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Paul Breiding, Bernd Sturmfels, and Sascha Timme. 2020. 3264 Conics in a Second. Notices Amer. Math. Soc 67 (1): 30–37.

T. Brysiewicz. 2020. Numerical Software to Compute Newton Polytopes and Tropical Membership. Mathematics in Computer Science.

T. Burggraf, M. Joswig, M. E. Pfetsch, M. Radons, and S. Ulbrich. 2020. Semi-Automatically Optimized Calibration of Internal Combustion Engines. Optimization and Engineering, no. 1.

Holger Eble, Michael Joswig, Lisa Lamberti, and Will Ludington. 2020. Higher-Order Interactions in Fitness Landscapes Are Sparse.

Michael Joswig. 2020. Essentials of Tropical Combinatorics.

Michael Joswig, Marek Kaluba, and Lukas Ruff. 2020. Geometric Disentanglement by Random Convex Polytopes.

Michael Joswig, and Ayush Kumar Tewari. 2020. Forbidden Patterns in Tropical Plane Curves. arXiv Preprint arXiv:2002.02270.

Michael Joswig, and Paul Vater. 2020. Real Tropical Hyperfaces by Patchworking in. In Mathematical Software – Icms 2020, edited by Anna Maria Bigatti, Jacques Carette, James H. Davenport, Michael Joswig, and Timo de Wolff. Vol. 12097. Lecture Notes in Computer Science. Springer.

M. Joswig, M. Panizzut, and B Sturmfels. 2020. The Schläfli Fan. Discrete & Computational Geometry. An International Journal of Mathematics and Computer Science. https://doi.org/10.1007/s00454-020-00215-x.

M. Kahle, and A. Newman. 2020. Topology and Geometry of Random 2-Dimensional Hypertrees.

Marek Kaluba, Benjamin Lorenz, and Sascha Timme. 2020. Polymake.jl: A New Interface to Polymake. http://arxiv.org/abs/2003.11381.

L. Kastner, and M Panizzut. 2020. Hyperplane Arrangements in Polymake. Edited by A. M. Bigatti, J. Carette, J. H. Davenport, M. Joswig, and T de Wolff. Springer International Publishing.

Ralph Morrison, and Ayush Kumar Tewari. 2020. Convex Lattice Polygons with All Lattice Points Visible. http://arxiv.org/abs/2005.04180.

M. Panizzut, E. Sertoz, and B Sturmfels. 2020. An Octanomial Model for Cubic Surfaces. Le Matematiche. https://doi.org/10.4418/2020.75.2.8.

Simon Telen, Sascha Timme, and Marc Van Barel. 2020. Backward Error Measures for Roots of Polynomials. Numerical Algorithms.

Ayush Kumar Tewari. 2020. Point-Line Geometry in the Tropical Plane. http://arxiv.org/abs/2006.04425.

Sascha Timme. 2020. Mixed Precision Path Tracking for Polynomial Homotopy Continuation. http://arxiv.org/abs/1902.02968.

Janko Boehm, Michael Joswig, Lars Kastner, and Andrew Newman. 2019. Random Growth on a Ramanujan Graph.

Laura Brustenga, Sascha Timme, and Madeleine Weinstein. 2019. 96120: The Degree of the Linear Orbit of a Cubic Surface. http://arxiv.org/abs/1909.06620.

T. Brysiewicz. 2019. Necklaces count polynomial parametric osculants. Journal of Symbolic Computation.

T. Brysiewicz, and F. Gesmundo. 2019. The Degree of Stiefel Manifolds. arXiv:1909.10085.

T. Brysiewicz, J. Rodriguez, F. Sottile, and T. Yahl. 2019a. Decomposable sparse polynomial systems. arXiv:2006.03154.

T. Brysiewicz, J. Rodriguez, F. Sottile, and T. Yahl. 2019b. Solving Decomposable Sparse Systems. arXiv:2001.04228.

F. Cools, M. D’Adderio, D. Jensen, and M Panizzut. 2019. Brill-Noether Theory of Curves on 1 × ℙ1: Tropical and Classical Approaches. Algebr. Comb 2 (3): 323–41.

F. Criado, and A. Newman. 2019. Randomized Construction of Complexes with Large Diameter.

Francisco Criado, Michael Joswig, and Francisco Santos. 2019. Tropical Bisectors and Voronoi Diagrams.

Holger Eble, Michael Joswig, Lisa Lamberti, and William B Ludington. 2019. Cluster Partitions and Fitness Landscapes of the Drosophila Fly Microbiome. J. Math. Biol 79 (3): 861–99. https://doi.org/10.1007/s00285-019-01381-0.

Simon Hampe, Michael Joswig, and Benjamin Schröter. 2019. Algorithms for Tight Spans and Tropical Linear Spaces. J. Symbolic Comput 91: 116–28. https://doi.org/10.1016/j.jsc.2018.06.016.

Robert Haraway, Robert Löwe, Dominic Tate, and Stephan Tillmann. 2019. On Moduli Spaces of Convex Projective Structures on Surfaces: Outitude and Cell-Decomposition in Fock-Goncharov Coordinates. http://arxiv.org/abs/1911.04176.

Olarte J., P. Marta, and Schröter B. 2019. On Local Dressians of Matroids. In Algebraic and Geometric Combinatorics on Lattice Polytopes, 309–29. Word Scientific Publishing.

Michael Joswig. 2019. Tropical Voronoi Diagrams. Oberwolfach Reports. https://doi.org/10.4171/OWR/2019/39.

Michael Joswig, Davide Lofano, Frank H. Lutz, and Mimi Tsuruga. 2019. Frontiers of Sphere Recognition in Practice.

Michael Joswig, and Georg Loho. 2019. Monomial Tropical Cones for Multicriteria Optimization. AIP Conference Proceedings 2070 (1): 020025. https://doi.org/10.1063/1.5089992.

Michael Joswig, Robert Löwe, and Boris Springborn. 2019. Secondary Fans and Secondary Polyhedra of Punctured Riemann Surfaces. Experimental Mathematics, 1–17. https://doi.org/10.1080/10586458.2018.1477078.

Michael Joswig, and Benjamin Schröter. 2019. The Tropical Geometry of Shortest Paths.

Michael Joswig, and Ben Smith. 2019. Convergent Puiseux Series and Tropical Geometry of Higher Rank.

Lars Kastner, and Robert Löwe. 2019. The Newton Polytope of the Discriminant of a Quaternary Cubic Form.

D. Lofano, and A. Newman. 2019. The Worst Way to Collapse a Simplex.

A. Newman. 2019. On the Complexity of Random Polytopes.

A Newman. 2019. Small Simplicial Complexes with Prescribed Torsion in Homology. Discrete Comput. Geom 62 (2): 433–60. https://doi.org/10.1007/s00454-018-9987-y.

M. Panizzut, and M Vigeland. 2019. Tropical Lines on Cubic Surfaces.

M. Radons. 2019a. A Note on Surjectivity of Piecewise Affine Mappings. Optim. Lett, no. 13.

M. Radons. 2019b. Generalized Perron Roots and Solvability of the Absolute Value Equation.

Bernd Sturmfels, Sascha Timme, and Piotr Zwiernik. 2019. Estimating Linear Covariance Models with Numerical Nonlinear Algebra. http://arxiv.org/abs/1909.00566.

Xavier Allamigeon, Pascal Benchimol, Stéphane Gaubert, and Michael Joswig. 2018. Log-Barrier Interior Point Methods Are Not Strongly Polynomial. SIAM J. Appl. Algebra Geom 2 (1): 140–78. https://doi.org/10.1137/17M1142132.

Klaus Altmann, Jarosław Buczyński, Lars Kastner, and Anna-Lena Winz. 2018. Immaculate Line Bundles on Toric Varieties. 2018. http://arxiv.org/abs/1808.09312.

Benjamin Assarf, Michael Joswig, and Julian Pfeifle. 2018. Webs of Stars or How to Triangulate Free Sums of Point Configurations. J. Combin. Theory Ser. A 159: 183–214. https://doi.org/10.1016/j.jcta.2018.05.007.

G. Balletti, M. Panizzut, and B Sturmfels. 2018. K3 Polytopes and Their Quartic Surfaces.

Paul Breiding, and Sascha Timme. 2018. HomotopyContinuation.jl: A Package for Homotopy Continuation in Julia. In International Congress on Mathematical Software, 458–65. Springer.

A. Griewank, R. Hasenfelder, M. Radons, L. Lehmann, and T. Streubel. 2018. Piecewise Linear Secant Approximation via Algorithmic Piecewise Differentiation. Optimization Methods and Software, no. 33.

Charles Jordan, Michael Joswig, and Lars Kastner. 2018. Parallel enumeration of triangulations. Electron. J. Comb 25 (3): research paper p3.6, 27.

Michael Joswig. 2018. Tropische Geometrie, Lineare Optimierung Und Netzwerke. Mitt. Dtsch. Math.-Ver 26 (4): 167–69. https://doi.org/10.1515/dmvm-2018-0051.

Michael Joswig, and Lars Kastner. 2018. New Counts for the Number of Triangulations of Cyclic Polytopes. In Mathematical Software – Icms 2018, edited by James H. Davenport, Manuel Kauers, George Labahn, and Josef Urban, 264–71. Cham: Springer International Publishing.

Michael Joswig, and Benjamin Schröter. 2018. The Degree of a Tropical Basis. Proc. Amer. Math. Soc 146 (3): 961–70. https://doi.org/10.1090/proc/13787.

M. Kahle, F. H. Lutz, A. Newman, and K. Parsons. 2018. Cohen–Lenstra Heuristics for Torsion in Homology of Random Complexes. Experimental Mathematics 0 (0): 0–0. https://doi.org/10.1080/10586458.2018.1473821.

Lars Kastner, Benjamin Lorenz, Andreas Paffenholz, and Anna-Lena Winz. 2018. Toric geometry in polymake. ACM Commun. Comput. Algebra 51 (3): 92–94.

A. Newman. 2018. A Lower Bound on the Number of Homotopy Types of Simplicial Complexes on n Vertices.

A. Newman, and E. Paquette. 2018. The Integer Homology Threshold in Yd(n, p).

M. Radons. 2018. O(n) Working Precision Inverses for Symmetric Tridiagonal Toeplitz Matrices with O(1) Floating Point Calculations. Optim. Lett, no. 12.

M. Radons, L. Lehmann, T. Streubel, and L. Lehmann. 2018. An Open Newton Method for Piecewise Smooth Functions.

Benjamin Assarf, Ewgenij Gawrilow, Katrin Herr, Michael Joswig, Benjamin Lorenz, Andreas Paffenholz, and Thomas Rehn. 2017. Computing Convex Hulls and Counting Integer Points with polymake. Math. Program. Comput 9 (1): 1–38. https://doi.org/10.1007/s12532-016-0104-z.

M. Brandt, J. Bruce, T. Brysiewicz, R. Krone, and E. Robeva. 2017. The Degree of SO(n, ℂ). In Combinatorial Algebraic Geometry, 229–46. Springer.

F. Cools, and M Panizzut. 2017. The Gonality Sequence of Complete Graphs. Electron. J. Combin 24 (4): Paper 4.1, 20.

T. Jiang, and A. Newman. 2017. Small Dense Subgraphs of a Graph. SIAM Journal on Discrete Mathematics 31 (1): 124–42. https://doi.org/10.1137/15M1007598.

Michael Joswig, Georg Loho, Benjamin Lorenz, and Rico Raber. 2017. MatchTheNet - An Educational Game on 3-Dimensional Polytopes (Multimedia Contribution). In 33rd International Symposium on Computational Geometry (Socg 2017), edited by Boris Aronov and Matthew J. Katz, 77:66:1–66:5. Leibniz International Proceedings in Informatics (Lipics). Dagstuhl, Germany: Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2017.66.

Lars Kastner, Kristin Shaw, and Anna-Lena Winz. 2017. Cellular Sheaf Cohomology in Polymake. In Combinatorial Algebraic Geometry: Selected Papers from the 2016 Apprenticeship Program, edited by Gregory G. Smith and Bernd Sturmfels, 369–85. New York, NY: Springer New York. https://doi.org/10.1007/978-1-4939-7486-3_17.

M. Panizzut. 2017. Gonality of Complete Graphs with a Small Number of Omitted Edges. Math. Nachr.

Michael Joswig, Georg Loho, Benjamin Lorenz, and Benjamin Schröter. 2016. Linear Programs and Convex Hulls over Fields of Puiseux Fractions. In Mathematical Aspects of Computer and Information Sciences, 9582:429–45. Lecture Notes in Comput. Sci. Springer, [Cham]. https://doi.org/10.1007/978-3-319-32859-1_37.

Lars Kastner. 2016. Ext and Tor on Two-Dimensional Cyclic Quotient Singularities. 2016. http://arxiv.org/abs/1601.05673.

M. Panizzut. 2016. Theta Characteristics of Hyperelliptic Graphs. Archiv Der Mathematik 106 (5): 445–55.

M. Radons. 2016. Direct Solution of Piecewise Linear Systems. Theoretical Computer Science 626.

Tristram Bogart, Christian Haase, Milena Hering, Benjamin Lorenz, Benjamin Nill, Andreas Paffenholz, Günter Rote, Francisco Santos, and Hal Schenck. 2015. Finitely Many Smooth d-Polytopes with n Lattice Points. Israel J. Math 207 (1): 301–29. https://doi.org/10.1007/s11856-015-1175-7.

A. Griewank, J. U. Bernt, M. Radons, and T. Streubel. 2015. Solving Piecewise Linear Systems in Abs-Normal Form. Linear Algebra and Its Applications 471.

Lars Kastner. 2015. Ext  On Affine Toric Varieties. PhD thesis, Freie Universität Berlin.

Benjamin Lorenz, and Benjamin Nill. 2015. On Smooth Gorenstein Polytopes. Tohoku Math. J. (2) 67 (4): 513–30. https://doi.org/10.2748/tmj/1450798070.

L. Balay-Wilson, and T. Brysiewicz. 2014. Points of Ninth Order on Cubic Curves. Rose-Hulman Undergraduate Mathematics Journal 15 (1).

T. Streubel, A. Griewank, M. Radons, and J. U. Bernt. 2014. Representation and Analysis of Piecewise Linear Functions in Abs-Normal Form. IFIP Advances in Information and Communication Technology 443.

Klaus Altmann, and Lars Kastner. 2013. Negative deformations of toric singularities that are smooth in codimension two. In Deformations of surface singularities, 13–55. Berlin: Springer; Budapest: János Bolyai Mathematical Society. https://doi.org/10.1007/978-3-642-39131-6_1.

Nathan Owen Ilten, and Lars Kastner. 2013. Calculating generators of multigraded algebras. J. Symb. Comput 51: 22–33. https://doi.org/10.1016/j.jsc.2012.03.005.

Christian Haase, Benjamin Lorenz, and Andreas Paffenholz. 2010. Generating Smooth Lattice Polytopes. In Mathematical Software—ICMS 2010, 6327:315–28. Lecture Notes in Comput. Sci. Springer, Berlin.

Michael Joswig, Benjamin Müller, and Andreas Paffenholz. 2009. **Polymake** and Lattice Polytopes. In 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 491–502. Discrete Math. Theor. Comput. Sci. Proc., Ak. Assoc. Discrete Math. Theor. Comput. Sci., Nancy.

A NewmanFreeness of the Random Fundamental Group. Journal of Topology and Analysis 0 (0): 1–7. https://doi.org/10.1142/S1793525319500468.

Franziska Hinkelmann, Lars Kastner, and Michael Stillman. n.d. A Web Application for Macaulay2. Journal of Software for Algebra and Geometry.

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