  Motivated by easy access to complete corepresentation (corep) data of all the
1651 magnetic space groups (MSGs) in three-dimensional space, we have developed
a Mathematica package MSGCorep to provide an offline database of coreps and
various functions to manipulate them, based on our previous package
SpaceGroupIrep. One can use the package MSGCorep to obtain the elements of any
MSG and magnetic little group, to calculate the multiplication of group
elements, to obtain the small coreps at any k-point and full coreps of any
magnetic k-star for any MSG and show them in a user-friendly table form, to
calculate and show the decomposition of direct products of full coreps between
any two specified magnetic k-stars, and to determine the small coreps of energy
bands. Both single-valued and double-valued coreps are supported. In addition,
the 122 magnetic point groups (MPGs) and their coreps are also supported by
this package. To the best of our knowledge, MSGCorep is the first package that
is able to calculate the direct product of full coreps for any MSG and able to
determine small coreps of energy bands for general purpose. In a word, the
MSGCorep package is an offline database and tool set for MSGs, MPGs, and their
coreps, and it is very useful to study the symmetries in magnetic and
nonmagnetic materials.
