12/04/28 13:03:58.71
>>506
>あんたはあの一次式をガロア分解式と呼んでるようだが
>じゃあそれの最小多項式はなんと言う？
>倉田令二郎はそれをガロア分解式と呼んでいる。
Galois resolventで検索をかけると下記ヒット。このサイトにどれだけの権威があるか不明だが、手っ取り早い根拠として挙げておく
URLﾘﾝｸ(fermatslasttheorem.blogspot.jp)
Definition 1: Galois Resolvent Function
For any equation f(x) with distinct roots, the Galois Resolvent Function is a function g(x1, ..., xn) of the roots that no matter how the roots are permuted on the function, no two of the values are equal.
Definition 2: Galois Resolvent
The Galois Resolvent is a value of the Galois Resolvent Function where the roots of the equation f(x) are passed in as parameters.
Lemma 2: Galois Resolvent Function Exists
Given any equation f(x) with distinct roots a,b,c,... one can always form a function V of the roots such that no two of the values one obtains by permuting the roots in this function are equal.
For example, one can take:
V = Aa + Bb + Cc + ...
A, B, C, ... being suitably chosen whole numbers.