The padic 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 padic calculations using Mathematica. It allows addition, subtraction, multiplication, and division of padic 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 padic Newton method.
Notebook
PDF
HTML
Introduction
padic Order and Valuation
Conversion to padics
Basic padic Arithmetic
Booleans and Selectors on padic Rationals
Function Expansion
VolkenbornIntegral
padic Newton Method
References
Additional Material


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