Plural - A Computer Algebra System for Noncommutative Polynomial Algebras

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

Volumn , Issue , 2003, Pages 176-183

  Levandovskyy, Viktor ^a   Schönemann, Hans ^a  

^a University of Koblenz Landau   (Germany)

Author keywords

Groebner bases; Noncommutative algebras

Indexed keywords

GROEBNER BASES; NONCOMMUTATIVE ALGEBRAS;

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER AIDED SOFTWARE ENGINEERING; COMPUTER PROGRAMMING; COMPUTER SOFTWARE; MATHEMATICAL OPERATORS;

POLYNOMIALS;

EID: 1542359932     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (23)

1. m). arXiv. math. QA/9911130, 1999.
2. Isaev, A. and Pyatov, P. and Rittenberg, V. Diffusion algebras. arXiv. math. QA/0103603, 2001.
3. J. Apel. Gröbnerbasen in nichtkommutativen algebren und ihre anwendung. Dissertation, Universität Leipzig, 1988.
4. J. Apel and U. Klaus. FELIX - an assistant for algebraists. In Proc. of the International Symposium on Symbolic and Algebraic Computation (ISSAC'91), pages 382-389. ACM Press, 1991.
5. O. Bachmann and H. Schönemann. Monomial Representations for Gröbner Bases Computations. In Proc. of the International Symposium on Symbolic and Algebraic Computation (ISSAC'98), pages 309-316. ACM Press, 1998.
6. G. Benkart and T. Roby. Down-up algebras. J. Algebra, 209(1):305-344, 1998.
7. F. Chyzak and B. Salvy. MGFUN - package for MAPLE: Non-commutative elimination in ore algebras proves multivariate identities. J. Symbolic Computation, 26 (2): 187-227, 1998.
8. D. Decker and D. Eisenbud. Sheaf algorithms using the exterior algebra. In Eisenbud, D.; Grayson, D.; Stillman, M.; Sturmfels, B., editor, Computations in algebraic geometry with Macaulay 2, 2001.
9. Y. Drozd and V. Kirichenko. Finite dimensional algebras. With an appendix by Vlastimil Dlab. Springer, 1994.
10. J. Gomez-Torrecillas and F. Lobillo. Global homological dimension of multifiltered rings and quantized enveloping algebras. J. Algebra, 225(2):522-533, 2000.
11. Greuel, G.-M. and Poster, G. with contributions by Bachmann, O. ; Lessen, C. and Schönemann, H. A SINGULAR Introduction to Commutative Algebra. Springer, 2002.
12. 3) Related to Quantum Gravity at q a Root of 1. In Proc. of IV Int. Conf. "Symmetry in Nonlinear Mathematical Physics", Kyiv, Ukraine, 2001.
13. A. Kandri-Rody and V. Weispfenning. Non-commutative gröbner bases in algebras of solvable type. J. Symbolic Computation, 9(1):l-26, 1990.
14. Klimyk, A. and Schmüdgen, K. Quantum groups and their representations. Springer, 1997.
15. H. Kredel. MAS Modula-2 Algebra System. In Proc. DISCO 90 Capri, pages 270-271. LNCS 429, 1990.
16. Kredel, H. Solvable polynomial rings. Shaker, 1993.
17. Levandovskyy, V. Gröbner bases of a class of non-commutative algebras. Master Thesis, Universität Kaiserslautern, 2000.
18. Levandovskyy, V. On Gröbner bases for non-commutative G-algebras. In Kredel, H. and Seiler, W.K., editor, Proceedings of the 8th Rhine Workshop on Computer Algebra, 2002.
19. Levandovskyy, V. PBW Bases, Non-Degeneracy Conditions and Applications. In Buchweitz, R.-O. and Lenzing, H., editor, Proceedings of the ICRA X conference, submitted.
20. Mora, T. An introduction to commutative and non-commutative Groebner bases. Theor. Comp. Sci., 134: 131-173, 1994.
21. T. Nüßler and H. Schönemann. Gröbner bases in algebras with zero-divisors. Preprint 244, Universität Kaiserslautern, 1993.
22. Schönemann, H. Singular in a Framework for Polynomial Computations. In Joswig, M. and Takayama, N., editor, Algebra, Geometry and Software Systems, pages 163-176. Springer, 2003.
23. T. Yan. The geobucket data structure for polynomials. J. Symbolic Computation, 25(3):285-294, March 1998.