Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Jie Wang
Pages: [31] - [49]
Received Date: May 17, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121832
This paper is devoted to studying difference indices of quasi-regular difference algebraic systems. We give the definition of difference indices through a family of pseudo-Jacobian matrices. Some properties of difference indices are proved. In particular, a Jacobi-type upper bound for the sum of the difference index and the order is given. As applications of difference indices, an upper bound of the Hilbert-Levin regularity and an upper bound of the order for the difference ideal membership problem are deduced.
difference index, difference algebraic system, Jacobi-type bound, Hilbert-Levin regularity, difference ideal membership problem.
