14/09/06 13:27:41.87
>>244
どうもです
スレ主です。
>解をみたいだけならライブラリとか、数式処理ソフト、数値計算ソフトで数値的に
>1行で全ての解を出してくれますけど。
>先人が関数用意してくれてるので。
はい、そうですね。いま２１世紀
degree = 7 URLﾘﾝｸ(en.wikipedia.org)
The general septic equation can be solved with the alternating or symmetric Galois groups A7 or S7.[1]
Such equations require hyperelliptic functions and associated theta functions of genus 3 for their solution.[1]
However, these equations were not studied specifically by the nineteenth-century mathematicians studying the solutions of algebraic equations,
because the sextic equations' solutions were already at the limits of their computational abilities without computers.[1]
（引用おわり）
これがnineteenth-century
Septics are the lowest order equations for which it is not obvious that their solutions may be obtained by superimposing continuous functions of two variables.
Hilbert's 13th problem was the conjecture this was not possible in the general case for seventh-degree equations.
Vladimir Arnold solved this in 1957, demonstrating that this was always possible.[2]
However, Arnold himself considered the genuine Hilbert problem to be whether the solutions of septics may be obtained by superimposing algebraic functions of two variables (the problem still being open).[3]
（引用おわり）
ここらが２０世紀