메뉴 건너뛰기




Volumn 44, Issue 3, 2009, Pages 242-260

A characteristic set method for ordinary difference polynomial systems

Author keywords

Ascending chain; Automated theorem proving; Characteristic set; Coherence; Difference polynomial; Irreducibility; Zero decomposition theorem

Indexed keywords


EID: 60249088243     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2007.05.005     Document Type: Article
Times cited : (33)

References (30)
  • 2
    • 0029182270 scopus 로고
    • Representation for the radical of a finitely generated differential ideal
    • ACM Press
    • Boulier F., Lazard D., Ollivier F., and Petitiot M. Representation for the radical of a finitely generated differential ideal. Proc. of ISSAC'95 (1995), ACM Press 158-166
    • (1995) Proc. of ISSAC'95 , pp. 158-166
    • Boulier, F.1    Lazard, D.2    Ollivier, F.3    Petitiot, M.4
  • 3
    • 0346789752 scopus 로고    scopus 로고
    • Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
    • Bouziane D., Kandri Rody A., and Maârouf H. Unmixed-dimensional decomposition of a finitely generated perfect differential ideal. J. Symbolic Comput. 31 (2001) 631-649
    • (2001) J. Symbolic Comput. , vol.31 , pp. 631-649
    • Bouziane, D.1    Kandri Rody, A.2    Maârouf, H.3
  • 4
    • 0013463217 scopus 로고
    • Automated reasoning in differential geometry and mechanics using the characteristic set method, Part I. An improved version of Ritt-Wu's decomposition algorithm
    • Chou S.C., and Gao X.S. Automated reasoning in differential geometry and mechanics using the characteristic set method, Part I. An improved version of Ritt-Wu's decomposition algorithm. J. Automat. Reason. 10 (1993) 161-172
    • (1993) J. Automat. Reason. , vol.10 , pp. 161-172
    • Chou, S.C.1    Gao, X.S.2
  • 5
    • 0032141037 scopus 로고    scopus 로고
    • Non-commutative elimination in Ore algebras proves multivariate indentities
    • Chyzak F., and Salvy B. Non-commutative elimination in Ore algebras proves multivariate indentities. J. Symbolic Comput. 26 (1998) 187-227
    • (1998) J. Symbolic Comput. , vol.26 , pp. 187-227
    • Chyzak, F.1    Salvy, B.2
  • 6
    • 33748963510 scopus 로고
    • Manifolds of difference polynomials
    • Cohn R.M. Manifolds of difference polynomials. Trans. AMS 64 (1948) 133-172
    • (1948) Trans. AMS , vol.64 , pp. 133-172
    • Cohn, R.M.1
  • 8
    • 27644512413 scopus 로고    scopus 로고
    • Sharp estimates for triangular sets
    • ACM Press, New York
    • Dahan X., and Schost E. Sharp estimates for triangular sets. Proc. of ISSAC'04 (2004), ACM Press, New York 103-110
    • (2004) Proc. of ISSAC'04 , pp. 103-110
    • Dahan, X.1    Schost, E.2
  • 9
    • 0010070016 scopus 로고
    • Birkhauser
    • Gallo G., and Mishra B. Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets. Progress in Mathematics vol. 94 (1991), Birkhauser 119-142
    • (1991) Progress in Mathematics , vol.94 , pp. 119-142
    • Gallo, G.1    Mishra, B.2
  • 10
    • 0348050312 scopus 로고
    • The dimension of ascending chains
    • Gao X.S., and Chou S.C. The dimension of ascending chains. Chinese Sci. Bull. 38 5 (1993) 396-399
    • (1993) Chinese Sci. Bull. , vol.38 , Issue.5 , pp. 396-399
    • Gao, X.S.1    Chou, S.C.2
  • 11
    • 0034178810 scopus 로고    scopus 로고
    • Factorization-free decomposition algorithms in differential algebra
    • Hubert E. Factorization-free decomposition algorithms in differential algebra. J. Symbolic Comput. 29 (2000) 641-662
    • (2000) J. Symbolic Comput. , vol.29 , pp. 641-662
    • Hubert, E.1
  • 12
    • 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. J. Symbolic Comput. 15 (1993) 143-167
    • (1993) J. Symbolic Comput. , vol.15 , pp. 143-167
    • Kalkbrener, M.1
  • 14
    • 0000069912 scopus 로고
    • A new method for solving algebraic systems of positive dimension
    • Lazard D. A new method for solving algebraic systems of positive dimension. Discrete Appl. Math. 33 (1991) 147-160
    • (1991) Discrete Appl. Math. , vol.33 , pp. 147-160
    • Lazard, D.1
  • 15
    • 0242648854 scopus 로고    scopus 로고
    • Coherent, regular and simple systems in zero decomposition of partial differential systems
    • Li Z., and Wang D.M. Coherent, regular and simple systems in zero decomposition of partial differential systems. J. Systems Sci. Math. Sci. 12 (1999) 43-60
    • (1999) J. Systems Sci. Math. Sci. , vol.12 , pp. 43-60
    • Li, Z.1    Wang, D.M.2
  • 17
    • 1542300112 scopus 로고    scopus 로고
    • Elimination theory for differential difference polynomials
    • ACM Press, New York
    • Mansfield E.L., and Szanto A. Elimination theory for differential difference polynomials. Proc. ISSAC,02 (2002), ACM Press, New York 191-198
    • (2002) Proc. ISSAC,02 , pp. 191-198
    • Mansfield, E.L.1    Szanto, A.2
  • 18
    • 84972029082 scopus 로고
    • Algorithms for reducing a system of PDEs to standard form
    • Reid G. Algorithms for reducing a system of PDEs to standard form. European J. Appl. Math. 2 (1991) 293-318
    • (1991) European J. Appl. Math. , vol.2 , pp. 293-318
    • Reid, G.1
  • 19
    • 0010708892 scopus 로고
    • Systems of algebraic difference equations
    • Ritt J.F., and Doob J.L. Systems of algebraic difference equations. Amer. J. Math. 55 (1933) 505-514
    • (1933) Amer. J. Math. , vol.55 , pp. 505-514
    • Ritt, J.F.1    Doob, J.L.2
  • 20
    • 60249083557 scopus 로고    scopus 로고
    • Ritt, J.F., 1950. Differential algebra, Amer. Math. Soc. Colloquium
    • Ritt, J.F., 1950. Differential algebra, Amer. Math. Soc. Colloquium
  • 21
    • 0000940301 scopus 로고
    • Specialization in differential algebra
    • Rosenfeld A. Specialization in differential algebra. Trans. AMS 90 (1959) 394-407
    • (1959) Trans. AMS , vol.90 , pp. 394-407
    • Rosenfeld, A.1
  • 23
    • 0025549971 scopus 로고
    • Gröbner basis, integration and transcendental functions
    • ACM Press, New York
    • Takayama N. Gröbner basis, integration and transcendental functions. Proc. of ISSAC'90 (1990), ACM Press, New York 152-156
    • (1990) Proc. of ISSAC'90 , pp. 152-156
    • Takayama, N.1
  • 26
    • 0003343439 scopus 로고
    • On the decision problem and the mechanization of theorem in elementary geometry
    • Wu W.T. On the decision problem and the mechanization of theorem in elementary geometry. Scientia Sinica 21 (1978) 159-172
    • (1978) Scientia Sinica , vol.21 , pp. 159-172
    • Wu, W.T.1
  • 27
    • 0347706652 scopus 로고
    • Springer
    • Wu W.T. A Constructive Theorey of Differential Algebraic Geometry. Lect. Notes in Math. No. 1255 (1987), Springer 173-189
    • (1987) Lect. Notes in Math. , vol.1255 , pp. 173-189
    • Wu, W.T.1
  • 30
    • 0001601404 scopus 로고
    • A holonomic systems approach to special function identities
    • Zeilberger D. A holonomic systems approach to special function identities. J. Comput. Appl. Math. 32 (1990) 321-368
    • (1990) J. Comput. Appl. Math. , vol.32 , pp. 321-368
    • Zeilberger, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.