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On the Conversion of Hensel Codes to Farey Rationals

Krishnamurthy, EV (1983) On the Conversion of Hensel Codes to Farey Rationals. In: IEEE Transactions on Computers, 32 (4). pp. 331-337.

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Abstract

Three different algorithms are described for the conversion of Hensel codes to Farey rationals. The first algorithm is based on the trial and error factorization of the weight of a Hensel code, inversion and range test. The second algorithm is deterministic and uses a pair of different p-adic systems for simultaneous computation; from the resulting weights of the two different Hensel codes of the same rational, two equivalence classes of rationals are generated using the respective primitive roots. The intersection of these two equivalence classes uniquely identifies the rational. Both the above algorithms are exponential (in time and/or space).

Item Type: Journal Article
Additional Information: Copyright 1983 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: reduced residue system;Conversion;Euclidean filtering algorithm;Euler's totient function;extended Euclidean algorithm;factorization;Farey rationals;greatest common divisor;Hensel code;index;isobaric set;multiplicative inverse;p-adic arithmetic;primitive root
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 06 Feb 2010 07:36
Last Modified: 19 Sep 2010 05:37
URI: http://eprints.iisc.ernet.in/id/eprint/21426

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