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Volumn 131, Issue 5, 2005, Pages 5885-5903

Univariate Ore polynomial rings in computer algebra

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EID: 27644495593     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10958-005-0449-8     Document Type: Article
Times cited : (41)

References (30)
  • 1
    • 0000614866 scopus 로고
    • Rational solutions of linear difference and differential equations with polynomial coefficients
    • S. A. Abramov, "Rational solutions of linear difference and differential equations with polynomial coefficients," USSR Comput. Maths. Math. Phys., 29, 7-12 (1989).
    • (1989) USSR Comput. Maths. Math. Phys. , vol.29 , pp. 7-12
    • Abramov, S.A.1
  • 2
    • 4344567591 scopus 로고    scopus 로고
    • Technical Report CS-2002-32, School of Computer Science, University of Waterloo, Ontario, Canada
    • S. A. Abramov, J. C. Carette, K. O. Geddes, and H. Q. Le, Symbolic Summation in Maple, Technical Report CS-2002-32, School of Computer Science, University of Waterloo, Ontario, Canada (2002).
    • (2002) Symbolic Summation in Maple
    • Abramov, S.A.1    Carette, J.C.2    Geddes, K.O.3    Le, H.Q.4
  • 3
    • 0346876958 scopus 로고    scopus 로고
    • Integration of solutions of linear functional equations
    • S. A. Abramov, M. van Hoeij, "Integration of solutions of linear functional equations," Integral Transform. Spec. Funct., 8, Nos. 1-2, 3-12 (1999).
    • (1999) Integral Transform. Spec. Funct. , vol.8 , Issue.1-2 , pp. 3-12
    • Abramov, S.A.1    Van Hoeij, M.2
  • 6
    • 0030397671 scopus 로고    scopus 로고
    • D'Alembertian solutions of inhomogeneous linear equations (differential, difference, and some other)
    • (Y. N. Lakshman, Ed.), ACM Press
    • S. A. Abramov and E. V. Zima, D'Alembertian solutions of inhomogeneous linear equations (differential, difference, and some other)," in: Proc. 1996 Int. Symp. Symbolic and Algebraic Computation (Y. N. Lakshman, Ed.), ACM Press (1997), pp. 232-240.
    • (1997) Proc. 1996 Int. Symp. Symbolic and Algebraic Computation , pp. 232-240
    • Abramov, S.A.1    Zima, E.V.2
  • 8
    • 0030576158 scopus 로고    scopus 로고
    • An introduction to pseudo-linear algebra
    • M. Bronstein and M. Petkovšek, "An introduction to pseudo-linear algebra," Theor. Comput. Sci., 157, 3-33 (1996).
    • (1996) Theor. Comput. Sci. , vol.157 , pp. 3-33
    • Bronstein, M.1    Petkovšek, M.2
  • 9
    • 0032141037 scopus 로고    scopus 로고
    • Noncommutative elimination in Ore algebras proves multivariate identities
    • F. Chyzak and B. Salvy, "Noncommutative elimination in Ore algebras proves multivariate identities," J. Symbolic Comput., 26, No. 2, 187-227 (1998).
    • (1998) J. Symbolic Comput. , vol.26 , Issue.2 , pp. 187-227
    • Chyzak, F.1    Salvy, B.2
  • 13
    • 0346460995 scopus 로고    scopus 로고
    • An algorithm of searching for the greatest common divisor for Ore polynomials with polynomial coefficients depending on a parameter
    • P. E. Glotov, "An algorithm of searching for the greatest common divisor for Ore polynomials with polynomial coefficients depending on a parameter," in: Program. Comput. Software, 24 No. 6, 275-283 (1998).
    • (1998) Program. Comput. Software , vol.24 , Issue.6 , pp. 275-283
    • Glotov, P.E.1
  • 14
    • 0038840100 scopus 로고
    • Decision procedure for indefinite hypergeometric summation
    • R. W. Gosper, "Decision procedure for indefinite hypergeometric summation," Proc. Natl. Acad. Sci. USA, 75, 40-42 (1978).
    • (1978) Proc. Natl. Acad. Sci. USA , vol.75 , pp. 40-42
    • Gosper, R.W.1
  • 15
    • 0036157415 scopus 로고    scopus 로고
    • FFT-like multiplication of linear differential operators
    • J. van der Hoeven, "FFT-like multiplication of linear differential operators," J. Symbolic Comput., 33, No. 1, 123-127 (2002).
    • (2002) J. Symbolic Comput. , vol.33 , Issue.1 , pp. 123-127
    • Van Der Hoeven, J.1
  • 16
    • 0009364726 scopus 로고
    • Pseudo-linear transformations
    • N. Jacobson, "Pseudo-linear transformations," Ann. Math., 38, No. 2, 484-507 (1937).
    • (1937) Ann. Math. , vol.38 , Issue.2 , pp. 484-507
    • Jacobson, N.1
  • 17
    • 84941388468 scopus 로고
    • Über irreduzible Differentialgleichungen
    • E. Landau, "Über irreduzible Differentialgleichungen," J. Reine Angew. Math., 124 115-120 (1902).
    • (1902) J. Reine Angew. Math. , vol.124 , pp. 115-120
    • Landau, E.1
  • 18
    • 0038742975 scopus 로고    scopus 로고
    • A direct algorithm to construct the minimal Z-pairs for rational functions
    • H. Q. Le, "A direct algorithm to construct the minimal Z-pairs for rational functions," Adv. Appl. Math., 30, 137-159 (2003).
    • (2003) Adv. Appl. Math. , vol.30 , pp. 137-159
    • Le, H.Q.1
  • 19
    • 0032514327 scopus 로고    scopus 로고
    • A subresultant theory for ore polynomials with applications
    • (O. Gloor, Ed.), ACM Press
    • Z. Li, "A subresultant theory for ore polynomials with applications," in: Proc. Int. Symp. Symbolic and Algebraic Computation, 1998 (O. Gloor, Ed.), ACM Press (1998), pp. 132-139.
    • (1998) Proc. Int. Symp. Symbolic and Algebraic Computation, 1998 , pp. 132-139
    • Li, Z.1
  • 20
    • 0030713241 scopus 로고    scopus 로고
    • A modular algorithm for computing greatest common right divisors of Ore polynomials
    • (W. Küchlin, Ed.), ACM Press
    • Z. Li and I. Nemes, "A modular algorithm for computing greatest common right divisors of Ore polynomials," in: Proc. Int. Symp. Symbolic and Algebraic Computation, 1997 (W. Küchlin, Ed.), ACM Press (1997), pp. 282-289.
    • (1997) Proc. Int. Symp. Symbolic and Algebraic Computation, 1997 , pp. 282-289
    • Li, Z.1    Nemes, I.2
  • 21
    • 0002148983 scopus 로고
    • Über reduzible lineare homogene Differentialgleichungen
    • A. Loewy, "Über reduzible lineare homogene Differentialgleichungen," Math. Ann., 56, 549-584 (1903).
    • (1903) Math. Ann. , vol.56 , pp. 549-584
    • Loewy, A.1
  • 22
    • 0002790739 scopus 로고
    • Über vollstandig reduzible lineare homogene Differentialgleichungen
    • A. Loewy, "Über vollstandig reduzible lineare homogene Differentialgleichungen," Math. Ann., 62 89-117 (1906).
    • (1906) Math. Ann. , vol.62 , pp. 89-117
    • Loewy, A.1
  • 24
    • 0001072553 scopus 로고
    • Theory of noncommutative polynomials
    • O. Ore, "Theory of noncommutative polynomials," Ann. Math., 34, 480-508 (1933).
    • (1933) Ann. Math. , vol.34 , pp. 480-508
    • Ore, O.1
  • 25
    • 0348250326 scopus 로고
    • Formale Theorie der linearen Differentialgleichungen, I
    • O. Ore, "Formale Theorie der linearen Differentialgleichungen, I," J. Reine Angew. Math., 167, 221-234 (1932).
    • (1932) J. Reine Angew. Math. , vol.167 , pp. 221-234
    • Ore, O.1
  • 26
    • 0010997730 scopus 로고
    • Formale Theorie der linearen Differentialgleichungen, II
    • O. Ore, "Formale Theorie der linearen Differentialgleichungen, II," J. Reine Angew. Math., 1, 233-252 (1932).
    • (1932) J. Reine Angew. Math. , vol.1 , pp. 233-252
    • Ore, O.1
  • 28
    • 0003171186 scopus 로고
    • Hypergeometric solutions of linear recurrences with polynomial coefficients
    • M. Petkovšek, "Hypergeometric solutions of linear recurrences with polynomial coefficients," J. Symbolic Comput., 14 243-264 (1992).
    • (1992) J. Symbolic Comput. , vol.14 , pp. 243-264
    • Petkovšek, M.1
  • 29
    • 0039035903 scopus 로고    scopus 로고
    • A Maple package for the symbolic construction of power series solutions to linear ordinary differential equations
    • A. Ryabenko, "A Maple package for the symbolic construction of power series solutions to linear ordinary differential equations," Program. Comput. Software, 25 No. 5, 296-305 (1999).
    • (1999) Program. Comput. Software , vol.25 , Issue.5 , pp. 296-305
    • Ryabenko, A.1
  • 30
    • 84941519029 scopus 로고
    • Noncommutative domains of integrity
    • J. H. M. Wedderburn, "Noncommutative domains of integrity," J. Reine Angew. Math., 167, 129-141 (1932).
    • (1932) J. Reine Angew. Math. , vol.167 , pp. 129-141
    • Wedderburn, J.H.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.