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Volumn 13, Issue 5, 2003, Pages 395-425

Resolvent representation for regular differential ideals

Author keywords

Computer algebra; Cyclic vector; Differential algebra; Differential primitive element; Resolvent

Indexed keywords

ALGORITHMS; LINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; POLES AND ZEROS; POLYNOMIALS; THEOREM PROVING; VECTORS;

EID: 0037331777     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00200-002-0110-4     Document Type: Article
Times cited : (26)

References (44)
  • 4
    • 0040620729 scopus 로고    scopus 로고
    • An algorithm for computing a companion block diagonal form for a system of linear differential equations
    • Barkatou, M.A.: An algorithm for computing a companion block diagonal form for a system of linear differential equations. AAECC, 4(3), 185-195 (2000)
    • (2000) AAECC , vol.4 , Issue.3 , pp. 185-195
    • Barkatou, M.A.1
  • 6
    • 51249192647 scopus 로고
    • Formal theory of irregular linear difference equations
    • Birkhoff, G.D.: Formal theory of irregular linear difference equations. Acta Mathematica, 54, 205-246 (1930)
    • (1930) Acta Mathematica , vol.54 , pp. 205-246
    • Birkhoff, G.D.1
  • 7
    • 0348055341 scopus 로고    scopus 로고
    • Diffalg, a MAPLE package. Description, help pages and examples of use; Symbolic Computation Group, University of Waterloo, Ontario, Canada
    • Boulier, F., Hubert, E.: Diffalg, a MAPLE package. Description, help pages and examples of use. Symbolic Computation Group, University of Waterloo, Ontario, Canada. 1998. Now accessible on http://www-sop.inria.fr/cafe/Evelyne.Hubert/web-diffalg
    • (1998)
    • Boulier, F.1    Hubert, E.2
  • 8
    • 0029182270 scopus 로고
    • Representation for the radical of a finitely generated differential ideal
    • In: A.H.M. Levelt (ed); ACM Press, New York
    • Boulier, F., Lazard, D., Ollivier, F., Petitot, M.: Representation for the radical of a finitely generated differential ideal. In: A.H.M. Levelt (ed) ISSAC'95, pp. 158-166, ACM Press, New York, 1995
    • (1995) ISSAC'95 , pp. 158-166
    • Boulier, F.1    Lazard, D.2    Ollivier, F.3    Petitot, M.4
  • 9
    • 0003921310 scopus 로고    scopus 로고
    • Computing representations for radicals of finitely generated differential ideals
    • Technical Report IT-306, LIFL
    • Boulier, F., Lazard, D., Ollivier, F., Petitot, M.: Computing representations for radicals of finitely generated differential ideals. Technical Report IT-306, LIFL, 1997. Revised version available at http://www.lifl.fr/~boulier
    • (1997)
    • Boulier, F.1    Lazard, D.2    Ollivier, F.3    Petitot, M.4
  • 10
    • 0033659532 scopus 로고    scopus 로고
    • Computing canonical representatives of regular differential ideals
    • In: C. Traverso (ed); ACM-SIGSAM, ACM
    • Boulier, F., Lemaire, F.: Computing canonical representatives of regular differential ideals. In: C. Traverso (ed) ISSAC, pp. 38-47. ACM-SIGSAM, ACM, 2000
    • (2000) ISSAC , pp. 38-47
    • Boulier, F.1    Lemaire, F.2
  • 11
    • 0346789752 scopus 로고    scopus 로고
    • Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
    • Bouziane, D., Kandri Rody, A., Maârouf, H.: Unmixed-dimensional decomposition of a finitely generated perfect differential ideal. Journal of Symbolic Computation, 31(6):631-649 (2001)
    • (2001) Journal of Symbolic Computation , vol.31 , Issue.6 , pp. 631-649
    • Bouziane, D.1    Kandri Rody, A.2    Maârouf, H.3
  • 13
    • 0013463217 scopus 로고
    • Automated reasonning in differential geometry and mechanics using the characteristic set method. Part I. An improved version of ritt-wu's decomposition algorithm
    • Chou, S-C., Gao, X-S.: Automated reasonning in differential geometry and mechanics using the characteristic set method. Part I. An improved version of Ritt-Wu's decomposition algorithm. Journal of Automated Reasonning, 10, 161-172 (1993)
    • (1993) Journal of Automated Reasonning , vol.10 , pp. 161-172
    • Chou, S.-C.1    Gao, X.-S.2
  • 15
    • 4244012397 scopus 로고    scopus 로고
    • Resolvent representation for regular differential ideals
    • Technical Report RR-4200, INRIA Sophia Antipolis
    • Cluzeau, T., Hubert, E.: Resolvent representation for regular differential ideals. Technical Report RR-4200, INRIA Sophia Antipolis, 2001. http://www.inria.fr/rrrt/rr-4200.html
    • (2001)
    • Cluzeau, T.1    Hubert, E.2
  • 16
    • 0013500940 scopus 로고
    • Formal solution of irregular linear differential equations. Part II
    • Cope, F.T.: Formal solution of irregular linear differential equations. Part II. American Journal of Mathematics, 58, 130-146 (1956)
    • (1956) American Journal of Mathematics , vol.58 , pp. 130-146
    • Cope, F.T.1
  • 19
    • 0000750175 scopus 로고
    • Algorithmes-disons rapides-pour la décomposition d'une variété algébrique en composantes irréductibles et équidimensionnelles
    • Birkhäuser Boston, Boston, MA
    • Giusti, M., Heintz, J.: Algorithmes-disons rapides-pour la décomposition d'une variété algébrique en composantes irréductibles et équidimensionnelles. In: Effective methods in algebraic geometry (Castiglioncello 1990), pp. 169-194. Birkhäuser Boston, Boston, MA, 1991
    • (1991) Effective Methods in Algebraic Geometry (Castiglioncello 1990) , pp. 169-194
    • Giusti, M.1    Heintz, J.2
  • 20
    • 0000936391 scopus 로고
    • La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial
    • Cambridge: Cambridge University Press
    • Giusti, M., Heintz, J.: La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial. In: Computational Algebraic Geometry and Commutative Algebra (Cortona 1991), pp. 216-256. Cambridge: Cambridge University Press
    • (1993) Computational Algebraic Geometry and Commutative Algebra (Cortona 1991) , pp. 216-256
    • Giusti, M.1    Heintz, J.2
  • 21
    • 0035294718 scopus 로고    scopus 로고
    • A gröbner free alternative for polynomial system solving
    • Giusti, M., Lecerf, G.I., Salvy, B.: A Gröbner free alternative for polynomial system solving. Journal of Complexity, 17(1), 154-211 (2001)
    • (2001) Journal of Complexity , vol.17 , Issue.1 , pp. 154-211
    • Giusti, M.1    Lecerf, G.I.2    Salvy, B.3
  • 22
    • 0001743074 scopus 로고    scopus 로고
    • Essential components of an algebraic differential equation
    • Hubert, E.: Essential components of an algebraic differential equation. Journal of Symbolic Computation, 28(4-5), 657-680 (1999)
    • (1999) Journal of Symbolic Computation , vol.28 , Issue.4-5 , pp. 657-680
    • Hubert, E.1
  • 23
    • 0034178810 scopus 로고    scopus 로고
    • Factorisation free decomposition algorithms in differential algebra
    • Hubert, E.: Factorisation free decomposition algorithms in differential algebra. Journal of Symbolic Computation, 29(4-5), 641-662 (2000)
    • (2000) Journal of Symbolic Computation , vol.29 , Issue.4-5 , pp. 641-662
    • Hubert, E.1
  • 24
    • 27644586410 scopus 로고    scopus 로고
    • Notes on triangular sets and triangulation-decomposition algorithms I: Polynomial systems
    • In: F. Winkler (ed); Springer, to appear
    • Hubert, E.: Notes on triangular sets and triangulation-decomposition algorithms I: Polynomial systems. In: F. Winkler (ed) Symbolic and Numerical Scientific Computations. Springer, to appear
    • Symbolic and Numerical Scientific Computations
    • Hubert, E.1
  • 25
    • 27644586410 scopus 로고    scopus 로고
    • Notes on triangular sets and triangulation-decomposition algorithms II: Differential systems
    • In: F. Winkler (ed); Springer, to appear
    • Hubert, E.: Notes on triangular sets and triangulation-decomposition algorithms II: Differential systems. In: F. Winkler (ed) Symbolic and Numerical Scientific Computations. Springer, to appear
    • Symbolic and Numerical Scientific Computations
    • Hubert, E.1
  • 26
    • 38249006658 scopus 로고
    • A generalized euclidean algorithm for computing triangular representations of algebraic varieties
    • Kalkbrener, M.: A generalized Euclidean algorithm for computing triangular representations of algebraic varieties. Journal of Symbolic Computation, 15(2), 143-167 (1993)
    • (1993) Journal of Symbolic Computation , vol.15 , Issue.2 , pp. 143-167
    • Kalkbrener, M.1
  • 27
    • 0001924189 scopus 로고
    • A simple algorithm for cyclic vectors
    • Katz, N.M.: A simple algorithm for cyclic vectors. Amer. J. Math. 109(1), 65-70 (1987)
    • (1987) Amer. J. Math. , vol.109 , Issue.1 , pp. 65-70
    • Katz, N.M.1
  • 29
    • 0000167385 scopus 로고
    • Solving zero dimensional algebraic systems
    • Lazard, D.: Solving zero dimensional algebraic systems. Journal of Symbolic Computation, 15, 117-132 (1992)
    • (1992) Journal of Symbolic Computation , vol.15 , pp. 117-132
    • Lazard, D.1
  • 30
    • 4243472110 scopus 로고
    • Differential gröbner bases
    • PhD thesis, University of Sydney
    • Mansfield, E.: Differential Gröbner Bases. PhD thesis, University of Sydney, 1991
    • (1991)
    • Mansfield, E.1
  • 31
    • 0001104863 scopus 로고    scopus 로고
    • The differential ideal [P]: M∞
    • Morrison, S.: The differential ideal [P]: M∞. Journal of Symbolic Computation, 28(4-5), 631-656 (1999)
    • (1999) Journal of Symbolic Computation , vol.28 , Issue.4-5 , pp. 631-656
    • Morrison, S.1
  • 33
    • 0030364642 scopus 로고    scopus 로고
    • Reduction of systems of nonlinear partial differential equations to simplified involutive forms
    • Reid, G.J., Wittkopf,A.D., Boulton,A.: Reduction of systems of nonlinear partial differential equations to simplified involutive forms. Eur. J. Appl. Math. 7, 604-635 (1996)
    • (1996) Eur. J. Appl. Math. , vol.7 , pp. 604-635
    • Reid, G.J.1    Wittkopf, A.D.2    Boulton, A.3
  • 34
    • 0003855155 scopus 로고
    • Les systèmes d'équations aux dérivées partielles
    • Gauthier-Villars, Paris
    • Riquier, C.: Les systèmes d'équations aux dérivées partielles. Gauthier-Villars, Paris, 1910
    • (1910)
    • Riquier, C.1
  • 35
  • 37
    • 0033131339 scopus 로고    scopus 로고
    • Solving zero-dimensional systems through the rational univariate representation
    • Rouillier, F.: Solving zero-dimensional systems through the rational univariate representation. AAECC, 9(5), 433-461 (1999)
    • (1999) AAECC , vol.9 , Issue.5 , pp. 433-461
    • Rouillier, F.1
  • 38
    • 0004156444 scopus 로고    scopus 로고
    • Rankings of derivatives for elimination algorithms and formal solvability of analytic partial differential equations
    • PhD thesis, University of Chicago, Illinois
    • Rust, C.: Rankings of derivatives for elimination algorithms and formal solvability of analytic partial differential equations. PhD thesis, University of Chicago, Illinois, 1998
    • (1998)
    • Rust, C.1
  • 39
    • 0033727483 scopus 로고    scopus 로고
    • A bound for the order of characteristic set elements of an ordinary prime differential ideal and some applications
    • Sadik, B.: A bound for the order of characteristic set elements of an ordinary prime differential ideal and some applications. AAECC, 10(3), 251-268 (2000)
    • (2000) AAECC , vol.10 , Issue.3 , pp. 251-268
    • Sadik, B.1
  • 40
    • 4243721208 scopus 로고    scopus 로고
    • Sur la résolution des systèmes polynomiaux à paramètres
    • PhD thesis, École polytechnique
    • Schost, E.: Sur la résolution des systèmes polynomiaux à paramètres. PhD thesis, École polytechnique, 2000
    • (2000)
    • Schost, E.1
  • 41
    • 84968518808 scopus 로고
    • Some basic theorems in differential algebra (characteristic p arbitrary)
    • Seidenberg, A.: Some basic theorems in differential algebra (characteristic p arbitrary). Transaction of the American Mathematical Society, 73, 174-190 (1952)
    • (1952) Transaction of the American Mathematical Society , vol.73 , pp. 174-190
    • Seidenberg, A.1
  • 42
    • 0346794374 scopus 로고    scopus 로고
    • An elimination method for differential polynomial systems. I
    • Wang, D.: An elimination method for differential polynomial systems. I. Systems Science and Mathematical Sciences, 9(3), 216-228, (1996)
    • (1996) Systems Science and Mathematical Sciences , vol.9 , Issue.3 , pp. 216-228
    • Wang, D.1
  • 43
    • 0000365195 scopus 로고
    • On the foundation of algebraic differential geometry
    • Wu, W-T.: On the foundation of algebraic differential geometry. Systems Science and Mathematical Sciences, 2(4), 289-312 (1989)
    • (1989) Systems Science and Mathematical Sciences , vol.2 , Issue.4 , pp. 289-312
    • Wu, W.-T.1
  • 44
    • 0003868126 scopus 로고
    • Springer-Verlag, New York; With the cooperation of I. S. Cohen, Corrected reprinting of the 1958 edition, Graduate Texts in Mathematics, No. 28
    • Zariski, O., Samuel, P.: Commutative algebra. Vol. 1, Springer-Verlag, New York, 1975. With the cooperation of I. S. Cohen, Corrected reprinting of the 1958 edition, Graduate Texts in Mathematics, No. 28
    • (1975) Commutative Algebra , vol.1
    • Zariski, O.1    Samuel, P.2


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