A Solution to the Polynomial Hensel Code Conversion Problem

The polynomial Hensel code of a rational function a(x)/ b(x) ϵ F(x), F is a field, is the pair (c(x) d-1(x) mod Xr, n); r is a positive integer and a(x)/ b(x) = (c(x))xn such that c(x) and d(x) have nonzero constant terms. Such a representation scheme was proposed, in analogy with the Hensel code re...

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Veröffentlicht in:IEEE transactions on computers Jg. C-36; H. 5; S. 634 - 637
1. Verfasser: MUKHOPADHYAY, A
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.05.1987
Institute of Electrical and Electronics Engineers
Schlagworte:
Algebraic simplification
algorithm design
Applied sciences
Arithmetic
Built-in self-test
Circuits
Codes
Coding, codes
Complexity theory
Computers
Euclidean algorithm
Exact sciences and technology
Fault tolerance
Fault tolerant systems
Hensel code
Information, signal and communications theory
Logic gates
Polynomials
rational function representation
Signal and communications theory
Telecommunications and information theory
Design
Algorithm
Code
Conversion
Rational function
ISSN:0018-9340, 1557-9956
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Zusammenfassung:The polynomial Hensel code of a rational function a(x)/ b(x) ϵ F(x), F is a field, is the pair (c(x) d-1(x) mod Xr, n); r is a positive integer and a(x)/ b(x) = (c(x))xn such that c(x) and d(x) have nonzero constant terms. Such a representation scheme was proposed, in analogy with the Hensel code representations of rational numbers, to facilitate arithmetic operations on rational functions and control intermediate expressions well. The difficulty with this scheme was the conversion of such a code to rational function form. In this correspondence, we have given sufficient conditions under which this can be done and have described an algorithm for effecting the conversion. We have also discussed an application, namely, the reduction of a rational function to its simplest form.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.1987.1676950