Edit Profile (opens in new tab) Hauenstein, Jonathan D. Co-Author Distance Author ID: hauenstein.jonathan-d Published as: Hauenstein, Jonathan D.; Hauenstein, Jonathan; Hauenstein, J. D. more...less External Links: MGP · ORCID · Wikidata Documents Indexed: 106 Publications since 2008, including 1 Book and 11 Additional arXiv Preprints 2 Contributions as Editor · 1 Further Contribution Software Indexed: 7 Packages Co-Authors: 100 Co-Authors with 104 Joint Publications 3,327 Co-Co-Authors all top 5 Co-Authors 4 single-authored 33 Sommese, Andrew John 18 Wampler, Charles W. II 16 Bates, Daniel J. 11 Mehta, Dhagash 10 Hao, Wenrui 8 Sottile, Frank 7 Peterson, Chris 6 Brake, Daniel A. 6 Daleo, Noah S. 6 Hu, Bei 6 Regan, Margaret H. 6 Szántó, Ágnes 6 Tang, Tingting 5 Liddell, Alan C. jun. 4 Rodriguez, Jose Israel 4 Sherman, Samantha N. 4 Zhang, Yongtao 3 Brake, Danielle A. 3 He, Yang-Hui Evariste 3 Ikenmeyer, Christian 3 Landsberg, Joseph Montague 3 Liu, Yuan 3 Mourrain, Bernard 2 Chen, Tianran 2 Cummings, Joseph 2 Di Rocco, Sandra 2 Dufresne, Emilie 2 Edwards, Parker B. 2 Griffin, Zachary A. 2 Harrington, Heather A. 2 Harris, Katherine M. 2 Haywood, Ian 2 Hein, Nickolas 2 Hong, Hoon 2 Leykin, Anton 2 McCoy, Timothy M. 2 Niemerg, Matthew E. 2 Oeding, Luke 2 Ottaviani, Giorgio Maria 2 Schreyer, Frank-Olaf 2 Sturmfels, Bernd 1 Ayyildiz Akoglu, Tulay 1 Bernal, Edgar A. 1 Bernardi, Alessandra 1 Besana, Gian Mario 1 Bisi, Cinzia 1 Blekherman, Grigoriy 1 Brake, Dani A. 1 Breiding, Paul 1 Brysiewicz, Taylor 1 Chiantini, Luca 1 Cleveland, Joseph 1 Cobian, Emma R. 1 Collins, Joseph B. 1 Coss, Owen 1 Cox, David A. 1 D’Andrea, Carlos 1 Decker, Wolfram 1 Dickenstein, Alicia M. 1 Dörfler, Florian 1 Dzugan, Jeffrey 1 Eklund, David 1 Gäfvert, Oliver 1 Gesmundo, Fulvio 1 Helmer, Martin 1 Hills, Caroline 1 Huang, Rijun 1 Kahle, David J. 1 Kevrekidis, Panayotis G. 1 Kotsireas, Ilias S. 1 Kulkarni, Avinash 1 Lerario, Antonio 1 Levandovskyy, Viktor 1 Lundberg, Erik 1 Mahdi, Adam 1 Manivel, Laurent 1 Matusevich, Laura Felicia 1 McPherson, Sanesha 1 Migliore, Juan Carlos 1 Molzahn, Daniel K. 1 Morse, Anthony Perry 1 Nezhad, Ali Mohammad 1 Ottem, John Christian 1 Pan, Victor Yakovlevich 1 Pessoa, Claudio 1 Pfister, Gerhard 1 Ranestad, Kristian 1 Robol, Leonardo 1 Schenck, Hal 1 Schlenk, Taylor 1 Sertöz, Emre Can 1 Shu, Chi-Wang 1 Sidman, Jessica 1 Simm, Nicholas J. 1 Smyth, Clifford 1 Stariolo, Daniel A. 1 Stillman, Michael Eugene 1 Szendrői, Balázs 1 Terlaky, Tamás 1 Tripoli, Paolo ...and 5 more Co-Authors all top 5 Serials 11 Journal of Symbolic Computation 9 Applied Mathematics and Computation 4 Numerical Algorithms 4 Experimental Mathematics 4 Foundations of Computational Mathematics 4 SIAM Journal on Applied Algebra and Geometry 3 Journal of High Energy Physics 3 Advances in Geometry 2 Mathematics of Computation 2 ACM Transactions on Mathematical Software 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Numerical Analysis 2 Journal of Scientific Computing 2 Vietnam Journal of Mathematics 1 Journal of Computational Physics 1 Nonlinearity 1 Bulletin of the London Mathematical Society 1 Compositio Mathematica 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Mathematics of Operations Research 1 Advances in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Applied Numerical Mathematics 1 Differential Geometry and its Applications 1 Notices of the American Mathematical Society 1 Chaos 1 Mechanism and Machine Theory 1 Nonlinear Analysis. Real World Applications 1 Portugaliae Mathematica. Nova Série 1 Software - Environments - Tools 1 Mathematics in Computer Science 1 Discrete and Continuous Dynamical Systems. Series S 1 ACM Communications in Computer Algebra 1 Journal of Algebraic Statistics 1 CBMS Regional Conference Series in Mathematics 1 Results in Applied Mathematics all top 5 Fields 70 Algebraic geometry (14-XX) 62 Numerical analysis (65-XX) 36 Computer science (68-XX) 23 Commutative algebra (13-XX) 7 Field theory and polynomials (12-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 6 Biology and other natural sciences (92-XX) 5 Partial differential equations (35-XX) 5 Operations research, mathematical programming (90-XX) 4 Functions of a complex variable (30-XX) 4 Quantum theory (81-XX) 3 Ordinary differential equations (34-XX) 2 General and overarching topics; collections (00-XX) 2 Mechanics of particles and systems (70-XX) 1 Mathematical logic and foundations (03-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 87 Publications have been cited 1,286 times in 577 Documents Cited by ▼ Year ▼ Numerically solving polynomial systems with Bertini. Zbl 1295.65057 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 160 2013 Software for numerical algebraic geometry: a paradigm and progress towards its implementation. Zbl 1143.65344 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. II 70 2008 Algorithm 921: alphaCertified: certifying solutions to polynomial systems. Zbl 1365.65148 Hauenstein, Jonathan D.; Sottile, Frank 67 2012 Regeneration homotopies for solving systems of polynomials. Zbl 1221.65121 Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 47 2011 Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core. Zbl 1238.35193 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 45 2012 Adaptive multiprecision path tracking. Zbl 1162.65026 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler II, Charles W. 43 2008 Witness sets of projections. Zbl 1203.14072 Hauenstein, Jonathan D.; Sommese, Andrew J. 35 2010 Isosingular sets and deflation. Zbl 1276.65029 Hauenstein, Jonathan D.; Wampler, Charles W. 34 2013 Numerically computing real points on algebraic sets. Zbl 1269.65048 Hauenstein, Jonathan D. 30 2013 A bootstrapping approach for computing multiple solutions of differential equations. Zbl 1294.65085 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Sommese, Andrew J. 30 2014 A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. Zbl 1349.65558 Hao, Wenrui; Hauenstein, Jonathan D.; Shu, Chi-Wang; Sommese, Andrew J.; Xu, Zhiliang; Zhang, Yong-Tao 30 2013 Continuation along bifurcation branches for a tumor model with a necrotic core. Zbl 1328.92032 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 29 2012 Algebraic boundaries of Hilbert’s SOS cones. Zbl 1273.13043 Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd 28 2012 A numerical local dimension test for points on the solution set of a system of polynomial equations. Zbl 1211.14066 Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 27 2009 A three-dimensional steady-state tumor system. Zbl 1238.92019 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Sommese, Andrew J. 27 2011 Algebraic geometrization of the Kuramoto model: equilibria and stability analysis. Zbl 1374.34115 Mehta, Dhagash; Daleo, Noah S.; Dörfler, Florian; Hauenstein, Jonathan D. 27 2015 Homotopy techniques for tensor decomposition and perfect identifiability. Zbl 1440.15019 Hauenstein, Jonathan D.; Oeding, Luke; Ottaviani, Giorgio; Sommese, Andrew J. 26 2019 Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1303.92044 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; McCoy, Timothy; Sommese, Andrew J. 23 2013 Regenerative cascade homotopies for solving polynomial systems. Zbl 1231.65190 Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 22 2011 Efficient path tracking methods. Zbl 1230.65059 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J. 22 2011 Stepsize control for path tracking. Zbl 1181.65071 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. II 21 2009 Maximum likelihood for matrices with rank constraints. Zbl 1345.62043 Hauenstein, Jonathan; Rodriguez, Jose Israel; Sturmfels, Bernd 19 2014 Membership tests for images of algebraic sets by linear projections. Zbl 1285.14066 Hauenstein, Jonathan D.; Sommese, Andrew J. 17 2013 On deflation and multiplicity structure. Zbl 1387.13063 Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 16 2017 Numerical algebraic geometry: a new perspective on gauge and string theories. Zbl 1397.81271 Mehta, Dhagash; He, Yang-Hui; Hauenstein, Jonathan D. 16 2012 Bertini_real: software for one- and two-dimensional real algebraic sets. Zbl 1437.14005 Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 15 2014 Equations for lower bounds on border rank. Zbl 1361.68098 Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, J. M. 14 2013 Cell decomposition of almost smooth real algebraic surfaces. Zbl 1271.65031 Besana, Gian Mario; Di Rocco, Sandra; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 14 2013 Recovering exact results from inexact numerical data in algebraic geometry. Zbl 1284.14084 Bates, Daniel J.; Hauenstein, Jonathan D.; McCoy, Timothy M.; Peterson, Chris; Sommese, Andrew J. 14 2013 An a posteriori certification algorithm for Newton homotopies. Zbl 1325.65074 Hauenstein, Jonathan D.; Haywood, Ian; Liddell, Alan C. jun. 13 2014 Certified predictor-corrector tracking for Newton homotopies. Zbl 1329.65110 Hauenstein, Jonathan D.; Liddell, Alan C. 13 2016 Experiments on the zeros of harmonic polynomials using certified counting. Zbl 1365.30002 Hauenstein, J. D.; Lerario, A.; Lundberg, E.; Mehta, D. 13 2015 Certifying isolated singular points and their multiplicity structure. Zbl 1345.68286 Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 13 2015 Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\). Zbl 1415.65121 Ayyildiz Akoglu, Tulay; Hauenstein, Jonathan D.; Szanto, Agnes 12 2018 Tensor decomposition and homotopy continuation. Zbl 1377.65057 Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard 12 2017 Numerical elimination and moduli space of vacua. Zbl 1342.83004 Hauenstein, Jonathan; He, Yang-Hui; Mehta, Dhagash 12 2013 Applications of polynomial systems. With contributions by Carlos D’Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, and Jessica Sidman. Zbl 1469.13001 Cox, David A. 11 2020 Unification and extension of intersection algorithms in numerical algebraic geometry. Zbl 1411.65075 Hauenstein, Jonathan D.; Wampler, Charles W. 11 2017 Numerical computation of Galois groups. Zbl 1442.14186 Hauenstein, Jonathan D.; Rodriguez, Jose Israel; Sottile, Frank 11 2018 Polynomials and the exponent of matrix multiplication. Zbl 1404.15020 Chiantini, Luca; Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, Joseph M.; Ottaviani, Giorgio 10 2018 Multiprojective witness sets and a trace test. Zbl 1448.65054 Hauenstein, Jonathan D.; Rodriguez, Jose Israel 10 2020 Mechanism mobility and a local dimension test. Zbl 1273.70004 Wampler, Charles W.; Hauenstein, Jonathan D.; Sommese, Andrew J. 9 2011 A hybrid symbolic-numerical approach to the center-focus problem. Zbl 1372.14053 Mahdi, Adam; Pessoa, Claudio; Hauenstein, Jonathan D. 9 2017 Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme. Zbl 1329.14108 Daleo, Noah S.; Hauenstein, Jonathan D. 8 2016 Numerical decomposition of the rank-deficiency set of a matrix of multivariate polynomials. Zbl 1191.14071 Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 8 2009 Foreword. What is numerical algebraic geometry? Zbl 1360.00098 8 2017 Algorithm 976: Bertini_real: numerical decomposition of real algebraic curves and surfaces. Zbl 1484.14109 Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 8 2017 Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety. Zbl 1410.65205 Bates, Daniel J.; Decker, Wolfram; Hauenstein, Jonathan D.; Peterson, Chris; Pfister, Gerhard; Schreyer, Frank-Olaf; Sommese, Andrew J.; Wampler, Charles W. 8 2014 Numerical computation of the Hilbert function and regularity of a zero dimensional scheme. Zbl 1315.13032 Griffin, Zachary A.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 7 2014 Multiple stable steady states of a reaction-diffusion model on zebrafish dorsal-ventral patterning. Zbl 1218.65043 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 7 2011 Real solutions to systems of polynomial equations and parameter continuation. Zbl 1309.65056 Griffin, Zachary A.; Hauenstein, Jonathan D. 7 2015 Locating and counting equilibria of the Kuramoto model with rank-one coupling. Zbl 1428.65003 Coss, Owen; Hauenstein, Jonathan D.; Hong, Hoon; Molzahn, Daniel K. 7 2018 Global structure of curves from generalized unitarity cut of three-loop diagrams. Zbl 1388.81392 Hauenstein, Jonathan D.; Huang, Rijun; Mehta, Dhagash; Zhang, Yang 7 2015 Validating the completeness of the real solution set of a system of polynomial equations. Zbl 1362.13027 Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell, Alan C. 6 2016 Newton polytopes and witness sets. Zbl 1304.14077 Hauenstein, Jonathan D.; Sottile, Frank 6 2014 Adaptive strategies for solving parameterized systems using homotopy continuation. Zbl 1427.65086 Hauenstein, Jonathan D.; Regan, Margaret H. 6 2018 A parallel endgame. Zbl 1238.14007 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J. 6 2011 A numerical toolkit for multiprojective varieties. Zbl 1451.65065 Hauenstein, Jonathan D.; Leykin, Anton; Rodriguez, Jose Israel; Sottile, Frank 6 2021 Numerically testing generically reduced projective schemes for the arithmetic Gorenstein property. Zbl 1460.14106 Daleo, Noah S.; Hauenstein, Jonathan D. 5 2016 Numerically intersecting algebraic varieties via witness sets. Zbl 1295.14054 Hauenstein, Jonathan D.; Wampler, Charles W. 4 2013 Computations and equations for Segre-Grassmann hypersurfaces. Zbl 1350.14034 Daleo, Noah S.; Hauenstein, Jonathan D.; Oeding, Luke 4 2016 On computing a cell decomposition of a real surface containing infinitely many singularities. Zbl 1437.14061 Bates, Daniel J.; Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 4 2014 Certifying solutions to square systems of polynomial-exponential equations. Zbl 1357.14071 Hauenstein, Jonathan D.; Levandovskyy, Viktor 4 2017 A primal-dual formulation for certifiable computations in Schubert calculus. Zbl 1360.14126 Hauenstein, Jonathan D.; Hein, Nickolas; Sottile, Frank 4 2016 Complexity of linear circuits and geometry. Zbl 1345.68157 Gesmundo, Fulvio; Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, J. M. 4 2016 Real monodromy action. Zbl 1433.65094 Hauenstein, Jonathan D.; Regan, Margaret H. 3 2020 Decomposing solution sets of polynomial systems using derivatives. Zbl 1434.14022 Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell, Alan C. jun. 3 2016 Machine learning the real discriminant locus. Zbl 1504.14104 Bernal, Edgar A.; Hauenstein, Jonathan D.; Mehta, Dhagash; Regan, Margaret H.; Tang, Tingting 3 2023 Exceptional Stewart-Gough platforms, Segre embeddings, and the special Euclidean group. Zbl 1455.65076 Hauenstein, Jonathan D.; Sherman, Samantha N.; Wampler, Charles W. 2 2018 A singular value homotopy for finding critical parameter values. Zbl 1470.65106 Collins, J. B.; Hauenstein, Jonathan D. 2 2021 Numerical computation of the dimensions of the cohomology of twists of ideal sheaves. Zbl 1185.14041 Hauenstein, Jonathan D.; Migliore, Juan C.; Peterson, Chris; Sommese, Andrew J. 2 2009 Numerical local irreducible decomposition. Zbl 1460.14131 Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J. 2 2016 Binomiality testing and computing sparse polynomials via witness sets. Zbl 1498.14152 Hauenstein, Jonathan D.; Matusevich, Laura; Peterson, Chris; Sherman, Samantha N. 2 2022 Smooth points on semi-algebraic sets. Zbl 1499.14098 Harris, Katherine; Hauenstein, Jonathan D.; Szanto, Agnes 2 2020 Probabilistic saturations and Alt’s problem. Zbl 1502.14146 Hauenstein, Jonathan D.; Helmer, Martin 2 2022 On computing the nonlinearity interval in parametric semidefinite optimization. Zbl 1528.90180 Hauenstein, Jonathan D.; Mohammad-Nezhad, Ali; Tang, Tingting; Terlaky, Tamás 2 2022 Singular value decomposition of complexes. Zbl 1428.14091 Brake, Danielle A.; Hauenstein, Jonathan D.; Schreyer, Frank-Olaf; Sommese, Andrew J.; Stillman, Michael E. 1 2019 A note on global Newton iteration over Archimedean and non-Archimedean fields. Zbl 1416.68221 Hauenstein, Jonathan D.; Pan, Victor Y.; Szanto, Agnes 1 2014 A counter example to an ideal membership test. Zbl 1410.68411 Hauenstein, Jonathan D. 1 2010 Homotopies for connected components of algebraic sets with application to computing critical sets. Zbl 1497.14121 Bates, Daniel J.; Brake, Dani A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 1 2017 Numerical algebraic geometry and semidefinite programming. Zbl 1476.90231 Hauenstein, Jonathan D.; Liddell, Alan C. jun.; McPherson, Sanesha; Zhang, Yi 1 2021 Using monodromy to statistically estimate the number of solutions. Zbl 07608753 Hauenstein, Jonathan D.; Sherman, Samantha N. 1 2022 Certifying reality of projections. Zbl 1396.14053 Hauenstein, Jonathan D.; Kulkarni, Avinash; Sertöz, Emre C.; Sherman, Samantha N. 1 2018 Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials. Zbl 1349.14177 Bates, Daniel J.; Hauenstein, Jonathan D.; Niemerg, Matthew E.; Sottile, Frank 1 2016 Special issue on algebraic geometry and machine learning. Zbl 07680286 1 2023 On the equations defining some Hilbert schemes. Zbl 1485.14111 Hauenstein, Jonathan D.; Manivel, Laurent; Szendrői, Balázs 1 2022 Evaluating and differentiating a polynomial using a pseudo-witness set. Zbl 1503.65111 Hauenstein, Jonathan D.; Regan, Margaret H. 1 2020 Machine learning the real discriminant locus. Zbl 1504.14104 Bernal, Edgar A.; Hauenstein, Jonathan D.; Mehta, Dhagash; Regan, Margaret H.; Tang, Tingting 3 2023 Special issue on algebraic geometry and machine learning. Zbl 07680286 1 2023 Binomiality testing and computing sparse polynomials via witness sets. Zbl 1498.14152 Hauenstein, Jonathan D.; Matusevich, Laura; Peterson, Chris; Sherman, Samantha N. 2 2022 Probabilistic saturations and Alt’s problem. Zbl 1502.14146 Hauenstein, Jonathan D.; Helmer, Martin 2 2022 On computing the nonlinearity interval in parametric semidefinite optimization. Zbl 1528.90180 Hauenstein, Jonathan D.; Mohammad-Nezhad, Ali; Tang, Tingting; Terlaky, Tamás 2 2022 Using monodromy to statistically estimate the number of solutions. Zbl 07608753 Hauenstein, Jonathan D.; Sherman, Samantha N. 1 2022 On the equations defining some Hilbert schemes. Zbl 1485.14111 Hauenstein, Jonathan D.; Manivel, Laurent; Szendrői, Balázs 1 2022 A numerical toolkit for multiprojective varieties. Zbl 1451.65065 Hauenstein, Jonathan D.; Leykin, Anton; Rodriguez, Jose Israel; Sottile, Frank 6 2021 A singular value homotopy for finding critical parameter values. Zbl 1470.65106 Collins, J. B.; Hauenstein, Jonathan D. 2 2021 Numerical algebraic geometry and semidefinite programming. Zbl 1476.90231 Hauenstein, Jonathan D.; Liddell, Alan C. jun.; McPherson, Sanesha; Zhang, Yi 1 2021 Applications of polynomial systems. With contributions by Carlos D’Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, and Jessica Sidman. Zbl 1469.13001 Cox, David A. 11 2020 Multiprojective witness sets and a trace test. Zbl 1448.65054 Hauenstein, Jonathan D.; Rodriguez, Jose Israel 10 2020 Real monodromy action. Zbl 1433.65094 Hauenstein, Jonathan D.; Regan, Margaret H. 3 2020 Smooth points on semi-algebraic sets. Zbl 1499.14098 Harris, Katherine; Hauenstein, Jonathan D.; Szanto, Agnes 2 2020 Evaluating and differentiating a polynomial using a pseudo-witness set. Zbl 1503.65111 Hauenstein, Jonathan D.; Regan, Margaret H. 1 2020 Homotopy techniques for tensor decomposition and perfect identifiability. Zbl 1440.15019 Hauenstein, Jonathan D.; Oeding, Luke; Ottaviani, Giorgio; Sommese, Andrew J. 26 2019 Singular value decomposition of complexes. Zbl 1428.14091 Brake, Danielle A.; Hauenstein, Jonathan D.; Schreyer, Frank-Olaf; Sommese, Andrew J.; Stillman, Michael E. 1 2019 Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\). Zbl 1415.65121 Ayyildiz Akoglu, Tulay; Hauenstein, Jonathan D.; Szanto, Agnes 12 2018 Numerical computation of Galois groups. Zbl 1442.14186 Hauenstein, Jonathan D.; Rodriguez, Jose Israel; Sottile, Frank 11 2018 Polynomials and the exponent of matrix multiplication. Zbl 1404.15020 Chiantini, Luca; Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, Joseph M.; Ottaviani, Giorgio 10 2018 Locating and counting equilibria of the Kuramoto model with rank-one coupling. Zbl 1428.65003 Coss, Owen; Hauenstein, Jonathan D.; Hong, Hoon; Molzahn, Daniel K. 7 2018 Adaptive strategies for solving parameterized systems using homotopy continuation. Zbl 1427.65086 Hauenstein, Jonathan D.; Regan, Margaret H. 6 2018 Exceptional Stewart-Gough platforms, Segre embeddings, and the special Euclidean group. Zbl 1455.65076 Hauenstein, Jonathan D.; Sherman, Samantha N.; Wampler, Charles W. 2 2018 Certifying reality of projections. Zbl 1396.14053 Hauenstein, Jonathan D.; Kulkarni, Avinash; Sertöz, Emre C.; Sherman, Samantha N. 1 2018 On deflation and multiplicity structure. Zbl 1387.13063 Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 16 2017 Tensor decomposition and homotopy continuation. Zbl 1377.65057 Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard 12 2017 Unification and extension of intersection algorithms in numerical algebraic geometry. Zbl 1411.65075 Hauenstein, Jonathan D.; Wampler, Charles W. 11 2017 A hybrid symbolic-numerical approach to the center-focus problem. Zbl 1372.14053 Mahdi, Adam; Pessoa, Claudio; Hauenstein, Jonathan D. 9 2017 Foreword. What is numerical algebraic geometry? Zbl 1360.00098 8 2017 Algorithm 976: Bertini_real: numerical decomposition of real algebraic curves and surfaces. Zbl 1484.14109 Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 8 2017 Certifying solutions to square systems of polynomial-exponential equations. Zbl 1357.14071 Hauenstein, Jonathan D.; Levandovskyy, Viktor 4 2017 Homotopies for connected components of algebraic sets with application to computing critical sets. Zbl 1497.14121 Bates, Daniel J.; Brake, Dani A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 1 2017 Certified predictor-corrector tracking for Newton homotopies. Zbl 1329.65110 Hauenstein, Jonathan D.; Liddell, Alan C. 13 2016 Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme. Zbl 1329.14108 Daleo, Noah S.; Hauenstein, Jonathan D. 8 2016 Validating the completeness of the real solution set of a system of polynomial equations. Zbl 1362.13027 Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell, Alan C. 6 2016 Numerically testing generically reduced projective schemes for the arithmetic Gorenstein property. Zbl 1460.14106 Daleo, Noah S.; Hauenstein, Jonathan D. 5 2016 Computations and equations for Segre-Grassmann hypersurfaces. Zbl 1350.14034 Daleo, Noah S.; Hauenstein, Jonathan D.; Oeding, Luke 4 2016 A primal-dual formulation for certifiable computations in Schubert calculus. Zbl 1360.14126 Hauenstein, Jonathan D.; Hein, Nickolas; Sottile, Frank 4 2016 Complexity of linear circuits and geometry. Zbl 1345.68157 Gesmundo, Fulvio; Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, J. M. 4 2016 Decomposing solution sets of polynomial systems using derivatives. Zbl 1434.14022 Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell, Alan C. jun. 3 2016 Numerical local irreducible decomposition. Zbl 1460.14131 Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J. 2 2016 Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials. Zbl 1349.14177 Bates, Daniel J.; Hauenstein, Jonathan D.; Niemerg, Matthew E.; Sottile, Frank 1 2016 Algebraic geometrization of the Kuramoto model: equilibria and stability analysis. Zbl 1374.34115 Mehta, Dhagash; Daleo, Noah S.; Dörfler, Florian; Hauenstein, Jonathan D. 27 2015 Experiments on the zeros of harmonic polynomials using certified counting. Zbl 1365.30002 Hauenstein, J. D.; Lerario, A.; Lundberg, E.; Mehta, D. 13 2015 Certifying isolated singular points and their multiplicity structure. Zbl 1345.68286 Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 13 2015 Real solutions to systems of polynomial equations and parameter continuation. Zbl 1309.65056 Griffin, Zachary A.; Hauenstein, Jonathan D. 7 2015 Global structure of curves from generalized unitarity cut of three-loop diagrams. Zbl 1388.81392 Hauenstein, Jonathan D.; Huang, Rijun; Mehta, Dhagash; Zhang, Yang 7 2015 A bootstrapping approach for computing multiple solutions of differential equations. Zbl 1294.65085 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Sommese, Andrew J. 30 2014 Maximum likelihood for matrices with rank constraints. Zbl 1345.62043 Hauenstein, Jonathan; Rodriguez, Jose Israel; Sturmfels, Bernd 19 2014 Bertini_real: software for one- and two-dimensional real algebraic sets. Zbl 1437.14005 Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 15 2014 An a posteriori certification algorithm for Newton homotopies. Zbl 1325.65074 Hauenstein, Jonathan D.; Haywood, Ian; Liddell, Alan C. jun. 13 2014 Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety. Zbl 1410.65205 Bates, Daniel J.; Decker, Wolfram; Hauenstein, Jonathan D.; Peterson, Chris; Pfister, Gerhard; Schreyer, Frank-Olaf; Sommese, Andrew J.; Wampler, Charles W. 8 2014 Numerical computation of the Hilbert function and regularity of a zero dimensional scheme. Zbl 1315.13032 Griffin, Zachary A.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 7 2014 Newton polytopes and witness sets. Zbl 1304.14077 Hauenstein, Jonathan D.; Sottile, Frank 6 2014 On computing a cell decomposition of a real surface containing infinitely many singularities. Zbl 1437.14061 Bates, Daniel J.; Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 4 2014 A note on global Newton iteration over Archimedean and non-Archimedean fields. Zbl 1416.68221 Hauenstein, Jonathan D.; Pan, Victor Y.; Szanto, Agnes 1 2014 Numerically solving polynomial systems with Bertini. Zbl 1295.65057 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 160 2013 Isosingular sets and deflation. Zbl 1276.65029 Hauenstein, Jonathan D.; Wampler, Charles W. 34 2013 Numerically computing real points on algebraic sets. Zbl 1269.65048 Hauenstein, Jonathan D. 30 2013 A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. Zbl 1349.65558 Hao, Wenrui; Hauenstein, Jonathan D.; Shu, Chi-Wang; Sommese, Andrew J.; Xu, Zhiliang; Zhang, Yong-Tao 30 2013 Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1303.92044 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; McCoy, Timothy; Sommese, Andrew J. 23 2013 Membership tests for images of algebraic sets by linear projections. Zbl 1285.14066 Hauenstein, Jonathan D.; Sommese, Andrew J. 17 2013 Equations for lower bounds on border rank. Zbl 1361.68098 Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, J. M. 14 2013 Cell decomposition of almost smooth real algebraic surfaces. Zbl 1271.65031 Besana, Gian Mario; Di Rocco, Sandra; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 14 2013 Recovering exact results from inexact numerical data in algebraic geometry. Zbl 1284.14084 Bates, Daniel J.; Hauenstein, Jonathan D.; McCoy, Timothy M.; Peterson, Chris; Sommese, Andrew J. 14 2013 Numerical elimination and moduli space of vacua. Zbl 1342.83004 Hauenstein, Jonathan; He, Yang-Hui; Mehta, Dhagash 12 2013 Numerically intersecting algebraic varieties via witness sets. Zbl 1295.14054 Hauenstein, Jonathan D.; Wampler, Charles W. 4 2013 Algorithm 921: alphaCertified: certifying solutions to polynomial systems. Zbl 1365.65148 Hauenstein, Jonathan D.; Sottile, Frank 67 2012 Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core. Zbl 1238.35193 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 45 2012 Continuation along bifurcation branches for a tumor model with a necrotic core. Zbl 1328.92032 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 29 2012 Algebraic boundaries of Hilbert’s SOS cones. Zbl 1273.13043 Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd 28 2012 Numerical algebraic geometry: a new perspective on gauge and string theories. Zbl 1397.81271 Mehta, Dhagash; He, Yang-Hui; Hauenstein, Jonathan D. 16 2012 Regeneration homotopies for solving systems of polynomials. Zbl 1221.65121 Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 47 2011 A three-dimensional steady-state tumor system. Zbl 1238.92019 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Sommese, Andrew J. 27 2011 Regenerative cascade homotopies for solving polynomial systems. Zbl 1231.65190 Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 22 2011 Efficient path tracking methods. Zbl 1230.65059 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J. 22 2011 Mechanism mobility and a local dimension test. Zbl 1273.70004 Wampler, Charles W.; Hauenstein, Jonathan D.; Sommese, Andrew J. 9 2011 Multiple stable steady states of a reaction-diffusion model on zebrafish dorsal-ventral patterning. Zbl 1218.65043 Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 7 2011 A parallel endgame. Zbl 1238.14007 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J. 6 2011 Witness sets of projections. Zbl 1203.14072 Hauenstein, Jonathan D.; Sommese, Andrew J. 35 2010 A counter example to an ideal membership test. Zbl 1410.68411 Hauenstein, Jonathan D. 1 2010 A numerical local dimension test for points on the solution set of a system of polynomial equations. Zbl 1211.14066 Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 27 2009 Stepsize control for path tracking. Zbl 1181.65071 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. II 21 2009 Numerical decomposition of the rank-deficiency set of a matrix of multivariate polynomials. Zbl 1191.14071 Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 8 2009 Numerical computation of the dimensions of the cohomology of twists of ideal sheaves. Zbl 1185.14041 Hauenstein, Jonathan D.; Migliore, Juan C.; Peterson, Chris; Sommese, Andrew J. 2 2009 Software for numerical algebraic geometry: a paradigm and progress towards its implementation. Zbl 1143.65344 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. II 70 2008 Adaptive multiprecision path tracking. Zbl 1162.65026 Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler II, Charles W. 43 2008 all cited Publications top 5 cited Publications all top 5 Cited by 758 Authors 64 Hauenstein, Jonathan D. 35 Hao, Wenrui 24 Sommese, Andrew John 19 Rodriguez, Jose Israel 19 Sturmfels, Bernd 18 Hu, Bei 18 Sottile, Frank 15 Leykin, Anton 13 Bates, Daniel J. 13 Bernardi, Alessandra 13 Peterson, Chris 13 Wu, Wenyuan 12 Mehta, Dhagash 11 Wampler, Charles W. II 10 Eklund, David 9 He, Yang-Hui Evariste 9 Landsberg, Joseph Montague 9 Michałek, Mateusz 9 Mourrain, Bernard 8 Breiding, Paul 8 Duff, Timothy 8 Ottaviani, Giorgio Maria 8 Safey El Din, Mohab 8 Szántó, Ágnes 8 Telen, Simon 7 Chiantini, Luca 7 Di Rocco, Sandra 7 Regan, Margaret H. 7 Zhi, Lihong 6 Ballico, Edoardo 6 Blekherman, Grigoriy 6 Helmer, Martin 6 Huang, Yaodan 6 Ikenmeyer, Christian 6 Lundberg, Erik 6 Niemerg, Matthew E. 6 Zhang, Yongtao 6 Zhang, Zhengce 6 Zhao, Xinyue Evelyn 5 Angelini, Elena 5 Brysiewicz, Taylor 5 Burr, Michael A. 5 Chen, Changbo 5 Chen, Tianran 5 Draisma, Jan 5 Feng, Yong 5 Gross, Elizabeth 5 Huang, Bo 5 Kubjas, Kaie 5 Liddell, Alan C. jun. 5 Schost, Éric 5 Timme, Sascha 5 Vannieuwenhoven, Nick 5 Verschelde, Jan 5 Xing, Ruixiang 5 Yap, Chee-Keng 4 Beltrán, Carlos E. 4 del Campo, Abraham Martín 4 Duhr, Claude 4 Faugère, Jean-Charles 4 Gesmundo, Fulvio 4 Harrington, Heather A. 4 Heaton, Alexander 4 Hein, Nickolas 4 Horobeţ, Emil 4 Krone, Robert 4 Lairez, Pierre 4 Lee, Tsung-Lin 4 Li, Nan 4 Li, Tien-Yien 4 Lim, Lek-Heng 4 Lin, Guang 4 Oeding, Luke 4 Shu, Chi-Wang 4 Tang, Tingting 4 Townsend, Alex 4 Tsigaridas, Elias P. 4 Van Barel, Marc 4 Vázquez-Leal, Héctor 4 Vinzant, Cynthia 4 Wang, Dongming 4 Wu, Junde 4 Zeng, Zhonggang 4 Zhang, Lei 4 Zheng, Chunyue 3 Améndola, Carlos 3 Ayyildiz Akoglu, Tulay 3 Batselier, Kim 3 Bender, Matías R. 3 Chen, Hongbin 3 Chen, Qipin 3 Daleo, Noah S. 3 de Wolff, Timo 3 Delabays, Robin 3 DeVille, Lee 3 Gäfvert, Oliver 3 Härkönen, Marc 3 He, Yinnian 3 Jacquod, Philippe 3 Jejjala, Vishnu ...and 658 more Authors all top 5 Cited in 159 Serials 60 Journal of Symbolic Computation 22 Journal of High Energy Physics 17 SIAM Journal on Applied Algebra and Geometry 16 Foundations of Computational Mathematics 15 Mathematics of Computation 15 Journal of Scientific Computing 13 Journal of Computational and Applied Mathematics 12 Journal of Computational Physics 12 Applied Mathematics and Computation 12 Chaos 11 Advances in Applied Mathematics 10 Numerical Algorithms 9 Experimental Mathematics 8 Journal of Mathematical Analysis and Applications 8 Journal of Differential Equations 8 Journal of Pure and Applied Algebra 6 Computers & Mathematics with Applications 6 Linear Algebra and its Applications 6 SIAM Journal on Optimization 6 Journal of Algebra and its Applications 5 Journal of Mathematical Physics 5 Journal of Algebra 5 SIAM Journal on Matrix Analysis and Applications 5 Mechanism and Machine Theory 5 Nonlinear Analysis. Real World Applications 5 Mathematics in Computer Science 4 Mathematical Methods in the Applied Sciences 4 Nonlinearity 4 Bulletin of Mathematical Biology 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Theoretical Computer Science 4 Computer Aided Geometric Design 4 Journal of Systems Science and Complexity 4 SIAM Journal on Applied Dynamical Systems 4 Arnold Mathematical Journal 4 European Journal of Mathematics 3 Journal of Mathematical Biology 3 Proceedings of the American Mathematical Society 3 Transactions of the American Mathematical Society 3 Discrete & Computational Geometry 3 SIAM Journal on Scientific Computing 3 Discrete and Continuous Dynamical Systems 3 Vietnam Journal of Mathematics 3 Advances in Geometry 3 Discrete and Continuous Dynamical Systems. Series B 3 Communications in Computational Physics 2 Computers and Fluids 2 Linear and Multilinear Algebra 2 Physics Letters. B 2 Advances in Mathematics 2 Automatica 2 Bulletin of the London Mathematical Society 2 Compositio Mathematica 2 Journal für die Reine und Angewandte Mathematik 2 Le Matematiche 2 Numerische Mathematik 2 Proceedings of the London Mathematical Society. Third Series 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 SIAM Journal on Numerical Analysis 2 Acta Applicandae Mathematicae 2 Physica D 2 Applied Numerical Mathematics 2 Journal of Complexity 2 Applied Mathematics Letters 2 Journal of the American Mathematical Society 2 Differential Geometry and its Applications 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 SIAM Review 2 Mathematical Programming. Series A. Series B 2 Journal of Dynamics and Differential Equations 2 Computational and Applied Mathematics 2 Advances in Computational Mathematics 2 Journal of Mathematical Chemistry 2 Mediterranean Journal of Mathematics 2 Acta Numerica 2 Journal of Statistical Mechanics: Theory and Experiment 2 Oberwolfach Reports 2 Nonlinear Analysis. Hybrid Systems 2 ACM Communications in Computer Algebra 2 Bollettino dell’Unione Matematica Italiana 2 Communications on Applied Mathematics and Computation 1 Acta Mechanica 1 American Mathematical Monthly 1 Classical and Quantum Gravity 1 Communications in Algebra 1 Communications in Mathematical Physics 1 Computer Physics Communications 1 Communications on Pure and Applied Mathematics 1 Discrete Mathematics 1 Journal of Engineering Mathematics 1 Journal of the Franklin Institute 1 Journal of Statistical Physics 1 Mathematical Biosciences 1 Nuclear Physics. B 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Beiträge zur Algebra und Geometrie 1 ACM Transactions on Mathematical Software 1 The Annals of Statistics ...and 59 more Serials all top 5 Cited in 53 Fields 247 Algebraic geometry (14-XX) 228 Numerical analysis (65-XX) 127 Computer science (68-XX) 107 Commutative algebra (13-XX) 77 Partial differential equations (35-XX) 55 Biology and other natural sciences (92-XX) 53 Linear and multilinear algebra; matrix theory (15-XX) 40 Ordinary differential equations (34-XX) 32 Quantum theory (81-XX) 27 Operations research, mathematical programming (90-XX) 26 Convex and discrete geometry (52-XX) 22 Statistics (62-XX) 19 Dynamical systems and ergodic theory (37-XX) 18 Field theory and polynomials (12-XX) 17 Mechanics of particles and systems (70-XX) 15 Functions of a complex variable (30-XX) 14 Combinatorics (05-XX) 13 Fluid mechanics (76-XX) 12 Systems theory; control (93-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Number theory (11-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Relativity and gravitational theory (83-XX) 6 Real functions (26-XX) 6 Potential theory (31-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Geometry (51-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Information and communication theory, circuits (94-XX) 5 Algebraic topology (55-XX) 5 Probability theory and stochastic processes (60-XX) 5 Mechanics of deformable solids (74-XX) 4 Associative rings and algebras (16-XX) 4 Group theory and generalizations (20-XX) 4 Approximations and expansions (41-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 General and overarching topics; collections (00-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Differential geometry (53-XX) 2 Operator theory (47-XX) 2 Manifolds and cell complexes (57-XX) 2 Astronomy and astrophysics (85-XX) 1 Mathematical logic and foundations (03-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Optics, electromagnetic theory (78-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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