Theory of Multiple Polynomial Remainder Sequence
Theory of Multiple Polynomial Remainder Sequence
复制标题
多项式余数列理论
DOI：
10.2977/prims/1195181611
复制
发表时间：
1984
影响因子：
1.2
通讯作者：
A. Furukawa
中科院分区：
文献类型：
--
作者：
Tateaki Sasaki;A. Furukawa
给出一组系数在整域I上的多项式{P GB，(#)，···>；POU)}j，我们可以生成一个余数集序列{P^(X)9...，Pf U)}，x=L，2 v.，通过/^Pffi^‘P^-a^h’，deg(Pffi))，0=1，.。，*，-！，*+！，…，ra，y，e{！，...，to}，其中ap°，#*>；e=7。。。，P，(*)}，f=L，2，.。。多重多项式余项序列(MULTI-PRS)。证明了对于每个多项式Pj“>；，都存在一个矩阵Mj^q^j<；i，使得Mj^Lm^i的第一列的每个非零元素都是x‘P^with/a非负整数和&e{！，…，m}，其他每个非零元素都是P$的系数，并给出了计算I上多项式的三种算法.
Given a set of polynomials {P£,(#), • • • > PoU)}j with coefficients in an integral domain I, we can generate a sequence of sets of remainders {P^(x)9 ..., Pf U)}, x=l ,2 v .., through /^Pffi^'P^-a^h', deg(Pffi) ), 0=1,.. . , *,-!, * + !,..., ra, y,e {!,..., TO}, with ap°, #*>e=7. We call the sequence of sets {PJ U C«) , . . . , P,(*)}, f=l , 2, . . . , multiple polynomial remainder sequence (multi-PRS). This paper proves that, for each polynomial Pj">, there exists a matrix M%\ Q^j<i, such that Pj^^lM^I, each nonzero element of the first column of MO? is x'P^ with / a nonnegative integer and &e {!,..., m}, and each of the other nonzero elements is a coefficient of P$. Furthermore, three algorithms for calculating multi-PRS over I are given.