Subresultant is a powerful tool for developing various algorithms in computer algebra. Subresultants for polynomials in standard basis (i.e., power basis) have been well studied so far. With the popularity of basis-preserving algorithms, resultants and subresultants in non-standard basis are drawing more and more attention. In this paper, we develop a formula for B\'ezout subresultants of univariate polynomials in general basis, which covers a broad range of non-standard bases. More explicitly, the input polynomials are provided in a given general basis and the resulting subresultants are B\'ezout-type expressions in the same basis. It is shown that the subresultants share the essential properties as the subresultants in standard basis.

翻译：子结式是为计算机代数中多种算法提供支持的有力工具。迄今为止，标准基（即幂基）下多项式的子结式已得到充分研究。随着基保持算法的普及，非标准基下的结式与子结式正受到越来越多的关注。本文发展了一个针对一般基下单变量多项式的Bézout子结式公式，该公式覆盖了广泛的非标准基情形。具体而言，输入多项式以给定的一般基表示，所得子结式为同一基下的Bézout型表达式。研究表明，这些子结式具有与标准基下子结式相同的基本性质。