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TitleOne class of planar rational involutions
Author(s) Zbigniew Leśniak, Yang Shiyun
TypeArticle in Journal
AbstractOur aim is to find one class of planar rational involutions φ λ : R 2 ∖ ( L 1 ∪ L 2 ) → R 2 ∖ ( L 1 ∪ L 2 ) of the form φ λ ( x , y ) : = ( a 1 x + a 2 y + a 3 a 4 x + a 5 y + a 6 , b 1 y + b 2 x + b 3 b 4 y + b 5 x + b 6 ) , where λ = ( a 1 , , a 6 , b 1 , , b 6 ) ∈ R 12 , and L 1 and L 2 denote two lines, a 4 x + a 5 y + a 6 = 0 and b 4 y + b 5 x + b 6 = 0 respectively. We give necessary and sufficient conditions on the 12 parameters a i , b i , i = 1 , 2 , , 6 , such that φ λ is an involution.
KeywordsInvolution, Planar rational map, Minimal primary decomposition, Gröbner basis, Elimination theory
ISSN0362-546X
URL http://www.sciencedirect.com/science/article/pii/S0362546X11003981
LanguageEnglish
JournalNonlinear Analysis: Theory, Methods & Applications
Volume74
Number17
Pages6097 - 6104
Year2011
Edition0
Translation No
Refereed No
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