>>595 追加 >https://joelshapiro.org/Pubvit/Downloads/Rulla_dftradicals.pdf >Solution by Radicals and the DFT January 11, 2019 Jim Rulla
(DFTとLagrange resolventとの関係) これのP8より The DFT of the roots is <下記は行列です。原文ご参照!> [1 1 1 1](r1)=(r1 + r2 + r3 + r4) ・・・・・(B4) [1 -i -1 i](r2) (r1 - r2i - r3 + r4i) [1 -1 1-1](r3) (r1 - r2 + r3 - r4) [1 i -1 -i](r4) (r1 + r2i - r3 - r4i) The top row, as always, is symmetric in the roots, and is - b. The second and fourth rows are similar ? they both qualify as Lagrange resolvents ? but the third row is different. (引用終り)
なお、Lagrange resolvent で、4次方程式が解けることは P9 の冒頭 Remark で ”One can also solve the quartic using the Lagrange resolvents.See Edwards6.” と記されている。(Edwards 6でなくても、他にもありと思うけど) 以上