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Fast Iterative Division of p-adic Numbers

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2 Author(s)
Krishnamurthy, E.V. ; Department of Applied Mathematics, Indian Institute of Science, Bangalore 560012, India, and the IDL—Nitro Nobel Basic Research Institute ; Murthy, V.K.

A fast iterative scheme based on the Newton method is described for finding the reciprocal of a finite segment p-adic numbers (Hensel code). The rate of generation of the reciprocal digits per step can be made quadratic or higher order by a proper choice of the starting value and the iterating function. The extension of this method to find the inverse transform of the Hensel code of a rational polynomial over a finite field is also indicated.

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Computers, IEEE Transactions on  (Volume:C-32 ,  Issue: 4 )