Bertini: Software for numerical algebraic geometry DJ Bates, JD Hauenstein, AJ Sommese, CW Wampler | 506 | 2006 |

Numerically solving polynomial systems with Bertini DJ Bates, AJ Sommese, JD Hauenstein, CW Wampler Society for Industrial and Applied Mathematics, 2013 | 439 | 2013 |

Adaptive multiprecision path tracking DJ Bates, JD Hauenstein, AJ Sommese, CW Wampler SIAM Journal on Numerical Analysis 46 (2), 722-746, 2008 | 120 | 2008 |

A numerical local dimension test for points on the solution set of a system of polynomial equations DJ Bates, JD Hauenstein, C Peterson, AJ Sommese SIAM Journal on Numerical Analysis 47 (5), 3608-3623, 2009 | 58 | 2009 |

Finding all real points of a complex curve Y Lu, DJ Bates, AJ Sommese, CW Wampler Contemporary Mathematics 448, 183, 2007 | 56 | 2007 |

Stepsize control for path tracking DJ Bates, JD Hauenstein, AJ Sommese, CW Wampler II Contemporary Mathematics 496, 21, 2009 | 52 | 2009 |

Efficient path tracking methods DJ Bates, JD Hauenstein, AJ Sommese Numerical Algorithms 58 (4), 451-459, 2011 | 46 | 2011 |

Toward a salmon conjecture DJ Bates, L Oeding Experimental Mathematics 20 (3), 358-370, 2011 | 45 | 2011 |

A numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set D Bates, C Peterson, AJ Sommese Journal of Complexity 22 (4), 475-489, 2006 | 40 | 2006 |

Numerical decomposition of the rank-deficiency set of a matrix of multivariate polynomials DJ Bates, JD Hauenstein, C Peterson, AJ Sommese Approximate Commutative Algebra, 55-77, 2009 | 37 | 2009 |

Khovanskii–Rolle continuation for real solutions DJ Bates, F Sottile Foundations of Computational Mathematics 11, 563-587, 2011 | 35 | 2011 |

Bertini: Software for numerical algebraic geometry, 2006 DJ Bates, JD Hauenstein, AJ Sommese, CW Wampler Software available at http://bertini. nd. edu, 0 | 30 | |

Numerical algebraic geometry for model selection and its application to the life sciences E Gross, B Davis, KL Ho, DJ Bates, HA Harrington Journal of The Royal Society Interface 13 (123), 20160256, 2016 | 29 | 2016 |

*Paramotopy*: Parameter Homotopies in ParallelD Bates, D Brake, M Niemerg Mathematical Software–ICMS 2018: 6th International Conference, South Bend …, 2018 | 27 | 2018 |

Recovering exact results from inexact numerical data in algebraic geometry DJ Bates, JD Hauenstein, TM McCoy, C Peterson, AJ Sommese Experimental Mathematics 22 (1), 38-50, 2013 | 27 | 2013 |

Bounds on the number of real solutions to polynomial equations DJ Bates, F Bihan, F Sottile International Mathematics Research Notices 2007 (9), rnm114-rnm114, 2007 | 24 | 2007 |

Bertini for Macaulay2 DJ Bates, E Gross, A Leykin, JI Rodriguez arXiv preprint arXiv:1310.3297, 2013 | 22 | 2013 |

BertiniLab: A MATLAB interface for solving systems of polynomial equations DJ Bates, AJ Newell, M Niemerg Numerical Algorithms 71, 229-244, 2016 | 21 | 2016 |

Numerical algebraic geometry for optimal control applications P Rostalski, IA Fotiou, DJ Bates, AG Beccuti, M Morari SIAM Journal on Optimization 21 (2), 417-437, 2011 | 20 | 2011 |

Numerical computation of the genus of an irreducible curve within an algebraic set DJ Bates, C Peterson, AJ Sommese, CW Wampler Journal of Pure and Applied Algebra 215 (8), 1844-1851, 2011 | 19 | 2011 |