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libtropicon: A Scalable Library for Computing Intersection Points of Generic Tropical Hyper-surfaces

  • Tianran ChenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)

Abstract

The computation of intersection points of generic tropical hyper-surfaces is a fundamental problem in computational algebraic geometry. An efficient algorithm for solving this problem will be a basic building block in many higher level algorithms for studying tropical varieties, computing mixed volume, enumerating mixed cells, constructing polyhedral homotopies, etc. libtropicon is a library for computing intersection points of generic tropical hyper-surfaces that provides a unified framework where the several conceptually opposite approaches coexist and complement one another. In particular, great efficiency is achieve by the data cross-feeding of the “pivoting” and the “elimination” step — data by-product generated by the pivoting step is selectively saved to bootstrap the elimination step, and vice versa. The core algorithm is designed to be naturally parallel and highly scalable, and the implementation directly supports multi-core architectures, computer clusters, and GPUs based on CUDA or ROCm/OpenCL technology. Many-core architectures such as Intel Xeon Phi are also partially supported. This library also includes interface layers that allows it to be tightly integrated into the existing ecosystem of software in computational algebraic geometry.

Keywords

Tropical hypersurfaces Mixed volume Mixed cells BKK bound Polyhedral homotopy 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Auburn University at MontgomeryMontgomeryUSA

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