Computing Tropical Prevarieties in Parallel

Anders Nedergaard Jensen, Jan Verschelde, Jeff Sommars

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review

Abstract

The computation of the tropical prevariety is the first step in the application of polyhedral methods to compute positive dimensional solution sets of polynomial systems. In particular, pretropisms are candidate leading exponents for the power series developments of the solutions. The computation of the power series may start as soon as one pretropism is available, so our parallel computation of the tropical prevariety has an application in a pipelined solver. We present a parallel implementation of dynamic enumeration. Our first distributed memory implementation with forked processes achieved good speedups, but quite often resulted in large variations in the execution times of the processes. The shared memory multithreaded version applies work stealing to reduce the variability of the run time. Our implementation applies the thread safe Parma Polyhedral Library (PPL), in exact arithmetic with the GNU Multiprecision Arithmetic Library (GMP), aided by the fast memory allocations of TCMalloc. Our parallel implementation is capable of computing the tropical prevariety of the cyclic 16-roots problem. We also report on computational experiments on the n-body and n-vortex problems; our computational results compare favorably with Gfan.

Original languageEnglish
Title of host publicationProceedings of the International Workshop on Parallel Symbolic Computation, PASCO 2017
PublisherAssociation for Computing Machinery
Publication date2017
Article numbera9
ISBN (Electronic)9781450352888
DOIs
Publication statusPublished - 2017
EventInternational Workshop on Parallel Symbolic Computation -
Duration: 23 Jul 201724 Jul 2017
Conference number: July 23 - 24, 2017

Workshop

WorkshopInternational Workshop on Parallel Symbolic Computation
Number July 23 - 24, 2017
Period23/07/201724/07/2017
SeriesPASCO 2017

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