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The local geometry of a Riemannian symmetric space is described completely bythe Riemannian metric and the Riemannian curvature tensor of the space. In thepresent article I describe how to compute these tensors for any Riemanniansymmetric space from the Satake diagram, in a way that is suited for the usewith computer algebra systems. As an example application, the totally geodesicsubmanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.  The submission also contains an example implementation of the algorithms andformulas of the paper as a package for Maple 10, the technical documentationfor this implementation, and a worksheet carrying out the computations for thespace SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.

Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram