Involutive bases of polynomial ideals

Mathematics and Computers in Simulation

Volumn 45, Issue 5-6, 1998, Pages 519-541

  Gerdt, Vladimir P ^a   Blinkov, Yuri A ^b  

^a JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^b SARATOV STATE UNIVERSITY   (Russian Federation)

Author keywords

Buchberger's chain criterion; Computer algebra; Gr bner bases; Involutive algorithm; Involutive bases; Involutive monomial division; Polynomial ideals; Polynomial reduction

Indexed keywords

ALGORITHMS; CALCULATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SET THEORY;

BUCHBERGER CHAIN CRITERION; COMPUTER ALGEBRA; INVOLUTIVE BASES; INVOLUTIVE MONOMIAL DIVISION;

POLYNOMIALS;

EID: 0032024774     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(97)00127-4     Document Type: Article

References (18)

1. B. Buchberger, An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-dimensional Polynomial Ideal (in German), PhD Thesis, University of Innsbruck, Austria, 1965.
2. B. Buchberger, Gröbner Bases: an Algorithmic Method in Polynomial Ideal Theory, in: N.K. Bose (Ed.), Recent Trends in Multidimensional System Theory, Reidel, Dordrecht, 1985, pp. 184-232.
3. T. Becker, V. Weispfenning, H. Kredel, Gröbner Bases. A Computational Approach to Commutative Algebra, Graduate Texts in Mathematics 141, Springer, New York, 1993.
4. T. Mora, Seven Variations on Standard Bases, Preprint No. 45, Dip. di Mathematica, Univ. di Genova, 1988.
5. A. Kandri-Rody, V. Weispfenning, Non-commutative Gröbner bases in algebras of solvable type, J. Symb. Comp. 9 (1990) 1-26.
6. G. Carra'Ferro, Gröbner bases and differential algebra, Lec. Not. in Comp. Sci. 356 (1987) 129-140.
7. F. Ollivier, Standard bases of differential ideals, Lec. Not. in Comp. Sci. 508 (1990) 304-321.
8. C. Requier, Les Systèmes d'Equations aux Dérivées Partielles, Gauthier-Villars, Paris, 1910.
9. M. Janet, Sur les systèmes d'équations aux dérivées partielles, J. Math, pure et Appl. 3 (1920) 65-151.
10. J. Thomas, Differential Systems, American Mathematical Society, New York, 1937.
11. J.F. Pommaret, Systems of Partial Differential Equations and Lie Pseudogroups, Gordon & Breach, New York, 1978.
12. V.P. Gerdt, Gröbner Bases and Involutive Methods for Algebraic and Differential Equations, in: J. Fleischer, J. Grabmeier, F.W. Hehl, W. Küchlin (Eds.), Computer Algebra in Science and Engineering, World Scientific, Singapore, 1995, pp. 117-137.
13. A.Yu. Zharkov, Yu.A. Blinkov, Involutive Approach to Investigating Polynomial Systems, in: Proceedings of "SC 93", International IMACS Symposium on Symbolic Computation: New Trends and Developments (Lille, June 14-17, 1993) Math. Comp. Simul 42 (1996) 323-332.
14. A.Yu. Zharkov, Yu.A. Blinkov, Involutive Bases of Zero-Dimentional Ideals, Preprint No. E5-94-318, Joint Institute for Nuclear Research, Dubna, 1994.
15. A.Yu. Zharkov, Solving Zero-Dimentional Involutive Systems, in: L. Gonzales-Vega, T. Recio (Eds.), Algorithms in Algebraic Geometry and Applications, Progress in Mathematics, Vol. 143, Birkhäuser, Basel, 1996, pp. 389-399.
16. B. Buchberger, A Criterion for Detecting Unnecessary Reductions in the Construction of Gröbner Bases. Proc. EUROSAM 79, in: E.W. Ng (Ed.), International Symposium on Symbolic and Algebraic Manipulation, Springer, Berlin, 1979, pp. 3-21.
17. A.Yu. Zharkov, Private communication, 1994.
18. J. Apel, A Gröbner approach to involutive bases, J. Symb. Comp. 19 (1995) 441-457.