An elementary proof of Sylvester's double sums for subresultants
An elementary proof of Sylvester's double sums for subresultants
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DOI：
10.1016/j.jsc.2006.09.003
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发表时间：
2006-04
期刊：
影响因子：
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通讯作者：
Carlos D'Andrea;Hoon Hong;T. Krick;Á. Szántó
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文献类型：
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作者：
Carlos D'Andrea;Hoon Hong;T. Krick;Á. Szántó
1853年，Sylvester陈述并证明了一个用输入多项式的根来表示多项式子结果的优美公式。Sylvester的公式最近也被Lascoux和Pragacz用多重舒尔函数和微分证明了。本文给出了只用矩阵乘法的基本性质和范德蒙行列式的初等证明。
In 1853 Sylvester stated and proved an elegant formula that expresses the polynomial subresultants in terms of the roots of the input polynomials. Sylvester’s formula was also recently proved by Lascoux and Pragacz using multi-Schur functions and divided differences. In this paper, we provide an elementary proof that uses only basic properties of matrix multiplication and Vandermonde determinants.