This subroutine uses a variant of Sloan’s method to calculate a symmetric permutation that aims to reduce the proﬁle and wavefront of a sparse matrix with a symmetric sparsity pattern. Alternatively, the Reverse Cuthill-McKee (RCM) method may be requested to reduce the bandwidth. There are optional facilities for looking for sets of columns with identical patterns and taking advantage of them. There is also an option for computing a row order that would be appropriate for use with a row-by-row frontal solver (for example, the equation entry to MA42 or MA43). These optional facilities may also be used independently.