Criteria for Finite Difference Gröbner Bases of Normal Binomial Difference Ideals
Authors: 
Yu-Ao Chen, Xiao-Shan GaoAuthors Info & Claims
Yu-Ao Chen, Xiao-Shan GaoAuthors Info & ClaimsAbstract
In 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 criteria are satisfied. The novelty of these criteria lies in the fact that complicated properties about difference polynomial ideals are reduced to elementary properties of univariate polynomials in Z[x].
References
[1]
Ruben Becker, Michael Sagraloff, Vikram Sharma, Juan Xu, and Chee Yap. 2016. Complexity analysis of root clustering for a complex polynomial. In Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation. ACM, 71--78.
[2]
Russell J Bradford and James H Davenport. 1988. Effective tests for cyclotomic polynomials. In International Symposium on Symbolic and Algebraic Computation. Springer, 244--251.
[3]
Richard-M Cohn. 1967. Difference algebra. (1967).
[4]
David Eisenbud and Bernd Sturmfels. 1996. Binomial ideals. Duke Mathematical Journal 84, 1 (1996), 1--45.
[5]
Xiao-Shan Gao, Zhang Huang, Jie Wang, and Chun-Ming Yuan. 2017. Toric Difference Variety. Journal of Systems Science and Complexity 30, 1 (2017), 173-- 195.
[6]
Xiao-Shan Gao, Zhang Huang, and Chun-Ming Yuan. 2017. Binomial difference ideals. Journal of Symbolic Computation 80 (2017), 665--706.
[7]
Xiao-Shan Gao, Yong Luo, and Chun-Ming Yuan. 2009. A characteristic set method for ordinary difference polynomial systems. Journal of Symbolic Compu- tation 44, 3 (2009), 242--260.
[8]
Vladimir P Gerdt. 2012. Consistency analysis of finite difference approximations to PDE systems. In Mathematical Modeling and Computational Science. Springer, 28--42.
[9]
Vladimir P Gerdt and Daniel Robertz. 2012. Computation of difference Gröbner bases. Comput. Sci. J. Mold. 20 (2012), 203--226.
[10]
Kei-ichiro Iima and Yuji Yoshino. 2009. Gröbner bases for the polynomial ring with infinite variables and their applications. Communications in Algebra 37, 10 (2009), 3424--3437.
[11]
Viktor Levandovskyy and Bernd Martin. 2012. A Symbolic Approach to Genera- tion and Analysis of Finite Difference Schemes of Partial Differential Equations. Numerical and Symbolic Scientific Computing (2012), 123--156.
[12]
Alexander Levin. 2008. Difference algebra. Vol. 8. Springer Science & Business Media.
[13]
Victoria Powers and Thorsten Wörmann. 1998. An algorithm for sums of squares of real polynomials. Journal of pure and applied algebra 127, 1 (1998), 99--104.
[14]
Vikram Sharma and Chee K Yap. 2012. Near optimal tree size bounds on a simple real root isolation algorithm. In Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation. ACM, 319--326.
[15]
Michael Wibmer. 2013. Algebraic difference equations. Preprint (2013).
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- Criteria for Finite Difference Gröbner Bases of Normal Binomial Difference Ideals
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Published In
July 2017
466 pages
ISBN:9781450350648
DOI:10.1145/3087604
- Editor:
- Michael Burr,
- General Chair:
- Chee K. Yap,
- Program Chair:
- Mohab Safey El Din
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Publication History
Published: 23 July 2017
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- Research-article
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- National Natural Science Foundation of China
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ISSAC '17
ISSAC '17: International Symposium on Symbolic and Algebraic Computation
July 23 - 28, 2017
Kaiserslautern, Germany
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Overall Acceptance Rate 395 of 838 submissions, 47%
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