Generalized Gröbner Bases and New Properties of Multivariate Difference Dimension Polynomials
Pages 273 - 280
Abstract
We present a method of Gröbner bases with respect to several term orderings and use it to obtain new results on multivariate dimension polynomials of inversive difference modules. Then we use the difference structure of the module of Kähler differentials associated with a finitely generated inversive difference field extension of a given difference transcendence degree to describe the form of a multivariate difference dimension polynomial of the extension.
References
[1]
A. Einstein. The Meaning of Relativity. Appendix II (Generalization of gravitation theory), 153--165. Princeton University Press, Princeton, NJ, 1953.
[2]
J. Johnson and W. Sit. On the differential transcendence polynomials of finitely generated differential field extensions. Amer. J. Math., 101 (1979), 1249--1263.
[3]
E. R. Kolchin. Differential Algebra and Algebraic Groups. Academic Press, 1973.
[4]
M. V. Kondrateva, A. B. Levin, A. V. Mikhalev, and E. V. Pankratev. Differential and Difference Dimension Polynomials. Kluwer Acad. Publ., 1999.
[5]
A. B. Levin. Reduced Gröbner bases, free difference-differential modules and difference-differential dimension polynomials. J. Symb. Comput., 30 (2000), 357--382.
[6]
A. B. Levin. Gröbner bases with respect to several orderings and multivariable dimension polynomials. J. Symb. Comput., 42 (2007), no. 5, 561--578.
[7]
A. B. Levin Computation of the Strength of Systems of Difference Equations via Generalized Gröbner Bases. Gröbner Bases in Symbolic Analysis, Walter de Gruyter, 2007, 43--73.
[8]
A. B. Levin. Multivariate dimension polynomials of inversive difference field extensions. Algebraic and algorithmic aspects of differential and integral operators. Lecture Notes in Comput. Sci., 8372 (2014), 146--163.
[9]
A. B. Levin Difference Algebra. Springer, New York, 2008.
[10]
A. B. Levin and A. V. Mikhalev. Type and Dimension of Finitely Generated G-algebras. Contemporary Mathematics, 184 (1995), 275--280.
[11]
P. Morandi. Field and Galois Theory. Springer-Verlag, New York, 1996.
[12]
M. Zhou and F. Winkler Computing difference-differential dimension polynomials by relative Grobner bases in difference-differential modules. J. Symb. Comput., 43 (2008), no. 10, 726--745.
Index Terms
- Generalized Gröbner Bases and New Properties of Multivariate Difference Dimension Polynomials
Recommendations
Dimension Polynomials of Intermediate Fields of Inversive Difference Field Extensions
MACIS 2015: Revised Selected Papers of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences - Volume 9582Let K be an inversive difference field, L a finitely generated inversive difference field extension of K, and F an intermediate inversive difference field of this extension. We prove the existence and establish properties and invariants of a numerical ...
Criteria for Finite Difference Gröbner Bases of Normal Binomial Difference Ideals
ISSAC '17: Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic ComputationIn this paper, we give decision criteria for normal binomial difference polynomial ideals in the univariate difference polynomial ring F{y to have finite difference Gröbner bases and an algorithm to compute the finite difference Gröbner bases if these ...
Reduced Gröbner Bases, Free Difference-Differential Modules and Difference-Differential Dimension Polynomials
Special issue on applications of the Gröbner basis methodWe define a special type of reduction in a free left module over a ring of difference differential operators and use the idea of the Gr bner basis method to develop a technique that allows us to determine the Hilbert function of a finitely generated ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
July 2021
379 pages
Copyright © 2021 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]
Sponsors
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 18 July 2021
Check for updates
Author Tags
Qualifiers
- Research-article
Funding Sources
- NSF
Conference
ISSAC '21
Sponsor:
ISSAC '21: International Symposium on Symbolic and Algebraic Computation
July 18 - 23, 2021
Virtual Event, Russian Federation
Acceptance Rates
Overall Acceptance Rate 395 of 838 submissions, 47%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 58Total Downloads
- Downloads (Last 12 months)10
- Downloads (Last 6 weeks)0
Reflects downloads up to 18 Dec 2024
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in