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On the Conversion of Hensel Codes to Farey Rationals
April 1983 (vol. 32 no. 4)
pp. 331-337
E.V. Krishnamurthy, IDL-Nitro Nobel Basic Research Institute, Bangalore-560012, India, and with the Department of Applied Mathematics and Computer Science, Indian Institute of Science
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).
Index Terms:
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
Citation:
E.V. Krishnamurthy, "On the Conversion of Hensel Codes to Farey Rationals," IEEE Transactions on Computers, vol. 32, no. 4, pp. 331-337, April 1983, doi:10.1109/TC.1983.1676233
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