  Difference schemes are considered for dynamical systems $ \dot x = f (x) $
with a quadratic right-hand side, which have $t$-symmetry and are reversible.
Reversibility is interpreted in the sense that the Cremona transformation is
performed at each step in the calculations using a difference scheme. The
inheritance of periodicity and the Painlev\'e property by the approximate
solution is investigated. In the computer algebra system Sage, such values are
found for the step $ \Delta t $, for which the approximate solution is a
sequence of points with the period $ n \in \mathbb N $. Examples are given and
hypotheses about the structure of the sets of initial data generating sequences
with the period $ n $ are formulated.
