Computer Science Technical Reports
CS at VT

The Algebraic Representation of Partial Functions

Wesselkamper, T. C. (1978) The Algebraic Representation of Partial Functions. Technical Report CS78009-R, Computer Science, Virginia Tech.

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The paper presents a generalization of the theorem which states that any (everywhere defined) function from a finite field GF(p^n) into itself may be represented at a polynomial over GF(p^n). The generalization is to partial functions over GF(p^n) and exhibits representations of a partial function f by the sum of a polynomial and a sum of terms of the form a/(x-b)i, where b is one of the points at which f is undefined. Three such representation theorems are given. The second is the analog of the Mittag-Leffler Theorem of the theory of functions of a single complex variable. The main result of the paper is that the sum of the degree of the polynomial part of the representation and the degrees of the principal parts of the representation need be no more than max(|A|, |B|) where A is the set upon which the function is defined and B is the set upon which the function is undefined.

Item Type:Departmental Technical Report
Keywords:Partial function, representation, finite field, principal part
Subjects:Computer Science > Historical Collection(Till Dec 2001)
ID Code:831
Deposited By:Administrator, Eprints
Deposited On:05 May 2006