递归多项式余项序列的次结式
Subresultants in Recursive Polynomial Remainder Sequence
摘要：
本文引入了递归多项式余项序列（PRS）和递归子结式的概念，并研究了它们的性质。在计算PRS时，如果存在初始多项式的GCD（最大公因数），我们用新的PRS对GCD及其导数进行“递归”计算，直到导出一个常数。我们称这样的PRS为递归PRS。我们定义递归子结式为用初始多项式的系数表示递归PRS中系数的行列式。最后，我们讨论了递归次结式在近似代数计算中的应用，这是本文工作的基础。
英文摘要：
We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," and investigate their properties. In calculating PRS, if there exists the GCD (greatest common divisor) of initial polynomials, we calculate "recursively" with new PRS for the GCD and its derivative, until a constant is derived. We call such a PRS a recursive PRS. We define recursive subresultants to be determinants representing the coefficients in recursive PRS by coefficients of initial polynomials. Finally, we discuss usage of recursive subresultants in approximate algebraic computation, which motivates the present work.
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