Let
be an Euclidean domain with a regular
Euclidean size
.
Let
be a prime element.
Let
and let
such that

,

,

.
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
20080131