Satellite Unknowns in Irreducible Differential Systems

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 

2. Panferov, A.A., Selected and satellite unknowns in linear differential systems, Adv. Appl. Math., 2017, vol. 85, pp. 1–11.

   Article  MathSciNet  MATH  Google Scholar 

3. Panferov, A.A., Partial algorithms for satellite unknowns determination, Program. Comput. Software, 2017, vol. 43, no. 2, pp. 119–125.

   Article  MathSciNet  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 

5. Minchenko, A., Ovchinnikov, A., and Singer, M.F., Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations, Int. Math. Res. Notices, 2015, vol. 215, no. 7, pp. 1733–1793.

   Article  MathSciNet  MATH  Google Scholar 

6. Hrushovski, E., Computing the Galois group of a linear differential equation, Banach Center Publications, 2002, vol. 58, pp. 97–138.

   Article  MathSciNet  MATH  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 

8. Abramov, S.A. and Bronshtein, M., Solution of linear differential and difference systems with respect to a part of the unknowns, Comput. Math. Math.Phys., 2006, vol. 46, no. 2, pp. 218–230.

   Article  MathSciNet  Google Scholar 

9. Feng, R., Hrushovski’s algorithm for computing the Galois group of a linear differential equation, Adv. Appl. Math., 2015, vol. 65, pp. 1–37.

   Article  MathSciNet  MATH  Google Scholar 

10. Panferov, A.A., Differential equation systems with selected part of the unknowns, Program. Comput. Software, 2015, vol. 41, no. 2, pp. 90–97.

    Article  MathSciNet  MATH  Google Scholar 

11. Panferov, A.A., Partitions of the set of selected unknowns in linear differential–algebraic systems, Program. Comput. Software, 2016, vol. 42, no. 2, pp. 84–89.

    Article  MathSciNet  MATH  Google Scholar 

12. Compoint, E. and Singer, M.F., Computing Galois groups of completely reducible differential equations, J. Symbol. Comput., 1999, vol. 28, pp. 473–494.

    Article  MathSciNet  MATH  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 

15. Beke, E., Die irreducibilität der homogenen linearen differentialgleichungen, Mathematische Annalen, 1894, vol. 45, pp. 185–195.

    MATH  Google Scholar 

16. Schwarz, F., A factorization algorithm for linear ordinary differential equations, Proc. ISSAC, 1989, pp. 17–25.

    Google Scholar 

17. Bronstein, M., On solutions of linear differential equations in their coefficient field, J. Symbol. Comput., 1992, vol. 13, pp. 413–439.

    Article  MathSciNet  MATH  Google Scholar 

18. Grigoriev, D.Yu., Complexity of factoring and calculating the gcd of linear ordinary differential operators, J. Symbol. Comput., 1990, vol. 10, pp. 7–37.

    Article  MathSciNet  Google Scholar 

19. Singer, M.F., Testing reducibility of linear differential operators: A group theory perspective, Appl. Algebra Eng. Commun. Comput., 1996, vol. 7, no. 2, pp. 77–104.

    Article  MATH  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 

21. van Hoeij, M., Factorization of differential operators with rational functions coefficients, J. Symbol. Comput., 1997, vol. 24, pp. 537–561.

    Article  MathSciNet  MATH  Google Scholar 

22. Grigoriev, D.Yu., Complexity of irreducibility testing for a system of linear ordinary differential equations, Proc. ISSAC, 1990, pp. 225–230.

    Chapter  Google Scholar 

Download references