#### Formulas for Linear Symbolic Newton Iteration.

Let be an Euclidean domain with a regular Euclidean size . Let be a prime element. Let and let such that
1. ,
2. ,
3. .
If is unknown, but and are known then we can compute a -adic expansion of as follows. Let be a -adic expansion of w.r.t. . Let be a positive integer. Recall that the element

 (1)

is a -adic approximation of at order . Let us denote by the canonical homomorphism from to . The following formula computes from :

 (2)

Marc Moreno Maza
2008-01-31