Real Tropical Hyperfaces by Patchworking in polymake

DOI10.1007/978-3-030-52200-1_20zbMath1506.14002arXiv2003.06326OpenAlexW3011444090WikidataQ117245031 ScholiaQ117245031MaRDI QIDQ5039573

Michael Joswig, Paul Vater

Publication date: 13 October 2022

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.06326

zbMATH Keywords

Hilbert's 16th problemtropical hypersurfacesreal algebraic hypersurfacesViro's patchworking

Mathematics Subject Classification ID

Geometric aspects of tropical varieties (14T20) Computational aspects of algebraic surfaces (14Q10) Software, source code, etc. for problems pertaining to algebraic geometry (14-04) Hypersurfaces and algebraic geometry (14J70)

Related Items (3)

A polyhedral homotopy algorithm for real zeros ⋮ A tropical count of real bitangents to plane quartic curves ⋮ Computing tropical bitangents to smooth quartic curves in polymake

Uses Software

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• PPL
• cellularSheaves
• patchworking

Cites Work

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• Triangulations. Structures for algorithms and applications
• From the sixteenth Hilbert problem to tropical geometry
• Critical points of real polynomials and topology of real algebraic \(T\)-surfaces
• Parallel enumeration of triangulations
• Cellular sheaf cohomology in polymake
• Viro theorem and topology of real and complex combinatorial hypersurfaces.
• Algorithms for tight spans and tropical linear spaces
• Computing convex hulls and counting integer points with \texttt{polymake}
• Patchworking algebraic curves disproves the Ragsdale conjecture

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