Computation of Difference Groebner Bases

作者: Daniel Robertz , Vladimir P. Gerdt

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摘要: This paper is an updated and extended version of our note [1] (cf. also [2]). To compute difference Grobner bases ideals generated by linear polynomials we adopt to polynomial rings the involutive algorithm based on Janet-like division. The has been implemented in Maple form package LDA (Linear Difference Algebra) describe main features package. Its applications are illustrated generation finite approximations partial differential equations reduction Feynman integrals. We present for ideal a set nonlinear polynomials. If terminates, then it constructs basis ideal.

参考文章(20)
Vladimir P. Gerdt, Involutive Algorithms for Computing Groebner Bases arXiv: Commutative Algebra. ,(2005)
E. V. Pankratiev, M. V. Kondratieva, A. B. Levin, A. V. Mikhalev, Differential and Difference Dimension Polynomials ,(1998)
Viktor Levandovskyy, Bernd Martin, A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations Texts & Monographs in Symbolic Computation. pp. 123- 156 ,(2012) , 10.1007/978-3-7091-0794-2_7
Heinz Kredel, Volker Weispfenning, Thomas Becker, Gröbner Bases: A Computational Approach to Commutative Algebra ,(2011)
François Ollivier, Standard Bases of Differential Ideals Applicable Algebra in Engineering, Communication and Computing. pp. 304- 321 ,(1990) , 10.1007/3-540-54195-0_60
Vladimir P. Gerdt, Daniel Robertz, Consistency of finite difference approximations for linear PDE systems and its algorithmic verification international symposium on symbolic and algebraic computation. pp. 53- 59 ,(2010) , 10.1145/1837934.1837950
Vladimir P. Gerdt, Gröbner Bases in Perturbative Calculations Nuclear Physics B - Proceedings Supplements. ,vol. 135, pp. 232- 237 ,(2004) , 10.1016/J.NUCLPHYSBPS.2004.09.011
W. Plesken, D. Robertz, Janet’s approach to presentations and resolutions for polynomials and linear pdes Archiv der Mathematik. ,vol. 84, pp. 22- 37 ,(2005) , 10.1007/S00013-004-1282-X
Vladimir P. Gerdt, Daniel Robertz, A Maple package for computing Grobner bases for linear recurrence relations Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment. ,vol. 559, pp. 215- 219 ,(2006) , 10.1016/J.NIMA.2005.11.171
A.V. Smirnov, Algorithm FIRE—Feynman Integral REduction Journal of High Energy Physics. ,vol. 2008, pp. 107- 107 ,(2008) , 10.1088/1126-6708/2008/10/107