  We give an extensive description of the renormalisation of the Higgs sector
of the minimal supersymmetric model in SloopS. SloopS is an automatised code
for the computation of one-loop processes in the MSSM. In this paper, the first
in a series, we study in detail the non gauge invariance of some definitions of
tan(beta). We rely on a general non-linear gauge fixing constraint to make the
gauge parameter dependence of different schemes for tan(beta) at one-loop
explicit. In so doing, we update, within these general gauges, an important
Ward-Slavnov-Taylor identity on the mixing between the pseudo-scalar Higgs,
A^0, and the Z^0. We then compare the tan(beta) scheme dependence of a few
observables. We find that the best tan(beta) scheme is the one based on the
decay A^0 -> tau^+ tau^- because of its gauge invariance, being unambiguously
defined from a physical observable, and because it is numerically stable. The
oft used DRbar scheme performs almost as well on the last count, but is usually
defined from non-gauge invariant quantities in the Higgs sector. The use of the
heavier scalar Higgs mass in lieu of tan(beta) though related to a physical
parameter induces too large radiative corrections in many instances and is
therefore not recommended.
