Home | Quick Search | Advanced Search | Bibliography submission | Bibliography submission using bibtex | Bibliography submission using bibtex file | Links | Help | Internal


TitleDiscussion on polynomials having polynomial iterative roots
Author(s) Lu Yang, Zhou Yujie, Weinian Zhang
TypeArticle in Journal
AbstractIn this paper, we discuss polynomial mappings which have iterative roots of the polynomial form. We apply the computer algebra system Singular to decompose algebraic varieties and finally find a condition under which polynomial functions have quadratic iterative roots of quadratic polynomial form. This condition is equivalent to, but simpler than Schweizer and Sklar’s and more convenient than Strycharz–Szemberg and Szemberg’s. We further find all polynomial functions which have cubic iterative roots of the quadratic polynomial form and compute all those iterative roots. Moreover, we find all 2-dimensional homogeneous polynomial mappings of degree 2 which have iterative roots of the polynomial form and obtain expressions of some iterative roots.
KeywordsIterative root, Polynomial mapping, Algebraic variety, Decomposition
URL http://www.sciencedirect.com/science/article/pii/S0747717111002318
JournalJournal of Symbolic Computation
Pages1154 - 1162
NoteSymbolic Computation and its Applications
Translation No
Refereed No