Title | **Discussion on polynomials having polynomial iterative roots** |

Author(s) | Lu Yang, Zhou Yujie, Weinian Zhang |

Type | Article in Journal |

Abstract | In 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. |

Keywords | Iterative root, Polynomial mapping, Algebraic variety, Decomposition |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717111002318 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 47 |

Number | 10 |

Pages | 1154 - 1162 |

Year | 2012 |

Note | Symbolic Computation and its Applications |

Edition | 0 |

Translation |
No |

Refereed |
No |