On polynomial functions from Zn1 × Zn2 × … × Znr to Zm

✍ Scribed by Zhibo Chen

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 367 KB
• Volume: 162
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(95)00305-g

✦ Synopsis

The well-known concept of a polynomial function (mod m) has been generalized to polynomial functions from Z, to Z m and a number of results have been obtained in (Chen, 1995). In the present paper, we further define the concept of polynomial functions from Z,, x Z.2 x ... x Z.r to Z,, and generalize the results of (Chen, 1995). We give a canonical representation and the counting formula for such polynomial functions. Then we obtain a necessary and sufficient condition on nl,n 2 ..... n r and m for all functions from Z,, x Z,2 x ... x Z,r to Zm to be polynomial functions. Further, we give an answer to the following problem: How to determine whether a given function from Z.