Theory of Multiple Polynomial Remainder Sequence
Tateaki Sasaki, Akio Furukawa · Publications of the Research Institute for Mathematical Sciences · 1984
Given a set of polynomials {P£, D (#), • • • > Po m) U)}j with coefficients in an integral domain I, we can generate a sequence of sets of remainders {P^(x) 9 ..., Pf w) 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, Cm) (*)}, f=l, 2,..., multiple polynomial remainder sequence (multi-PRS).This paper proves that, for each polynomial Pj">, there exists a matrix M%\ Q^j