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This article is cited in 1 scientific paper (total in 1 paper)
Matrices of scalar differential operators: divisibility and spaces of solutions
S. A. Abramova, M. A. Barkatoub, M. Petkovšekc a Dorodnicyn Computing Center of Federal Research Center "Computer Science and Control" of the Russian Academy
of Science, Vavilova str., 40, Moscow, 119333, Russia
b University of Limoges, CNRS, XLIM UMR 7252, MATHIS, 123, Av. A. Thomas, 87060 Limoges cedex, France
c University of Ljubljana, Faculty of Mathematics and Physics, Jadranska, 19, SI-1000, Ljubljana, Slovenia
Abstract:
We investigate the connection between divisibility of full-rank square matrices of linear scalar differential operators over some differential field $K$, and the solution spaces of these matrices over the universal Picard–Vessiot extension of $K$. We establish some properties of the solution spaces of the greatest common right divisor and the least common left multiple of such matrices.
Key words:
computer algebra algorithms, differential operator matrices, divisibility of square matrices of differential operators, solution space, greatest common right divisor, least common left multiple.
Received: 20.07.2019 Revised: 31.08.2019 Accepted: 18.09.2019
Citation:
S. A. Abramov, M. A. Barkatou, M. Petkovšek, “Matrices of scalar differential operators: divisibility and spaces of solutions”, Zh. Vychisl. Mat. Mat. Fiz., 60:1 (2020), 116–117; Comput. Math. Math. Phys., 60:1 (2020), 109–118
Linking options:
https://www.mathnet.ru/eng/zvmmf11020 https://www.mathnet.ru/eng/zvmmf/v60/i1/p116
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Abstract page: | 62 | References: | 3 |
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