张量积在线性递归序列复杂性的研究

Tensor Products with Applications to Linear Recurring Sequences

中文摘要:

      设R是有单位元的交换环,设f(x)是R上的首一多项式,记S(f(x))为R中由f(x)生成的所有齐次线性递归序列集合.S(f(x))S(g(x))定义为所有乘积st,S∈S(f(x)),l∈S(g(x)),生成的R模,本文的目的是要确定h(x)∈R[x],使得S(f(x))S(g(x))=S(h(x)).当R是一个域时,我们进一步给出确定h(x)的可计算的方法,使得S(f(x))S(g(x))=S(h(x)).

英文摘要:

      Let R be a commutative ring with unit. Let f(x) be a monic polynomial over R. S(f(x)) denotes the set of all homogeneous linear resurring sequences in R generated by f(x). S(f(x))S(g(x)) is defined to be the R-module spanned by all the products st, with s e S(f(x)), t ∈ S(g(x)). The object of this paper is to determine h(x) in R[x], such that S(f(x)S(g(x)) = S(h(x). When R is a field, we can furthermore give an explicit and computaionally feasible determination of h(x) such that S(h(x)) = S(f(x))S(g(x)).