Symmetries of planar algebraic vector fields
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F24%3A43972083" target="_blank" >RIV/49777513:23520/24:43972083 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0167839624000244?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0167839624000244?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cagd.2024.102290" target="_blank" >10.1016/j.cagd.2024.102290</a>
Alternative languages
Result language
angličtina
Original language name
Symmetries of planar algebraic vector fields
Original language description
In this paper, we address the computation of the symmetries of polynomial (and thus also rational) planar vector fields using elements from Computer Algebra. We show that they can be recovered from the symmetries of the roots of an associated univariate complex polynomial which is constructed as a generator of a certain elimination ideal. Computing symmetries of the roots of the auxiliary polynomial is a task considerably simpler than the original problem, which can be done efficiently working with classical Computer Algebra tools. Special cases, in which the group of symmetries of the polynomial roots is infinite, are separately considered and investigated. The presented theory is complemented by illustrative examples. The main steps of the procedure for investigating the symmetries of a given polynomial vector field are summarized in a flow chart for clarity.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GF21-08009K" target="_blank" >GF21-08009K: Generalized Symmetries and Equivalences of Geometric Data</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Computer Aided Geometric Design
ISSN
0167-8396
e-ISSN
1879-2332
Volume of the periodical
111
Issue of the periodical within the volume
June 2024
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
12
Pages from-to
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UT code for WoS article
001238529000001
EID of the result in the Scopus database
2-s2.0-85191971455