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In 2010, M. Sakai and the first author showed that the topological complexityof a space $X$ coincides with the fibrewise unpointed L-S category of a pointedfibrewise space $\operatorname{pr}_{1} : X \times X \to X$ with the diagonalmap $\Delta : X \to X \times X$ as its section. In this paper, we describe ouralgorithm how to determine the fibrewise L-S category or the TopologicalComplexity of a topological spherical space form. Especially, for $S^3/Q_8$where $Q_8$ is the quaternion group, we write a python code to realise thealgorithm to determine its Topological Complexity.

Topological Complexity of $S^3/Q_8$ as fibrewise L-S category