Characteristic set method for differential-difference polynomial systems

Journal of Symbolic Computation

Volumn 44, Issue 9, 2009, Pages 1137-1163

  Gao, X S ^a   Van der Hoeven, J ^b   Yuan, C M ^a   Zhang, G L ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

^b CNRS   (France)

Author keywords

Characteristic set; Differential and difference polynomial; Irreducible ascending chain; Perfect ideal membership problem; Regular ascending chain; Zero decomposition algorithm

Indexed keywords

EID: 67349126177     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2008.02.010     Document Type: Article

References (24)

1. Aubry P., Lazard D., and Maza M.M. On the theory of triangular sets. Journal of Symbolic Computation 28 (1999) 105-124
2. 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, New York 158-166
3. Bouziane D., Kandri Rody A., and Maârouf H. Unmixed-dimensional decomposition of a finitely generated perfect differential ideal. Journal of Symbolic Computation 31 (2001) 631-649
4. Chou S.C., and Gao X.S. Ritt-Wu's decomposition algorithm and geometry theorem proving. In: Stickel M.E. (Ed). CADE'10. LNCS vol. 449 (1990), Springer-Verlag 207-220
5. Chou S.C., and Gao X.S. Automated reasoning in differential geometry and mechanics: Part I. An improved version of Ritt-Wu's decomposition algorithm. Journal of Automated Reasoning 10 (1993) 161-172
6. Cohn R.M. Difference Algebra (1965), Interscience Publishers
7. Cohn R.M. Manifolds of difference polynomials. Transactions of AMS 64 (1948) 133-172
8. Gao X.S., and Chou S.C. The dimension of ascending chains. Chinese Science Bulletin 38 5 (1993) 396-399
9. Gao X.S., Luo Y., and Yuan C.M. A characteristic set method for ordinary difference polynomial systems. Journal of Symbolic Computation 44 (2009) 242-260
10. Gao X.S., Luo Y., and Zhang G. A characteristic set method for ordinary difference polynomial systems. MM-Preprints vol. 25 (2006) 84-102
11. Gao X.S., and Yuan C. Resolvent systems of difference polynomial ideals. Proc. ISSAC 2006 (2006), ACM Press, New York 101-108
12. Hubert É. Factorization-free decomposition algorithms in differential algebra. Journal of Symbolic Computation 29 (2000) 641-662
13. Kolchin E. Differential Algebra and Algebraic Groups (1973), Academic Press, New York
14. Kondratieva M.V., Levin A.B., Mikhalev A.V., and Pankratiev E.V. Differential and Difference Dimension Polynomials (1999), Kluwer Academic Publishers
15. Ritt J.F. Differential Algebra (1950), American Mathematical Society
16. Ritt J.F., and Doob J.L. Systems of algebraic difference equations. American Journal of Mathematics 55 (1933) 505-514
17. Ritt J.F., and Raudenbush H.W. Ideal theory and algebraic difference equations. Transactions of AMS 46 (1939) 445-452
18. Rosenfeld A. Specialization in differential algebra. Transactions of American Mathematical Society 90 (1959) 394-407
19. Wang D. Elimination Methods (2000), Springer, Berlin
20. van der Hoeven, J., 1996. Differential and mixed differential-difference equations from the effective viewpoint. Preprints
21. Wu W.T. On the foundation of algebraic differential polynomial geometry. Systems Science & Mathematical Sciences 2 4 (1989) 289-312
22. Wu W.T. Basic Principle of Mechanical Theorem Proving in Geometries (1984), Science Press, Beijing English translation, Springer, Wien, 1994
23. Wu W.T. Mathematics Machenization (2001), Science Press/Kluwer, Beijing
24. Yang L., Zhang J.Z., and Hou X.R. Non-linear Algebraic Equations and Automated Theorem Proving (1996), ShangHai Science and Education Pub., Shanghai (in Chinese)