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Uncovering symmetries in polynomial systems

Larsson, Viktor LU and Åström, Kalle LU (2016) In Lecture Notes in Computer Science (LNCS) 9907. p.252-267
Abstract

In this paper we study symmetries in polynomial equation systems and how they can be integrated into the action matrix method. The main contribution is a generalization of the partial p-fold symmetry and we provide new theoretical insights as to why these methods work. We show several examples of how to use this symmetry to construct more compact polynomial solvers. As a second contribution we present a simple and automatic method for finding these symmetries for a given problem. Finally we show two examples where these symmetries occur in real applications.

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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Lecture Notes in Computer Science (LNCS)
editor
Leibe, Bastian; Matas, Jiri; Sebe, Nicu; Welling, Max; ; ; and
volume
9907
pages
16 pages
publisher
Springer Verlag
external identifiers
  • scopus:84990041155
  • wos:000389384800016
ISSN
0302-9743
1611-3349
ISBN
978-3-319-46486-2
978-3-319-46487-9
DOI
10.1007/978-3-319-46487-9_16
language
English
LU publication?
yes
id
1506a56c-c165-4b88-89cd-9dbfc521c5d5
date added to LUP
2016-10-24 07:41:26
date last changed
2017-09-18 11:28:17
@inproceedings{1506a56c-c165-4b88-89cd-9dbfc521c5d5,
  abstract     = {<p>In this paper we study symmetries in polynomial equation systems and how they can be integrated into the action matrix method. The main contribution is a generalization of the partial p-fold symmetry and we provide new theoretical insights as to why these methods work. We show several examples of how to use this symmetry to construct more compact polynomial solvers. As a second contribution we present a simple and automatic method for finding these symmetries for a given problem. Finally we show two examples where these symmetries occur in real applications.</p>},
  author       = {Larsson, Viktor and Åström, Kalle},
  booktitle    = {Lecture Notes in Computer Science (LNCS)},
  editor       = {Leibe, Bastian and Matas, Jiri and Sebe, Nicu and Welling, Max},
  isbn         = { 978-3-319-46486-2},
  issn         = {0302-9743},
  language     = {eng},
  pages        = {252--267},
  publisher    = {Springer Verlag},
  title        = {Uncovering symmetries in polynomial systems},
  url          = {http://dx.doi.org/10.1007/978-3-319-46487-9_16},
  volume       = {9907},
  year         = {2016},
}