The Mathematica Journal
Volume 9, Issue 2


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p-adic Arithmetic
Stany De Smedt

The p-adic numbers were introduced by K. Hensel in 1908 in his book Theorie der algebraïschen Zahlen, Leipzig, 1908. In this article we present a package that does p-adic calculations using Mathematica. It allows addition, subtraction, multiplication, and division of p-adic numbers written in Hensel expansion. Functions, such as sqrt, log, exp, sin, cos, sinh, and cosh, are defined using their power series expansion. We also calculate the coefficients of a continuous function with respect to the Mahler and Vanderput bases, and implement the p-adic Newton method.





  *p-adic Order and Valuation

  *Conversion to p-adics

  *Basic p-adic Arithmetic

  *Booleans and Selectors on p-adic Rationals

  *Function Expansion


  *p-adic Newton Method


  *Additional Material

Stany De Smedt
KBC Bank & Verzekeringen
Havenlaan 12,1080 Brussels, Belgium

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