Resolvent systems of difference polynomial ideals

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn 2006, Issue , 2006, Pages 101-108

  Xiao Shan, Gao ^a   Yuan, Chun Ming ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

Difference ascending chain; Difference polynomial; Difference variety; Resolvent; Unmixed decomposition

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; DIFFERENCE EQUATIONS; LINEAR ALGEBRA; PROBLEM SOLVING; THEOREM PROVING;

DIFFERENCE ASCENDING CHAINS; DIFFERENCE POLYNOMIALS; DIFFERENCE VARIETY; RESOLVENT SYSTEMS; UNMIXED DECOMPOSITION;

POLYNOMIALS;

EID: 33748975678     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. T. Cluzeau and E. Hubert, Resolvent Representation for Regular Differential Ideals, AAECC, 29, 395-425, 2003.
2. R.M. Cohn, Difference Algebra, Interscience Pbulishers, 1965.
3. R.M. Cohn, Manifolds of Difference Polynomials, Trans. of AMS, 64, 133-172, 1948.
4. S.C. Chou, Mechanical Geometry Theorem Proving, D.Reidel Publishing Company, 1988.
5. X.S. Gao and S.C. Chou, On the Parameterization of Algebraic Curves, AAECC, 3, 27-38, 1992.
6. X.S. Gao and S.C. Chou, On the Dimension for Arbitrary Ascending Chains, Chinese Bull, of Scis., vol. 38, 396-399, 1993.
7. X.S. Gao and S.C. Chou, On the Theory of Resolvents and its Applications, Sys. Sci. and Math. Sci., 12, 17-30, 1999,
8. X.S. Gao and Y. Luo, A Characteristic Set Method for Difference Polynomial Systems, Inter Conf on Poly Sys. Sol., Nov. 24-26, Paris, 2004. Submitted to JSC.
9. P. Gianni and T. Mora, Algebraic Solution of Systems of Polynomial Equations Using Gröbnert bases, 247-257, LNCS, vol. 356, Springer-Verlag, 1987.
10. D. Grigoriev, Complexity of Quantifier Elimination in the Theory of Ordinary Differential Equations, LNCS, vol. 378, 11-25, 1989.
11. R. Loos, Computing in Algebraic Extensions, in Computer Algebra (Ed. by B. Buchberger, et al), 173-187, Springer-Verlag, New York. 1982.
12. H. Kobayashi, S. Moritsugu and R.W. Hogan, Solving Systems of Algebraic Equations, Proc. of ISSAC-88, pp.139-149, LNCS No. 358, Springer-Verlag, 1988.
13. E. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973.
14. E.L. Mansfield and A. Szanto, Elimination Theory for Differential Difference Polynomials, Proc. ISSAC 2002, 191-198, ACM Press.
15. J.F. Ritt, Differential Algebra, Amer. Math. Soc. Colloquium, 1950.
16. J.F. Ritt and J.L. Doob, Systems of Algebraic Difference Equations, American Journal of Mathematics, 55, 505-514, 1933.
17. B.M. Trager, Algebraic Factoring and Rational Integration, Proc. of ACM Sym. on Symbolic and Algebraic Computation, 1976.
18. D. Wang and D. Lin, A Method for Multivariate Polynomial Factorization over Successive Algebraic Extension Fields, Mathematics and Mathematics Mechanization, 138-172, 2001.
19. J. van der Hoeven, Differential and Mixed Differential-difference Equations from the Effetive Viewpoint, Preprints, 1996.
20. W.T. Wu, Basic Principle of Mechanical Theorem Proving in Geometries, Science Press, Beijing, 1984; Springer, Wien, 1994.
21. K. Yokoyama, M. Noro and T. Takeshima, Computing Primitive Elements of Extension Fields, Journal of Symbolic Computation, 8, 553-580, 1989.