  In recent years, great success has been achieved on the classification of
symmetry-protected topological (SPT) phases for interacting fermion systems by
using generalized cohomology theory. However, the explicit calculation of
generalized cohomology theory is extremely hard due to the difficulty of
computing obstruction functions. In this paper, based on the physical picture
of topological invariants and mathematical techniques in homotopy algebra, we
develop an algorithm to resolve this hard problem. It is well known that
cochains in the cohomology of the symmetry group, which are used to enumerate
the SPT phases, can be expressed equivalently in different linear bases, known
as the resolutions. By expressing the cochains in a reduced resolution
containing much fewer basis than the choice commonly used in previous studies,
the computational cost is drastically reduced. In particular, it reduces the
computational cost for infinite discrete symmetry groups, like the wallpaper
groups and space groups, from infinity to finity. As examples, we compute the
classification of two-dimensional interacting fermionic SPT phases, for all 17
wallpaper symmetry groups
