Computing complex and real tropical curves using monodromy |
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| Affiliation: | 1. Department of Mathematics, University of Wisconsin-Eau Claire, Eau Claire, WI 54701, United States of America;2. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, United States of America;3. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States of America;1. School of Mathematics and Big Data, Foshan University, Guangdong, 528000, PR China;2. Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq;3. Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21101 Novi Sad, Serbia;4. Centre for Research in Mathematics, School of Computing, Engineering and Mathematics, Western Sydney University, Locked Bag 1797, Penrith, NSW 2751, Australia;5. Department of Mathematics, University of York, Heslington, York YO10 5DD, UK;1. University of California Los Angeles, Los Angeles, CA 90095, United States of America;2. Elon University, Elon, NC 27244, United States of America;1. Department of Mathematics, Stanford University, Stanford, CA 94305, United States of America;2. Department of Mathematics and Statistics, SUNY, Albany, NY 12222, United States of America |
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| Abstract: | Tropical varieties capture combinatorial information about how coordinates of points in a classical variety approach zero or infinity. We present algorithms for computing the rays of a complex and real tropical curve defined by polynomials with constant coefficients. These algorithms rely on homotopy continuation, monodromy loops, and Cauchy integrals. Several examples are presented which are computed using an implementation that builds on the numerical algebraic geometry software Bertini. |
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| Keywords: | 14T05 14Q05 14P05 |
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