  We introduce some general tools to design exact splitting methods to compute
numerically semigroups generated by inhomogeneous quadratic differential
operators. More precisely, we factorize these semigroups as products of
semigroups that can be approximated efficiently, using, for example,
pseudo-spectral methods. We highlight the efficiency of these new methods on
the examples of the magnetic linear Schr{\"o}dinger equations with quadratic
potentials, some transport equations and some Fokker-Planck equations.
