Termination of algorithm for computing relative Gröbner bases and difference differential dimension polynomials

We introduce the concept of difference-differential degree compatibility on generalized term orders. Then we prove that in the process of the algorithm the polynomials with higher and higher degree would not be produced, if the term orders ‘ ≺ ’ and ‘ ≺ ′ ’ are difference-differential degree compati...

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Bibliographic Details
Published in:Frontiers of mathematics in China 2015-06, Vol.10 (3), p.635-648
Main Authors: HUANG, Guanli, ZHOU, Meng
Format: Article
Language:English
Subjects:
Algebra
Algorithms
bivariate dimension polynomial
China
Computation
Decomposition
difference-differential module
Differential equations
Mathematical models
Mathematics
Mathematics and Statistics
Modules
Polynomials
Relative Gröbner basis
Research Article
Studies
termination of algorithm
Theorems
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Summary:We introduce the concept of difference-differential degree compatibility on generalized term orders. Then we prove that in the process of the algorithm the polynomials with higher and higher degree would not be produced, if the term orders ‘ ≺ ’ and ‘ ≺ ′ ’ are difference-differential degree compatibility. So we present a condition on the generalized orders and prove that under the condition the algorithm for computing relative Gröbner bases will terminate. Also the relative Gröbner bases exist under the condition. Finally, we prove the algorithm for computation of the bivariate dimension polynomials in difference-differential modules terminates.
ISSN:1673-3452
1673-3576
DOI:10.1007/s11464-015-0439-1