PyTables seems to be the correct data storage

The PyTables package is a Python interface to HDF5, which is a general purpose library and file format for storing scientific data made at NCSA. HDF5 can store two primary objects: datasets and groups. A dataset is essentially a multidimensional array of data elements, and a group is a structure for organizing objects in an HDF5 file (very similar to a directory in a filesystem).

Need to check GiNaC to provide algebraic manipulation to my software

Found “GiNaC is Not a CAS“, a symbolic algebra manipulation system. Through swiginac it will be possible to use it from Python. The only concern is that may be an overkill.