Algorithms for computing bases for 3-variable homogeneous integer-valued polynomials

JOURNAL OF ALGEBRA

卷:559

Article

关键词: Integer valued polynomials;    Polynomial rings;    Homogeneous polynomials;    Smith normal form;    Hermite normal form;   

DOI  :  10.1016/j.jalgebra.2020.04.014

来源: Elsevier

【 摘 要 】

A polynomial f in Q [x, y, z] is integer-valued if f (x, y, z) is an element of Z, whenever x, y, z are integers. This work will look at the case where f is homogeneous and will present algorithms for constructing polynomials f/p(k) with f is an element of Z[x, y, z] such that k is as large as possible for a given degree. From this we will find bases for the modules of homogeneous integer-valued polynomials (IVPs) in a range of degrees. IVPs have been studied for their topological applications, including the homogeneous ones. We explain the connection between 3-variable homogeneous IVPs of degree m and 3-variable IVPs of degree m, as well as with 2-variable IVPs of degree m evaluated at odd values only, then use linear algebra to calculate bases for both cases in a range of degrees. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free