16

Didier Henrion Simone Naldi Mohab Safey El Din Exact Algorithms for Linear Matrix Inequalities. 2512-2539 2016 26 SIAM J. Optim. 4 https://doi.org/10.1137/15M1036543 db/journals/siamjo/siamjo26.html#HenrionND16

Bernard Bonnard Jean-Charles Faugère Alain Jacquemard Mohab Safey El Din Thibaut Verron Determinantal Sets, Singularities and Application to Optimal Control in Medical Imagery. 103-110 2016 ISSAC https://doi.org/10.1145/2930889.2930916 conf/issac/2016 db/conf/issac/issac2016.html#BonnardFJDV16 Mohab Safey El Din Pierre-Jean Spaenlehauer Critical Point Computations on Smooth Varieties: Degree and Complexity Bounds. 183-190 2016 ISSAC https://doi.org/10.1145/2930889.2930929 conf/issac/2016 db/conf/issac/issac2016.html#DinS16

Bernard Bonnard Jean-Charles Faugère Alain Jacquemard Mohab Safey El Din Thibaut Verron Determinantal sets, singularities and application to optimal control in medical imagery. 2016 abs/1605.00887 CoRR http://arxiv.org/abs/1605.00887 db/journals/corr/corr1605.html#BonnardFJDV16

Mohab Safey El Din Pierre-Jean Spaenlehauer Critical Point Computations on Smooth Varieties: Degree and Complexity bounds. 2016 abs/1605.02518 CoRR http://arxiv.org/abs/1605.02518 db/journals/corr/corr1605.html#DinS16

Mohab Safey El Din Éric Schost Bit complexity for multi-homogeneous polynomial system solving Application to polynomial minimization. 2016 abs/1605.07433 CoRR http://arxiv.org/abs/1605.07433 db/journals/corr/corr1605.html#DinS16a

Didier Henrion Simone Naldi Mohab Safey El Din SPECTRA -a Maple library for solving linear matrix inequalities in exact arithmetic. 2016 abs/1611.01947 CoRR http://arxiv.org/abs/1611.01947 db/journals/corr/corr1611.html#HenrionND16

Ivan Bannwarth Mohab Safey El Din Probabilistic Algorithm for Computing the Dimension of Real Algebraic Sets. 37-44 2015 ISSAC https://doi.org/10.1145/2755996.2756670 conf/issac/2015 db/conf/issac/issac2015.html#BannwarthD15 Feng Guo 0007 Mohab Safey El Din Chu Wang Lihong Zhi Optimizing a Parametric Linear Function over a Non-compact Real Algebraic Variety. 205-212 2015 ISSAC https://doi.org/10.1145/2755996.2756666 conf/issac/2015 db/conf/issac/issac2015.html#GuoDWZ15 Didier Henrion Simone Naldi Mohab Safey El Din Real Root Finding for Rank Defects in Linear Hankel Matrices. 221-228 2015 ISSAC https://doi.org/10.1145/2755996.2756667 conf/issac/2015 db/conf/issac/issac2015.html#HenrionND15 Béatrice Bérard Serge Haddad Claudine Picaronny Mohab Safey El Din Mathieu Sassolas Polynomial Interrupt Timed Automata. 20-32 2015 RP https://doi.org/10.1007/978-3-319-24537-9_3 conf/rp/2015 db/conf/rp/rp2015.html#BerardHPDS15

Didier Henrion Simone Naldi Mohab Safey El Din Real root finding for rank defects in linear Hankel matrices. 2015 abs/1502.02473 CoRR http://arxiv.org/abs/1502.02473 db/journals/corr/corr1502.html#HenrionND15

Béatrice Bérard Serge Haddad Claudine Picaronny Mohab Safey El Din Mathieu Sassolas Polynomial Interrupt Timed Automata. 2015 abs/1504.04541 CoRR http://arxiv.org/abs/1504.04541 db/journals/corr/corr1504.html#BerardHPDS15

Didier Henrion Simone Naldi Mohab Safey El Din Real root finding for low rank linear matrices. 2015 abs/1506.05897 CoRR http://arxiv.org/abs/1506.05897 db/journals/corr/corr1506.html#HenrionND15a

Didier Henrion Simone Naldi Mohab Safey El Din Exact algorithms for linear matrix inequalities. 2015 abs/1508.03715 CoRR http://arxiv.org/abs/1508.03715 db/journals/corr/corr1508.html#HenrionND15b

Saugata Basu Marie-Françoise Roy Mohab Safey El Din Éric Schost A Baby Step-Giant Step Roadmap Algorithm for General Algebraic Sets. 1117-1172 2014 14 Found. Comput. Math. 6 https://doi.org/10.1007/s10208-014-9212-1 db/journals/focm/focm14.html#BasuRDS14

Bernd Bank Marc Giusti Joos Heintz Mohab Safey El Din Intrinsic complexity estimates in polynomial optimization. 430-443 2014 30 J. Complex. 4 https://doi.org/10.1016/j.jco.2014.02.005 db/journals/jc/jc30.html#BankGHD14

Aurélien Greuet Mohab Safey El Din Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set. 1313-1343 2014 24 SIAM J. Optim. 3 https://doi.org/10.1137/130931308 db/journals/siamjo/siamjo24.html#GreuetD14

Alin Bostan Thierry Combot Mohab Safey El Din Computing necessary integrability conditions for planar parametrized homogeneous potentials. 67-74 2014 ISSAC https://doi.org/10.1145/2608628.2608662 conf/issac/2014 db/conf/issac/issac2014.html#BostanCD14

Alin Bostan Thierry Combot Mohab Safey El Din Computing necessary integrability conditions for planar parametrized homogeneous potentials. 2014 abs/1405.5342 CoRR http://arxiv.org/abs/1405.5342 db/journals/corr/corr1405.html#BostanCM14

Didier Henrion Simone Naldi Mohab Safey El Din Real root finding for determinants of linear matrices. 2014 abs/1412.5873 CoRR http://arxiv.org/abs/1412.5873 db/journals/corr/corr1412.html#HenrionND14

Jean-Charles Faugère Mohab Safey El Din Thibaut Verron On the complexity of computing Gr{ö}bner bases for weighted homogeneous systems. 2014 abs/1412.7547 CoRR http://arxiv.org/abs/1412.7547 db/journals/corr/corr1412.html#FaugereDV14

Jean-Charles Faugère Mohab Safey El Din Pierre-Jean Spaenlehauer On the complexity of the generalized MinRank problem. 30-58 2013 55 J. Symb. Comput. https://doi.org/10.1016/j.jsc.2013.03.004 db/journals/jsc/jsc55.html#FaugereDS13

Mohab Safey El Din Critical point methods and effective real algebraic geometry: new results and trends. 5-6 2013 ISSAC https://doi.org/10.1145/2465506.2465928 conf/issac/2013 db/conf/issac/issac2013.html#Din13 Jean-Charles Faugère Mohab Safey El Din Thibaut Verron On the complexity of computing gröbner bases for quasi-homogeneous systems. 189-196 2013 ISSAC https://doi.org/10.1145/2465506.2465943 conf/issac/2013 db/conf/issac/issac2013.html#FaugereDV13 Qingdong Guo Mohab Safey El Din Lihong Zhi Computing rational solutions of linear matrix inequalities. 197-204 2013 ISSAC https://doi.org/10.1145/2465506.2465949 conf/issac/2013 db/conf/issac/issac2013.html#GuoDZ13

Jean-Charles Faugère Mohab Safey El Din Thibaut Verron Computing Gröbner bases for quasi-homogeneous systems http://arxiv.org/abs/1301.5612 2013 CoRR abs/1301.5612 db/journals/corr/corr1301.html#abs-1301-5612

Mohab Safey El Din Elias P. Tsigaridas A probabilistic algorithm to compute the real dimension of a semi-algebraic set http://arxiv.org/abs/1304.1928 2013 CoRR abs/1304.1928 db/journals/corr/corr1304.html#abs-1304-1928

Bernd Bank Marc Giusti Joos Heintz Mohab Safey El Din Intrinsic complexity estimates in polynomial optimization http://arxiv.org/abs/1304.5214 2013 CoRR abs/1304.5214 db/journals/corr/corr1304.html#abs-1304-5214

Mohab Safey El Din Éric Schost A nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets. 2013 CoRR http://arxiv.org/abs/1307.7836 abs/1307.7836 db/journals/corr/corr1307.html#DinS13

Aurélien Greuet Mohab Safey El Din Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set. 2013 CoRR http://arxiv.org/abs/1307.8281 abs/1307.8281 db/journals/corr/corr1307.html#GreuetD13

Aurélien Greuet Feng Guo 0007 Mohab Safey El Din Lihong Zhi Global optimization of polynomials restricted to a smooth variety using sums of squares. 503-518 2012 47 J. Symb. Comput. 5 https://doi.org/10.1016/j.jsc.2011.12.003 db/journals/jsc/jsc47.html#GreuetGDZ12

Hoon Hong Mohab Safey El Din Variant quantifier elimination. 883-901 2012 47 J. Symb. Comput. 7 https://doi.org/10.1016/j.jsc.2011.05.014 https://www.wikidata.org/entity/Q57431347 db/journals/jsc/jsc47.html#HongD12

Jean-Charles Faugère Mohab Safey El Din Pierre-Jean Spaenlehauer Critical points and Gröbner bases: the unmixed case. 162-169 2012 ISSAC https://doi.org/10.1145/2442829.2442855 conf/issac/2012 db/conf/issac/issac2012.html#FaugereDS12

Saugata Basu Marie-Françoise Roy Mohab Safey El Din Éric Schost A baby step-giant step roadmap algorithm for general algebraic sets http://arxiv.org/abs/1201.6439 2012 CoRR abs/1201.6439 db/journals/corr/corr1201.html#abs-1201-6439

Jean-Charles Faugère Mohab Safey El Din Pierre-Jean Spaenlehauer Critical Points and Gröbner Bases: the Unmixed Case http://arxiv.org/abs/1202.0179 2012 CoRR abs/1202.0179 db/journals/corr/corr1202.html#abs-1202-0179

Mohab Safey El Din Éric Schost A Baby Steps/Giant Steps Probabilistic Algorithm for Computing Roadmaps in Smooth Bounded Real Hypersurface. 181-220 2011 45 Discret. Comput. Geom. 1 https://doi.org/10.1007/s00454-009-9239-2 db/journals/dcg/dcg45.html#DinS11

Jean-Charles Faugère Mohab Safey El Din Pierre-Jean Spaenlehauer Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree (1, 1): Algorithms and complexity. 406-437 2011 46 J. Symb. Comput. 4 https://doi.org/10.1016/j.jsc.2010.10.014 db/journals/jsc/jsc46.html#FaugereDS11

Aurélien Greuet Mohab Safey El Din Deciding reachability of the infimum of a multivariate polynomial. 131-138 2011 ISSAC https://doi.org/10.1145/1993886.1993910 conf/issac/2011 db/conf/issac/issac2011.html#GreuetD11

Jean-Charles Faugère Mohab Safey El Din Pierre-Jean Spaenlehauer On the Complexity of the Generalized MinRank Problem http://arxiv.org/abs/1112.4411 2011 CoRR abs/1112.4411 db/journals/corr/corr1112.html#abs-1112-4411

Bernd Bank Marc Giusti Joos Heintz Mohab Safey El Din Éric Schost On the geometry of polar varieties. 33-83 2010 21 Appl. Algebra Eng. Commun. Comput. 1 https://doi.org/10.1007/s00200-009-0117-1 db/journals/aaecc/aaecc21.html#BankGHDS10

Mohab Safey El Din Lihong Zhi Computing Rational Points in Convex Semialgebraic Sets and Sum of Squares Decompositions. 2876-2889 2010 20 SIAM J. Optim. 6 https://doi.org/10.1137/090772459 db/journals/siamjo/siamjo20.html#DinZ10

Feng Guo 0007 Mohab Safey El Din Lihong Zhi Global optimization of polynomials using generalized critical values and sums of squares. 107-114 2010 ISSAC https://doi.org/10.1145/1837934.1837960 conf/issac/2010 db/conf/issac/issac2010.html#GuoDZ10 Jean-Charles Faugère Mohab Safey El Din Pierre-Jean Spaenlehauer Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology. 257-264 2010 ISSAC https://doi.org/10.1145/1837934.1837984 conf/issac/2010 db/conf/issac/issac2010.html#FaugereDS10

Jean-Charles Faugère Mohab Safey El Din Pierre-Jean Spaenlehauer Gröbner Bases of Bihomogeneous Ideals generated by Polynomials of Bidegree (1,1): Algorithms and Complexity http://arxiv.org/abs/1001.4004 2010 CoRR abs/1001.4004 db/journals/corr/corr1001.html#abs-1001-4004

Hazel Everett Daniel Lazard Sylvain Lazard Mohab Safey El Din The Voronoi Diagram of Three Lines. 94-130 2009 42 Discret. Comput. Geom. 1 https://doi.org/10.1007/s00454-009-9173-3 db/journals/dcg/dcg42.html#EverettLLD09

Hoon Hong Mohab Safey El Din Variant real quantifier elimination: algorithm and application. 183-190 2009 ISSAC https://doi.org/10.1145/1576702.1576729 conf/issac/2009 db/conf/issac/issac2009.html#HongD09

Mohab Safey El Din Éric Schost A baby steps/giant steps Monte Carlo algorithm for computing roadmaps in smooth compact real hypersurfaces http://arxiv.org/abs/0902.1612 2009 CoRR abs/0902.1612 db/journals/corr/corr0902.html#abs-0902-1612

Mohab Safey El Din Lihong Zhi Computing rational points in convex semi-algebraic sets and SOS decompositions http://arxiv.org/abs/0910.2973 2009 CoRR abs/0910.2973 db/journals/corr/corr0910.html#abs-0910-2973

Mohab Safey El Din Computing the global optimum of a multivariate polynomial over the reals. 71-78 2008 ISSAC https://doi.org/10.1145/1390768.1390781 conf/issac/2008 db/conf/issac/issac2008.html#Din08 Jean-Charles Faugère Guillaume Moroz Fabrice Rouillier Mohab Safey El Din Classification of the perspective-three-point problem, discriminant variety and real solving polynomial systems of inequalities. 79-86 2008 ISSAC https://doi.org/10.1145/1390768.1390782 conf/issac/2008 db/conf/issac/issac2008.html#FaugereMRD08

Mohab Safey El Din Testing Sign Conditions on a Multivariate Polynomial and Applications. 177-207 2007 1 Math. Comput. Sci. 1 https://doi.org/10.1007/s11786-007-0003-9 db/journals/mics/mics1.html#Din07

Mohab Safey El Din Practical and Theoretical Issues for the Computation of Generalized Critical Values of a Polynomial Mapping. 42-56 2007 ASCM https://doi.org/10.1007/978-3-540-87827-8_4 conf/ascm/2007 db/conf/ascm/ascm2007.html#Din07 Hazel Everett Sylvain Lazard Daniel Lazard Mohab Safey El Din The voronoi diagram of three lines. 255-264 2007 conf/compgeom/2007 SCG https://doi.org/10.1145/1247069.1247116 db/conf/compgeom/compgeom2007.html#EverettLLD07 Mohab Safey El Din Philippe Trebuchet POSIX threads polynomials(PTPol): a scalable implementation of univariate arithmetic operations. 104-106 2007 conf/issac/2007pasco PASCO https://doi.org/10.1145/1278177.1278198 db/conf/issac/pasco2007.html#DinT07

Mohab Safey El Din Philippe Trebuchet Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry http://arxiv.org/abs/cs/0610051 2006 CoRR abs/cs/0610051 db/journals/corr/corr0610.html#abs-cs-0610051

Mohab Safey El Din Éric Schost Properness Defects of Projections and Computation of at Least One Point in Each Connected Component of a Real Algebraic Set. 417-430 2004 32 Discret. Comput. Geom. 3 https://doi.org/10.1007/s00454-004-1107-5 db/journals/dcg/dcg32.html#DinS04

Mohab Safey El Din Éric Schost Polar varieties and computation of one point in each connected component of a smooth real algebraic set. 224-231 2003 conf/issac/2003 ISSAC https://doi.org/10.1145/860854.860901 db/conf/issac/issac2003.html#DinS03

Philippe Aubry Fabrice Rouillier Mohab Safey El Din Real Solving for Positive Dimensional Systems. 543-560 2002 34 J. Symb. Comput. 6 https://doi.org/10.1006/jsco.2002.0563 db/journals/jsc/jsc34.html#AubryRD02

Fabrice Rouillier Marie-Françoise Roy Mohab Safey El Din Finding at Least One Point in Each Connected Component of a Real Algebraic Set Defined by a Single Equation. 716-750 2000 16 J. Complex. 4 https://doi.org/10.1006/jcom.2000.0563 db/journals/jc/jc16.html#RouillierRD00

Henri Lombardi Marie-Françoise Roy Mohab Safey El Din New Structure Theorem for Subresultants. 663-689 2000 29 J. Symb. Comput. 4-5 db/journals/jsc/jsc29.html#LombardiRD00 https://doi.org/10.1006/jsco.1999.0322

Fabrice Rouillier Mohab Safey El Din Éric Schost Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study. 26-40 2000 conf/adg/2000 Automated Deduction in Geometry https://doi.org/10.1007/3-540-45410-1_3 db/conf/adg/adg2000.html#RouillierDS00 Philippe Aubry Bernd Bank Ivan Bannwarth Saugata Basu Béatrice Bérard Jérémy Berthomieu Bernard Bonnard Alin Bostan Sébastien Briot Michael A. Burr Jose Capco Damien Chablat François Chaumette Frédéric Chyzak Alessandro Colotti Thierry Combot Christian Eder Jesse Elliott Hazel Everett Jean-Charles Faugère Hamza Fawzi Andrew Ferguson Jorge García Fontán Louis Gaillard Mark Giesbrecht Edern Gillot Marc Giusti Alexandre Goldsztejn Sriram Gopalakrishnan Aurélien Greuet Feng Guo 0007 Qingdong Guo Serge Haddad Jonathan D. Hauenstein Joos Heintz Didier Henrion Hoon Hong Alain Jacquemard Olivier Kermorgant Robin Kouba George Labahn Pierre Lairez Daniel Lazard Sylvain Lazard Huu Phuoc Le Henri Lombardi Victor Magron Philippe Martinet Marc Mezzarobba Jared Miller Rafael Mohr Guillaume Moroz Simone Naldi Abhilash Nayak Vincent Neiger Hadrien Notarantonio Tomás Pajdla Beatriz Pascual-Escudero Claudine Picaronny Rémi Prébet Cordian Riener Elisabetta Rocchi James Rohal Fabrice Rouillier Marie-Françoise Roy Durgesh Haribhau Salunkhe Mathieu Sassolas Josef Schicho Georgy Scholten Éric Schost Markus Schweighofer Pierre-Jean Spaenlehauer Adrien Taylor Philippe Trebuchet Emmanuel Trélat Pavel Trutman Elias P. Tsigaridas Thibaut Verron Thi Xuan Vu Trung Hieu Vu Chu Wang Weijia Wang Philippe Wenger Timo de Wolff Zhi-Hong Yang Chee-Keng YapChee K. YapChee Yap Lihong Zhi