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10.1145/800136.804479acmconferencesArticle/Chapter ViewAbstractPublication PagesaplConference Proceedingsconference-collections
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The geometric primitives of APL

Published: 30 May 1979 Publication History

Abstract

The roles of φ, θ, 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 ⊤ 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 φ, θ, and ⦰. These similarities are heightened by considering the partitioning of all permutations of a given order according to their internal symmetries.

Reference

[1]
K.E.Iverson, "Formalism in Programming Languages", Communications of the A.C.M., Vol. 7 No. 2, Feb. 1964 pp.80-88.

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cover image ACM Conferences
APL '79: Proceedings of the international conference on APL: part 1
May 1979
403 pages
ISBN:9781450374408
DOI:10.1145/800136
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 30 May 1979

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