The geometric primitives of APL

Authors:
N. D. Thomson
Affiliations:
Education and Training Dept., IBM (UK) Laboratories Ltd., Hursley Park,Wlnchester, Hants., ENGLAND
Venue:
APL '79 Proceedings of the international conference on APL: part 1
Year:
1979

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Abstract

The roles of &fgr;, &THgr;, and @@@@ in describing the symmetries of the square are investigated. This leads to relationships between the results of these functions and the cyclic and dihedral groups of orders 2 and 4. Numerical modelling of these groups is accomplished through the primitives @@@@ and &Tgr; which are thus seen to play an important auxiliary role. Next the behavior of the functions @@@@ and @@@@ applied to permutation vectors is investigated, and parallels are observed between these primitives and the primitives &fgr;, &THgr;, and @@@@. These similarities are heightened by considering the partitioning of all permutations of a given order according to their internal symmetries.