Bertini.m2 swMATH ID: 8784 Software Authors: Jose I. Rodriguez; D. Bates; E. Gross; A. Leykin Description: Bertini for Macaulay2. Numerical algebraic geometry is the field of computational mathematics concerning the numerical solution of polynomial systems of equations. Bertini, a popular software package for computational applications of this field, includes implementations of a variety of algorithms based on polynomial homotopy continuation. The Macaulay2 package Bertini.m2 provides an interface to Bertini, making it possible to access the core run modes of Bertini in Macaulay2. With these run modes, users can find approximate solutions to zero-dimensional systems and positive-dimensional systems, test numerically whether a point lies on a variety, sample numerically from a variety, and perform parameter homotopy runs. In this talk, a short tutorial will be given for the Macaulay2 package Bertini.m2 and details to an application in algbebraic statistics involving maximum likelihood estimation. Homepage: https://github.com/Macaulay2/M2/blob/master/M2/Macaulay2/packages/Bertini.m2 Source Code: https://github.com/Macaulay2/M2/blob/master/M2/Macaulay2/packages/Bertini.m2 Dependencies: Macaulay2; Bertini Related Software: Macaulay2; Bertini; PHCpack; NumericalAlgebraicGeometry; SageMath; NumericalNP; MPFR; Matplotlib; LearningAlgebraicVarieties; triangulation; LamanGraphs; Traces; nauty; Mathematica; NumericalImplicitization; RAGlib Cited in: 10 Publications all top 5 Cited by 17 Authors 4 Rodriguez, Jose Israel 2 Brysiewicz, Taylor 1 Bernstein, Daniel Irving 1 Chen, Justin 1 del Campo, Abraham Martín 1 Eklund, David 1 Farnsworth, Cameron 1 Gross, Elizabeth 1 Harrington, Heather A. 1 Hauenstein, Jonathan D. 1 Kileel, Joe 1 Leykin, Anton 1 Maxim, Laurentiu G. 1 Rosen, Zvi 1 Sottile, Frank 1 Sturmfels, Bernd 1 Wang, Botong all top 5 Cited in 8 Serials 2 Advances in Applied Mathematics 1 Bulletin of Mathematical Biology 1 Journal of Pure and Applied Algebra 1 Journal of Symbolic Computation 1 Foundations of Computational Mathematics 1 Mathematics in Computer Science 1 ACM Communications in Computer Algebra 1 The Journal of Software for Algebra and Geometry all top 5 Cited in 11 Fields 8 Algebraic geometry (14-XX) 5 Numerical analysis (65-XX) 2 Commutative algebra (13-XX) 2 Computer science (68-XX) 1 Combinatorics (05-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) Citations by Year