Geodesic
Simple and generalized elements search in nested arrays and their replacement
Čebyševskij sbornik, Tome 16 (2015) no. 3, pp. 460-478.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article provides a series of custom recursive functions for a variety of tasks of searching and replacing elements in nested arrays. The latter are defined recursively, as is done in the system of engineering and scientific calculations, PTC Mathcad Prime, then there are matrices whose elements can be scalars, strings, and again the nesting arrays. Some problems of the search are considered in [1-4]. Our goal was the development of existing and creation of new means associated with both simple and generalized searching and replacing elements in nested arrays. Let A be a scalar, a string, or a nested array, B — nested array. The problem with generalized occurrences of A in B (generalized searching A in B) and replaced of such occurrences arise when A or B to be included by special elements associated with any scalar, string or nested array. In the article are formulated 10 problems. For each suggested one or more solutions as functions in a programming language PTC Mathcad Prime. All the features are tested on a large number of examples, but the tests are not completely. Bibliography: 7 titles.
Keywords: nested array, matrix, tree, recursion, recursive function, search and replace, generalized searching, PTC Mathcad. 
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S. G. Grigoryev; A. R. Esayan. Simple and generalized elements search in nested arrays and their replacement. Čebyševskij sbornik, Tome 16 (2015) no. 3, pp. 460-478. http://geodesic.mathdoc.fr/item/CHEB_2015_16_3_a22/

[1] Esayan A. R., Dobrovolsky N. M., “Nested arrays and recursion”, Proc. XXIII Int. Conf. “Algebra, number theory and discrete geometry. Modern problems and applications” (Tula, May 25–30, 2015), 2015, 319–321 (in Russian)

[2] Esayan A. R., Yakushin A. V., “Vectorization and nested arrays”, Proc. XXIII Int. Conf. “Algebra, number theory and discrete geometry. Modern problems and applications” (Tula, May 25–30, 2015), 2015, 328–330 (in Russian)

[3] Esayan A. R., Dobrovolsky N. M., “Nested arrays and recursion”, Chebyshevskii Sb., 16:3(55) (2015), 479–495 (in Russian)

[4] Esayan A. R., Yakushin A. V., “Vectorization and nested arrays”, Chebyshevskii Sb., 16:3(55) (2015), 496–509 (in Russian)

[5] Esayan A. R., Teaching algorithmization based on recursion, TGPU, Tula, 2001, 215 pp. (in Russian)

[6] Maxfield B., Essential PTC Mathcad Prime 3.0. A Guide for New and Current Users, Academic Press is an imprint of Elsevier, New York, Nov. 11, 2013, 563 pp.

[7] Nans Wessenlingh and Hans de Waard, Calculate Communicate with Mathcad Prime 3.0, First edition, Delft Academic Press, The Netherlands, 2014