关于Bezoutiant的不变量理论
On the invariant theory of the Bezoutiant
摘要：
研究了二元形式对A，B的Bezoutiant R（A，B）的经典不变量理论。证明了R（A，B）允许一个泰勒展开式，其系数（本质上）为奇transvectant（A，B）2 r +1}.此外，R（A，B）完全由前两项M =（A，B）_1，N =（A，B）_3决定.利用Plucker关系，给出了高阶transvector（A，B）_5，（A，B）_7表示为M，N的等变公式。我们还描述了一个“归约公式”，它根据A和R（A，B）的知识计算B。
英文摘要：
We study the classical invariant theory of the Bezoutiant R(A,B) of a pair of binary forms A,B. It is shown that R(A,B) admits a Taylor expansion whose coefficients are (essentially) the odd transvectants (A,B)_{2r+1}. Moreover, R(A,B) is entirely determined by the first two terms M = (A,B)_1, N =(A,B)_3. Using the Plucker relations, we give equivariant formulae which express the higher transvectants (A,B)_5, (A,B)_7 in terms of M,N. We also describe a `reduction formula' which calculates B from the knowledge of A and R(A,B).
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