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Volumn 20, Issue 1 SPEC. ISS., 2009, Pages 73-121

Computing representations for radicals of finitely generated differential ideals

Author keywords

Computer algebra; Differential algebra

Indexed keywords

ALGEBRA; COMPUTATION THEORY;

EID: 65049090438     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00200-009-0091-7     Document Type: Article
Times cited : (72)

References (46)
  • 5
    • 0346789752 scopus 로고    scopus 로고
    • Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
    • D. Bouziane A. Kandri Rody H. Maârouf 2001 Unmixed-dimensional decomposition of a finitely generated perfect differential ideal J. Symb. Comput. 31 631 649
    • (2001) J. Symb. Comput. , vol.31 , pp. 631-649
    • Bouziane, D.1    Kandri Rody, A.2    Maârouf, H.3
  • 6
    • 84980263493 scopus 로고
    • A criterion for detecting unnecessary reductions in the construction of gröbner bases
    • Springer, New York
    • Buchberger, B.: A Criterion for Detecting Unnecessary Reductions in the Construction of Gröbner Bases. Lecture Notes in Computer Science, vol. 72, pp. 3-21. Springer, New York (1979)
    • (1979) Lecture Notes in Computer Science , vol.72 , pp. 3-21
    • Buchberger, B.1
  • 7
    • 0003368162 scopus 로고
    • Gröbner bases and differential ideals
    • Springer, Menorca
    • Carra-Ferro, G.: Gröbner bases and differential ideals. In: Proceedings of AAECC 5, pp. 129-140, Springer, Menorca (1987)
    • (1987) Proceedings of AAECC , vol.5 , pp. 129-140
    • Carra-Ferro, G.1
  • 8
    • 0003908675 scopus 로고
    • Ideals, varieties and algorithms. An introduction to computational algebraic geometry and commutative algebra
    • Springer, New York
    • Cox, D., Little, J., O'Shea, D.: Ideals, Varieties and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra. Undergraduate Texts in Mathematics. Springer, New York (1992)
    • (1992) Undergraduate Texts in Mathematics
    • Cox, D.1    Little, J.2    O'Shea, D.3
  • 9
    • 0003243860 scopus 로고
    • Commutative algebra with a view toward algebraic geometry
    • Springer, New York
    • Eisenbud, D.: Commutative Algebra with a View Toward Algebraic Geometry. Graduate Texts in Mathematics, vol. 150. Springer, New York (1995)
    • (1995) Graduate Texts in Mathematics , vol.150
    • Eisenbud, D.1
  • 10
    • 84955591390 scopus 로고
    • Some constructions in rings of differential polynomials
    • G. Gallo B. Mishra F. Ollivier 1991 Some constructions in rings of differential polynomials Lect. Notes Comput. Sci. 539 171 182
    • (1991) Lect. Notes Comput. Sci. , vol.539 , pp. 171-182
    • Gallo, G.1    Mishra, B.2    Ollivier, F.3
  • 11
    • 0001596387 scopus 로고
    • On an installation of Buchberger's algorithm
    • R. Gebauer H.M. Möller 1988 On an installation of Buchberger's algorithm J. Symb. Comput. 6 2-3 275 286
    • (1988) J. Symb. Comput. , vol.6 , Issue.23 , pp. 275-286
    • Gebauer, R.1    Möller, H.M.2
  • 13
    • 0002856938 scopus 로고
    • Systèmes d'équations aux dérivées partielles
    • Gauthier-Villars, Paris
    • e Série, vol. 3. Gauthier-Villars, Paris (1920)
    • (1920) e Série , vol.3
    • Janet, M.1
  • 14
    • 4243928791 scopus 로고
    • Leçons sur les systèmes d'équations aux dérivées partielles
    • Gauthier-Villars, Paris
    • Janet, M.: Leçons sur les Systèmes d'Équations aux Dérivées Partielles. Cahiers Scientifiques, vol. IV. Gauthier-Villars, Paris (1929)
    • (1929) Cahiers Scientifiques , vol.4
    • Janet, M.1
  • 15
    • 38249006658 scopus 로고
    • A generalized euclidean algorithm for computing triangular representations of algebraic varieties
    • M. Kalkbrener 1993 A generalized euclidean algorithm for computing triangular representations of algebraic varieties J. Symb. Comput. 15 143 167
    • (1993) J. Symb. Comput. , vol.15 , pp. 143-167
    • Kalkbrener, M.1
  • 19
    • 0000167385 scopus 로고
    • Solving zero-dimensional algebraic systems
    • D. Lazard 1992 Solving zero-dimensional algebraic systems J. Symb. Comput. 13 117 131
    • (1992) J. Symb. Comput. , vol.13 , pp. 117-131
    • Lazard, D.1
  • 20
    • 0042524551 scopus 로고
    • The low power theorem for partial differential equations
    • H. Levi 1945 The low power theorem for partial differential equations Ann. Math. Soc. 46 113 119
    • (1945) Ann. Math. Soc. , vol.46 , pp. 113-119
    • Levi, H.1
  • 28
    • 0003345224 scopus 로고
    • Applications of Lie Groups to Differential Equations
    • 2nd edn. Springer, New York
    • Olver, P.J.: Applications of Lie Groups to Differential Equations. Graduate Texts in Mathematics, vol. 107, 2nd edn. Springer, New York (1993)
    • (1993) Graduate Texts in Mathematics , vol.107
    • Olver, P.J.1
  • 31
    • 84972029082 scopus 로고
    • Algorithms for reducing a system of PDEs to standard form determining the dimension of its solution space and calculating its Taylor series solution
    • G.J. Reid 1991 Algorithms for reducing a system of PDEs to standard form determining the dimension of its solution space and calculating its Taylor series solution Eur. J. Appl. Math. 2 293 318
    • (1991) Eur. J. Appl. Math. , vol.2 , pp. 293-318
    • Reid, G.J.1
  • 32
    • 0030364642 scopus 로고    scopus 로고
    • Reduction of systems of nonlinear partial differential equations to simplified involutive forms
    • G.J. Reid A.D. Wittkopf A. Boulton 1996 Reduction of systems of nonlinear partial differential equations to simplified involutive forms Eur. J. Appl. Math. 7 6 635 666
    • (1996) Eur. J. Appl. Math. , vol.7 , Issue.6 , pp. 635-666
    • Reid, G.J.1    Wittkopf, A.D.2    Boulton, A.3
  • 33
    • 0039842239 scopus 로고    scopus 로고
    • Differential elimination-completion algorithms for DAE and PDAE
    • G.J. Reid P. Lin A.D. Wittkopf 2001 Differential elimination-completion algorithms for DAE and PDAE Stud. Appl. Math. 106 1 1 45
    • (2001) Stud. Appl. Math. , vol.106 , Issue.1 , pp. 1-45
    • Reid, G.J.1    Lin, P.2    Wittkopf, A.D.3
  • 36
    • 0004119251 scopus 로고
    • Dover, New York
    • Ritt, J.F.: Differential Algebra. Dover, New York (1950). http://www.ams.org/online-bks/coll33
    • (1950) Differential Algebra
    • Ritt, J.F.1
  • 37
    • 0000940301 scopus 로고
    • Specializations in differential algebra
    • A. Rosenfeld 1959 Specializations in differential algebra Trans. Am. Math. Soc. 90 394 407
    • (1959) Trans. Am. Math. Soc. , vol.90 , pp. 394-407
    • Rosenfeld, A.1
  • 39
    • 84968518808 scopus 로고
    • Some basic theorems in differential algebra(characteristic p arbitrary)
    • A. Seidenberg 1952 Some basic theorems in differential algebra(characteristic p arbitrary) Trans. Am. Math. Soc. 73 174 190
    • (1952) Trans. Am. Math. Soc. , vol.73 , pp. 174-190
    • Seidenberg, A.1
  • 41
    • 84968484220 scopus 로고
    • Abstract differential algebra and the analytic case
    • A. Seidenberg 1958 Abstract differential algebra and the analytic case Proc. Am. Math. Soc. 9 159 164
    • (1958) Proc. Am. Math. Soc. , vol.9 , pp. 159-164
    • Seidenberg, A.1
  • 42
    • 84968503787 scopus 로고
    • Abstract differential algebra and the analytic case II
    • A. Seidenberg 1969 Abstract differential algebra and the analytic case II Proc. Am. Math. Soc. 23 689 691
    • (1969) Proc. Am. Math. Soc. , vol.23 , pp. 689-691
    • Seidenberg, A.1
  • 45
    • 0002352629 scopus 로고
    • On the foundation of algebraic differential geometry
    • (research preprints)
    • W.W. Tsün 1989 On the foundation of algebraic differential geometry Mechanization Math. 3 2 27 (research preprints)
    • (1989) Mechanization Math. , vol.3 , pp. 2-27
    • Tsün, W.W.1
  • 46
    • 0003868126 scopus 로고
    • Van Nostrand, New York Also volumes 28 and 29 of the Graduate Texts in Mathematics. Springer, New York
    • Zariski, O., Samuel, P.: Commutative Algebra. Van Nostrand, New York (1958). Also volumes 28 and 29 of the Graduate Texts in Mathematics. Springer, New York
    • (1958) Commutative Algebra
    • Zariski, O.1    Samuel, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.