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Designing for geometrical symmetry exploitation

Symmetry-exploiting software based on the generalized Fourier transform (GFT) is presented from a practical design point of view. The algorithms and data structures map closely to the relevant mathematical abstractions, which primarily are based upon representation theory for groups. Particular care has been taken in the design of the data layout of the performance-sensitive numerical data structures. 
 
The use of a vanilla strategy is advocated for the design of flexible mathematical software libraries: An efficient general-purpose routine should be supplied, to obtain a practical and useful system, while the possibility to extend the library and replace the default routine with a special-purpose - even more optimized - routine should be supported. 
 
Compared with a direct approach, the performance results show the superiority of the GFT-based approach for so-called dense equivariant systems. The GFT application is found to be well suited for parallelism.