International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, pp. 8788

The matrix is its own contragredient, and hence (Section 1.3.2.4.2.2) the transform of a symmetric (respectively antisymmetric) function is symmetric (respectively antisymmetric). In this case the group acts in both real and reciprocal space as . If with both factors diagonal, then acts byi.e.
The symmetry or antisymmetry properties of X may be writtenwith for symmetry and for antisymmetry.
The computation will be summarized aswith the same indexing as that used for structurefactor calculation. In both cases it will be shown that a transform with and M diagonal can be computed using only partial transforms instead of .