Abstract. In a recent comment Sneddon discussed the set of fourteen algebraic invariants of the Riemann curvature tensor in four dimensions. The focus was rectification of an error (in the form of lack of independence) in an earlier construction and the presentation of a corrected set suitable for application. Several authors who have worked on this problem were mentioned. The comment, however, did not mention the work of Narlikar and Karmarkar who presented a set of invariants well before the earliest work cited in the comment. The original publication by Narlikar and Karmarkar may not be readily available so we list and make a few comments on their set.Recently, Sneddon (1986) discussed briefly the form in which several authors have presented the fourteen independent algebraic invariants (Haskins 1902)$ of the Riemann curvature tensor in four dimensions. Among the authors mentioned were GChCniau and Debever (1956a, b, c) with implied priority of publication. This accords with common usage in which these scalars are almost universally referred to as the 'GChCniau-Debever' scalars. The fact is that Narlikar and Karmarkar (1948) published such a set substantially earlier.

In this paper we discuss the package DESOLV written for the algebraic computing system MAPLE. DESOLV has routines which will systematically obtain with considerably flexibility, all resulting integrability conditions for any system of linear, coupled, partial differential equations. It also contains routines which will automatically generate and attempt to integrate the determining equations for the Lie symmetries of differential equations.

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We consider all purely magnetic, locally rotationally symmetric (LRS) spacetimes. It is shown that such spacetimes belong to either LRS class I or III by the Ellis classification. For each class the most general solution is found exhibiting a disposable function and three parameters. A Segré classification of purely magnetic LRS spacetimes is given together with the compatibility requirements of two general energy–momentum tensors. Finally, implicit solutions are obtained, in each class, when the energy–momentum tensor is a perfect fluid.

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