By default, the group elements acting on a ring are passed as onerow substitution matrices as those accepted by substitute. Setting Sub=>false allows the user to pass these elements as square matrices.
The example below sets up the action of a symmetric group on the resolution of a monomial ideal. The symmetric group acts by permuting the four variables of the ring. The conjugacy classes of permutations are determined by their cycle types, which are in bijection with partitions. In this case, we consider five permutations with cycle types, in order: 4, 31, 22, 211, 1111. For simplicity, we construct these matrices by permuting columns of the identity.





Similarly, setting Sub=>false causes ringActors and inverseRingActors to return the group elements acting on the ring as square matrices. With the default setting Sub=>true, the same elements are returned as onerow substitution matrices.



