A common problem in the practical implementation of quantum many-body theory [whether for quantum chemistry, solid state physics, or nuclear physics] goes like this. One starts with a Hamiltonian and observables that are written in terms of second quantised operators. Real calculations of observables requires diagonalising the Hamiltonian matrix. It must then be written as a symmetric real matrix in some basis of many-body states.
To do this means manipulating large numbers of creation and annihilation operators. This can quickly become cumbersome, particularly for fermions. It is easy to loose track of signs when calculating matrix elements. It would be nice to be able to do this in an automated way, e.g., using Mathematica.
Sriram Shastry and John Wright have developed a Mathematica program DiracQ that will do all this. It can be downloaded for free and is described in detail in a preprint. The latter contains some highly non-trivial examples, e.g., finding the conserved quantities of the one-dimensional Hubbard model.
This should be very useful, both for research and teaching.