伪多项式的联合微分预解式
Joint differential resolvents for pseudopolynomials
摘要：
对于给定常微分域中系数的普通多项式的任意根z，存在z^alpha的线性微分预解式，其中alpha是关于给定域的导数的不定常数。在本文中，我们考虑几个阿尔法。我们将把变量v的不定幂的有限和称为v中的伪多项式。我们将把单个单项式z^alpha的单个多项式的微分预解式的定义推广到根中的伪多项式的多个多项式的微分预解式的定义。我们还将推广预解式的定义，使其具有非连续导数。我们将证明作者的幂和公式可以用来计算这个更一般的微分预解式。
英文摘要：
The existence of linear differential resolvents for z^alpha for any root z of an ordinary polynomial with coefficients in a given ordinary differential field has been established, where alpha is an indeterminate constant with respect to the derivation of the given field. In this paper we consider several alphas. We will call a finite sum of indeterminate powers of a variable v a pseudopolynomial in v. We will generalize the definition of a differential resolvent of a single polynomial for a single monomial z^alpha to the definition of a differential resolvent of several polynomials for a pseudopolynomial in the roots. We will also generalize the definition of a resolvent to have non-consecutive derivatives. We will show that the authors powersum formula may be used to compute this more general differential resolvent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
