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Volumn 22, Issue 2, 1996, Pages 179-200

Note on Kovacic's algorithm

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EID: 0030209957     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1996.0047     Document Type: Article
Times cited : (57)

References (27)
  • 2
    • 85008411704 scopus 로고
    • Solutions of linear differential equations in their coefficient field
    • Bronstein, M. (1992). Solutions of linear differential equations in their coefficient field. J. Symbolic Computation 13, 413-439.
    • (1992) J. Symbolic Computation , vol.13 , pp. 413-439
    • Bronstein, M.1
  • 3
    • 0000761723 scopus 로고
    • Kovacic's algorithm and its application to some families of special functions
    • Duval, A., Loday-Richaud, M. (1992) Kovacic's algorithm and its application to some families of special functions. Appl. Alg. in Eng. Comm. and Comp. 3, 211-246.
    • (1992) Appl. Alg. in Eng. Comm. and Comp. , vol.3 , pp. 211-246
    • Duval, A.1    Loday-Richaud, M.2
  • 4
    • 0011419932 scopus 로고
    • Ueber die linearen differentialgleichungen zweiter ordnung, welche algebraische integrale besitzen, zweite abhandlung
    • Fuchs, L. (1878). Ueber die linearen Differentialgleichungen zweiter Ordnung, welche algebraische Integrale besitzen, zweite Abhandlung. J. für Math. 85, 1-25.
    • (1878) J. Für Math. , vol.85 , pp. 1-25
    • Fuchs, L.1
  • 5
    • 85027600141 scopus 로고
    • A rationality result for Kovacic's algorithm
    • New York: ACM press
    • Hendriks, P., van der Put, M. (1993) A rationality result for Kovacic's algorithm Proceedings ISSAC'93, New York: ACM press.
    • (1993) Proceedings Issac'93
    • Hendriks, P.1    Van der Put, M.2
  • 6
    • 0001331665 scopus 로고
    • Galois action on solutions of linear differential equations
    • Hendriks, P., van der Put, M. (1995). Galois action on solutions of linear differential equations. J. Symbolic Computation 19, 559-576.
    • (1995) J. Symbolic Computation , vol.19 , pp. 559-576
    • Hendriks, P.1    Van der Put, M.2
  • 7
    • 0011515848 scopus 로고
    • Mémoire sur les équations différentielles linéaires à intégrale algébrique
    • Jordan, C. (1878). Mémoire sur les équations différentielles linéaires à intégrale algébrique. J. für Math. 84, 89-215.
    • (1878) J. Für Math. , vol.84 , pp. 89-215
    • Jordan, C.1
  • 9
    • 0002007894 scopus 로고
    • Algebraic matrix groups and the picard-vessiot theory of homogeneous linear ordinary differential equations
    • Kolchin, E. R. (1948). Algebraic matrix groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations., Annals of Math. 49, 1-42.
    • (1948) Annals of Math. , vol.49 , pp. 1-42
    • Kolchin, E.R.1
  • 10
    • 41549083615 scopus 로고
    • An algorithm for solving second order linear homogeneous differential equations
    • Kovacic, J. (1986). An algorithm for solving second order linear homogeneous differential equations. J. Symbolic Computation 2, 3-43.
    • (1986) J. Symbolic Computation , vol.2 , pp. 3-43
    • Kovacic, J.1
  • 12
    • 33749555740 scopus 로고
    • Sur la détermination des intégrales dont la valeur est algébrique
    • Liouville, J. (1833). Sur la détermination des intégrales dont la valeur est algébrique. J. de l'École Polytechnique 22, 149-193.
    • (1833) J. De L'école Polytechnique , vol.22 , pp. 149-193
    • Liouville, J.1
  • 13
    • 0011413520 scopus 로고
    • Méthode pour obtenir les intégrales algébriques des équations différentielles linéaires du second ordre
    • Pépin, P.TH. (1881). Méthode pour obtenir les intégrales algébriques des équations différentielles linéaires du second ordre. Atti dell' Accad. Pont. de Nuovi Lincei, XXXIV, 243-388.
    • (1881) Atti Dell' Accad. Pont. De Nuovi Lincei , vol.34 , pp. 243-388
    • Pépin, P.T.H.1
  • 14
    • 0001072553 scopus 로고
    • Theory of non-commutative polynomials
    • Ore, O. (1933). Theory of non-commutative polynomials. Ann. of Math. 34, 480-508.
    • (1933) Ann. of Math. , vol.34 , pp. 480-508
    • Ore, O.1
  • 16
    • 0000594770 scopus 로고
    • Liouvillian solutions of nth order homogeneous linear differential equations
    • Singer, M.F. (1981). Liouvillian solutions of nth order homogeneous linear differential equations. Amer. J. Math. 103, 661-682.
    • (1981) Amer. J. Math. , vol.103 , pp. 661-682
    • Singer, M.F.1
  • 17
    • 0002075795 scopus 로고
    • An outline of differential galois theory
    • ed E. Tournier, New York: Academic Press
    • Singer, M.F. (1990). An outline of differential Galois theory. In Computer Algebra and Differential Equations, ed E. Tournier, New York: Academic Press.
    • (1990) Computer Algebra and Differential Equations
    • Singer, M.F.1
  • 18
    • 0000163677 scopus 로고
    • Liouvillian solutions of linear differential equations with Liouvillian coefficients
    • Singer, M.F. (1991). Liouvillian solutions of linear differential equations with Liouvillian coefficients. J. Symbolic Computation 11, 251-273.
    • (1991) J. Symbolic Computation , vol.11 , pp. 251-273
    • Singer, M.F.1
  • 19
    • 0041523852 scopus 로고    scopus 로고
    • Testing reducibility of linear differential operators: A group theoretic perspective
    • Singer, M.F. (1996). Testing reducibility of linear differential operators: a group theoretic perspective. Appl. Alg. in Eng. Comm. and Comp. 7, 77-104.
    • (1996) Appl. Alg. in Eng. Comm. and Comp. , vol.7 , pp. 77-104
    • Singer, M.F.1
  • 20
    • 43949170180 scopus 로고
    • Galois groups of second and third order linear differential equations
    • Singer, M.F., Ulmer, F. (1993a). Galois groups of second and third order linear differential equations. J. Symbolic Computation 16, 1-36.
    • (1993) J. Symbolic Computation , vol.16 , pp. 1-36
    • Singer, M.F.1    Ulmer, F.2
  • 21
    • 38249003324 scopus 로고
    • Liouvillian and algebraic solutions of second and third order linear differential equations
    • Singer, M.F., Ulmer, F. (1993b). Liouvillian and algebraic solutions of second and third order linear differential equations. J. Symbolic Computation 16, 37-73.
    • (1993) J. Symbolic Computation , vol.16 , pp. 37-73
    • Singer, M.F.1    Ulmer, F.2
  • 22
    • 0029230902 scopus 로고
    • Necessary conditions for Liouvillian solutions of (third order) linear differential equations
    • Singer, M.F., Ulmer, F. (1994). Necessary conditions for Liouvillian solutions of (third order) linear differential equations. Appl. Alg. in Eng. Comm. and Comp. 6, 1-22.
    • (1994) Appl. Alg. in Eng. Comm. and Comp. , vol.6 , pp. 1-22
    • Singer, M.F.1    Ulmer, F.2
  • 24
    • 0003834321 scopus 로고
    • Texts and Monographs in Symbolic Computation, Wien: Springer-Verlag
    • Sturmfels, B. (1993). Algorithms in Invariant Theory, Texts and Monographs in Symbolic Computation, Wien: Springer-Verlag.
    • (1993) Algorithms in Invariant Theory
    • Sturmfels, B.1
  • 25
    • 0000570124 scopus 로고
    • On Liouvillian solutions of differential equations
    • Ulmer, F. (1992). On Liouvillian solutions of differential equations. Appl. Alg. in Eng. Comm. and Comp. 2, 171-193.
    • (1992) Appl. Alg. in Eng. Comm. and Comp. , vol.2 , pp. 171-193
    • Ulmer, F.1
  • 26
    • 0000880341 scopus 로고
    • Linear differential equations of prime order
    • Ulmer, F. (1994) Linear differential equations of prime order. J. Symbolic Computation 18, 385-401.
    • (1994) J. Symbolic Computation , vol.18 , pp. 385-401
    • Ulmer, F.1
  • 27
    • 0011458741 scopus 로고
    • The use of the special semi-groups for solving quasi-linear differential equations
    • New York: ACM press
    • Weil, J.-A. (1994), The use of the Special semi-groups for solving quasi-linear differential equations Proceedings ISSAC'94, New York: ACM press.
    • (1994) Proceedings ISSAC'94
    • Weil, J.-A.1


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