Given a matrix group G with base ring R, construct a new matrix group H with base ring S derived from G by coercing entries of the generators of G from R into S.

ChangeRing(G, S, f) : GrpMat, Rng, Map -> GrpMat, Map

Given a matrix group G with base ring R, construct a new matrix group H with base ring S derived from G by applying f to the entries of the generators of G.

Given a matrix group G with base ring K, a finite field, and S a subfield of K, construct the matrix group H with base ring S obtained by restricting the scalars of the components of elements of G into S, together with the restriction map from G onto H.

Given a matrix group G with base ring K, a finite field, and L an extension of K, construct the matrix group H with base ring L obtained by lifting the components of elements of G into L, together with the inclusion homomorphism from G into H.