References
References
- Adams, W. W. and Loustaunau, P., An Introduction to Gröbner Bases. American Mathematical Society, 1994.
- Apel, J., The theory of involutive divisions and an application to Hilbert function computations. J. Symbolic Computation, vol. 2
- 5(6) (1998), 683-704.
- Apel, J. and Hemmecke, R., Detecting unnecessary reductions in an involutive basis computation. J. Symbolic Computation, vol. 40(4-5) (2005), 1131-1149.
- Becker, T. and Weispfenning, V., Gröbner Bases. A Computational Approach to Commutative Algebra. Springer, 1993.
- Blinkov, Y. A., Cid, C. F., Gerdt, V. P., Plesken, W. and Robertz, D., The MAPLE Package Janet: I. Polynomial Systems. II. Linear Partial Differential Equations, Proc. 6th Int. Workshop on Computer Algebra in Scientific Computing, Passau, 2003, pp. 31-40 resp. 41-54. Involutive.ps, Involutive.pdf, Janet.ps, Janet.pdf.
- Buchberger, B., Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, PhD thesis, Univ. Innsbruck, Austria, 1965.
- Chyzak, F. and Salvy, B., Non-commutative elimination in Ore algebras proves multivariate identities. J. Symbolic Computation, vol. 26 (1998), pp. 187-227.
- Cohn, P. M., Free Rings and their Relations. Second edition. Academic Press, 1985.
- Evans, G. A. and Wensley, C. D., Complete involutive rewriting systems. J. Symbolic Computation, vol. 42 (2007), pp. 1034-1051.
- Fabianska, A. and Quadrat, A., Applications of the Quillen-Suslin theorem to multidimensional systems theory. In: H. Park et G. Regensburger (eds.), Gröbner Bases in Control Theory and Signal Processing, Radon Series on Computational and Applied Mathematics 3, de Gruyter, 2007, pp. 23-106.
- Gerdt, V. P., Involutive Algorithms for Computing Gröbner Bases. In: Cojocaru, S. and Pfister, G. and Ufnarovski, V. (eds.), Computational Commutative and Non-Commutative Algebraic Geometry, NATO Science Series, IOS Press, pp. 199-225.
- Gerdt, V. P., On Computation of Gröbner Bases for Linear Difference Systems, Nuclear Instruments and Methods in Physics Research, A: Accelerators, Spectrometers, Detectors and Associated Equipment, 559(1):211-214, 2006.
- Gerdt, V. P. and Blinkov, Y. A., Involutive bases of polynomial ideals. Minimal involutive bases. Mathematics and Computers in Simulation, vol. 45 (1998), pp. 519-541 resp. 543-560.
- Gerdt, V. P. and Blinkov, Y. A., Janet-like Monomial Division. Janet-like Gröbner Bases. In: Ganzha, V. G. and Mayr, E. W. and Vorozhtsov, E. V. (eds.), Computer Algebra in Scientific Computing CASC 2005, Springer, pp. 174-183 resp. 184-195.
- Gerdt, V. P. and Robertz, D. A Maple package for computing Gröbner bases for linear recurrence relations. Nuclear Instruments and Methods in Physics Research Section A 559(1):215-219, 2006. http://arxiv.org/abs/cs/0509070
- Kredel, H., Solvable Polynomial Rings. Shaker, Aachen, 1993.
- Janet, M., Leçons sur les systèmes des équationes aux dérivées partielles, Gauthiers-Villars, Cahiers Scientifiques IV, 1929.
- Plesken, W. and Robertz, D., Janet's approach to presentations and resolutions for polynomials and linear pdes, Archiv der Mathematik, vol. 84(1) (2005), pp. 22-37.
- Plesken, W. and Robertz, D., Constructing Invariants for Finite Groups, Experimental Mathematics, vol. 14(2) (2005), pp. 175-188.
- Plesken, W. and Robertz, D., Representations, commutative algebra, and Hurwitz groups, Journal of Algebra, vol. 300 (2006), pp. 223-247.
- Plesken, W. and Robertz, D. Some elimination problems for matrices. In: Ganzha, V. G., Mayr, E. W., Vorozhtsov, E. V. (Eds.), Computer Algebra in Scientific Computing, 10th International Workshop, CASC 2007, Bonn, Germany, Proceedings Series: Lecture Notes in Computer Science, Vol. 4770, Springer, 2007, pp. 350-359.
- Pommaret, J.-F., Partial Differential Equations and Group Theory: New Perspectives for Applications, Kluwer, 1994.
- Rehm, H. P., Differential-Algebra, Lecture Notes, Univ. of Karlsruhe, Germany, winter semester 2001/2002.
- Robertz, D., Formal Computational Methods for Control Theory, PhD thesis, RWTH Aachen, Germany, 2006, available at http://darwin.bth.rwth-aachen.de/opus/volltexte/2006/1586.
- Robertz, D. Janet Bases and Applications, In: Rosenkranz, M., Wang, D. (eds.), Groebner Bases in Symbolic Analysis, Radon Series on Computational and Applied Mathematics 2, de Gruyter, 2007, pp. 139-168.