Using SAGBI bases to compute invariants

Journal of Pure and Applied Algebra

Volumn 139, Issue 1, 1999, Pages 285-302

  Stillman, Michael ^a   Tsai, Harrison ^b  

^a Cornell University ^*  (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033147401     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(99)00015-8     Document Type: Article

References (17)

1. A. Conca, J. Herzog, G. Valla, Sagbi bases with applications to blow-up algebras, J. Reine Angew. Math. 474 (1996) 113-138.
2. J. Dalbec, Geometry and Combinatorics of Chow Forms, PhD Thesis, Cornell University, 1995.
3. H. Derksen, Constructive Invariant Theory and the Linearization Problem, PhD Thesis, University of Basel, 1997.
4. H. Derksen, Polynomial Bounds for Rings of Invariants, Preprint.
5. J. Fogarty, Invariant Theory, W.A. Benjamin, New York, 1969.
6. D. Grayson, M. Stillman, Macaulay 2: A Computer Algebra System for Algebraic Geometry and Commutative Algebra, 1996, available at http://www.math.uiuc.edu/Macaulay2.
7. T. Hibi, H. Ohsugi, Toric Ideals Generated by Quadratic Binomials, Preprint.
8. D. Kapur, K. Madlener, A completion procedure for computing a canonical basis of a k-subalgebra, in: Kaltofen and Watt (Eds.). Proc. Computers and Mathematics 89, MIT, Cambridge, MA, 1989.
9. J. Miller, Analogs of Gröbner bases in polynomial rings over a ring, J. Symbol. Comput. 21 (1996) 139-153.
10. J. Miller, Effective algorithms for intrinsically computing SAGBI-Gröbner bases in a polynomial ring over a field, in: B. Buchberger, F. Winkler (Eds.), Gröbner Bases and Applications, London Mathematical Society, London, London Mathematical Society, Lecture Note Series, vol. 251, 998, pp. 421-433.
11. L. Robbiano, On the theory of graded structures, J. Symbol. Comput. 2 (1986) 139-170.
12. L. Robbiano, M. Sweedler, Subalgebra bases, in: W. Brans, A. Simis (Eds.), Commutatitve Algebra, Proc. Salvador, 1988, Lecture Notes in Mathematics vol, 1430, Springer, Berlin, 1990, pp. 61-87.
13. A. Schrijver, Theory of Linear and Integer Programming, Wiley-Interscience, Chichester, 1986.
14. B. Sturmfels, Algorithms in Invariant Theory, Springer, Vienna, 1993.
15. B. Sturmfels, Gröbner Bases and Convex Polytopes, American Mathematical Society, Providence, RI, 1996.
16. a-action on an affine variety, J. Symbol. Comput. 16 (1993) 551-555.
17. W. Vasconcelos, Computational Methods in Commutative Algebra and Algebraic Geometry, Springer, Berlin, 1997.