How to flatten a soccer ball

Kaie Kubjas, Pablo A. Parrilo, Bernd Sturmfels

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

4 Citations (Scopus)

Abstract

This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general instances, the boundary of the image is given by two highly singular curves. We determine these curves and show how they demarcate the "flattened soccer ball". We explore cylindrical algebraic decompositions, by working through concrete examples. Maps onto convex polygons and connections to convex optimization are also discussed.
Original languageEnglish
Title of host publicationHomological and Computational Methods in Commutative Algebra
Subtitle of host publicationDedicated to Winfried Bruns on the Occasion of his 70th Birthday
EditorsAldo Conca, Joseph Gubeladze, Tim Römer
PublisherSpringer
Pages141-162
ISBN (Electronic)978-3-319-61943-9
ISBN (Print)978-3-319-61942-2
DOIs
Publication statusPublished - 2017
MoE publication typeA3 Book section, Chapters in research books

Publication series

NameSpringer INdAM series
PublisherSpringer
Volume20

Keywords

  • Mathematics - Algebraic Geometry
  • Mathematics - Optimization and Control

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