Satellite Unknowns in Irreducible Differential Systems
- 12 Downloads
In this paper, the concept of satellite unknowns in differential systems with selected unknowns is considered in the context of irreducible systems. It is proved that any unselected unknown in an irreducible differential system is linearly satellite for any nonempty set of selected unknowns. An algorithm for factorization of differential systems is proposed that is not always applicable but executable in polynomial time. Cases where the algorithm cannot be applied are also recognized in polynomial time.
Unable to display preview. Download preview PDF.
- 1.Panferov, A.A., On determination of satellite unknowns in linear differential systems, Materialy mezhdunarodnoi konferentsii Komp’yuternaya algebra (Proc. Int. Conf. Computer Algebra), Moscow, 2016, pp. 78–80.Google Scholar
- 4.van der Put, M. and Singer, M.F., Galois theory of linear differential equations, Grundlehren der mathematischen Wissenschaften, Berlin: Springer, 2003.Google Scholar
- 7.Panferov, A.A., Symbolic algorithm for recognition of satellite unknowns in linear differential systems with selected unknowns, Nauchnaya konferentsiya Lomonosovskie chteniya (Sci. Conf. Lomonosov Readings) (Moscow, 2017), Moscow: MAKS Press, 2017, pp. 122–122.Google Scholar
- 13.Cluzeau, T., Factorization of differential systems in characteristic p, Proc. ISSAC, 2003, pp. 58–65.Google Scholar
- 14.Bolibrukh, A.A., Obratnye zadachi monodromii v analiticheskoi teorii differentsial’nykh uravnenii (Inverse Monodromy Problems in the Analytical Theory of Differential Equations), Moscow: Moscow Cent. Contin. Math. Educ., 2009.Google Scholar
- 16.Schwarz, F., A factorization algorithm for linear ordinary differential equations, Proc. ISSAC, 1989, pp. 17–25.Google Scholar
- 20.Tsarev, S.P., An algorithm for complete enumeration of all factorizations of a linear ordinary differential operator, Proc. ISSAC, 1996, pp. 226–231.Google Scholar