Issue No. 04 - April (1983 vol. 32)
E.V. Krishnamurthy , Department of Applied Mathematics, Indian Institute of Science, Bangalore 560012, India, and the IDL?Nitro Nobel Basic Research Institute
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.
reciprocal, Hensel code, Hensel lemma, higher order convergence, iterate, Newton method, p-adic numbers, quadratic convergence
V. Murthy and E. Krishnamurthy, "Fast Iterative Division of p-adic Numbers," in IEEE Transactions on Computers, vol. 32, no. , pp. 396-398, 1983.