Symmetries of planar algebraic vector fields
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Symmetries of planar algebraic vector fields
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Symmetries of planar algebraic vector fields
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
<a href="/cs/project/GF21-08009K" target="_blank" >GF21-08009K: Zobecněné symetrie a ekvivalence geometrických dat</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2024
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Computer Aided Geometric Design
ISSN
0167-8396
e-ISSN
1879-2332
Svazek periodika
111
Číslo periodika v rámci svazku
June 2024
Stát vydavatele periodika
NL - Nizozemsko
Počet stran výsledku
12
Strana od-do
—
Kód UT WoS článku
001238529000001
EID výsledku v databázi Scopus
2-s2.0-85191971455