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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 1, Pages 116–117 (Mi zvmmf11020)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-001174
Ministry of Education, Science and Sport of Slovenia research programme P1-0294
Abramov’s research was supported in part by the Russian Foundation for Basic Research, project no. 19-01-00032-a. PetkovЕЎek’s research was supported in part by the Ministry of Education, Science, and Sport of Slovenia research program P1-0294.


DOI: https://doi.org/10.31857/S0044466920010044


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:1, 109–118

Bibliographic databases:

UDC: 517.929
Received: 20.07.2019
Revised: 31.08.2019
Accepted:18.09.2019
Language:

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

Citation in format AMSBIB
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\paper Matrices of scalar differential operators: divisibility and spaces of solutions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 1
\pages 116--117
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\crossref{https://doi.org/10.31857/S0044466920010044}
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