The theory of involutive divisions and an application to Hilbert function computations

Journal of Symbolic Computation

Volumn 25, Issue 6, 1998, Pages 683-704

  Apel, Joachim ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032089281     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1997.0194     Document Type: Article

References (15)

1. Apel, J. (1995). A Gröbner approach to involutive bases. J. Symb. Comput. 19/5, 441-457.
2. Apel, J. (1998). The computation of Gröbner bases using an alternative algorithm. In Bronstein, M., Grabmeier, J. and Weispfenning, V. eds, Proc. Workshop on Symbolic Rewriting Techniques, Monte-Verita, 1995, pp 35-45. Birkhauser.
3. Becker, T., Weispfenning, V., in cooperation with Kredel, H. (1993). Gröbner Bases, A Computational Approach to Commutative Algebra. Springer, New York, Berlin, Heidelberg.
4. Buchberger, B. (1965). Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, PhD Thesis, University of Innsbruck, Austria.
5. Buchberger, B. (1985). An algorithmic method in polynomial ideal theory. In Bose, N. K. ed., Recent Trends in Multidimensional System Theory, D. Reidel, Dordrecht.
6. Gerdt, V.P., Blinkov, Yu.A. (1996). Involutive bases of polynomial ideals. Preprint 01/96, Naturwissenschaftlich-Theoretisches Zentrum, University of Leipzig.
7. Giovini, A., Mora, T., Niesi, G., Robbiano, L., Traverse, C. (1991). "One sugar cube, please," or selection strategies in the Buchberger algorithm. In Watt, S. M. ed., Proc. ISSAC'91, pp. 49-54. ACM Press, New York.
8. Janet, M. (1929). Lecons sur les Systèmes d'equations aux Dérivées Partielles. Gauthier-Villars, Paris.
9. Mall, D. (1995). A Note on Pommaret Bases. Private communication.
10. Nischke, K. Private communication about an implementation of involutive bases.
11. Pommaret, J.F. (1978). Systems of Partial Differential Equations and Lie Pseudogroups. Gordon and Breach, New York.
12. Renschuch, B. (1976). Elementare und Praktische Idealtheorie. Deutscher Verlag der Wissenschaften, Berlin.
13. Seiler, W. (1994). On the arbitrariness of the general solution of an involutive partial differential equation. J. Math. Phys. 35, 486-498.
14. Thomas, J. (1937). Differential Systems. American Mathematical Society, New York.
15. Zharkov, A. Yu., Blinkov, Yu. A. (1993). Involution approach to solving systems of algebraic equations. Proc. IMACS'93, pp. 11-16.