Let
be a real
multiquadratic field and
be a set of prime ideals of
.
In this paper, we present a heuristic algorithm for the computation of the
-class group and
the
-unit group
that runs in time
where
and
is the
discriminant of
.
We use this method to compute the ideal class group of the maximal order
of
in time
. When
for some
constant
,
these methods run in polynomial time. We implemented our algorithm using Sage
7.5.1.
Keywords
ideal class group, $S$-unit group, multiquadratic fields