  Semiclassical techniques have proven to be a very powerful method to extract
physical effects from different quantum theories. Therefore, it is expected
that in the near future they will play a very prominent role in the context of
quantum gravity. In this work we develop systematic tools to derive
semiclassical approximations for any quantum theory with one degree of freedom.
In our approach, the wave function is decomposed in terms of an infinite set of
moments, which encode the complete quantum information of the system.
Semiclassical regimes can then be properly described by truncation of this
infinite system. The use of efficient computer algebra tools allows us to
compute the equations of motion up to a very high order. In this way, we can
study very precisely the quantum back reaction of the system as well as the
convergence of the method with the considered order. Finally, these tools are
applied to the particular case of a homogeneous universe filled with a massless
scalar field and positive cosmological constant, which provide interesting
physical results.
